Cancers of the head and ne¬ck and their treatment can cause disfigurement and loss of functioning, with a profound negative impact on the person’s self-image and psychosocial wellbeing. This can lead to experiences of shame and stigma, which are important targets for psychosocial interventions. Accurate measurement and identification of these problems enables clinicians to offer appropriate interventions and monitor patients’ progress. This study aimed to validate the Canadian version of the Shame and Stigma Scale (SSS) among French and English speaking head and neck cancer patients. Data from 258 patients from two major Canadian hospitals was analysed. The existing 4-factor structure of the SSS was supported, with the following subscales: Shame with Appearance, Sense of Stigma, Regret, and Social/Speech Concerns. The Canadian SSS showed adequate convergent and divergent validity and test-retest reliability. Rasch analysis suggested scale improvement by removing two misfitting item and two items with differential functioning between French and English speaking patients. The final 16-item scale version had adequate fit to the Rasch model. The SSS provides more accurate measures for people with high levels of shame and stigma, and thus has utility in identifying patients with more severe symptoms who may be in need of psychosocial interventions.

This work demonstrates that a plasmid can function as an efficient biocatalyst in mediating the nitroaldol (Henry) reaction at high temperatures in ultrapure water. Compared with ssDNA, the plasmid displayed a remarkable catalytic efficiency (97% yield within 20 min). Aromatic aldehydes which bear strong or moderate electron-withdrawing groups reacted satisfactorily with nitromethane, which afforded the corresponding β-nitroalcohols in good yields within 2 h (up to 98%). By contrast, aliphatic and aromatic aldehydes with electron-donating groups did not react. Moreover, the yield significantly dropped when the size of the carbanion increased, and the yield was only 10% when nitropropane was used as the donor.

The importance of frailty in older people is getting constant recognition as an important aspect both in terms of public health, as well in personal level for the appropriate management of an older person health condition. This is reflected by the continuously increasing number of research studies carried out in several settings across different countries. Sometimes this is very solid, but in other cases there is a considerable gap in terms of accurate and well grounded documentation of frailty status. This is the case in Greece, where we are missing clinically validated tools to approach frailty. We are missing frailty screening tools, such as for instance PRISMA 7, the gold standard tool of Fried criteria is somehow problematic since the question referring to physical activity originates from a questionnaire that has not been translated and validated, while Clinical Frailty Scale has been validated for the translation but not for the capacity to detect frailty. Aim of this study is to validate these tools for their accuracy to detect frailty by using a measurable index of frailty, previously proposed for use in clinical studies: the Short Physical Performance Battery (SPPB). 74 male and female participants have been evaluated for their frailty status using different tools. We observed that PRISMA 7 translation detects frailty only when one question is removed at a cut-off of ≥ 2 and indicated a sensitivity of 88.1%, and specificity of 99.9% with a good correlation with SPPB measurements (r = 0.858; p < 0.001). When CFS was validated using SPPB it demonstrated a very good correlation (r = -0.838; p < 0.001 respectively) as it was the case for the modified Fried Criteria (r = -0.725; p < 0.001). All items demonstrated a good correlation between them. We can here propose that we can accurately assess frailty status in the community setting by using a modified version of Fried criteria, Clinical Frailty Scale translation in Greek and we can screen for frailty by using the Greek translation of PRISMA 7 only after removing the item 6 of the questionnaire.

There is a deep link existing between symmetry and nature that may be best apprehended by using group theory. In physics, giving a symmetry group is entirely equivalent to fix natural laws (Noether’s theorem). Within such a framework, it follows that all fundamental mechanical laws may be given by defining a group of symmetry operations belonging to the Gal(3,1) symmetry group having ten generators (3 + 3 + 3 + 1 = 10). The move to special relativity amounts simply to substitute another group ISO(3,1) to Gal(3,1) and having the same number of generators. In both cases, one immediately perceives that we live in universe with 3 dimensions of space and 1 dimension of time. A further progress could be made by looking for the symmetry group that leaves Maxwell’s equations invariant. The answer to this fundamental question is the group ISO(4,2)⊗U(2)⊗U(2) characterized by 23 generators : 15 = 10 + 5 for the conformal group ISO(4,2), 4 for U(2) and hence 8 = 4 + 4 for the compact part U(2)⊗U(2) that could be related to the existence of quantum physics besides relativity. As ISO(3,1) is a sub-group of ISO(4,2), the two numbers 4 and 2 suggests that, taking into account the existence of light besides matter, we live in an universe having 4 spacelike dimensions and 2 time-like dimensions. Here, it is proposed that, as music is characterized by a scale-invariant symmetry operation (transposition by octaves) and that as time may be perceived differently in shamanic trance for instance, the two “new” dimensions of our universe may be related to music and consciousness. Related to the fifth dimension of music, the notion of diapason linking physical frequencies to a musical note is revisited. It is thus proposed to adopt a new A4 = 429.62 Hz value based on universal physical constants of our universe and on the mass of the water molecule H₂O, the most abundant molecule in the universe. Demonstration is done that this new diapason is superior to other diapasons based on frequencies of 440 Hz or even 432 Hz

The study was conducted to prepare juice blend by using Orange, Carrot and Tiger-nut juices. Fully mature raw Orange, Tiger-nut and Carrot were processed into juice forms and combined in different ratios which were analyzed for their composition and Consumer’s acceptability. The analysis showed that the juice with higher Orange juice content had higher levels of acidity. This implies that they would last longer as they are not susceptible to spoilage by most organisms. The Juice with higher orange juice content was also found to be very rich in Vitamin C, due to inherent high amount of Vitamin C in raw Orange Fruit. However, it scored lowest in terms of general acceptability because the raw fruit was purchased separately and there’s a likelihood some of the Orange used in the Juice preparation were sour. This led to a sour taste in this Juice blend. The Juice blend that contained equal proportions of all three juices was the most acceptable to the consumers in terms of color, taste and Nutritional composition. It gave equal amounts of the unique properties of each fruit and provided a unique color and taste that was very appealing to the panelists. This product makes it possible to properly utilize these fruits, reduce post harvest losses, cater to different health needs of the consumers and ensure food security. It is recommended that further work should be done on antioxidant properties, other fruit blends and storage stability of the beverage to determine the shelf-life.

This article presents an overview of the first AI-human collaborated album, Hello World, by SKYGGE, which utilizes Sony’s Flow Machines technologies. This case study is situated within an overview of current and emerging uses of AI in popular music production, and connects those uses with myths and fears that have circulated in discourses concerning the use of AI in general, but also in music specifically. By proposing the concept of an audio uncanny valley in relation to AIPM (artificial intelligence popular music), this article offers a lens through which to examine the more novel and unusual melodies and harmonisations made possible through AI music generation, and questions how this content relates to wider speculations about posthumanism, sincerity, and authenticity in both popular music, and more wider assumptions of anthropocentric creativity. In its documentation of the emergence of a new era of popular music, the AI era, this article surveys: (1) the current landscape of artificial intelligence popular music focusing on the use of Markov models for generative purposes; (2) posthumanist creativity and the potential for an audio uncanny valley; and (3) issues of perceived authenticity in the technologically mediated “voice”.

A series of MgAl-layered double hydroxide (MgAl-HT), the calcined form at 500^oC (MgAlO_x) and the re-hydrated one at 25^oC (MgAl-HT-RH) were synthesized. Physicochemical properties of the catalysts were characterized by x-ray diffraction (XRD), scanning electron microscopy (SEM). Surface area of the as-synthesized, calcined and re-hydrated catalysts was determined by N₂ physisorption at -196^oC. CO₂-teperature programmed desorption (CO₂-TPD) was applied to determine the basic sites of catalysts. The catalytic test reaction was carried out using benzaldehyde and their derivatives with nitromethane and their derivatives. The Henry products (1-15) were obtained in a very good yield using MgAl-HT-RH catalyst either by conventional method at 90^oC in liquid phase, or under microwave irradiation method. The mesoporous structure and basic nature of re-hydrated solid catalyst were responsible for their superior catalytic efficiency. The robust nature was determined by using the same catalyst for five times, where the product % yield was almost unchanged significantly.

Although Lov\'{a}sz introduced the graph exponential $G^K$ in 1967, this product has received little attention. This paper focuses on the number of components in $G^K$ when exponent $K$ is a complete graph $K_n$. For a connected bipartite $G$, when $K$ is $K_2$, $G^{K_2}$ has three components; and when $K$ is $K_n$ with $n>2$, $G^{K_n}$ produces $\lceil\frac{n+1}{2}\rceil$ components. A connected $G$ with an odd cycle produces one component in $G^{K_n}$.

Introduced in 1967 by Lov\'{a}sz, graph exponentiation has received little attention over the past several decades. Since graph exponentiation produces large graphs and any graph can be constructed utilizing its adjacency matrix, we provide a four step linear construction algorithm that generates the adjacency matrix for the graph exponential.

Clustering coefficient measures are key complex network analysis tools. We examine local and global clustering coefficient measures with respect to the lexicographic graph product. As a preliminary condition, we analyze the $K_3$ subgraph structure focused on vertex inclusion with respect to the product graph. From this structure, we determine both the clustering coefficient for the product graph vertices and the average clustering coefficient for the product graph.

In this research article, the notions of SuperHyperDominating and SuperHyperResolving are defined in the setting of neutrosophic SuperHyperGraphs. Some ideas are introduced on both notions of SuperHyperDominating and SuperHyperResolving, simultaneously and as the same with each other. Some neutrosophic SuperHyperClasses are defined based on the notion, SuperHyperResolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, SuperHyperDominating and SuperHyperResolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted SuperHyperVertices, there’s only one SuperHyperVertex in the intended set. There are some instances and some clarifications to make sense about what’s happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

The kind of set which is based on edges, is introduced. The analysis on this set is done in the matter of operation which are the classes of graphs. The general notion which is related to this concept, is up. The set of edges is seen in the matter of common vertex, entitled neighbor edges and the set of edges which has specific condition on the vertices of graphs, entitled ghost set. The kind of viewpoint when the edges are up so the kind of efforts to assign some notions which get the sensible result of edges which make sense about these two types of notions. Notions of having some attributes about vertices concerning edges and edges' attributes to get result about edges in the matter of vertices.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

In this article, the connections amid matroid and other notions have been studied. The structure of matroid could be a reflection of some other structure in lattice theory, group theory, other algebraic structure, graph theory, combinatorics and enumeration theory.

