Despite the partial disclosure of driving scenario knowledge graphs, they still fail to meet the comprehensive needs of intelligent connected vehicles for driving knowledge. Current issues include the high complexity of pattern layer construction, insufficient accuracy of information extraction and fusion, and limited performance of knowledge reasoning models. To address these challenges, a hybrid knowledge graph method was adopted in the construction of the Driving Scenario Knowledge Graph (DSKG). Firstly, core concepts in the field were systematically sorted and classified, laying the foundation for the construction of a multi-level classified knowledge graph top-level ontology. Subsequently, by deeply exploring and analyzing the Traffic Genome data, 34 entities and 51 relations were extracted and integrated with the ontology layer, achieving the expansion and updating of the knowledge graph. Then, in terms of knowledge reasoning models, an analysis of the training results of the TransE, Complex, Distmult, and Rotate models in the entity linking prediction task of DSKG revealed that the Distmult model performed the best in metrics such as hit rate, making it more suitable for inference in DSKG. Finally, a standardized and widely applicable Driving Scenario Knowledge Graph was proposed. The DSKG and related materials have been publicly released for use by industry and academia.

Aiming at the limitations of single-functionality, limited applicability, and complex designs prevalent in current metasurfaces, we propose a terahertz multifunctional and multiband tunable metasurface utilizing a VO2-metal hybrid structure. This metasurface structure comprises a top VO2-metal resonance layer, a middle polyimide dielectric layer, and a gold film reflective layer at the bottom. This metasurface exhibits multifunctionality, operating independently of polarization and incident angle. The varying conductivity states of the VO2 layers, enable the metasurface to achieve various terahertz functionalities, including single-band absorption, broadband THz absorption, and multiband perfect polarization conversion for linear (LP) and circularly polarized (CP) incident waves. Finally, we believe that the functional adaptability of the proposed metasurface expands the repertoire of options available for future terahertz device designs.

Being able to express broad families of equivariant or invariant attributed graph functions is a popular measuring stick of whether graph neural networks should be employed in practical applications. However, it is equally important to learn deep local minima of losses (i.e., with much smaller loss values than other minima), even when architectures cannot express global minima. In this work we introduce the architectural property of attracting GNN optimization trajectories to local minima as a means of achieving smaller losses. We take first steps in satisfying this property for losses defined over attributed undirected unweighted graphs with a novel architecture, called Universal Local Attractor (ULA). The latter refines each dimension of end-to-end trained node feature embeddings based on graph structure to track the optimization trajectories of losses satisfying some mild conditions. The refined dimensions are then linearly pooled to create predictions. We experiment on 10 tasks, from node classification to clique detection, on which ULA is comparable with or significantly outperforms popular alternatives of similar or greater theoretical expressive power.

Information molecules of DNA and RNA should obey principles of quantum mechanics where unitary operators in form of unitary matrices have key meanings. Unitary matrices are the basis of calculations in quantum computers. This article presents some author's results, which show that matrix forms of the representation of structured systems of molecular-genetic alphabets can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation each other. Decompositions of numeric genetic matrices into sets of sparse unitary matrices are connected with the logical operation of modulo-2 addition used in quantum computers as well. Tensor (or Kronecker) families of unitary genetic matrices with their fractal-like properties are also considered. The described results are discussed in the frame of development of quantum-information approaches for modeling genetic systems.

In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey number was established as R_trans (3,3)=5. Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ=lim┬(N→∞)⁡〖N_g/N_r 〗, where N is the total number of green and red seeds, N_g and N_r, were found ζ=0.272±0.001 (Voronoi) and ζ= 0.47±0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as S= 1.690±0.001 and for the Poisson line tessellation as S =1.265±0.015.

We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

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 paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.

This work is devoted to the construction and study of commutative gates for a two-qubit quantum system. Using four-dimensional algebra developed by the Kazakh mathematician Abenov M.M. all groups of commutative gates have been constructed, and among all states of a two-qubit quantum system, unitary states with which a specific gate is connected have been identified. An explicit type of gate is described that transfers a quantum system from one unitary state to another unitary state. The proposed approach opens up new possibilities for the design of quantum algorithms not only for two-qubit quantum systems, but also for $n$-qubit quantum systems.

This study introduces a novel computational approach for testing conditional independence (BB CI test) within causal Directed Acyclic Graphs (DAGs), leveraging Bayesian non-parametric bootstrap and machine learning techniques. Our method offers an alternative for validating the assumptions underpinning causal DAGs. Through simulation studies and an industrial case analysis, we demonstrate the test procedure in accurately assessing conditional independence, comparing it with the Generalized Covariance Measure (GCM) test. Our findings suggest that the BB CI test is advantageous in scenarios where existing methods may falter due to violations of model assumptions. This research contributes to the causal inference literature by providing a computational tool for researchers and practitioners to validate causal models.

Brand trust holds significant importance in the Mongolian cashmere industry. This study examines the primary predictors of customer brand trust among Mongolian cashmere users. Our research includes a survey with 800 participants and 20 individual interviews conducted among both Mongolian cashmere users and non-users. We utilized an online platform to reach participants, employing convenience sampling. The study investigates the relationship between various factors and brand trust within the context of Mongolian cashmere brands. Through a combination of in-dividual interviews and statistical analysis, we test six hypotheses. The findings indicate that higher brand quality, a strong reputation, greater transparency, effective issue resolution, commitment to environmental and social responsibility, and pre-purchase research on such commitments positively impact brand trust. Key insights gleaned from the interviews emphasize the importance of quality, reputation, transparency, customer service, and environmental responsibility in shaping consumer trust. These results offer valuable implications for cashmere brands aiming to bolster consumer trust and foster loyalty.

To address the problems of insufficient semantic fusion between text and questions and the lack of consideration of global semantic information encountered in machine reading comprehension models, we proposed a machine reading comprehension model called BERT_hybrid based on BERT and hybrid attention mechanism. In this model, BERT is utilized to separately map the text and questions into the feature space. Through the integration of Bi-LSTM, attention mechanism, and self-attention mechanism, the proposed model achieves comprehensive semantic fusion between text and questions. The probabilities distribution of answers is computed using Softmax. Experimental results on the public dataset DuReader demonstrate that the proposed model achieves improvements in BLEU-4 and ROUGE-L scores compared to existing models. Furthermore, to validate the effectiveness of the proposed model design, we analyze the factors influencing the model’s performance.

The article is devoted to algebraic modeling of universal rules of stochastic organization of genomic DNA of higher and lower organisms, previously published by the author. The proposed algebraic apparatus, which uses formalisms of quantum mechanics and quantum informatics and which is based on the so-called tensor-unitary transformations of vectors that generate families of interrelated stochastic-deterministic vectors of increased dimensions. The features of the vectors' interconnections in these families model the stochastic-deterministic properties of the named phenomenological rules. There are new approaches to modeling of developing multi-parameter biosystems, whose number of parameters increases in the course of step-by-step development. In the light of the presented materials, the issues of fractal-like organization in genetically inherited biosystems are considered. The development of the theory of stochastic determinism as an antipode of deterministic chaos is discussed.

Partially state-owned firms are common in both developed and developing countries and contribute around 10% of the world's GDP. This has led to a rich literature exploring various aspects of competition between such “mixed”-ownership firms. This paper contributes to the existing literature by studying the effects of mixed ownership on the intensity of competition in oligopoly markets. Our findings indicate that state ownership exerts an anti-competitive influence, with a higher state ownership share resulting in less aggressive behavior by firms in the product market. This result implies that industries with a higher proportion of state ownership yield lower total surplus. Further, when considering factors such as taxes, soft budget constraints, and weak property rights, the anti-competitive effects of state ownership are accentuated.

