With the rapid development of technology and the advancement of Internet technology, various social networking platforms are gradually coming into people's view and occupying a higher and higher position. In the recommendation scenario, the user-item interaction naturally forms a bipartite heterogeneous graph structure and with the development of graph embedding and graph neural network technologies based on deep learning to process graph domain information, the combination of graph information and recommendation systems shows strong research potential and application prospects. The methodological improvement of the recommendation algorithm based on collaborative filtering takes advantage of the nature that user-items can form a bipartite graph in the recommendation scenario. The existing methods still have some shortcomings. The methods that only use weights or convolutional recurrent neural networks to implicitly model different historical behaviors lack explicit modeling of video switching relationships in serialized behaviors. The user's interest is changing all the time, so it is not possible to recommend based on the user's history, and it is necessary to consider both the long-term and short-term interest of the user according to the video content in order to achieve accurate recommendation of short videos. In this paper, we design a recommendation model based on graph neural network, which models users' long-term and short-term interests by two vector propagation methods, respectively.

Traffic congestion and frequent traffic accidents have become main problems affecting urban traffic. Effective location prediction of vehicle trajectory can help alleviate traffic congestion, reduce the occurrence of traffic accidents, and optimize the urban traffic system. Vehicle trajectory is closely related to the surrounding Points of Interest (POI). POI can be considered as the spatial feature and can be fused with trajectory points to improve prediction accuracy. A Local Dynamic Graph Spatiotemporal- Long Short-Term Memory (LDGST-LSTM) is proposed in this paper to extract and fuse the POI knowledge and realize next location prediction. POI semantic information is learned by constructing the traffic knowledge graph, and spatial and temporal features are extracted by combining Graph Attention Network (GAT) and temporal attention mechanism. Moreover, the weights of POI that influence location prediction are visualized to improve the interpretability of the proposed model. The effectiveness of LDGST-LSTM is verified on two datasets, including Chengdu taxi trajectory data in October 2018 and August 2014. The accuracy and robustness of the proposed model are significantly improved compared with the benchmark models.

We revise the definition of graph operations in [WDK2018] and adapt correspondingly the construction of graph term algebras. As a first contribution to a prospective research field Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. Especially, we generalize the concept generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct for any graph operation expression a corresponding derived graph operation in any graph algebra.

Keywords: mHealth; peritoneal dialysis; functionality; usability

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

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

Background: Post-acute sequelae of SARS-CoV-2 infection (PASC) is a complicated disease that affects millions of people all over the world. Previous studies have shown that PASC impacts 10% of SARS-CoV-2 infected patients of which 50-70% are hospitalized. It has also been shown that 10-12% of those vaccinated against COVID-19 were affected with PASC and its complications. The severity and the later development of PASC symptoms is positively associated with the early intensity of the infection. Results: The generated health complications caused by PASC involve a vast variety of organ systems. Patients affected by PASC have been diagnosed with neuropsychiatric and neurological symptoms. Cardiovascular system also has been involved and several diseases such as myocarditis, pericarditis, and coronary artery diseases were reported. Chronic hematological problems such as thrombotic endothelialitis and hypercoagulability were described as a condition that could increase the risk of clotting disorders and coagulopathy in PASC patients. Chest pain, breathlessness, and cough in PASC patients were associated with respiratory system in long COVID-19 causing respiratory distress syndrome. The observed immune complications were notable, involving several diseases. Renal system also was impacted and result in raising the risk of diseases such as thrombotic issues, fibrosis, and sepsis. Endocrine gland malfunction can lead to diabetes, thyroiditis, and male infertility. Symptoms such as diarrhea, nausea, loss of appetite and taste were also among reported observations due to several gastrointestinal disorders. Skin abnormalities might be an indication of infection and long-term implications such as persistent cutaneous complaints were linked to PASC. Conclusions: Long COVID is a multidimensional syndrome with considerable public health implications, affecting several physiological systems and demanding thorough medical therapy as well as more study to address its underlying causes and long-term effects.