In this research, assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then an “δ−SuperHyperForcing” is a minimal SuperHyperForcing of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : |S∩N(s)|>|S∩(V \N(s))|+δ, |S∩N(s)|<|S∩(V \N(s))|+δ.Thefirst Expression, holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an “δ−SuperHyperDefensive”; a“neutrosophic δ−SuperHyperForcing” is a minimal neutrosophic SuperHyperForcing of SuperHyperVertices with minimum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperForcing. Since there’s more ways to get type-results to make SuperHyperForcing more understandable. For the sake of having neutrosophic SuperHyperForcing, there’s a need to “redefine” the notion of “SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new notions, namely, SuperHyperDegree and Co-SuperHyperDegree. Two different types of definitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The cancer’s treatments are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “cancer’s treatments”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “cancer’s treatments”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. If there’s a SuperHyperEdge between two SuperHyperVertices, then these two SuperHyperVertices are called SuperHyperNeighbors. The number of SuperHyperNeighbors for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperNeighbors for some SuperHyperVertices is called Co-SuperHyperDegree for them and used SuperHyperVertices are called Co-SuperHyperNeighbors. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The number of SuperHyperEdges for a given SuperHyperVertex is called SuperHyperDegree. The number of common SuperHyperEdges for some SuperHyperVertices is called Co-SuperHyperDegree for them. The number of SuperHyperVertices for a given SuperHyperEdge is called SuperHyperDegree. The number of common SuperHyperVertices for some SuperHyperEdges is called Co-SuperHyperDegree for them. The model proposes the specific designs. The model is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this model, The “specific” cells and “specific group” of cells are modeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are modeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise model which in this case the model is called “neutrosophic”. In the future research, the foundation will be based on the caner’s treatment and the results and the definitions will be introduced in redeemed ways. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperAlliances and Neutrosophic SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperAlliances, then it’s officially called “SuperHyperAlliances” but otherwise, it isn’t SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperAlliances. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperAlliances” and “neutrosophic SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperAlliances are redefined “neutrosophic SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperAlliances.] SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperAlliances or the strongest SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperAlliances, called SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

In this research, new setting is introduced for new SuperHyperNotions, namely, an 1-failed SuperHyperForcing and Neutrosophic 1-failed SuperHyperForcing. Assume a SuperHyperGraph. Then an ``1-failed SuperHyperForcing'' $\mathcal{Z}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a ``neutrosophic 1-failed SuperHyperForcing'' $\mathcal{Z}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an ``$\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

The research is on the SuperHyperGirth and the neutrosophic SuperHyperGirth. A SuperHyperGraph has SuperHyperGirth where it’s the longest SuperHyperCycle. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperGirth. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. This SuperHyperClass is officially called “SuperHyperFlower”. If there’s a need to have all SuperHyperCycles until the SuperHyperGirth, then it’s officially called “SuperHyperOrder” but otherwise, it isn’t SuperHyperOrder. There are two instances about the clarifications for the main definition titled “SuperHyperGirth”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperGirth and they’re called “SuperHyperFlower.” A SuperHyperGraph has “neutrosophic SuperHyperGirth” where it’s the strongest [the maximum value from all SuperHyperCycles amid the minimum value amid all SuperHyperEdges from a SuperHyperCycle.] SuperHyperCycle. In “Cancer’s Recognitions”, the aim is to find either the longest SuperHyperCycle or the strongest SuperHyperCycle in those neutrosophic SuperHyperModels. For the longest SuperHyperCycle, called SuperHyperGirth, and the strongest SuperHyperCycle, called neutrosophic SuperHyperGirth, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

: Extra- and intra-cellular activity occurs under the direction of numerous inter-molecular interactions, and in any tissue or cell, molecules are densely packed, thus promoting those molecular interactions. Galectins and chemokines, the focus of this review, are small, protein effector molecules that mediate various cellular functions, in particular cell adhesion and migration, as well as cell signaling/activation. In the past, researchers have reported that combinations of these (and other) effector molecules act separately, yet sometimes in concert, but nevertheless physically apart and via their individual cell receptors. This view that each effector molecule functions independently of the other limits our thinking about functional versatility and cooperation, and, in turn, ignores the prospect of physiologically important inter-molecular interactions, especially when both molecules are present or co-expressed in the same cellular environment. This review is focused on such protein-protein interactions with chemokines and galectins, their homo- and hetero-oligomeric structures that they can form, and the functional consequences of those paired interactions.

Crosstalk between the BMP and TGF-β signaling pathways regulates many complex developmental processes from the earliest stages of embryogenesis throughout adult life. In many situations, the two signaling pathways act reciprocally. For example, TGF-β signaling is generally pro-fibrotic whereas BMP signaling is anti-fibrotic and pro-calcific. Sex-specific differences occur in many diseases including cardiovascular pathologies. Differing ratios of fibrosis and calcification in stenotic valves suggests that BMP/TGF-β signaling may vary in men and women. In this review, we focus on the current understanding of the interplay between sex and BMP/TGF-β signaling and pose several unanswered questions.

In this research, the extreme SuperHyperNotion, namely, extreme SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty extreme SuperHyperEdges but $E_2$ is a loop extreme SuperHyperEdge and $E_4$ is an extreme SuperHyperEdge. Thus in the terms of extreme SuperHyperNeighbor, there's only one extreme SuperHyperEdge, namely, $E_4.$ The extreme SuperHyperVertex, $V_3$ is extreme isolated means that there's no extreme SuperHyperEdge has it as an extreme endpoint. Thus the extreme SuperHyperVertex, $V_3,$ is excluded in every given extreme SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an extreme SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an extreme SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an extreme R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an extreme R-SuperHyperGirth SuperHyperPolynomial.}} $ The following extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices] is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of extreme SuperHyperEdges[SuperHyperVertices], is the extreme type-SuperHyperSet of the extreme SuperHyperGirth. The extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is an extreme type-SuperHyperSet with the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive sequence of the extreme SuperHyperVertices and the extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are not only four extreme SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious extreme SuperHyperGirth isn't up. The obvious simple extreme type-SuperHyperSet called the extreme SuperHyperGirth is an extreme SuperHyperSet includes only less than four extreme SuperHyperVertices. But the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended extreme SuperHyperSet. Thus the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth isn't up. To sum them up, the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth. Since the extreme SuperHyperSet of the extreme SuperHyperEdges[SuperHyperVertices], is an extreme SuperHyperGirth $\mathcal{C}(ESHG)$ for an extreme SuperHyperGraph $ESHG:(V,E)$ is the extreme SuperHyperSet $S$ of extreme SuperHyperVertices[SuperHyperEdges] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle given by that extreme type-SuperHyperSet called the extreme SuperHyperGirth and it's an extreme SuperHyperGirth . Since it 's the maximum extreme cardinality of an extreme SuperHyperSet $S$ of extreme SuperHyperEdges[SuperHyperVertices] such that there's only one extreme consecutive extreme sequence of extreme SuperHyperVertices and extreme SuperHyperEdges form only one extreme SuperHyperCycle. There are only less than four extreme SuperHyperVertices inside the intended extreme SuperHyperSet, thus the obvious extreme SuperHyperGirth, is up. The obvious simple extreme type-SuperHyperSet of the extreme SuperHyperGirth, is: ,is the extreme SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected extreme SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple extreme type-SuperHyperSet called the extreme SuperHyperGirth amid those obvious[non-obvious] simple extreme type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with extreme SuperHyperGirth theory, SuperHyperGraphs, and extreme SuperHyperGraphs theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Bipartite and Neutrosophic SuperHyper-Path are introduced. More instances and more clarifications alongside sufficient references.