The wellness economy has developed rapidly recently, particularly in wellness tourism. Wellness tourism transforms sustainable strategy through the availability of extended multi-actor engagement in service innovation to further the tourism experience. Therefore, when operating a wellness tourism destination, it is necessary to encourage multi-actor engagement in service innovation to achieve sustainable development. This paper introduces a mixed research method with the SWOT-AHP-QSPM, as it qualitatively analyzes the advantages, disadvantages, opportunities, and threats, constructs an evaluation index system, conducts quantitative analysis using the analytic hierarchy process, determines the index weight and weighted score, and calculate the sustainable development strategy, which is appropriate for wellness development of Chongqing Tea Mountain and Bamboo Forest National Forest Park. Purposive field surveys and personal interviews were conducted in Chongqing forest tourism destinations, involving 356 effective respondents. The research reveals that multi-actor engagement significantly enhances sustainable development. These findings bridge service innovation knowledge gaps and provide valuable insights for forest tourism destination management and sustainable policy strategies to elevate multi-actor engagement in forest sites.

Commercially cultivated Prunus species are commonly grown in adjacent or mixed orchards, and can be infected with unique or commonly shared viruses. Apple (Malus domestica), another member of the Rosacea and distantly related to Prunus, can share the same growing regions and common pathogens. Pollen can be a major route for virus transmission, and analysis of the pollen virome in tree fruit orchards can provide insights into these virus pathogen complexes from mixed production sites. Commercial honey bee (Apis mellifera) pollination is essential for improved fruit set and yield in tree fruit production systems. Here we describe the metagenomics-based detection of plant viruses through bee and pollen samples collected during the spring bloom period from a mixed Prunus and Malus orchard. Twenty-one unique viruses were detected in samples collected during apricot (Prunus armeniaca), sweet cherry (Prunus avium), peach (Prunus persica), and apple blooms. Ilarviruses prune dwarf virus (PDV) and prunus necrotic ringspot virus (PNRSV), Secoviridae family members tomato necrotic ringspot virus, tobacco necrotic ringspot virus, and prunus virus F, and Capillovirus cherry virus A (CVA) were detected in all time points, while other viruses were detected with restricted ranges. These results demonstrate the benefits of area-wide monitoring through bee pollination activities, and provide new insights into the diversity of viruses in tree fruit pollination ecosystems.

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.

We address the problem of finding a unique graph embedding that best describes a graph's "topology". This issue is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are termed tessellate, those that do not decussate. We give examples of decussate and tessellate graphs that are finite and 3-periodic. We conjecture that a graph has at most one tessellate embedding. We give reasons for considering this the default "topology" of periodic graphs.

In this paper, we give all non splitting bi-unitary superperfect polynomials divisible by one or two irreducible polynomials over the prime field of two elements. We prove the nonexistence of odd bi-unitary superperfect polynomials over F2.

Symmetry, as a key concept in geometry and the foundational principle of mathematical concepts, is a fundamental part of geometry and nature, creating patterns that help us conceptually organize our world. It is often linked with aesthetic beauty and can be observed in both natural phenomena and human-made objects, such as artworks and manufactured products, across the globe. The automorphism group of a graph is a mathematical structure that captures all the symmetries of the graph. symmetry refers to the property of a graph, indicating that it can be transformed without changing its structure, while the automorphism group is the collection of all permutations of the vertices that preserve the graph's adjacency relationships. In graph theory, the concepts of symmetry group and automorphism group play fundamental roles in understanding the symmetries and structural properties of graphs. This paper aims to explore the relationship between symmetry groups and automorphism groups, shedding light on their interconnected nature and their significance in graph theory. We delve into the definitions and properties of both symmetry groups and automorphism groups, highlighting their similarities and distinctions. Furthermore, we discuss their applications in various fields, including computer science, chemistry, and network analysis. Through this exploration, we aim to provide a comprehensive understanding of the relationship between symmetry groups and automorphism groups, deepening our comprehension of the symmetries and structures inherent in graphs.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

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 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.

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

We introduce a new variation on the domination theme which we call vertex domination as reducing waste of time in transportation planning and optimization of transport routes. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs. The bounds is obtained for it. In fuzzy graphs, monotone decreasing property and monotone increasing property are introduced. We prove both of the vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for vertex domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied. Finally, we discuss about vertex dominating set of a fuzzy tree by using the bridges and $\alpha$-strong edges equivalence.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another de nitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

A popular approach to learning about admixture from population genetic data is by computing the allele-sharing summary statistics known as f-statistics. Compared to some methods in population genetics, f-statistics are relatively simple, but interpreting them can still be complicated at times. In addition, f-statistics can be used to build admixture graphs (multi-population trees allowing for admixture events), which provide more explicit and thorough modeling capabilities but are correspondingly more complex to work with. Here, I discuss some of these issues to provide users of these tools with a basic guide for protocols and procedures. My focus is on the kinds of conclusions that can or cannot be drawn from the results of f₄-statistics and admixture graphs, illustrated with real-world examples involving human populations.

Fe-(9, 19, 28, 37)wt.% Cr alloys were corroded at 700 and 800 ^oC for 70 h under 1 atm of N₂, 1 atm of N₂/3.2%H₂O-mixed gas, and 1 atm of N₂/3.1%H₂O/2.42%H₂S-mixed gas. The corrosion rate of Fe-9Cr alloy increased with the addition of H₂O, and furthermore with the addition of H₂S in N₂ gas. Fe-9Cr alloy was always nonprotective. In contrast, Fe-(19, 28, 37) wt.%Cr alloys were protective in N₂ and N₂/H₂O-mixed gas because of formation of the Cr₂O₃ layer. They were, however, nonprotective in N₂/H₂O/H₂S-mixed gas because sulfidation dominated to form the outer FeS layer and the inner Cr₂S₃ layer containing some FeCr₂S₄.

In forests, the microbial populations living in the soil can directly affect the carbon decomposed by the surface plants, and promote carbon storage and stability. In this study, 3 plots of 25.82 m×25.82 m were set up in 5 stand types, respectively. Soil samples were collected from 0~20 cm, 20~40 cm and 40~60 cm layers. Soil microbial composition, organic carbon component, pH, water content, bulk density, nitrogen, phosphorus, potassium and other physicochemical indexes and correlations were determined, and the correlations between soil carbon components and soil microbial functional modules in different mixed modes were analyzed. The results showed that: (1) The SOC of the same soil layer varied significantly, which also showed significant differences on the composition of soil bacteria and fungal microbial communities. Moreover, the bacterial community was more sensitive to the vegetation change environment, and the fungal community structure was more resistant to the influence of soil environment changes. (2) Fun_mod 1,6 and Bac_mod 7 were the microbial functional modules that played a decisive role in the process of soil carbon pool change, and the diversity and composition of bacterial community had more positive effects on soil organic carbon than that of fungal community. (3) Linear fitting and RDA results showed that POC in soil had the strongest correlation with SOC content, indicating that soil microorganisms affected the storage and stability of soil carbon mainly by regulating the conversion of surface plants (carbon sources) into POC. The soil environment of different mixed modes has different effects on soil carbon accumulation. Soil microorganisms affect soil carbon storage and stability mainly by regulating the conversion of surface plants (carbon sources) into POC forms.

The study on graphs emerging from different algebraic structures like groups, rings, fields, vector spaces, etc. is a prominent area of research in mathematics, as algebra and graph theory are two mathematical fields that focuses on creating and analysing structures. There are numerous studies linking algebraic structures and graphs, which began with the introduction of Cayley graphs of groups. Several algebraic graphs have been defined on rings, which have huge-growing literature. In this article, we systematically review the literature on some variants of Cayley graphs that are defined on rings, to understand the research in this area.

In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then shows that “whether there is a protection routing to the destination” is NP-complete. Tapolcai find that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we propose dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we propose a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs Kn, complete bipartite graphs Km,n, hypercubes Qn, locally twisted cubes LTQn as examples, we provide a recursive method to construct dual-PRTs on them. This article will show that there are no two CISTs on K3,3, Q3, and LTQ3, but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Qn and LTQn, we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs.

Graph entropies have been used to interpret the complexity of the networks. There are various graph entropies in the literature. In this note a new graph entropy is defined which is based on the dominating sets of the graphs. Moreover the entropy of some classes of the graphs is obtained

The canonical decomposition of a bipartite graph is a new decompositionmethod that involves three operators, parallel, series and K+S. The class of weak bisblit graphs is totally decomposable with respect of these operators, and the class of bicographs is totally decomposable with respect of parallel and series operators. We prove in this paper that the class of bipartite (P_6,C_6)-free graphs is exactly the class of bipartite graphs that are totally decomposable with respect of parallel and K+S operators. We simplify the recognition algorithm of weak-bisplit graphs to adepte with bipartite (P_6,C_6)-free graphs. As a result of this adapted algorithm, we prsent efficient solutions in this class of graphs for two optimization graph problems, the first is the maximm balanced bi-clique problem and the the second is the maximum independent set problem.