Graph theory plays significant role in every field of science as well as technology. Every situation can be articulated in terms of suitable graphs by using various approaches of graph theory. Considering the recent pandemic in the world and the precautions taken for prevention of the COVID 19, it is the most appropriate way to exercise the graph models with theoretical as well as practical aspects to control this epidemic. This paper defines the variable set, variable graphs and their types with respect to variable vertex sets and variable edge sets. Depending upon the nature of the pandemic, there are four types of Virus graphs. Virus graph I and III are not so perilous for all living beings. Although, Virus graphs II and IV are extremely hazardous for the harmony of the world. In view of different aspects for expand of pandemic, growth types of virus graphs are divided in 1-1, 1-P and 1-all growth types. The COVID19 initially was in Virus graph-I type, but presently it is in Virus graph-II types. We present the table involving the number of infected people after n days with respect to different values of P and growth rates with I0 = 100. Moreover, the country wise starting dates of stages of the virus graph-I and II are specified. The concept of cut sets is applicable for prevention of COVID19 and the whole world is using the same analogy.

The properties of the annual, semiannual and triennial oscillations (AO, SAO and TO) in the middle atmosphere have been investigated using the TIMED/SABER temperature data. The Lomb-Scargle and wavelet spectra were used to determine the dominant oscillations in the background temperature field. The AO is prominent at the mid-latitudes. The AO amplitudes present an asymmetry between the two Hemispheres, being larger in the mesosphere than in the stratosphere. The SAO dominates the tropical regions, with three amplitude maxima at altitudes of 45, 75, and 85 km. The SAOs in the upper mesosphere (75 km) are out of phase with those in the mesopause (85 km) in the tropical regions, which can generate an enhancement of 11 K at each equinox, contributing to the lower mesospheric inversion layer. The TO is significant in the tropical region, with amplitude being maximum at 35, 45 and 85 km. Result shows that there may be potential interaction by the TO with SAO at 85km at the equator. The relation between ENSO and TO has also been discussed. The ENSO signal may modulate the amplitude of the TO, mainly in the lower stratosphere. The real origin of the TO may lie in the wave-mean-flow interaction.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel subgroup. In the absence of mass, particle states are disentangled into left and right handed chiral states, governed by the maximal solvable subgroups sol2± of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, it is argued how the spin-flip contribution is closely related to the occurrence of nonphysical spin operators.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns out, this space reduction could be understood as another definition of inflation. It is shown that the introduction of the non-associativity of the algebra of physical fields in a homogeneous space leads to a nonlinear equation, the solutions of which can be considered as two-stage inflation. Using the example of reduction $T\times R^7$ to $T\times R^3$, it is shown that there is a continuous cross-linking of the Friedmann and inflationary stages of algebraic inflation at times $10^{-15}$ with the number of baryons $10^{80}$ in the Universe. In this paper, we construct a new gravitational constant based on a nonassociative octonion algebra.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

Among the various generalizations of persistent topology, the one based on rank functions and leading to indexing-aware functions appears to be particularly suited to catch graph-theoretical properties without the need for a simplicial construction and a homology computation. This paper defines and studies "simple" and "single-vertex" features in directed and undirected graphs, by which several indexing-aware persistence functions are produced, within the scheme of steady and ranging sets. The implementation of the "sink" feature and its application to trust networks provide an example of the ease of use and meaningfulness of the method.

Long-term safety of a nutraceutical combination based on agnus castus and magnolia extracts combined with soy isoflavones (SI) and lactobacilli, and effectiveness on vasomotor symptoms and sleep disorders in postmenopausal women, were assessed. A controlled study was carried-out in menopausal women comparing this nutraceutical combination (ESP group) with formulation containing isoflavones alone (C group), at the dosage recommended. Kuppermann index, PSQI, and SF-36 were determined at baseline, 3, 6 and 12 months. Endometrial thickness, mammary density and liver function were evaluated at baseline and after 12 months. 180 women (100 in ESP group and 80 in C group, mean age 55.5 years, in menopause for about 36 months) were enrolled in the study. At the treatment end, mammary density, endometrial thickness, and hepatic function did not show substantial differences between groups. Kuppermann index, and particularly hot flushes, were progressively and significantly decreased in frequency and severity during ESP versus C treatment. No adverse events were observed. Agnus castus and magnolia, combined with SI + lactobacilli, can effectively and safely be used in symptomatic postmenopausal women, mainly when quality of sleep is the most disturbing complaint. Endometrium, mammary glands and liver function, were unaffected after 12 months treatment.