In this research, assume a SuperHyperGraph. Then an extreme SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; an extreme R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; an extreme R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. Assume a SuperHyperGraph. Then $\delta-$SuperHyperMatching is a maximal of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta-$SuperHyperDefensive; a neutrosophic $\delta-$SuperHyperMatching is a maximal neutrosophic of SuperHyperVertices with maximum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S$ there are: $|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta;$ and $ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperOffensive. And the second Expression, holds if $S$ is a neutrosophic $\delta-$SuperHyperDefensive It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with Extreme SuperHyperMatching theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, new setting is introduced for new SuperHyperNotion, namely, 11 Neutrosophic 1-failed SuperHyperForcing. Two different types of SuperHyperDefinitions 12 are debut for them but the research goes further and the SuperHyperNotion, 13 SuperHyperUniform, and SuperHyperClass based on that are well-defined and 14 well-reviewed. The literature review is implemented in the whole of this research. For 15 shining the elegancy and the significancy of this research, the comparison between this 16 SuperHyperNotion with other SuperHyperNotions and fundamental 17 SuperHyperNumbers are featured. The definitions are followed by the examples and the 18 instances thus the clarifications are driven with different tools. The applications are 19 figured out to make sense about the theoretical aspect of this ongoing research. The 20 “Cancer’s Neutrosophic Recognition” are the under research to figure out the challenges 21 make sense about ongoing and upcoming research. The special case is up. The cells are 22 viewed in the deemed ways. There are different types of them. Some of them are 23 individuals and some of them are well-modeled by the group of cells. These types are all 24 officially called “SuperHyperVertex” but the relations amid them all officially called 25 “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic 26 SuperHyperGraph” are chosen and elected to research about “Cancer’s Neutrosophic 27 Recognition”. Thus these complex and dense SuperHyperModels open up some avenues 28 to research on theoretical segments and “Cancer’s Neutrosophic Recognition”. Some 29 avenues are posed to pursue this research. It’s also officially collected in the form of 30 some questions and some problems. Assume a SuperHyperGraph. Then a “1-failed 31 SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 32 is the maximum cardinality of a SuperHyperSet S of black SuperHyperVertices 33 (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn’t 34 turned black after finitely many applications of “the color-change rule”: a white 35 SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white 36 SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred 37 by “1-” about the usage of any black SuperHyperVertex only once to act on white 38 SuperHyperVertex to be black SuperHyperVertex; a “neutrosophic 1-failed 39 SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 40 is the maximum neutrosophic cardinality of a SuperHyperSet S of black 41 SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such 42 that V (G) isn’t turned black after finitely many applications of “the color-change rule”: 43 a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only 44 1/128 white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is 45 referred by “1-” about the usage of any black SuperHyperVertex only once to act on 46 white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. 47 Then an “δ−1-failed SuperHyperForcing” is a maximal 1-failed SuperHyperForcing of 48 SuperHyperVertices with maximum cardinality such that either of the following 49 expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : 50 |S ∩N(s)| > |S ∩(V \N(s))|+δ, |S ∩N(s)| < |S ∩(V \N(s))|+δ. The first Expression, 51 holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an 52 “δ−SuperHyperDefensive”; a“neutrosophic δ−1-failed SuperHyperForcing” is a maximal 53 neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with maximum 54 neutrosophic cardinality such that either of the following expressions hold for the 55 neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > 56 |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. 57 The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the 58 second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to 59 define “neutrosophic” version of 1-failed SuperHyperForcing. Since there’s more ways to 60 get type-results to make 1-failed SuperHyperForcing more understandable. For the sake 61 of having neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the 62 notion of “1-failed SuperHyperForcing”. The SuperHyperVertices and the 63 SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this 64 procedure, there’s the usage of the position of labels to assign to the values. Assume a 65 1-failed SuperHyperForcing. It’s redefined neutrosophic 1-failed SuperHyperForcing if 66 the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, 67 HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” 68 with the key points, “The Values of The Vertices & The Number of Position in 69 Alphabet”, “The Values of The SuperVertices&The maximum Values of Its Vertices”, 70 “The Values of The Edges&The maximum Values of Its Vertices”, “The Values of The 71 HyperEdges&The maximum Values of Its Vertices”, “The Values of The 72 SuperHyperEdges&The maximum Values of Its Endpoints”. To get structural examples 73 and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph 74 based on 1-failed SuperHyperForcing. It’s the main. It’ll be disciplinary to have the 75 foundation of previous definition in the kind of SuperHyperClass. If there’s a need to 76 have all SuperHyperConnectivities until the 1-failed SuperHyperForcing, then it’s 77 officially called “1-failed SuperHyperForcing” but otherwise, it isn’t 1-failed 78 SuperHyperForcing. There are some instances about the clarifications for the main 79 definition titled “1-failed SuperHyperForcing”. These two examples get more scrutiny 80 and discernment since there are characterized in the disciplinary ways of the 81 SuperHyperClass based on 1-failed SuperHyperForcing. For the sake of having 82 neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the notion of 83 “neutrosophic 1-failed SuperHyperForcing” and “neutrosophic 1-failed 84 SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned 85 by the labels from the letters of the alphabets. In this procedure, there’s the usage of 86 the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. 87 It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And 88 1-failed SuperHyperForcing are redefined “neutrosophic 1-failed SuperHyperForcing” if 89 the intended Table holds. It’s useful to define “neutrosophic” version of 90 SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make 91 neutrosophic 1-failed SuperHyperForcing more understandable. Assume a neutrosophic 92 SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended 93 Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, 94 SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are 95 “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic 96 SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic 97 2/128 SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table 98 holds. A SuperHyperGraph has “neutrosophic 1-failed SuperHyperForcing” where it’s 99 the strongest [the maximum neutrosophic value from all 1-failed SuperHyperForcing 100 amid the maximum value amid all SuperHyperVertices from a 1-failed 101 SuperHyperForcing.] 1-failed SuperHyperForcing. A graph is SuperHyperUniform if it’s 102 SuperHyperGraph and the number of elements of SuperHyperEdges are the same. 103 Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as 104 follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given 105 SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one 106 SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s 107 only one SuperVertex as intersection amid all SuperHyperEdges; it’s 108 SuperHyperBipartite it’s only one SuperVertex as intersection amid two given 109 SuperHyperEdges and these SuperVertices, forming two separate sets, has no 110 SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as 111 intersection amid two given SuperHyperEdges and these SuperVertices, forming multi 112 separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one 113 SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has 114 one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes 115 the specific designs and the specific architectures. The SuperHyperModel is officially 116 called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this 117 SuperHyperModel, The “specific” cells and “specific group” of cells are 118 SuperHyperModeled as “SuperHyperVertices” and the common and intended properties 119 between “specific” cells and “specific group” of cells are SuperHyperModeled as 120 “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, 121 indeterminacy, and neutrality to have more precise SuperHyperModel which in this case 122 the SuperHyperModel is called “neutrosophic”. In the future research, the foundation 123 will be based on the “Cancer’s Neutrosophic Recognition” and the results and the 124 definitions will be introduced in redeemed ways. The neutrosophic recognition of the 125 cancer in the long-term function. The specific region has been assigned by the model 126 [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is 127 identified by this research. Sometimes the move of the cancer hasn’t be easily identified 128 since there are some determinacy, indeterminacy and neutrality about the moves and 129 the effects of the cancer on that region; this event leads us to choose another model [it’s 130 said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s 131 happened and what’s done. There are some specific models, which are well-known and 132 they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves 133 and the traces of the cancer on the complex tracks and between complicated groups of 134 cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, 135 SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). 136 The aim is to find either the longest 1-failed SuperHyperForcing or the strongest 137 1-failed SuperHyperForcing in those neutrosophic SuperHyperModels. For the longest 138 1-failed SuperHyperForcing, called 1-failed SuperHyperForcing, and the strongest 139 SuperHyperCycle, called neutrosophic 1-failed SuperHyperForcing, some general results 140 are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have 141 only two SuperHyperEdges but it’s not enough since it’s essential to have at least three 142 SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of 143 any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, 144 literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph 145 theory and neutrosophic SuperHyperGraph theory are proposed.

New ideas on the framework of Neutrosophic SuperHyperGraph for different styles of Neutrosophic SuperHyper-Wheel and Neutrosophic SuperHyper-Star are introduced. More instances and more clarifications alongside sufficient references are featured with a specific type of independency of SuperHyperVertices.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Neutrosophic Failed SuperHyperClique theory, SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Extreme SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

The apicomplexan parasite, Sarcocystis neurona causes the degenerative neurological equine protozoal myeloencephalitis (EPM) disease of horses. Due to its host range expansion, S. neurona is an emerging threat that requires close monitoring. In apicomplexans, protein kinases (PKs) have been implicated in a myriad of critical functions such as host cell invasion, cell cycle progression and host immune responses evasion. Here, we used various bioinformatics methods to define the kinome of S. neurona and phylogenetic relatedness of its PKs to other apicomplexans. Further, three-dimensional (3D) homology models for selected S. neurona putative PKs were constructed and evaluated for inhibitor docking. We identified 92 putative PKs clustering within the AGC, CAMK, CK1, CMGC, STE, TKL, aPK and OPK groups. Although containing the universally conserved PKA (AGC group), S. neurona kinome was devoid of PKB and PKC, but contained the six apicomplexan conserved CDPKs (CAMK group). The OPK group was represented by ROPKs 19A, 27, 30, 33, 35 and 37, but was devoid of the virulence-associated ROPKs 5, 6, 18 and 38. Two out of the three S. neurona CK1 enzymes had high sequence similarities to T. gondii TgCK1-α and TgCK1-β and the Plasmodium PfCK1. Docking of four inhibitors onto homology models of putative ROP27 and PKA indicated that inhibition of S. neurona PKs is feasible, but needs to be experimentally tested. The essentiality of apicomplexan PKs makes the elucidation of S. neurona kinome a key milestone for development of novel therapeutics for EPM.

In this research, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty neutrosophic SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is an neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as an neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ is excluded in every given neutrosophic SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an neutrosophic SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an neutrosophic SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an neutrosophic R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an neutrosophic R-SuperHyperGirth SuperHyperPolynomial.}} $ The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic type-SuperHyperSet with the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperGirth isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth is an neutrosophic SuperHyperSet includes only less than four neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth isn't up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth and it's an neutrosophic SuperHyperGirth . Since it 's the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are only less than four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, thus the obvious neutrosophic SuperHyperGirth, is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth, is: ,is the neutrosophic SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with neutrosophic SuperHyperGirth theory, SuperHyperGraphs, and neutrosophic SuperHyperGraphs theory are proposed.

In this research, new setting is introduced for assuming a SuperHyperGraph. Then a ``SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperClique'' is a \underline{maximal} SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperClique'' is a \underline{maximal} neutrosophic SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme SuperHyperClique theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with neutrosophic SuperHyperMatching theory, SuperHyperGraphs theory, and neutrosophic SuperHyperGraphs theory are proposed.

In this research, Assume a neutrosophic SuperHyperGraph. Then a ``Failed SuperHyperStable $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common; a ``neutrosophic Failed SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's a neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperStable'' $\mathcal{I}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