Let G[F,Vk, Huv] be the graph with k pockets, where F is a simple graph of order n ≥ 1,Vk= {v1,v2,··· ,vk} is a subset of the vertex set of F and Hvis a simple graph of order m ≥ 2,v is a specified vertex of Hv. Also let G[F,Ek, Huv] be the graph with k edge pockets, where F is a simple graph of order n ≥ 2, Ek= {e1,e2,···ek} is a subset of the edge set of F and Huvis a simple graph of order m ≥ 3, uv is a specified edge of Huvsuch that Huv− u is isomorphic to Huv− v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk, Hv] and G[F,Ek, Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.

To address the insufficient mechanical properties of calcined phosphogypsum, this research aims to investigate the utilization of basalt fiber and calcium carbonate whiskers as reinforcing agents. The study examines their impact on the flexural and compressive strength, toughness, water resistance, and tensile strength of calcined phosphogypsum. In the individual tests, basalt fibers with different lengths (3 mm, 6 mm, 9 mm, and 18 mm) were added at dosages of 0%, 0.5%, 1.0%, and 1.5% respectively. The findings demonstrate that basalt fiber effectively enhances the flexural and compressive strength, toughness, and tensile strength of calcined phosphogypsum, albeit potentially compromising water resistance. Among the various fiber lengths, the 6 mm fibers exhibit the most advantageous influence on the performance of calcined phosphogypsum. A subsequent test was conducted to investigate the impact of cross-scale fibers on the properties of calcined phosphogypsum by mixing 6 mm basalt fibers and calcium carbonate whiskers. The results illustrate that calcium carbonate whisker refines the pores, thereby improving the flexural strength and toughness of calcined phosphogypsum. Furthermore, it compensates for the water resistance limitations associated with the sole utilization of basalt fiber while further augmenting the tensile strength and strain capacity. However, it should be noted that increasing the dosage of both calcium carbonate whiskers and basalt fibers concurrently leads to increased porosity of phosphogypsum and reduced compressive strength.

Sugarcane mosaic virus (SCMV) and sugarcane streak mosaic virus (SCSMV) are the primary viruses responsible for mosaic diseases in sugarcane. In this study, the mosaic viruses SCMV and SCSMV with the involvement of sorghum mosaic virus (SrMV) were surveyed from eight commercial sugarcane cultivars grown in fields at four locations in East Java, Indonesia. Sugarcane leaves with mosaic symptoms were assessed for disease incidence and severity, and symptomatic leaves were collected for analysis. The incidence and severity of mosaic symptoms were the highest in the PS881 and NX04 cultivars grown in Kediri compared to the other cultivars. RT-PCR analysis showed that SCSMV was present in all sugarcane cultivars and locations. Interestingly, double mixed infections with SCMV were found in PS881, PS882, and Cening, whereas triple mixed infections with SrMV were found in the PS881 cultivar. Phylogenetic analysis grouped SCSMV, SCMV, and SrMV together with isolates from Thailand (KP987832.1), Florida, USA (MT725538.1), and Agentina (EU189037.1). The expression of ascorbate peroxidase gene (Apx) was increased in the virus-infected sugarcane cultivars and prominently elevated in the triple mixed infection of PS881 cultivars. However, the catalase gene (Cat) was slightly upregulated in the mixed infection group. The chlorophyll content was significantly reduced in the leaves of PS58, PS881, PS882, NX04, and HW Merah, in parallel with the expression of the photosystem I gene (PsaA). The expression of photosynthetic genes, such as ribulose-1,5 bisphosphate carboxylase small sub-unit (RbcS), phosphoenolpyruvate carboxylase (Pepc), sucrose-phosphate synthase (Sps1), and PsaA, was significantly reduced and almost depleted in the triple mixed infection of PS881, except for Pepc expression, which remained approximately half of that in the control healthy sugarcane. The decrease in photosynthetic activity was confirmed by the decrease in ribulose-1,5 bisphosphate carboxylase (Rubisco) and PEPC proteins, as detected by immunoblot analysis. The decrease in photosynthetic parameters indicated that the mosaic viral infection substantially reduced the growth and yield of sugarcane.

Breast cancer (BC) is the most common invasive neoplasm and affects many women of working age. The return to work (RTW) of female survivors (BCSs) is associated with a better quality of life and longer survival. A tailored intervention to promote RTW was launched in 2022. A year later, the women were contacted to find out if RTW had occurred regularly and what their health conditions were compared to baseline. BCSs reported excessive fatigue, poor sleep quality, anxiety, depression and reduced work ability; these parameters had not improved significantly compared to baseline. Thematic analysis of the interviews confirmed the presence of personal, company and societal factors that could hinder or favor RTW. The interviews demonstrated that, even in an economically developed country that has provided numerous benefits for BCSs, protection is not always effective. Personalized intervention seems necessary to complete the process of reintegrating BCSs into their future working careers.

Soot combustion experiments with 5%O2/He were conducted using model soot, and four distinct compositions of CexPr1-xO2-δ oxides were prepared, varying nominal cerium com-positions (x=0, 0.2, 0.3, and 1). The catalyst samples were comprehensively characterized using techniques such as XRD, Raman spectroscopy, HR-TEM, N2 adsorption at −196 °C, XPS, O2-TPD, H2-TPR, and work function measurements. The Pr-rich compositions, rang-ing from Ce0.3Pr0.7O2-δ to PrO2-δ, resulted in a significant increase in the total evolved O2 amounts and enhanced catalyst reducibility. However, a decrease in textural properties of the catalysts was noted, being particularly important for the pure praseodymia under the synthesis route conducted. The catalytic activity was investigated under two contact modes of mixing between soot and catalyst: loose and tight. The results revealed that the catalytic performance is associated with the surface contact in tight contact mode and with the combination of surface/subsurface/bulk oxygen mobility and the BET surface ar-ea in loose contact mode. Notably, the T10 and T50 parameters were achieved at much lower temperatures than the uncatalyzed soot combustion, even under loose contact conditions. Specifically, the 50% conversion was achieved at 511℃ and 538℃ for Ce0.3Pr0.7O2 and Ce0.2Pr0.8O2, respectively. While no direct correlation between catalytic activity and work function was observed a significant relationship emerges between work function values and the formation of oxy-gen vacancies, whatever the conditions used for these measurements. On the other hand, the ability to generate a high population of oxygen vacancies at low temperatures, rather than the direct activation of gas-phase O2, influences the catalytic performance of Pr-doped ceria catalysts, highlighting the importance of surface/subsurface oxygen vacancy generation, which was the parameter which showed better correlation with the catalytic activity, whatever the soot conversion value or the mode of contact considered.

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size large; a tight limitation on the temporal step size ($\delta t <<1$) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Knowledge graphs (KGs) play a crucial role in many applications, such as question answering, but incompleteness is an urgent issue for their broad application. Much research in knowledge graph completion (KGC) has been performed to resolve this issue. The methods of KGC can be classified into two major categories: rule-based reasoning and embedding-based reasoning. The former has high accuracy and good interpretability, but a major challenge is to obtain effective rules on large-scale KGs. The latter has good efficiency and scalability, but it relies heavily on data richness and cannot fully use domain knowledge in the form of logical rules. We propose a novel method that injects rules and learns representations iteratively to take full advantage of rules and embeddings. Specifically, we model the conclusions of rule groundings as 0-1 variables and use a rule confidence regularizer to remove the uncertainty of the conclusions. The proposed approach has the following advantages: 1) It combines the benefits of both rules and knowledge graph embeddings (KGEs) and achieves a good balance between efficiency and scalability. 2) It uses an iterative method to continuously improve KGEs and remove incorrect rule conclusions. Evaluations on two public datasets show that our method outperforms the current state-of-the-art methods, improving performance by 2.7% and 4.3% in mean reciprocal rank (MRR).