The influence of short term water absorption on the mechanical properties of halloysite nanotubes-multi layer graphene reinforced polyester hybrid nanocomposites has been investigated. The addition of nano-fillers significantly increased the flexural strength; tensile strength and impact strength in dry and wet conditions. After short term water exposure; the maximum microhardness; tensile; flexural and impact toughness values were observed at 0.1 wt% MLG. The microhardness increased up to 50.3%; tensile strength increased up to 40% and flexural strength increased up to 44%. Compared to dry samples; the fracture toughness and surface roughness of all types of produced nanocomposites were increased that may be attributed to plasticization effect. Scanning electron microscopy revealed that the main failure mechanism is caused by the weakening of nano-filler-matrix interface induced by water absorption. It was further observed that synergistic effects were not effective at concentration of 0.1 wt% to produce considerable improvement in mechanical properties of produced hybrid nanocomposites.

(1) Background: Thrombophilia is a tendency towards hypercoagulability, and it is increased by pregnancy, peaking around delivery. Research question: does thrombophilia stimulate the in-flammatory state of the patient, already suppressed by pregnancy? (2) Methods: Eighty thrombo-philia patients admitted for delivery between 1/10/2017 and 1/12/2021 were prospectively stud-ied, together with eighty age- and para-matched control patients. Patients were admitted for de-livery at term by means of cesarean section. The inflammation indexes from the complete blood count values analysis during both the 24 hours before and after labor—extracted from the hospi-tal’s medical records—were calculated and then correlated with uterine involution. (3) Results: Except for the PLR, most of the numerous inflammation indexes studied were not significantly different in treated thrombophilia patients, before and after delivery, compared to non-thrombophilia patients. Only when we split the patients, based on the uterine haematometra in the first 24-48 hours postpartum, we found out that the few treated thrombophilia patients with haematometra (14 with haematometra out of 79 with treated thrombophilia) had elevated SII and AISI antepartum. In pregnant patients treated for thrombophilia, MLR is higher in pa-tients without the Rh factor than in those with the Rh factor. In non-thrombophilia patients, MCVL and NLPR increased with age and before labor, while SII and AISI increased with age postpartum. (4) Conclusions: Thrombophilia did not stimulate the inflammatory state of the pa-tient, already suppressed by pregnancy.

Background: The validation of laser usage during laparoscopic procedures, notably by Camran Nezhat in the late 1980s, has been significant. Lasers offer precision and depth control in tissue vaporization without bleeding. Surgical intervention remains central in managing endometrio-sis-associated pain and infertility, especially for patients unresponsive to hormonal therapy. Methods: This retrospective cohort study included 200 patients with SPE who underwent laparo-scopic laser vaporization. Surgery was performed using a CO2 laser, and histological confirma-tion of endometriosis was obtained for all cases. Pain scores and SF-36 questionnaire domains were assessed preoperatively and postoperatively. Fertility outcomes were evaluated among pa-tients desiring pregnancy. Results: Significant improvements in pain score and SF-36 questionnaire domains were ob-served postoperatively (p-value

Sentiment analysis plays a crucial role in understanding customer feedback, guiding product development, and informing business decisions. This paper introduces term sentiment entropy (TSE), a novel weighting method that leverages the distribution of sentiment labels associated with words to enhance text classification accuracy. TSE complements traditional TF-IDF techniques by capturing the nuances of sentiment variation across different contexts. Experiments across diverse public datasets demonstrate TSE's potential to improve sentiment analysis performance, especially in capturing subtle sentiment shifts and adapting to specific domains. While computational cost and label quality pose challenges, TSE offers a promising avenue for refining sentiment analysis and opening new research frontiers.