in this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic SuperHyperStable. In this research article, there are some research segments for ``Neutrosophic SuperHyperStable'' about some researches on neutrosophic SuperHyperStable. With researches on the basic properties, the research article starts to make neutrosophic SuperHyperStable theory more understandable. Assume a neutrosophic SuperHyperGraph. Then a ``neutrosophic SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an SuperHyperStable and Neutrosophic SuperHyperStable. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognitions'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognitions''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognitions''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a``SuperHyperStable'' $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's no SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperStable'' is a \underline{maximal} SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperStable'' is a \underline{maximal} neutrosophic SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. It's useful to define a ``neutrosophic'' version of an SuperHyperStable. Since there's more ways to get type-results to make an SuperHyperStable more understandable. For the sake of having neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of an ``SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume an SuperHyperStable. It's redefined a neutrosophic SuperHyperStable if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph'' with the key points, ``The Values of The Vertices \& The Number of Position in Alphabet'', ``The Values of The SuperVertices\&The maximum Values of Its Vertices'', ``The Values of The Edges\&The maximum Values of Its Vertices'', ``The Values of The HyperEdges\&The maximum Values of Its Vertices'', ``The Values of The SuperHyperEdges\&The maximum Values of Its Endpoints''. To get structural examples and instances, I'm going to introduce the next SuperHyperClass of SuperHyperGraph based on an SuperHyperStable. It's the main. It'll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there's a need to have all SuperHyperConnectivities until the SuperHyperStable, then it's officially called an ``SuperHyperStable'' but otherwise, it isn't an SuperHyperStable. There are some instances about the clarifications for the main definition titled an ``SuperHyperStable''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on an SuperHyperStable. For the sake of having a neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of a ``neutrosophic SuperHyperStable'' and a ``neutrosophic SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It's redefined ``neutrosophic SuperHyperGraph'' if the intended Table holds. And an SuperHyperStable are redefined to an ``neutrosophic SuperHyperStable'' if the intended Table holds. It's useful to define ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic SuperHyperStable more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are ``neutrosophic SuperHyperPath'', ``neutrosophic SuperHyperCycle'', ``neutrosophic SuperHyperStar'', ``neutrosophic SuperHyperBipartite'', ``neutrosophic SuperHyperMultiPartite'', and ``neutrosophic SuperHyperWheel'' if the intended Table holds. A SuperHyperGraph has a ``neutrosophic SuperHyperStable'' where it's the strongest [the maximum neutrosophic value from all the SuperHyperStable amid the maximum value amid all SuperHyperVertices from an SuperHyperStable.] SuperHyperStable. A graph is a SuperHyperUniform if it's a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It's SuperHyperPath if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it's SuperHyperCycle if it's only one SuperVertex as intersection amid two given SuperHyperEdges; it's SuperHyperStar it's only one SuperVertex as intersection amid all SuperHyperEdges; it's SuperHyperBipartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it's SuperHyperMultiPartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it's a SuperHyperWheel if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph''. In this SuperHyperModel, The ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperVertices'' and the common and intended properties between ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperEdges''. Sometimes, it's useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``neutrosophic''. In the future research, the foundation will be based on the ``Cancer's Recognitions'' and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be neutrosophic SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperStable or the strongest SuperHyperStable in those neutrosophic SuperHyperModels. For the longest SuperHyperStable, called SuperHyperStable, and the strongest SuperHyperCycle, called neutrosophic SuperHyperStable, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn't any formation of any SuperHyperCycle but literarily, it's the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn't form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperDefensive SuperHyperAlliances and Neutrosophic SuperHyperDefensive SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperDefensive SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperDefensive SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperDefensive SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperDefensive SuperHyperAlliances, then it’s officially called “SuperHyperDefensive SuperHyperAlliances” but otherwise, it isn’t SuperHyperDefensive SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperDefensive SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperDefensive SuperHyperAlliances. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperDefensive SuperHyperAlliances” and “neutrosophic SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperDefensive SuperHyperAlliances are redefined “neutrosophic SuperHyperDefensive SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperDefensive SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperDefensive SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperDefensive SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperDefensive SuperHyperAlliances.] SuperHyperDefensive SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperDefensive SuperHyperAlliances or the strongest SuperHyperDefensive SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperDefensive SuperHyperAlliances, called SuperHyperDefensive SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperDefensive SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously; failed independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Failed-Independent Number,” and “Setting of Failed Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, two neighbors, form maximal set but with slightly differences, in cycle-neutrosophic graphs, two neighbors forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of all vertices leads us to neutrosophic failed-independent number and failed independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices containing only center and one other vertex, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices including two vertices from different parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of t vertices from different parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic failed-independent number but the neutrosophic cardinality of a set has eligibility to call failed independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connections amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

Constructing new graph from the graph's parameters and related notions in the way that, the study on the new graph and old graph in their parameters could be facilitated. As graph, new graph has some characteristics and results which are related to the structure of this graph. For this purpose, regular graph is considered so the internal relation and external relation on this new graph are studied. The kind of having same number of edges when this number is originated by common number of graphs like maximum degree, minimum degree, domination number, coloring number and clique number, is founded in the word of having regular graph

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

In this outlet, I’ve devised the concept of relation amid two points where these points are coming up to make situation which in that the set of objects are greed to represent the story of how to be in whatever situations when these two points have the styles of being everywhere in the highlights of the concept which are coming from the merits of these points where are eligible to make capable situation to overcome every situation when they’re participant in the hugely diverse situations which mean too styles of graphs with have the name or the general results for the general situation as possible as are.

This paper examines the most prominent “progressive” American religious groups’ (as defined by those that liberalized early on the issue of birth control, circa 1930) views of women between the first and second waves of the feminist movement (1930-1965). We find that some groups have indeed had a long and outspoken support for women’s equality. Using their modern-day names, these groups, the United Church of Christ, the Unitarian Universalist Church, and to a lesser extent, the Society of Friends, or Quakers, professed strong support for women’s issues, early, and often. However, we also find that prominent progressive groups –the Protestant Episcopal Church, the Methodist Episcopal Church and the United Presbyterian Church, were virtually silent on the issue of women’s rights – even as the second wave of the feminist movement was picking up steam – as late as 1965.

Following an initial mechanical insult, traumatic spinal cord injury (SCI) induces a secondary wave of injury, resulting in a toxic lesion environment inhibitory to axonal regeneration. This review focuses on the glial cell line-derived neurotrophic factor (GDNF) and its application, also in combination with other factors and cell transplantations, for repairing the injured spinal cord. As recent decades of studies strongly suggest combinational treatment approaches hold the greatest therapeutic potential for the central nervous system (CNS) trauma, future directions of combinational therapies will also be discussed.

Background: The antimalarial drug chloroquine and antimicrobial drug azithromycin have received significant attention during the current COVID-19 pandemic. Both drugs can alter cardiac electrophysiology and have been associated with drug-induced arrhythmias. Meanwhile, sympathetic activation is commonly observed during systemic inflammation and oxidative stress (e.g., in SARS-CoV-2 infection), and may influence the electrophysiological effects of chloroquine and azithromycin. Here, we investigated the effect of beta-adrenergic stimulation on proarrhythmic properties of chloroquine and azithromycin using a detailed in silico model of ventricular electrophysiology. Methods: Concentration-dependent chloroquine and azithromycin-induced alterations in ion-channel function were incorporated into the Heijman canine ventricular cardiomyocyte model. Single and combined drug effects on action-potential (AP) properties were analyzed using a population of 592 models accommodating inter-individual variability. Sympathetic stimulation was simulated by an increase in pacing rate and experimentally validated isoproterenol-induced changes in ion-channel function. Results: At 1 Hz pacing, therapeutic doses of chloroquine and azithromycin (5 and 20 µM, respectively) individually prolonged AP duration (APD) by 33% and 13%. Their combination produced synergistic APD prolongation (+161%) with incidence of proarrhythmic early afterdepolarizations in 53.5% of models. Increasing the pacing frequency to 2 Hz shortened APD and together with 1 µM isoproterenol corrected the drug-induced APD prolongation. No afterdepolarizations occurred following increased rate and simulated application of 0.1-1 µM isoproterenol. Conclusion: Sympathetic stimulation limits chloroquine- and azithromycin-induced proarrhythmia by reducing their APD-prolonging effect, suggesting the importance of heart rate and autonomic status monitoring in particular conditions (e.g., COVID-19).

Recent years have seen a massive increase in research on mindfulness as both a therapeutic practice as well as a protective health factor. While many associations have been made between mindfulness and clinical outcomes, understanding of the underlying mechanistic processes is still in its infancy. In this review, associations between mindfulness and other established frameworks in cognitive control are explored—in particular the dual modes of control framework in cognitive control theory. Studies in mindfulness providing evidence towards a dual-mode mindfulness model are reviewed and compared with the proactive and reactive modes of cognitive control to identify common underlying principles. Studies involving cognitive testing, advanced neuroimaging, and neurotransmitter levels and their associations with proactive and reactive control are reviewed in the context of the dual modes of mindfulness. While evidence supporting relationships between proactive and reactive modes of mindfulness and cognitive control are preliminary, existing literature on mindfulness already supports the notion of two components of mindfulness and is in line with the hypothesis that cognitive control and mindfulness are closely related. Since preliminary evidence suggests that proactive forms of mindfulness are more associated with improvement in clinical outcomes, mindfulness programs could be modified to target proactive mindfulness practices to maximize outcomes. The implications of proactive and reactive mindfulness on therapy, limitations of the framework, and necessity of studies providing direct evidence are further discussed.

A checklist of parasitic cymothoids from Malaysian waters is presented based on available literature and material collected from 2010 to 2020. Most of the collected specimens were recorded from waters of Terengganu, east coast of Peninsular Malaysia (facing South China Sea), whereas literature records were represented from Sarawak, along the Miri coast of northwest Borneo. The checklist comprises 18 species under 10 genera, seven of which are new records from Malaysia, which includes Anilocra nemipteri Bruce, 1987; Ceratothoa barracuda Martin, Bruce and Nowak, 2015; Ceratothoa carinata (Bianconi, 1869); Cymothoa epimerica Avdeev, 1979; Elthusa sigani Bruce, 1990; Joryma engraulidis (Barnard, 1936) and Renocila richardsonae Williams and Bunkley-Williams, 1992. Eight new host records are based on collected specimens: Anilocra nemipteri was dorsally attached on Nemipterus nemurus (Bleeker 1857), Nemipterus nematophorus (Bleeker 1854), Nemipterus tambuloides (Bleeker 1853), and Nemipterus thosaporni Russell 1991 (family Nemipteridae); Ceratothoa carinata was found in the buccal cavity of Decapterus macrosoma Bleeker 1851 (family Carangidae); Cymothoa eremita (Brunnich, 1783) was attached in the buccal cavity of Nemipterus tambuloides and Nemipterus furcosus (Valenciennes 1830); Elthusa sigani was found attached on Pterois russelli Bennett 1831 (family Scorpaenidae); and Renocila richardsonae was attached on the caudal fin of Upeneus japonicus (Houttuyn 1782) (family Mullidae). All cymothoid species listed here are known to have a Central Indo Pacific distribution, with some ranging as far as the western Indian Ocean. The cymothoid-host association is here listed from 28 fish families, with the most common reported from Carangidae (pompanos, jack mackerels, runners, scads), Engraulidae (anchovies) and Leiognathidae (ponyfishes, slipmouths). This paper is the first comprehensive treatment to update both verified literature data and deposited specimens, with a key for the family Cymothoidae in Malaysian waters.