When an aircraft malfunctions, quickly and accurately identifying the faulty unit is essential for ensuring normal operation. Unfortunately, maintenance engineers often struggle to acquire the necessary fault-related knowledge due to poor management and utilization of aircraft fault documents. To address this issue, we introduce knowledge graph technology into the field of aircraft fault diagnosis, exploring its construction and application for effective knowledge management. Our work starts by analyzing the critical knowledge elements required for aircraft fault diagnosis and designing a schema layer for fault knowledge graphs. We then we then combine deep learning and heuristic rules to extract fault knowledge from both structured and unstructured data, enabling the construction of aircraft fault knowledge graphs. Finally, we develop a fault question-answering system based on fault knowledge graphs that can accurately give solutions to questions posed by maintenance engineers. Our practice demonstrates that knowledge graphs provide an effective means of managing aircraft fault knowledge, assisting engineers in locating fault reasons accurately and quickly.

The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

The Collatz conjecture is a well-known number theory puzzle that states that every positive integer would eventually converge to the trivial cycle of 1, 2, 1, 2,... when repeatedly exposed to a particular transformation. In this transformation, even numbers are divided in half, odd numbers are tripled, and one is added. In this study, we present a new method for creating a directed graph and using it to display and analyze Collatz sequences. Our technique creates what we call a Collatz directed graph by joining an endless number of simple directed graphs, each of which corresponds to a natural number. We show by careful mathematical analysis that all positive integers are included in this Collatz directed graph. Moreover, we give an evidence that verifies the Collatz conjecture by showing that the sole cycle in this graph is the trivial cycle of 1, 2, 1, 2,... We also prove that there is no sequence that diverges to infinity in this graph. Our results provide insights into the fundamental structure of Collatz sequences and further our knowledge of the Collatz conjecture .

In large-scale parallel computing and communication systems, an interconnect network structure is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. In a graph, the vertices and edges are likely to fail, so we must think about the fault tolerance of a graph. Connectivity is an important parameter in the study of faulty tolerance for a graph. In this paper, we study a special class of connectivity: $m$-component connectivity, this is a natural generalization of the classical connectivity of graphs defined in terms of the minimum vertex-cut. Let $F$ is a vertex set of $G$ $(i.e, F\subseteq V(G))$, if the following conditions are satisfied, we say $F$ is a $m$-component cut: $(1)$ $G-F$ is disconnected; $(2)$ the number of components in $G-F$ is greater than or equal to $m$. In another word, the $m$-component connectivity $c\kappa_{m}(G)$ is defined as $min\{|F|~|~F\subseteq V(G)$ and $F$ is a $m$-component cut$\}$. Determining $m$-component connectivity is still unsolved in most interconnection networks even for small $m'$s. Leaf-sort graph is a special Cayley graph, it has many special properties that are different from other Cayley graphs. So we need to pay attention to some of it's special properties when we study it. In this paper, we can get the values: $c\kappa_{3}(CF_{n})=3n-6$ $(n$ is odd$)$ and $c\kappa_{3}(CF_{n})=3n-7$ $(n$ is even$)$ for $n\geq3$; $c\kappa_{4}(CF_{n})=\frac{9n-21}{2}$ $(n$ is odd$)$ and $c\kappa_{4}(CF_{n})=\frac{9n-24}{2}$ $(n$ is even$)$ for $n\geq4$; $c\kappa_{5}(CF_{n})=6n-16$ $(n$ is odd$)$ and $c\kappa_{5}(CF_{n})=6n-18$ $(n$ is even$)$ for $n\geq5$.

During the creation and integration of a health care system based on medical knowledge graphs, it is necessary to review and select the vocabularies and definitions that best fit the information requirements of the system being developed. This implies the reuse of medical knowledge graphs; however, full importation of knowledge graphs is not a tractable solution in terms of memory requirements. In this paper we present a modularization-based method for knowledge graph reuse. A case study of graph reuse is presented by transforming the original model into a lighter one.

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 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 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.

For the first time, We do fuzzification the concept of domination in crisp graph on a generalization of fuzzy graph by using membership values of vertices, α-strong edges and edges. In this paper, we introduce the first variation on the domination theme which we call vertex domination. We determine the vertex domination number γ_v for several classes of t-norm fuzzy graphs which include complete t-norm fuzzy graph, complete bipartite t-norm fuzzy graph, star t-norm fuzzy graph and empty t-norm fuzzy graph. The relationship between effective edges and α-strong edges is obtained. Finally, we discuss about vertex dominating set of a fuzzy tree with respect to a t-norm ⨂ by using the bridges and α-strong edges equivalence.

Hybrid power plants have recently emerged as reliable and flexible electricity generation stations by combining multiple renewable energy sources, energy storage systems (ESS), and fossil-based output. However, the effective operation of the hybrid power plants to ensure continuous energy dispatch under challenging conditions is a complex task. This paper proposes a dispatch engine (DE) based on mixed-integer linear programming (MILP) for the planning and management of hybrid power plants. To maintain the committed electricity output, the dispatch engine will provide schedules for operation over extended time periods as well as monitor and reschedule the operation in real-time. Through precise prediction of the PV and wind power output, the proposed approach guarantees optimum scheduling. The precise prediction of the PV and wind power are achieved by employing a predictor of Feed-Forward Neural Network (FFNN) type. With such a dispatch engine, the operational cost of the hybrid power plants, and the use of diesel generators (DGs) are both minimized. A case study is carried out to assess the proposed dispatch engine feasibility. A real-time measurement data pertaining to load, wind, and PV power outputs is obtained from different locations in the Sultanate of Oman. The real-time data is utilized to predict the future output power from PV and the Wind farm over 24 hours. The predicted powers are then used in combination with a PV-Wind-DG-ESS-Grid hybrid plant to evaluate the performance of the proposed dispatch engine. The proposed approach is implemented and simulated using MATLAB. The results of the simulation reveal the proposed Feed-Forward Neural Network’s (FFNN) powerful forecasting abilities. In addition, the results demonstrate that adopting the proposed DE can minimize the use of DG units and reduce plant running expenses.

With the advancement of technology, signal modulation types are becoming increasingly diverse and complex. The phenomenon of signal time-frequency overlap during transmission poses significant challenges for the classification and recognition of mixed signals, including poor recognition capabilities and low generality. This paper presents a recognition model for fine-grained analysis of mixed signal characteristics, proposing a Geometry Coordinate attention mechanism and introducing a low-rank bilinear pooling module to more effectively extract signal features for classification. The model employs a residual neural network as its backbone architecture and utilizes the Geometry Coordinate attention mechanism for time-frequency weighted analysis based on information geometry theory. This analysis targets multiple-scale features within the architecture, producing time-frequency weighted features of the signal. These weighted features are further analyzed through a low-rank bilinear pooling module, combined with the backbone features, to achieve fine-grained feature fusion. This results in a fused feature vector for mixed signal classification. Experiments were conducted on a simulated dataset comprising 39,600 mixed signal time-frequency plots. The model was benchmarked against a baseline using a residual neural network. The experimental outcomes demonstrated an improvement of 9% in the exact match ratio and 5% in the Hamming score. These results indicate that the proposed model significantly enhances the recognition capability and generalizability of mixed signal classification.

Electrochromic measurements have been performed throughout the full composition range of reactive magnetron-sputtered mixed Titanium oxide and Molybdenum oxide (TiO2-MoO3) to search for enhanced Coloration Efficiency (CE). Optical parameters and composition have been determined and mapped by using Spectroscopic Ellipsometry (SE). Scanning Electron Microscopy (SEM) with Energy-Dispersive X-ray Spectroscopy (EDS). EDS has been used to check the SE results as it was used in our earlier paper [N. T. Ismaeel et al, Materials 2023, 16(12), 4204] for (TiO2-SnO2). Ti and Mo targets were put separately from each other, and the Indium-Tin-Oxide (ITO) covered glass and Si-probes on a glass substrate (30 cm × 30 cm) were moved under the two separated targets (Ti and Mo) in a reactive Argon-Oxygen (Ar-O2) gas mixture. By using this combinatorial process, all the compositions (from 0 to 100%) were achieved in the same sputtering chamber after one sputtering process. The CE (the change of light transmission for the unit electric charge) of mixed metal oxides (TiO2-MoO3) that are deposited by reactive sputtering has been studied in an electrochemical cell. This paper aims to assess the results of investigations of such materials showing the enhanced electrochromic behavior compared to the pure materials and to enhance the Coloration Efficiency.

The Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph and some special graphs.

Chellali et al. introduced two degree concepts, ve-degree and ev-degree (Chellali et al, 2017). The ve-degree of a vertex equals to number of different edges which are incident to a vertex from the closed neighborhod of v. Moreover the ev-degree of an edge e=ab equals to the number of vertices of the union of the closed neighborhoods of a and b. The most private feature of these degree concepts is, total number of ve-degrees and total number of ev-degrees equal to first Zagreb index of the graphs for triangle-free graphs. In this paper we introduce ve-degree entropy, ev-degree entropy and investigate the relations between these entropies and the first Zagreb index entropy. Finally we obtain the maximal trees with respect to ve-degree irregularity index.

Background: Health insurance (HI) run by government is providing health care service to large population. Due to poor accountability, participation and sustainability, cooperative health insurance is becoming more popular and effective in low and middle income and some high-income countries too. In Nepal, there are public and cooperative HI is in practice. The aim of this study is to compare the effectiveness of public (government) and cooperative HI in relation to benefit packages, population coverage, inclusiveness, health care utilization, and promptness for treatment in these two health insurance models in Nepal. Method: This is an institution based concurrent mixed study consists of qualitative and quantitative variables from public and cooperative groups. We included all public HI operated by government hospitals and cooperatives groups those purchased hospital service in contract. Two separate study tools were applied to access the effectiveness of insurance models. The key questions were asked for the representatives of government and private health insurance. The numeric information consisted of in quantitative data and subjective response was included in qualitative approach. Descriptive statistics and Mean Whitney U test was applied in numeric data and qualitative information were analyzed by inductive approach Results: The study revealed that new enrolment was not increased, health care utilization rate was increased and the benefit package was almost same in both groups. The overall inclusiveness was higher for the government HI, but enrolment from the religious minority, proportion of negotiated amount during treatment were significantly higher (p<0.05). During illness, the response time to reach hospital was significantly faster in cooperative health insurance than government health insurance. Qualitative findings showed that level of participation, accountability, transparency and recording system was better in cooperative health insurance than public. Conclusion: Cooperative HI could be more sustainable and accountable to the community for all; low, middle and high-income countries.

In different fields in our life, like physics, coding theory and computer science, graph labeling dramas an vital role and appears in many applications. A labeling of a graph is a map which assign each element in with a positive integer number. An edge irregular total -labeling is a function such that where and are weights for any two distinct edges. In this case, has total edge irregularity strength (TEIS) if is minimum. In our paper, we defined a new type of graphs called a triple star snake graph and star snake graph . Also, we investigated TEIS for a triple star snake graph . After that, we generalized the results for star snake graph .

Tracking information diffusion is a non-trivial task and it has been widely studied across different domains and platforms. The advent of social media has led to even more challenges, given the higher speed of information propagation and the growing impact of social bots and anomalous accounts. Nevertheless, it is crucial to derive a trustworthy information diffusion graph, which is capable of highlighting the importance of specific nodes in spreading the original message. The paper introduces the interaction strength, a novel metric to model retweet cascade graphs by exploring users’ interactions. Initial findings show the soundness of the approaches based on this new metric with respect to the state-of-the-art model, and its ability to generate a denser graph, revealing crucial nodes that participated in the retweet propagation. Reliable retweet graph generation will enable a better understanding of the diffusion path of a specific tweet.

The numerical simulation of entropy generation at mixed natural free and forced convection flow in a square lid-driven cavity filled with an eletrically conducting binary fluids saturated porous media in the presence of a magnetic field is performed in this investigation. Both the top and bottom horizontal walls of the cavity are kept at constant and different temperatures while the left and right vertical walls are adiabatic and insulated. The magnetic field is applied in normal direction to the cavity. The Darcy model, including Brinkman term relative to viscous effects and Forchheimer term due to inertial forces, is used for the momentum equations, and the SIMPLER algorithm, based on the control volume finite-element method approach is used to solve the pressure –velocity coupling. The flow pattern and the heat transfer characteristics inside the cavity are presented in the form of isotherms, streamlines and isentropic lines and average Nusselt number trend. The entropy generation rate is determined for various values of Darcy number (10^-3 ≤ Da ≤ 1) and for a range of Hartmann number (0 ≤ Ha ≤ 10²). This study is limited to Pr = 7 which corresponds to water. It is observed that entropy generation is very affected by the variations of dimensionless control parameters considered.

A total $m$-labelling $\alpha$ on graph $\Gamma$ is called an edge irregular total $m$-labelling if for any two different edges of $\Gamma$, their weights respect to $\alpha$ are distinct, where the weight of any edge is defined as the sum of its label and the labels of its end vertices. We determine the minimum $m$ such that $\Gamma$ can be labelled by an edge irregular total $m$-labelling whenever $\Gamma$ is an odd staircase graph or an even staircase graph.

A signed graph is an undirected graph such that all of its edges are labeled positive or negative. Let D be an embedding of a signed graph G in the Euclidean line. If in D for all of the vertices their positive neighbors are closer than the negative neighbors, then D is called a valid drawing of G. In this paper we show that signed trees, unicyclic graphs, and ladder graphs have a valid drawing in the Euclidean line.

The realization of the third-generation artificial intelligence (AI) requires the evolution from perceptual intelligence to cognitive intelligence, where knowledge graphs may not meet the practical needs anymore. Based on the dual channel theory, cognitive graphs are established and developed through coordinating the implicit extraction module and the explicit reasoning module as well as integrating knowledge graphs, cognitive reasoning and logical expressions, which have achieved successes in multi-hop question answering. It is desired for cognitive graphs to be widely used in advanced AI applications such as large-scale knowledge representations and intelligent responses, promoting the development of Al dramatically. This review discusses cognitive graphs systematically and elaborately, including basic concepts, generations, theories and technologies. Moreover, we try to predict the development of cognitive intelligence in the short-term future and further enlighten more researches and studies.

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the average lower 2-domination number of a graph is a measure of the graph vulnerability and it is defined by ${\gamma }_{2av}\left(G\right)=\frac{1}{\left|V\left(G\right)\right|}{\sum }_{v\in V\left(G\right)}{\gamma }_{2v}\left(G\right)$, where the lower 2-domination number, denoted by ${\gamma }_{2v}\left(G\right)$, of the graph G relative to v is the minimum cardinality of 2-domination set in G that contains the vertex v. In this paper, the average lower 2-domination number of wheels and some related networks namely gear graph, friendship graph, helm graph and sun flower graph are calculated. Then, we offer an algorithm for computing the 2-domination number and the average lower 2-domination number of any graph G.

We characterize the form of the order divisor graph of cyclic groups based on the group order. Furthermore, we describe some topological indices of the order divisor graph of cyclic groups, including the Wiener index, Harary index, first Zagreb index, and second Zagreb index.

It has recently been shown that, contrary to the wide belief that a shift-enabled condition (necessary for any shift-invariant filter to be representable by a graph shift matrix) can be ignored because any non-shift-enabled matrix can be converted to a shift-enabled matrix, such a conversion in general may not hold for a directed graph with non-symmetric shift matrix. This paper extends this prior work, focusing on undirected graphs where the shift matrix is generally symmetric. We show that while, in this case, the shift matrix can be converted to satisfy the original shift-enabled condition, the converted matrix is not associated with the original graph, that is, it does not capture anymore the structure of the graph signal. We show via a counterexample, that a non-shift-enabled matrix cannot be converted to a shift-enabled one and still maintain the topological structure of the underlying graph, which is necessary to facilitate localized signal processing.

This paper presents a new method : HIVEC to learn latent vector representations of graphs in a manner that captures the semantic dependencies of sub-structures. The representations can then be used in machine learning algorithms for tasks such as graph classification, clustering etcetera. The method proposed is unsupervised and uses the information of co-occurrence of sub-structures. It introduces a notion of hierarchical embeddings that allows us to avoid repetitive learning of sub-structures for every new graph. As an alternative to deep learning methods, the edit distance similarity between sub-structures is also used to learn vector representations. We compare the performance of these methods against previous work.