Industrial hemp (Cannabis sativa L.) is an attractive candidate for sustainable pest management due to its abundance of bioactive compounds with potential pesticidal properties. Solvent choice has a significant impact on the extraction efficiency of bioactive compounds. Deep Eutectic Solvents (DESs) are gaining popularity in extraction because they are safe and environmentally friendly, making them viable alternatives to organic solvents (OSs). This research first compared the extraction efficiency of OSs on the extraction of phytochemicals from the infloresences of two hemp varieties, Citrus and Cherry Dwarf. Inflorescences were extracted using three OSs, ethanol, ethyl acetate, and hexane. The highest level of cannabidiol (CBD; 0.69%) was extracted from Cherry Dwarf using ethanol while the level of delta-9 tetrahydrocannabinol THC (0.19%) was essentially the same in both. Therefore, Cherry Dwarf was selected to compare the extraction efficiency of DESs to the OSs. The DESs were choline chloride/ethylene glycol, citric acid/ethylene glycol, menthol/lauric acid, choline chloride/urea and choline chloride/glycerol. In the targeted analysis, choline chloride/ethylene glycol extracted the highest amount of CBD (0.87%) followed by choline chloride/urea (0.78%). As some DESs outperformed ethanol, the popular solvent for extracting cannabinoids, DESs are viable candidates to replace organic solvents.

PdRe/Al2O3 catalysts are highly selective for hydrogenation of furfural to furfuryl alcohol (FAL). Moreover, synergy between the metals can result in greater specific activity (higher turnover frequency, TOF) than exhibited by either metal alone. Bimetallic catalyst structure depends strongly on the metal precursors employed and their addition sequence to the support. In this work, PdRe/Al2O3 catalysts were prepared by: (i) co impregnation (CI) and sequential impregnation (SI) of  Al2O3 using HReO4 and Pd(NO3)2, (ii) SI using NH4ReO4 and [Pd(NH3)4(NO3)2], (iii) HReO4 addition to a reduced and passivated Pd/Al2O3 catalyst, and (iv) impregnation with the double complex salt (DCS), [Pd(NH3)4(ReO4)2]. Raman spectroscopy and temperature-programmed reduction (TPR) evidence larger supported PdO crystallites in catalysts prepared using Pd(NO3)2 than [Pd(NH3)4(NO3)2]. Surface [ReO4]- species detected by Raman exhibit TPR peak temperatures from ranging 85 to 260°C (versus 375°C for Re/Al2O3). After H2 reduction at 400°C, the catalysts were characterized by chemisorption, temperature-programmed hydride decomposition (TPHD), CO diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), and scanning transmission electron microscopy (STEM) with energy-dispersive x-ray (EDX) spectroscopy. The CI catalyst containing supported Pd-Re alloy crystallites had a TOF similar to Pd/Al2O3 but higher (61%) FAL selectivity. In contrast, catalysts prepared by methods (ii-iv) containing supported Pd-Re nanoparticles exhibit higher TOFs and up to 78% FAL selectivity.

This study investigates the pivotal areas where Artificial Intelligence (AI) integration in healthcare warrants further exploration, leveraging insights from Boston Specialists, a forefront healthcare provider in AI adoption. Employing a qualitative case study approach, enriched by in-depth interviews and comprehensive literature reviews, we identify three main domains for potential AI expansion: scheduling efficiency, clinical documentation, and AI-driven medical research. Our results underscore the substantial enhancements AI brings to operational workflows and patient care, notably through improved scheduling systems, accuracy in medical documentation, and the facilitation of data-driven research methodologies. These findings suggest a critical need for healthcare institutions to further invest in AI technologies, focusing on these key areas to harness AI's full potential in personalizing care, optimizing efficiency, and advancing medical knowledge. The study concludes with a call for continued investigation into AI's integration within healthcare settings, emphasizing the importance of a supportive organizational infrastructure, ethical considerations, and data security in realizing AI's transformative impact on healthcare delivery and patient outcomes.

Most commercial Cannabis sativa L. (cannabis) genotypes are short-day plants and cultivators typically use a 12.0 h uninterrupted dark period to induce flowering; however, scientific information is lacking to prove this is the optimal dark period for all genotypes, and cultivar specific photoperiods may increase productivity. Tissue culture can be used for research requiring multiple treatments, proper replication, and in a controlled environment on a smaller scale compared to greenhouse and indoor facilities. To determine whether cannabis explants can flower under varied photoperiods in vitro, explants were grown under one of six photoperiod treatments: 12.0, 13.2, 13.8, 14.4, 15.0, and 16.0 h for four weeks. The percentage of flowering explants was highest under 12.0 and 13.2 h treatments. There were no treatment effects on the fresh weight, final height, or growth index of the explants. The results suggest an uninterrupted dark period of at least 10.8 h (i.e. 13.2 h photoperiod) is needed to induce the flowering of this genotype. In vitro flowering could provide a unique and high throughput approach to study floral/seed development and secondary metabolism in cannabis under highly controlled conditions. Further research should determine if this response is the same on a whole plant level.

Current instrumental technology in evaluating performance of skin care creams is still rather limited and there are no industrial standard testing equipment, method and performance specifications for it. In this paper, we report our attempt in using an instrument called PhabrOmeter for this purpose. PhabrOmeter is a commercialized instrument for sensory performance evaluation of textiles, leather, paper and nonwoven and has been designated by American Association of Textile Chemists and Colorists (AATCC) as a standard test method for textiles, AATCC TM 202 in 2013. By adopting artificial skin samples treated with skin care creams, we have developed a procedure to apply this instrument for evaluation of skin care creams from sample preparation, measurement to data analysis and interpretation. The results using commercial skin care creams to demonstrate the feasibility and advantages of this instrument are provided.

The presence of potentially pathogenic bacteria on veterinary clinic surfaces may be problematic. In this study we collected swab samples (Fisherbrand, double transport swabs with Stuart’s liquid medium) and water samples from five veterinary rehabilitation clinics. Swabs and water samples were transported to a microbiology lab for processing. At the lab swabs were used to inoculated Hardy’s Cdiff Banana broth (for Clostridium difficile [Cdiff]), and five different types of bacterial growth media, including: Hardy CHROM MRSA agar (methicillin resistant Staphylococcus aureus [MRSA], and S. pseudintermedius [SIM]), Mannitol Salt Agar (S. aureus), Eosin Methylene Blue agar (enterics [ENT]), Pseudomonas Isolation agar (Pseudomonas sp.), and Tryptic Soy Agar [TSA] (non-specific). The most prominent species cultured was Cdiff (on nearly 55% of swabs). Bacillus sp. and Enterics were encountered on nearly 35% of swabs, with MRSA and SIM on just over 10% of swabs. The most contaminated sample site was harnesses/life jackets used with the underwater treadmill (33% of swabs). Underwater treadmill water had total bacterial counts from 1.6 to 2.7 e3 cfu/ml. Of all bacterial species detected SIM tends to be more pathogenic for dogs. Targeted cleaning/disinfecting in these clinics could help reduce risks for both animals and caregivers utilizing these clinics.

Although the vegetative stage of indoor cannabis production can be relatively short in duration, there is a high energy demand due to higher light intensities (LI) than the clonal propagation stage and longer photoperiods than the flowering stage (i.e., 16 – 24 hours vs. 12 hours). While electric lighting is a major component of both energy consumption and overall production costs, there is a lack of scientific information to guide cultivators in selecting a LI that corresponds to their vegetative stage production strategies. To determine the vegetative plant responses to LI, clonal plants of ‘Gelato’ were grown for 21 days with canopy-level photosynthetic photon flux densities (PPFD) ranging between 135 and 1430 µmol·m^-2·s^-1 on a 16-hour photoperiod (i.e., daily light integrals of ≈ 8 to 80 mol·m^-2·d^-1). Plant height and growth index responded quadratically; the number of nodes, stem thickness, and aboveground dry weight increased asymptotically; and internode length and water content of aboveground tissues decreased linearly with increasing LI. Foliar attributes had varying responses to LI. Chlorophyll content index increased asymptotically, leaf size decreased linearly and specific leaf weight increased linearly with increasing LI. Generally, PPFD levels of ≈ 900 µmol·m^-2·s^-1 produced compact, robust plants that are commercially relevant, while PPFD levels of ≈ 600 µmol·m^-2·s^-1 promoted plant morphology with more open architecture – to increase airflow and reduce the potential foliar pests in compact (i.e., indica-dominant) genotypes.

Universe created with the fundamental laws of science. Nature is lazy and needs to form with the least possible to be perfect. A natural pattern, such as pinecones, sunflowers, pineapples, and cacti, has a double spiral structure. Once we look at these plants' centers, we will see the seeds line up in spirals shape. The number of spirals whirling in each direction will give us the Fibonacci numbers. We can give more examples representing these natural patterns; however, one example is unique and remarkable. The similarities between spiral galaxies- Milky Way and hurricanes. Are they similar in every property or just in shape and rotational movements? What are the similarities between them? This short review article will try to find these questions' answers by reviewing some literature articles. The first part of this article gave some information about hurricanes and galaxies. The second of this article focused on the comparison between hurricanes and galaxies. Finally, we will conclude the article with our remarks.

The mechanisms of treatment-resistant epilepsy remain unclear. We have previously shown that frontline administration of therapeutic doses of lamotrigine (LTG), which preferentially inhibits the fast-inactivation state of sodium channels, during corneal kindling of mice promotes cross-resistance to several other antiseizure medicines (ASMs). However, whether this phenomenon extends to monotherapy with ASMs that stabilize the slow inactivation state of sodium channels is unknown. Therefore, this study assessed whether lacosamide (LCM) monotherapy during corneal kindling would promote future development of drug-resistant focal seizures in mice. Male CF-1 mice (n=40/group; 18-25 g) were administered an anticonvulsant dose of LCM (4.5 mg/kg, ip), LTG (8.5 mg/kg, ip), or vehicle (0.5% methylcellulose) twice daily for two weeks during kindling. A subset of mice (n=10/group) were euthanized 1 day after kindling for immunohistochemical assessment of astrogliosis, neurogenesis, and neuropathology. The dose-related antiseizure efficacy of distinct ASMs, LTG, LCM, carbamazepine, levetiracetam, gabapentin, perampanel, valproic acid, phenobarbital, and topiramate was then assessed in remaining kindled mice. Neither LCM nor LTG administration prevented kindling: 29/39 vehicle-exposed mice were kindled; 33/40 LTG-exposed mice were kindled; and 31/40 LCM-exposed mice were kindled. Mice administered LCM or LTG during kindling became resistant to escalating doses of LCM, LTG, and carbamazepine. Perampanel, valproic acid, and phenobarbital were less potent in LTG- and LCM-kindled mice, whereas levetiracetam and gabapentin retained equivalent potency across groups. Notable differences in reactive gliosis and neurogenesis were also appreciated. This study indicates that early, repeated administration of sodium channel blocking ASMs, regardless of inactivation state preference, promotes pharmacoresistant chronic seizures. Inappropriate ASM monotherapy in newly diagnosed epilepsy may thus be one driver of future drug-resistance, with resistance being highly ASM class-specific.