One route to reducing CO2 emissions is to improve the energy efficiency of machines. For example, conventional combustion engines are being downsized (and down-speeded), are now running on lower viscosity engine lubricants (such as SAE 0W-20 or lower viscosity grades) and often also have stop-start systems fitted (to prevent engine idling when the vehicle is stopped). Some of these changes result in higher levels of mixed and boundary friction, and so accurate estimation of mixed/boundary friction losses is becoming of increased importance, both for estimating friction losses, and also for estimating wear volumes. Traditional approaches to estimating mixed/boundary friction, which employ real area of contact modelling such as the Greenwood-Tripp model [1] are widely used, but recent experimental data suggests that these approaches underestimate mixed/boundary friction losses [2-5]. A new model has been developed, based on experimental data, which estimates the proportion of mixed/boundary lubrication, X, as a function of the value (where is the ratio of the oil film thickness separating the surfaces to the combined root mean square surface roughness of the interface surfaces). The precise equation that describes the way in which X varies with takes the form of a “reverse S-curve”, which makes physical sense since S-curves arise naturally in growth processes, and in mixed/boundary lubrication, the real area of contact of rough surfaces grows as the load (and 1/) increases. Numerical estimates of mixed/boundary lubrication losses in internal combustion engines are presented here and compared with published data [2,6]. In addition, the improved method described here is used to estimate both the financial cost of mixed/boundary lubrication for today’s passenger car fleet, and the CO2 emissions associated with these friction losses.

The accurate diagnosis and effective treatment of mental health disorders such as depression remain challenging owing to the complex underlying causes and varied symptomatology. Traditional information extraction methods struggle to adapt to evolving diagnostic criteria such as the Diagnostic and Statistical Manual of Mental Disorders fifth edition (DSM-5) and to contextualize rich patient data effectively. This study proposes a novel approach for enhancing information extraction from mental health data by integrating medical knowledge graphs and large language models (LLMs). Our method leverages the structured organization of knowledge graphs specifically designed for the rich domain of mental health combined with the powerful predictive capabilities and zero-shot learning abilities of LLMs. This research enhances the quality of knowledge graphs through entity linking and demonstrates superiority over traditional information extraction techniques, making a significant contribution to the field of mental health. It enables a more fine-grained analysis of the data and the development of new applications. Our approach redefines the manner in which mental health data are extracted and utilized. By integrating these insights with existing healthcare applications, the groundwork is laid for the development of real-time patient monitoring systems. The performance evaluation of this knowledge graph highlights its effectiveness and reliability, indicating significant advancements in automating medical data processing and depression management.

Quantum entanglement is a fascinating topic with both theoretical and technological impacts. Yet, even in the simplest scenarios, there are still various open questions involving pure state and mixed state entanglement. Here we present the simplest entangled mixed states. We consider both qubits (quantum bits) and qudits (quantum digits). We first provide our simplest yet most important result for rank-2 bi-partite states, and we then generalize our results to go beyond rank-2 and to go beyond bi-partite states.

The most common form of mixed dementia (MixD) is constituted by abnormal protein deposits associated with Alzheimer´s disease (AD) that coexist with vascular disease. Although olfactory dysfunction is considered a clinical sign of AD-related de-mentias, little is known about the impact of this sensorial impairment in MixD at molecular level. To address this gap in knowledge, we have assessed olfactory bulb (OB) proteome-wide expression in MixD subjects (n=6) respect to neurologically intact controls (n=7). Around 9% of the quantified proteins were differentially expressed, pinpointing aberrant proteostasis involved in synaptic transmission, nucleoside monophosphate and carbohydrate metabolisms and neuron projection regeneration. In addition, net-work-driven proteomics revealed a modulation in cell-survival related pathways such as ERK, AKT and PDK1-PKC axis. Part of the differential OB protein set was not specific of MixD, being also deregulated across different tauopathies, synucleinopathies and tardopathies. However, the comparative functional analysis of OB proteome data between MixD and pure AD pathologies deciphered commonalities and differences between both related phenotypes. Finally, olfactory proteomics allowed to propose serum Prolow-density lipoprotein receptor-related protein 1 (LRP1) as a candidate marker to differentiate AD from MixD phe-notypes.

Conceptual distance refers to the degree of proximity between two concepts within a conceptualization. It is closely linked with semantic similarity and relationship, but its computation relies entirely on the context of the given concepts. The DIS-C algorithm, which requires using search algorithms such as Breadth First Search, represents an advance in computing the semantic similarity/relation regardless of the type of knowledge structure and semantic relationships. The shortest path algorithm facilitates the determination of the semantic closeness between two indirectly connected concepts in an ontology by propagating local distances. This process is implemented for each concept pair to establish the most effective and efficient paths to connect these concepts. The algorithm identifies the shortest path between the concepts, allowing for the inference of the most relevant relationships between them. This approach contributes to developing a comprehensive understanding of the ontology and enhances the accuracy and precision of the semantic representation of the concepts. However, one of the critical issues is associated with the computational complexity due to the nature of the algorithm, which is errorn3. This paper studies alternatives to accelerate the DIS-C based on approximation and optimized algorithms, focusing on Dijkstra, pruned Dijkstra, and Sketched-based algorithms to compute conceptual distance. Based on the experiments, we discovered that the bottleneck can be avoided using the proposed 2-hop coverages, bringing DIS-C almost linearity.

Wireless sensor networks (WSNs) are a critical research area with numerous practical applications. WSNs are utilized in real-life scenarios, including environmental monitoring, healthcare, industrial automation, smart homes, and agriculture. As WSNs advance and become more sophisticated, they offer limitless opportunities for innovative solutions in various fields. However, due to their unattended nature, it is essential to develop strategies to improve their performance without draining the battery power of the sensor nodes, which is their most valuable resource. This paper proposes a novel sink mobility model based on constructing a bipartite graph from a deployed wireless sensor network. Using the bipartite graph’s properties, the mobile sink node can visit stationary sensor nodes in an optimal way to collect data and transmit it to the base station. We evaluated the proposed approach through simulations using the NS-2 simulator to investigate the performance of wireless sensor networks when adopting this mobility model. Our results show that using the proposed approach can significantly enhance the performance of wireless sensor networks while conserving the energy of the sensor nodes.

Recent years have seen the growing adoption of non-relational data models for representing diverse, incomplete data. Among these, the RDF graph-based data model has seen ever-broadening adoption, particularly on the Web. This adoption has prompted the standardization of the SPARQL query language for RDF, as well as the development of a variety of local and distributed engines for processing queries over RDF graphs. These engines implement a diverse range of specialized techniques for storage, indexing, and query processing. A number of benchmarks, based on both synthetic and real-world data, have also emerged to allow for contrasting the performance of different query engines, often at large scale. This survey paper draws together these developments, providing a comprehensive review of the techniques, engines and benchmarks for querying RDF knowledge graphs.

Let G be a graph with n vertices and let 1; 2; : : : ; n be the eigenvalues of Randic matrix. The Randic Estrada index of G is REE(G) = Ón i=1 ei . In this paper, we establish lower and upper bounds for Randic index in terms of graph invariants such as the number of vertices and eigenvalues of graphs and improve some previously published lower bounds.

We compute explicitly traces of one-dimensional diffusion processes. The obtained trace forms can be regarded as Dirichlet forms on graphs. Then we discuss conditions ensuring the trace forms to be conservative. Finally, the obtained results are applied to the one-dimensional diffusion related to the Bessel’s process of order $\nu$.

In mathematics, one always aims to obtain new frameworks from specific ones. This also stratified to the regality of graphs, where one can produce numerous new graphs from a specific set of graphs. In this work we define some classes of pyramid graphs created by a gear graph and we derive straightforward formulas of the complexity of these graphs, using linear algebra matrix analysis techniques and employing knowledges of Chebyshev polynomials.

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In this paper, bounds for the Randić, general Randić, sum-connectivity, the general sum-connectivity and harmonic indices for tensor product of graphs are determined by using the combinatorial inequalities and combinatorial computing.

In the last decade several projects have been developed for the digitization and semantization of cultural heritage data. They were developed to preserve and maintain this heritage, but bringing it closer to all types of users and allowing access to this information to other sectors such as tourism, education, etc. In these developments, web technologies are combined, along with the use of knowledge graphs and interactive visualisation tools. Although remarkably interesting projects have been developed, in those projects, the data visualization tools are usually focused on the project context. This makes it difficult to reuse these jobs. Additionally, there are peculiarities of cultural heritage data considered with little depth, such as uncertainty, spatial and temporal granularity, as well as other aspects, such as relationships between data. In this article, these problems are described and based on other works such as VUMO or VISO, the design of an ontology that formalizes how to visualise this information is proposed, considering these problems. In addition, the development of a platform that allows the visualisation of this information through a web application and its evaluation of its use in projects such as SILKNOW, or Arxiu Valencià del Disseny is exposed

In this work, we will study at a basic level, a series of possible new three-dimensional monoclinic allotropes of silicon, with sp3 hybridization, of the bct type; where hexahedrons and octahedrons are combined, with other cluster shapes, with basic silicon geometries such as: triangles ( Si3 ), squares ( Si4 ), pentagons ( Si5 ) and hexagons ( Si6 ); similar to two-dimensional, sp2 hybridized graphene allotropes. Calculating its electron density, bandgap energy and electronic mobility.

The aim of the paper is to investigate Nash equilibria and correlated equilibria of classical and quantum games in the context of their Pareto optimality. We study four games: the prisoner's dilemma, battle of the sexes and two versions of the game of chicken. The correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device. We analyze the quantum extension of these games in the Eisert-Wilkens-Lewenstein formalism with the full SU(2) space of players’ strategy parameters. It has been shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counterparts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also analyzed.

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs) and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no". Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been done to evaluate the method.

We will try to use the approach of labeled cycle cover sum to count the number of hamiltonian cycles in a special type of bipartite graphs, with 4k + 2 vertices which can also be considered as an alternative method to check hamiltonicity in such bipartite graphs. This graph is such that, there exists at least 1 vertex which is not a part of any cycle of size 4m + 2 where m < k, in O∗(1.414n) time. The algorithm is inspired by Bjorklund’s approach where instead of working on the field of GF(2k), we will be working on C.

A simple undirected graph $\Gamma=(V_\Gamma,E_\Gamma)$ admits an $H$-covering if every edge in $E_\Gamma$ belongs to at least one subgraph of $\Gamma$ that isomorphic to a graph $H$. For any graph $\Gamma$ admitting $H$-covering, a total Labelling $\beta: V_\Gamma \cup E_\Gamma \longrightarrow \{1,2,\dots,p\}$ is called an $H$-irregular total $p$-labelling of $\Gamma$ if every two different subgraphs $H_1$ and $H_2$ of $\Gamma$ isomorphic to $H$ have distinct weights where the weight $w_\beta(K)$ of subgraph $K$ of $\Gamma$ is defined as $w_f(K):=\displaystyle \sum_{v\in V_K} f(v) + \sum_{e\in E_K} f(e)$. The smallest number $p$ for which a graph $\Gamma$ admits an $H$-irregular total $p$-labelling is called the total $H$-irregularity strength of $\Gamma$ and is denoted by $ths(\Gamma)$. In this paper, we determine the total $H$-irregularity strength of edge comb product of two graphs.

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, fi nite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

This paper presents a new framework to classify floor plan elements and represent them in a vector format. Unlike existing approaches using image-based learning frameworks as the first step to segment the image pixels, we first convert the input floor plan image into vector data and utilize graph neural network. Our framework consists of three steps. (1) image pre-processing and vectorization of the floor plan image. (2) region adjacency graph conversion. (3) graph neural network on converted floor plan graphs. Our approach is able to capture different types of indoor elements including basic elements such as walls, doors, and symbols as well as spatial elements such as rooms and corridors. In addition, the proposed method can also detect element shapes. Experimental results show that our framework can classify indoor elements with an F1 score of 95%, with scale and rotation invariance. Furthermore, we propose a new graph neural network model that takes the distance between nodes into account, which is a valuable feature of spatial network data.

A double Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2, 3} 2 with the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for 3 which f(v) = 3 or two vertices v1 and v2 for which f(v1) = f(v2) = 2, and every vertex u for which 4 f(u) = 1 is adjacent to at least one vertex v for which f(v) ≥ 2. The weight of a double Roman dominating function f is the value w(f) = ∑u∈V(G) 5 f(u). The minimum weight over all double 6 Roman dominating functions on a graph G is called the double Roman domination number γdR(G) 7 of G. In this paper we determine the exact value of the double Roman domination number of the 8 generalized Petersen graphs P(n, 2) by using a discharging approach.

Recent advancements in communication technology have catalyzed the widespread adoption of realistic content, with augmented reality (AR) emerging as a pivotal tool for seamlessly inte-grating virtual elements into real-world environments. In construction, architecture, and urban design, the integration of mixed reality (MR) technology enables rapid interior spatial mapping, providing clients with immersive experiences to envision their desires. The rapid advancement of MR devices, or devices that integrate MR capabilities, offers users numerous opportunities for enhanced entertainment experiences. However, to support designers at a high level of expertise, it is crucial to ensure the accuracy and reliability of the data provided by these devices. This study explores the potential of utilizing spatial mapping within various methodologies for surveying architectural interiors. The objective is to identify optimized spatial mapping procedures and determine the most effective applications for their use. Experiments were conducted to evaluate the interior survey performance, using HoloLens 2, iPhone 13 Pro for spatial mapping, and photogrammetry. The findings indicate that HoloLens 2 is most well-suited for the tasks exam-ined in the scope of experiments. Nonetheless, based on the acquired parameters, the author also proposes approaches to apply the other technologies in specific real-world scenarios.

AbstractCurrently, public health researchers are investigating several complex and multi-faced health problems that require mixed-method approaches (MMA) to clearly understand problems and design proper intervention approaches and policy formulation. Besides, a comprehensive comprehension of the complex operation of society is vital. The MMA helps in having a broader understanding of the functioning and structure of the community at large. MMA deliberately integrates qualitative and quantitative approaches carefully to build on the merits of each other and confirm that the findings of research are closer to the truth. Therefore, public health scholars must have an excellent comprehension of the MMA and its philosophical foundations for discovering the complex conditions that challenge public health nowadays. However, public health researchers do not clearly understand the theoretical underpinnings and practical application of MMA, despite its popularity in developing countries. Therefore, this article aimed to provide comprehensive evidence on the theoretical underpinnings and practical application of MMA.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