Coral reefs are critical ecosystems globally for marine fauna, biodiversity and through the services they provide to humanity. However, they are significantly threatened by anthropogenic stressors, such as climate change. By combining 9 environmental variables and ecological and health-based thresholds obtained from the available literature, we develop, using fuzzy logic (discontinuous functions), a Coral Reef Stress Exposure Index (CRSEI) for remotely monitoring coral reef exposure to environmental stressors. Our approach capitalises on the abundance of readily available satellite Earth Observation (EO) data available in the Google Earth Engine (GEE) cloud-based geospatial processing platform. CRSEI values from 3157 distinct reefs were generated and mapped across 12 important coral reef ecosystem regions. Quantitative analyses indicated that the index detected significant temporal differences in stress and was, therefore, able to capture historic change at a global scale. We also applied the CRSEI to three case-study reef ecosystems, previously well-monitored for stress and disturbance using other methods. PCA analysis indicated that depth, current, sea surface temperature (SST) and SST anomaly accounted for the greatest contribution to the variance in stress in these three regions. The CRSEI corroborated temporal and spatial differences in stress exposure from known disturbances within these reference regions, in addition to identifying the potential drivers of inter- and intra-region differences in stress, namely depth, degree heating weeks and SST anomaly. We discuss how the index can be further improved in future with site-specific thresholds for each stress variable, and the incorporation of additional variables not currently available in GEE. This index provides an open access tool, built around a free and powerful processing platform, that has broad potential to assist in the regular monitoring of our increasingly imperilled coral reef ecosystems, and, in particular, those that are remote or inaccessible.

Higher consumption of fruit and vegetables has been associated with a lower risk of various chronic diseases including coronary heart disease, obesity, and certain cancers. Recently, fruit and vegetable intake has also been linked with mental health, including depression. This systematic review aimed to evaluate the association between fruit and vegetable intake and depressive symptoms in young people and adults aged 15-45. The systematic review focused on peer-reviewed cohort studies published from 1 January 2000 to 31 August 2020 using searches of six electronic databases. The exposure was fruit and vegetable consumption analysed both separately and/or together, and the outcome was depression or depressive symptoms. Data from eligible studies were extracted according to predefined criteria and the studies were appraised using the Newcastle-Ottawa Scale (NOS) for Cohort Studies to evaluate for study quality and risk of bias. To evaluate the association between fruit and vegetable consumption and depressive symptoms, a narrative synthesis was conducted. Of 9667 potentially relevant studies that were screened for title and abstracts, 144 full text studies were evaluated, and 12 studies from seven countries were deemed eligible and included in the qualitative synthesis. Using the NOS framework one study was categorised as ‘very good’ quality, ten studies were ‘good’ quality, and two studies were ‘moderate’ quality. With respect to combined fruit and vegetable consumption, two studies demonstrated an inverse association with depression. When the effects of fruit and vegetable on depression were analysed separately, five studies showed significant associations in fruit consumption, and two studies showed significant associations in vegetable consumption. Four studies showed no association between combined fruit and vegetable consumption and depression, one study showed no association between fruit consumption and depression, and two studies showed no association between vegetable consumption and depression. Despite some contradictory results in the studies included in this review, the evidence seems to be building that a possible association exists, and this may have implications for addressing the burden of mental illness in young people and adults aged 15-45 years. Well-designed prospective cohort studies are needed to provide more robust evidence on the diet-depression relationship.

This paper aims to investigate the rate of expansion and extraction within the solar system. We carried out the Solar system expansion calculations to do such a review. The Universe is expected to look the same from every point in it. After the big bang, Universe is expanding at some speed. Astrophysicists have been in a race to measure precisely how fast the Universe is expanding since Hubble announced that galaxies were systematically moving away from Milky Way Galaxy with a current speed in 1929. Hubble’s observations came after Einstein’s general relativity, which inspired the big bang theory. According to the Big Bang theory, the Universe has created billions of years ago with an explosion and started to expand until today. The expansion of the Universe mostly happens in vast spaces, so clusters of galaxies move away from each other. For example, raising bread during baking will expand, but the raisings will stay the same size while moving each other to expand the bread. Observers have proven that an object (galaxies, a cluster of planets) held together by gravity has a patch of nonexpanding space produced by a gravitational field. However, some observers claimed the solar system is not expanding, while others claimed it is expanding. Does our solar system expand in an expanding Universe? The cosmological expansion of local systems is reviewed in the modern cosmological models. We showed answers related to this question with the help of literature. This review article revisited the proof of the Solar System’s expansion and its speed with about 0.32 nm/s in an expanding Universe.

This article examines older physical education (PE) teachers’ wellbeing over the course of their career in Finland. The study highlights challenges to physical and mental functioning as well as how teachers respond to these challenges. The six interviewees were over 55-year-old PE teachers, whose career had lasted for more than 30 years. Qualitative methods were used in the collection, transcription and analysis of the research data. The qualitative analysis consisted of a series of interpretations that visualised the world described by the interviewees. All the research participants had physical problems that affected their teaching and make teachers consider a potential career change. To be able to teach, teachers adapted their ways of working according to the challenges brought by age and injuries. The research participants found that the challenges caused by musculoskeletal problems and ageing were an inevitable part of the profession. They emphasised the positive sides of the work: the profession permits varied workdays. In addition, the teachers noted that their work provides them with opportunities to remain physically fit. Teaching health education is a means to lighten the workload of older teachers. PE teachers enjoy their profession and are dedicated to it, despite all the challenges. The interviewed participants clearly experienced work engagement. Our development proposal for teacher education is that future PE teachers be informed about the risks involved in the profession. Such activity helps young teachers reflect proactively on the measures taken to maintain their functioning during their career and on perspectives related to the ways of working.

In order to remain competitive in the highly competitive construction industry, it is crucial for construction organizations to continually improve their overall performance, as project performance is a key determinant of their relevance. Despite the industry's competitiveness and risk, it has been reported that the construction industry has the lowest return margins compared to other industries (Jackson, 1999), suggesting that the project performance of construction organizations in the industry has not been up to par. This issue can be attributed to several factors, with motivation being the primary factor. Unfortunately, motivation is often disregarded in the construction industry due to the short duration of many construction projects and the high rate of employee turnover. The impact of employee dissatisfaction and related work attitudinal problems on performance in the construction industry is a matter of concern, particularly in developing countries where working conditions may be unappealing. The severity of this issue cannot be overstated.The objective of this research is to evaluate the effectiveness of motivational techniques in enhancing project performance in Nigeria. The study employed a survey research design and targeted the management staff of construction firms in Lagos State, Nigeria. The questionnaire was used to collect data, and the respondents were purposively selected from the population. Data analysis was conducted using percentage, mean ranking, and chi-square. The findings reveal that the opportunity to learn new skills, with a mean score of 0.85, and wage increment, with a mean score of 0.82, were the most widely adopted motivational techniques for management staff and skilled labor, respectively, in construction firms. Additionally, the study found that most of the motivational schemes tested did not produce statistically significant results, indicating low adoption and limited effectiveness in enhancing project performance. As a result, it is suggested that construction companies in Nigeria should implement and enforce financial and non-financial incentives to enhance the performance of their employees and consequently, improve project performance.

This study determines the threshold for the computational rate of actuator motor controllers for unmanned underwater vehicles necessary to accurately follow discontinuous square wave commands. Motors must track challenging square-wave inputs, and identification of key computational rates permit application of deterministic artificial intelligence (D.A.I.) to achieve tracking to a machine-precision degree of accuracy in direct comparison to other state-of-art approaches. All modeling approaches are validated in MATLAB simulations where the motor process is discretized at varying step-sizes (inversely proportional to computational rate). At a large step-size (fast computational rate), discrete D.A.I. shows a mean error more than three times larger than that of a ubiquitous model-following approach. Yet, at a smaller step size (slower computational rate), the mean error decreases by a factor of 10, only three percent larger than that of continuous D.A.I. Hence, the performance of discrete D.A.I. is critically affected by the sampling period for discretization of the system equations and computational rate. Discrete D.A.I. should be avoided when small step-size discretization is unavailable. In fact, continuous D.A.I. has surpassed all modeling approaches which makes it the safest and most viable solution to future commercial applications in unmanned underwater vehicles.

Advanced cutaneous melanoma is considered the most aggressive type of skin cancer with variable rates of treatment response. Nowadays, there are available some classes of immunotherapy and target therapy for its treatment. Immunotherapy can inhibit tumor growth and its recurrence by triggering host's immune system, while targeted therapy acts inhibiting specific molecules or signaling pathways. However, melanoma response to these treatments are highly heterogenous, and frequently become resistant. Epigenome (DNA/histone modification) contribute to cancer initiation and progression. Epigenetic alterations are divided into four levels of gene expression regulation: DNA methylation, histone modification, chromatin remodeling and non-coding RNAs regulation. The deregulation of lysine methyltransferase enzymes is associated with tumor initiation, invasion, development of metastases, changes in immune microenvironment and drug resistance. The study of lysine histone methyltransferase (KMT) inhibitors is important to cancer epigenetic mechanisms understanding and to biological processes. In addition to immunotherapy and target therapy, the research and development of KMT inhibitors is ongoing. Many studies are exploring the therapeutic implications and possible side effects of these compounds, besides their adjuvant potential to the approved current therapies. Importantly, as with any drug development, safety, efficacy, and specificity are crucial considerations when developing KMT inhibitors for clinical applications.