The origins of directed acyclic graphs (DAGs) date back to the emergence of ‘graph theory’ in the early 1700s (Biggs et al. 1986). DAGs are conceptual or literal, diagrammatic representations of causal paths between variables which are constructed – as their name suggests – on the basis of two over-riding principles: first, that all causal paths are ‘directed’ (i.e. for each pair of variables, only one can represent the cause, while the other must be its consequence); and second, that no direct cyclical paths, or indirect cyclical pathways (comprising sequences of consecutive paths) are allowed, such that no consequence can be considered its own direct or indirect cause (hence ‘acyclic’; Law et al., 2012). As such DAGs reflect the knowledge, presumptions, assumptions and/or speculation of the analyst(s) concerned regarding the causal relationships between each of the variables included therein. Current convention dictates that variables are represented as nodes/vertices, and that any causal paths between variables are represented as directed arcs/edges/lines, often in the form of arrows (see Figure 1). Although each arc indicates the presence and direction of a known/presumed/assumed/speculative causal relationship between the two variables concerned, drawing an arc does not require the sign, magnitude, precision or shape of the relationship to be known or declared (Tennant et al., 2021). In this respect, DAGs provide a simple, uncomplicated, accessible and entirely nonparametric approach for postulating causal relationships amongst any variables of interest even when these are uncertain, unknown or entirely speculative (Ellison, 2020). Nonetheless, as a result of the parametric constraints imposed by the presence/absence of possible arcs within any given DAG, these also reflect and support a number of more sophisticated statistical applications which make it possible to use DAGs to inform the design of multivariable statistical models that reflect the causal structure(s) involved – albeit without the need to know or understand the mathematical technicalities on which these are based (Lewis and Kuerbis, 2016). These features make DAGs attractive cognitive, educational and analytical tools for strengthening the epistemological, theoretical and empirical basis of causal inference, and there has been a recent proliferation in the use of DAGs across a range of applied scientific disciplines (e.g. Knight and Winship, 2013), and an associated upsurge in analytical methods training (e.g. Elwert, 2011; Gilthorpe, 2017; Hernán 2018; Roy, 2021; Hünermund, 2021). This Chapter reflects on a decade of delivering medical statistics training to undergraduate medical students at the University of Leeds between 2012-2021 in which the third year research, evaluation and special studies module (‘RESS3’) has used DAGs to support the development of applied statistical skills relevant to the extended student-selected research and evaluation projects (ESREP) students undertake in their fourth and final years (Ellison, 2021; Ellison et al., 2014a,b). Based on successive iterations of the structure and content of the RESS3 module, together with notes made during formal and informal planning and review meetings with module leads, lecturers, tutors and students, we draw on the claims and criticisms made of DAGs in the epidemiological literature to identify a number of explicit strengths (and associated, often implicit. weaknesses) that are central to their use in prediction and causal inference modelling. While using DAGs requires (and benefits from) a clear understanding of their non-parametric nature and parametric implications, the weaknesses of DAGs seem likely to reflect both: the challenges inherent in the modelling of data generating processes when these are imperfectly understood; and troublesome cognitive and heuristic tendencies common to all analytical tools – in which the tool facilitates the task in hand by reducing the necessity (and benefits of) exploring uncertainties and identifying assumptions. These, more epistemological considerations appear particularly challenging for medical undergraduates to grasp (Ellison, 2021), but also appear poorly understood by many established analysts and clinical epidemiologists (Ellison, 2020).

In this paper, we propose a method for assessing the effectiveness of entropy features using several chaotic mappings. We anlyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) on four discrete mappings: the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn is shown to have improved global efficiency (GEFMCC) in the classification task compared to NNetEn. At the same time, there are local areas of the time series dynamics in which the classification efficiency NNetEn is higher than FuzzyEn. The results of using horizontal visibility graphs (HVG) instead of the raw time series are also shown. GEFMCC decreases after HVG time series transformation, but there are local areas of the time series dynamics in which the classification efficiency increases after including the HVG. The scientific community can use the results to explore the efficiency of entropy-based classification of time series.

The minimum vertex cover (MVC) problem is a canonical NP-hard combinatorial optimization problem, aiming to find a smallest set of vertices such that every edge has at least one endpoint in the set, which has extensive applications in cyber security, scheduling, and monitoring link failures in wireless sensor networks (WSNs). Numerous local search algorithms have been proposed to obtain a “good” vertex cover. However, due to the NP-hard nature, it is challenging to efficiently solve the MVC problem, especially on large graphs. In this paper, we propose an efficient local search algorithm for MVC called TIVC, which is based on two main ideas: A 3-improvements (TI) framework with tiny perturbation, and an edge selection strategy. We conducted experiments on real-world large instances of a massive graph benchmark. Compared with two state-of-the-art MVC algorithms, TIVC shows superior performance in accuracy and possesses a remarkable ability to identify significantly smaller vertex covers on many graphs.

The independent set, IS, on a graph $G=(V,E)$ is $V^{*}\subseteq V$ such that no two vertices in $V^{*}$ have an edge between them. The MIS problem on G seeks to identify an IS with maximum cardinality, i.e. MIS. $V^{*}\subseteq V$ is a vertex cover, i.e. VC of $G=(V,E)$ if every $e\in E$ is incident upon at least one vertex in $V^{*}$ . $V^{*}\subseteq V$ is dominating set, DS, of $G=(V,E)$ if $\forall v\in V$ either $v\in V^{*}$ or $\exists u\in V^{*}$ and $(u,v)\in E$ . The MVC problem on G seeks to identify a vertex cover with minimum cardinality, i.e. MVC. Likewise, MCV seeks a connected vertex cover, i.e. VC which forms one component in G, with minimum cardinality, i.e. MCV. A connected DS, CDS, is a DS that forms a connected component in G. The problems MDS and MCD seek to identify a DS and a connected DS i.e. CDS respectively with minimum cardinalities. MIS, MVC, MDS, MCV and MCD on a general graph are known to be NP-complete. Polynomial time algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs for some of these problems. We introduce a novel graph class, layered graph, where each layer refers to a subgraph containing at most some k vertices. Inter layer edges are restricted to the vertices in adjacent layers. We show that if $k=\Theta (log\mid V\mid )$ then MIS, MVC and MDS can be computed in polynomial time and if $k=O\left({(log\mid V\mid )}^{\alpha }\right)$ , where $\alpha <1$ , then MCV and MCD can be computed in polynomial time. If $k=\Theta \left({(log\mid V\mid )}^{1+ϵ}\right)$ , for $ϵ>0$ , then MIS, MVC and MDS require quasi-polynomial time. If $k=\Theta (log\mid V\mid )$ then MCV, MCD require quasi-polynomial time. Layered graphs do have constraints such as bipartiteness, planarity and acyclicity.

We derive a quantum speed limit for unitary evolution for the case of mixed quantum states using the stronger uncertainty relation for mixed quantum states. This bound can be optimized over different choices of Hermitian operators for a better bound. We illustrate this with some examples and show its better performance with respect to three existing bounds for mixed quantum states.

Polypropylene (PP) is commonly used in the polymer processing industry. Its feature is a good chemical resistance, it is non-toxic and not harmful to people. Polypropylene is widely used in the manufacturing of food packages, laboratory and medical equipment, electric cables insulators, automotive parts, toys and furniture. The application of this material enables us to obtain complicated shapes of big surfaces. It is also highly recyclable. Polylactide (PLA) is a product of the so called “green chemistry” because it is obtained from the renewable raw materials (biomass). As its price is higher compared to the traditional polymers, its repeated use (recycling) is of high interest. Due to the same reason (cost) the mixtures of PLA with other polymers are applied. In this paper the results of testing the PP/PLA mixtures of various mass ratio of the components are presented. Technical terms of preparing and processing such mixtures have been practically tested. Also the mechanical strength was determined based on the static tensile tests. The results showed that those mixtures can be repeatedly processed. Even five-times reprocessing does not cause essential drop of mechanical properties

Triple-negative breast cancer (TNBC) is a subtype of breast cancer characterized by the lack of estrogen receptors (ER), progesterone receptors, and HER-2 receptors. Thus, TNBC tumours do not benefit from the current therapies targeting ER or HER-2. Therefore, there is an urgent need to develop novel treatment for this subtype of breast cancer. Marijuana is a common name given to Cannabis plants, a group of plants in the Cannabis genus of the Cannabaceae family. Cannabis plants are among the oldest cultivated crops, traced back at least 12,000 years and are well known for their multi-purpose usage, including medicinal purposes. The main active compounds extracted from Cannabis plants are 21-carbon-containing terpenophenolics, which are referred to as phytocannabinoids. Of these, the tetrahydrocannabinol (THC) group contains highly potent cannabinoids, including delta-9-tetrahydrocannabinol (∆9-THC) and delta-8-tetrahydrocannabinol (∆8-THC), which are the most abundant THCs and are largely responsible for psychological and physiological effects of marijuana. The use of Cannabis plants for medicinal purposes was first recorded in 2337 BC in China, where Cannabis plants were used to treat pains, rheumatism, and gout. Recently, several cannabinoids have been approved for a number of treatments, one of which is the treatment of nausea and vomiting caused by chemotherapy in cancer patients. Furthermore, increasing evidence shows that cannabinoids not only attenuate side effects due to cancer treatment, but might also potentially possess direct antitumor effects in several cancer types, including breast cancer. However, anti-tumour activity of marijuana has been variable in different studies and even promoted tumour growth in some cases. In addition, the mechanisms of cannabinoid action in cancer remain unclear. This review summarizes evidence about the mixed actions of cannabinoids in cancer in general and triple-negative breast cancer in particular.