The 2019 Coronavirus Disease (COVID-19) is a major cause of morbidity and mortality worldwide. Since late November 2021, Omicron variant has emerged as the primary cause of COVID-19 and caused a huge increase in the reported incidence around the world. To date, 32-34 spike mutations have been reported, 15 of which were located in the receptor-binding domain that interacts with the cell surface of the host cells, while the rest were located in the N-terminal domain and around the Furin cleavage site. At present, both the genomic and clinical profiles of this novel variant are being investigated. Here, we aim to discuss the recent reports on the transmissibility and severity of Omicron variant from both the genetic and clinical perspectives. Afterward, we also take the chance to deliver our personal view on the topic.

In this work, we report on the first attempt using size-controlled ZnO nanoparticles (NPs) to analyze role of thioacetamide (TAA) in forming ZnS nanostructures from ZnO. The size-controlled B(blue)_, G(green)_, Y(yellow)_ZnO QDs, and NC (nanocrystalline)_ZnO NPs were synthesized by sol-gel process as well as hydrothermal method, respectively and then reacted with an ethanolic TAA solution as sulfur source. After reacting with TAA, the formation of ZnS QDs was observed over time. The chemical reactions were identified using X-ray diffraction (XRD), Transmission Electron Microscope (TEM), UV-vis spectroscopy, and Photoluminescence (PL). All results indicate that ZnS formation is due to direct crystal growth and/or chemical conversion of ZnO to ZnS. Our results enable a broader understanding of the synthetic mechanisms involved in the use of TAA as a sulfur source in forming ZnS nanostructures from ZnO.

In the first year of its appearance, the 2019 coronavirus disease (COVID-19) has affected more than 150 million individuals and killed 3 million people worldwide. The pandemic has also triggered numerous global initiatives to tackle the newly emerging disease, including the development of SARS-CoV-2 vaccines and the attempt to discover potential pharmacological therapies. Nonetheless, despite the success of SARS-CoV-2 vaccines development, COVID-19 therapy remains challenging. Several repurposed drugs that were documented to be useful in small clinical trials have been shown to be ineffective in larger studies. Additionally, the pathophysiology of SARS-CoV-2 infection displayed the predominance of hyperinflammation and immune dysregulation in inducing multiorgan damage. Therefore, the potential benefits of both immune modulation and suppression in COVID-19 have been extensively discussed. Here, we reviewed the roles of immunomodulation as potential COVID-19 pharmacological modalities based on the existing data and proposed several new immunologic targets to be tested in the foreseeable future.

Climate change, recognized as a global crisis, is not only altering our environment but also significantly impacting human health. Particularly, its influence on non-communicable diseases (NCDs), a leading cause of global mortality, is becoming increasingly evident yet underexplored. This review aims to synthesize current research on the impact of climate change on NCDs, addressing a critical gap in our understanding of how environmental changes affect human health. We examine the complex interplay between climate change and NCDs, drawing insights from recent studies that highlight the adverse effects of climate variables on chronic diseases, such as cardiovascular and kidney diseases, and the role of food and nutrition security in this nexus. Furthermore, the review explores the disproportionate impact on vulnerable regions and populations, particularly in Pacific Island countries and territories, underscoring the urgent need for context-specific solutions and a cross-sectoral approach. By integrating findings from various disciplines, this review aims to inform policy and public health interventions, highlighting the necessity of collaborative efforts to mitigate the burgeoning burden of NCDs in a rapidly changing climate.

Childhood obesity is one of the most prevalent public health challenges in the United States and although rates are declining overall, rates among children living in underserved neighborhoods are increasing. This five-year intervention project seeks to empower teachers (n=92) to invest in their own health and then to integrate nutrition concepts into core subjects’ lessons in elementary schools. The professional development sessions reflect the concepts in the Whole Child, Whole School, Whole Community model. Results indicate that teachers who attended professional development sessions were more likely to implement nutrition lessons in the classroom (r = 0.54, p&lt;0.01) and students demonstrated a significant increase in nutrition knowledge (p &lt; .001, df = 2, F = 9.66). Investing in school-based programs that ensure teacher well-being and professional development can yield positive benefits for both teachers and students.

We report the production of metal oxide (TiFe₂O₄, ZnFe₂O₄) nanoparticles by pulsed laser ablation technique in liquid environment. We used nano second Nd: YAG laser systems working at 532 nm and 1064 nm of wavelength, the energy of the laser beam was kept constant at 80 mJ. Absorbance spectra, surface plasmon resonance, optical band-gap and nanoparticle morphology were investigated using ultraviolet-visible (UV-Vis) spectroscopy, Fourier transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). Changing the wavelength of the laser for growth, nanoparticles shown shift between the absorbance and surface plasmon resonance peaks in their UV-Vis spectra, this implies that the optical properties of the colloid nanoparticles depends on laser parameters, this was confirmed with the variation of the band gap energy. Furthermore, red shift for the absorbance peak was observed for samples as-growth at 532 nm around the 150 nm as function of time preparation. Whereas, for the samples as-growth at 1064 nm there is no shift in the absorbance spectra, this can be due to agglomeration and formation of larger particles. The characterization results shown appropriate plasmonic photo-catalysts properties of the particles, hence the photo activation of the nanoparticles was examined on antibacterial effect using colonies of Staphylococcus Aureus and Escherichia coli.

Robot-assisted rehabilitation has emerged as a promising approach for enhancing motor function in stroke survivors. However, the feasibility and effectiveness of home-based robotic training in this population are underexplored, especially in low/middle-income countries. This feasibility study aimed to address this gap by examining the feasibility and effectiveness of independent home-based training using PLUTO, a robotic device for hand training. A total of 7 chronic stroke survivors were recruited, with 5 completing the study. The results revealed high engagement and adherence to the home-based training program, with participants averaging 1659.8 minutes of training over 24.8 days. The PLUTO system demonstrated excellent usability and elicited positive user perceptions. Significant improvements were observed in functional outcomes, as evidenced by a noteworthy increase in Fugl-Meyer Assessment scores (mean increase of 6.2 points, exceeding the minimal clinically important difference (MCID) of 5.35 points). Furthermore, participants showed improvements in the ABILHAND measure (mean improvement of 1.24 logits, surpassing the MCID of 0.2 logits) and the Barthel Index (mean increase of 8.8 points). These findings demonstrate the feasibility and effectiveness of home-based robotic rehabilitation for chronic stroke survivors. This has implications for expanding access to rehabilitation services in low- and middle-income countries, enhancing patient engagement and adherence, and improving functional outcomes. Larger controlled studies are warranted to evaluate the effectiveness of home-based robotic rehabilitation programs.

In radiotherapy, accurate deposition of energy to the targeted volume is vital to ensure effective treatment. Gel dosimeters are attractive detection systems, as tissue substitutes with potential to yield three-dimensional dose distributions. Radio-fluorogenesis is creation fluorescent chemical products in response to energy deposition from high-energy radiation. This report shares studies of a radio-fluorogenic gel dosimetry system, gelatin with coumarin-3-carboxlyic acid (C3CA), for the quantification of imparted energy. Aqueous solutions exposed to ionizing radiation result in the production of hydroxyl free radicals through water radiolysis. Interactions between hydroxyl free radicals and coumarin-3-carboxylic acid produce a fluorescent product. 7-hydroxy-coumarin-3-carboxylic acid has a blue (445 nm) emission, following UV to near UV (365–405 nm) excitation. Effects of C3CA concentration and pH buffers were investigated for this system. The response of the system was explored with respect to strength, type, and exposure rate of high-energy radiation. Results show a linear dose response relationship with a dose-rate dependency and no energy or type dependencies. This report supports the utility of gelatin-C3CA for phantom studies of radio-fluorogenic processes.

In this paper we explore how we can use catchment resilience as a unifying concept to manage and regulate catchments, using structured reviews to support our perspective. River catchments are physical boundaries which delineate where all surface water (e.g. precipitation, snow, meltwater) falling on a piece of land runs off or flows to a single point at a lower elevation, where the river meets a larger body of water (e.g. sea, lake). Catchments are complex systems with interrelated natural, social, and technical aspects. The exposure, vulnerability, and resilience of these aspects (separately and in combination) are the latent conditions which when triggered by a specific hazard, result in catchment impacts. In complex catchment systems, resilience is the ability to bounce-back, the ability to absorb, and the ability to transform. When all three abilities are accounted for, we are forced to consider the interactions of the catchment system. Six main complexity concepts can be used to frame how we approach evaluating catchment resilience. These concepts are: natural-social-technical aspects, interactions, spatial scales, time scales, multiple forms of evidence, and uncertainty. In analysing these complexity concepts we have found that there are several gaps in current practice. For example critical interactions which need further methodological study are the linkages between the natural-social-technical realms, as well as across spatial scales (e.g. households or communities) and time scales (e.g. days or years). Requirements for future methodological approaches are suggested. Central to these is (1) the study of interactions linking the short- to medium-term time scales (2) better integration of bottom-up and top-down approaches, to link local context with higher-level decision-making, and (3) developing ‘hazard-agnostic’ methods which can address the impacts of floods, droughts – even acknowledging dormant ‘socio-technical hazards’. There is no ‘one size fits all’ approach to catchment resilience. Mixed method approaches are required and their selection will depend on contextual issues identified early in the process for specific catchments. Central to any effective approach is the incorporation of a linking systems or interaction analysis, which draws together the natural-social-technical system in a meaningful way. If our approaches do not begin to acknowledge the interdependencies and interactions, we may miss substantial opportunities to enhance catchment resilience.

The emergence of the COVID-19 pandemics prompted a fast development of novel diagnostic methods of the etiologic virus SARS-CoV-2. Methods based on CRISPR-Cas systems have been particularly promising because they can achieve a similar sensitivity and specificity to the golden standard RT-qPCR, especially when coupled to an isothermal pre-amplification step. Furthermore, they have also solved inherent limitations of RT-qPCR that impede its decentralized use and deployment in the field, such as the need for expensive equipment, high cost per reaction, and delivery of results in hours, among others. In this review, we evaluate publicly available methods to detect SARS-CoV-2 that are based on CRISPR-Cas and isothermal amplification. We critically analyze the steps required to obtain a successful result from clinical samples and pinpoint key experimental conditions and parameters that could be optimized or modified to improve clinical and analytical outputs. The COVID outbreak has propelled intensive research in a short time, which is paving the way to develop effective and very promising CRISPR-Cas systems for the precise detection of SARS-CoV-2. This review could also serve as an introductory guide to new labs delving into this technology.

Neurodegeneration is becoming one of the leading causes of death worldwide as the population expands and grows older. There is a growing desire to understand the mechanisms behind prion proteins as well as the prion-like proteins that make up neurodegenerative diseases (NDs) including Alzheimer’s Disease (AD). Both amyloid β (Aβ) and hyperphosphorylated tau (p-tau) proteins behave in ways similar to that of the infectious form of the prion protein, PrPSc, such as aggregating, seeding, and replicating under not yet fully understood mechanisms, thus the designation of prion-like. This review aims to highlight the shared mechanisms between prion-like proteins and prion proteins in the structural variations associated with aggregation and disease development. These mechanisms are largely focusing on the dysregulation of protein homeostasis, self-replication, and protein aggregation, and how this knowledge could contribute to diagnoses and treatments for the given NDs.

Enhanced food and nutrition security remains a primary goal for every community. Several interventions have been promoted in dry areas to improve issues on food and nutrition security. However, studies on the level of knowledge, cultural norms, perceptions and attitudes that are key drivers in adoption and uptake to highlight gaps and provide evidence for improvement are limited. This study investigated variables influencing the adoption and implementation of an integrated crop-dairy goat farming system in Elgeyo Marakwet. A descriptive cross-sectional survey entailing qualitative and quantitative approaches among farmers practicing integrated farming was undertaken. A thematic questionnaire was used to collect quantitative data, while key informant interviews and focus groups discussions were used in qualitative research. This study utilized the multi-stage sampling procedure to sample the farmers and sample size was calculated based on Krejcie and Morgan table. Data analysis for quantitative data was done using SPSS software while qualitative data utilized N-vivo software The findings show that farmers have knowledge on the integrated farming system. Age, level of education, land size, gender, perceptions and attitudes influence adoption. Small animals like dairy goats are associated to women in this community hence increasing their participation in access, control and decision making of agricultural resources. The key findings of this study provide baseline data that can form evidence to help inform policy on the indicators contributing to adoption of integrated crop-dairy goat systems to enhance food and nutrition security

The ejido system in Mexico based on communal land was transformed for private ownership due to neoliberal trends during 1990. This research describes the evolution of Mexican land policies that changed the ejido system into private development to answer why land tenure change is shaping urban growth. To demonstrate this, municipalities of San Andrés Cholula and Ocoyucan were selected as a case study. Within this context, we evaluated how much ejido land is being urbanized due to real estate market forces and what type of urbanization model is created. These two areas represent different development scales: S.A. Cholula where its ejidos were expropriated as part of a regional urban development plan; and Ocoyucan where its ejidos and rural land were reached by private developers without local planning. To analyze both municipalities, historical satellite images from Google Earth were used with GRASS GIS 7.4 and corrected with QGIS 2.18. We found that privatization of ejidos fragmented and segregated the rural world for the construction of massive gated-communities. Therefore, a disturbing land tenure change occurred during the last 30 years, hence this research questions the role of local authorities in permitting land use change without regulations or local planning. The resulting urbanization model is a private sector development that isolates rural communities in their own territories, for which we provide recommendations.

Object detection is important in many applications, such as autonomous driving. While 2D images are lack of depth information and are sensitive to environmental conditions, 3D point cloud can provide accurate depth information and a more descriptive environment. However, sparsity is always a challenge in single-frame point cloud object detection. This paper introduces a two-stage proposal-based feature fusion method for object detection using multiple frames. The proposed method, called proposal features fusion (PFF), utilizes a cosine-similarity approach to associate proposals from multiple frames and employs an attention weighted fusion module to merge features from these proposals. It allows for feature fusion specific to individual objects and offers lower computational complexity while achieving higher precision. The experimental results on the nuScenes dataset demonstrate the effectiveness of our approach, achieving a mAP of 46.7%, which is 1.3% higher than the state-of-the-art 3D object detection method.

Speech emotion recognition remains a heavy lifting in natural language processing. It has strict requirements to the effectiveness of feature extraction and that of acoustic model. With that in mind, a Heterogeneous Parallel Convolution Bi-LSTM model is proposed to address these challenges. It consists of two heterogeneous branches: the left one contains two dense layers and a Bi-LSTM layer, while the right one contains a dense layer, a convolution layer, and a Bi-LSTM layer. It can exploit the spatiotemporal information more effectively, and achieves 84.65%, 79.67%, and 56.50% unweighted average recall on the benchmark databases EMODB, CASIA, and SAVEE, respectively. Compared with the previous research results, the proposed model achieves better performance stably.

Inflammasomes are multimolecular complexes with potent inflammatory activity. As such, their activity is tightly regulated at the transcriptional and post-transcriptional levels. In this review, we present the transcriptional regulation of inflammasome genes from sensors (e.g NLRP3) to substrates (e.g. IL-1β). Lineage-determining transcription factors shape inflammasome responses in different cell types with profound consequences on the responsiveness to inflammasome-activating stimuli. Pro-inflammatory signals (sterile or microbial) have a key transcriptional impact on inflammasome genes, which is largely mediated by NF-κB and, that translates into higher antimicrobial immune responses. Furthermore, diverse intrinsic (e.g. circadian clock, metabolites) or extrinsic (e.g. xenobiotics) signals are integrated by signal-dependent transcription factors and chromatin structure changes to modulate transcriptionally inflammasome responses. Finally, anti-inflammatory signals (e.g. IL-10) counterbalance inflammasome genes induction to limit deleterious inflammation. Transcriptional regulations thus appear as the first line of inflammasome regulation to raise the defense level in front of stress and infections but also to limit excessive or chronic inflammation.

Fibrosis is a ubiquitous pathology, and prior studies have indicated that various artemisinin (ART) derivatives (including artesunate (AS), artemether (AM), and dihydroartemisinin (DHA)) can reduce fibrosis in vitro and in vivo. The medicinal plant, Artemisia annua L., is the natural source of ART and is widely used, especially in underdeveloped countries, to treat a variety of diseases including malaria, while A. afra contains no ART but is also antimalarial. Using human dermal fibroblasts (CRL-2097), we compared the effects of A. annua and A. afra tea infusions, ART, AS, AM, DHA, and a liver metabolite of ART, deoxyART (dART), on fibroblast viability and expression of key fibrotic marker genes after 1 and 4 days of treatment. AS, DHA, and Artemisia tea significantly reduced fibroblast viability at 1 and 4 d post-treatment. After 4 d post treatment, AS, DHA, and A. afra tea downregulated ACTA2, and upregulated MMP3, with other genes either being unaffected or differentially affected. ART and AM had no significant effect on either fibroblast viability or fibrotic gene expression. Although A. annua contains ART, it had a significantly greater anti-fibrotic effect than ART alone. Immunofluorescent staining for smooth muscle α-actin (α-SMA) correlated well with transcriptional responses of drug-treated fibroblasts. Together, proliferation, qPCR, and immunofluorescence results show that treatment with ART, AS, DHA, and the two Artemisia teas yield differing responses, including those related to fibrosis, in human dermal fibroblasts.

Recent research has suggested that working memory training interventions may benefit children with Developmental Language Disorder (DLD). The current study investigated a short and engaging adaptive working memory intervention that targeted executive skills and aimed to improve both language comprehension and working memory abilities in children with DLD. Forty-seven 6- to 10-year-old children with DLD were randomly allocated to an executive working memory training intervention (n=24) or an active control group (n=23). A pre-test/intervention/post-test/9-month-follow-up design was used. Outcome measures included assessments of language (to evaluate far transfer of the training) and working memory (to evaluate near transfer of the training). Hierarchical multiple regression analyses controlling for pre-intervention performance and age found group to be a significant predictor of sentence comprehension and of performance on six untrained working memory measures at post-intervention and 9-month follow-up. Children in the intervention group showed significantly higher language comprehension and working memory scores at both time points than children in the active control group. The intervention programme showed potential to improve working memory and language comprehension in children with DLD and demonstrated several advantages: it involved short sessions over a short period; caused little disruption in the school day; and was enjoyed by children.

The production and secretion of very-low density lipoproteins (VLDL) by hepatocytes has a direct impact on liver fat content as well as the concentration of cholesterol and triglycerides in the circulation and thus affects liver and cardiovascular health, respectively. Importantly, excess caloric intake and lack of physical activity are associated with overproduction of VLDL, hepatic steatosis, and increased levels of atherogenic lipoproteins. Cholesterol as well as triglycerides in remnant particles after VLDL lipolysis are risk factors for atherosclerotic cardiovascular disease (ASCVD) and have garnered increasing attention over the last few decades. To date, however, increased risk of ASCVD is not the only concern when considering today’s cardiometabolic patients, as they often also suffer from hepatic steatosis. This notion highlights the importance of understanding the molecular regulation of VLDL biogenesis. Fortunately, there has been a resurgence of interest in the intracellular assembly, trafficking, degradation, and secretion of VLDL by hepatocytes, that has led to many exciting new molecular insights, the topic of this review. We think that increasing our understanding of the biology of this pathway will help improve the health of the cardiometabolic patient in the long term.

We construct a Bayesian estimator for the dilution of a wastewater sample. When wastewater is diluted by rainwater an estimate of the level of dilution is required if we are to normalise sample measurements of disease markers such as SARS-CoV-2 RNA. We consider the situation where flow measurements are available, but will regularly be unreliable because of the action of combined sewer outflows (CSOs) and wastewater storage tanks, which divert wastewater away from treatment plants when the flow is excessive. However, we also have proxies for the flow from various chemical markers (e.g.\ phosphate, ammonium, electrical conductivity), whose level per unit of population is fixed. The new flow estimator has multiple advantages compared to existing procedures: credible intervals for the estimates; optimal weighting of the chemical markers; systematic handling of missing and censored values; and model based smoothing without lags.