This article is the first part of a scientific project under the general title "Geometrized Vacuum Physics". This study is based on two main postulates: 1) independence of the propagation velocity of electromagnetic waves in vacuum from their frequency; 2) the constancy of the averaged zero vacuum balance, associated with the assertion that only mutually opposite formations are born from vacuum, so that on average they completely compensate for each other's manifestations. In this part of the "Geometrized Vacuum Physics" the foundations of the Algebra of Stignatures are laid, which is the mathematical and logical foundation of the entire project. In the next articles of this project it will be shown that the Algebra of Stignatures can be used for the development of "zero" (vacuum) technologies, algebraic genetics, vacuum cosmology, the vacuum standard model of "elementary particles", vacuum gravity and levitation, vacuum energy, ethics and aesthetics and many other branches of knowledge. At the end of this article, one of the many possible applications of the Algebra of Stignatures is given, in particular, the basics of the stignature-spectral analysis are outlined, with the help of which the possibilities of communication channels can be significantly expanded.

This article is the second part of a scientific project under the general name "Geometrized vacuum physics". On the basis of the Algebra of Stignatures presented in the previous article [1], this article develops the main provisions of the Algebra of Signatures. Both of the above algebras are aimed at studying the properties of an ideal vacuum, but at the same time they are universal and can be applied in various branches of knowledge. It is shown that the signature of a quadratic form is related to the topology of the metric space for which the given quadratic form is a metric. Conditions are given under which an additive imposition of metric spaces with different topologies (or signatures) leads to a total Ricci flat space similar to a Calabi-Yau manifold. A spin-tensor representation of metrics with different signatures is considered and a Dirac bundle of quadratic forms is presented. This article does not contain physical applications of the Algebra of Signatures, but the potential power of this mathematical apparatus will be demonstrated in subsequent articles of this project.

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

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

Graph databases (GDBs) are becoming increasingly popular across scientific disciplines, being highly suitable to store and connect complex heterogeneous data. In systems biology, they are used as a backend solution for biological data repositories, ontologies, networks, pathways, and knowledge graph (KG) databases. In this review, we analyse all publications using or mentioning graph databases retrieved from PubMed and PubMed Central full-text search, focusing on the top 16 available GDB technologies. Relevant publications are then categorised according to their domain and application. We detail different approaches and highlight advantages of outstanding resources, such as UniProtKB, Disease Ontology, and Reactome, which provide graph-based solutions. We discuss ongoing efforts of the systems biology community to standardise and harmonise KG creation and the maintenance of integrated resources. Outlining prospects, including the use of GDBs as a way of communication between biological data repositories, we conclude that efficient design, querying, and maintenance of GDBs will be key for knowledge generation in systems biology and other research fields with heterogeneous data.

Background/Objectives: Vitamin B12 deficiency can cause variable symptoms, which may be irreversible if not diagnosed and treated in a timely manner. We aimed to develop a widely accepted expert consensus to guide the practice of diagnosing and treating B12 deficiency. Methods: We conducted a scoping review of the literature published in PubMed since January 2003. Data were used to design a two-round Delphi survey to study the level of consensus among 42 experts. Results: The panelists agreed on the need for educational and organizational changes in the current medical practices for diagnosing and treating B12 deficiency. Recognition of clinical symptoms should receive the highest priority in establishing the diagnosis. There is agreement that the serum B12 concentration is useful as a screening marker, whereas methylmalonic acid or homocysteine can support the diagnosis. Patient lifestyle, disease history and medications can provide clues to the cause of B12 deficiency. Regardless of the cause of the deficiency, initial treatment with parenteral B12 was regarded as the first choice for patients with acute and severe manifestations of B12 deficiency. The use of high-dose oral B12 at different frequencies may be considered for long-term treatment. Prophylactic B12 supplementation should be considered for specific high-risk groups. Conclusions: There is a consensus that clinical symptoms need to receive more attention in establishing a diagnosis. B12 laboratory markers can support the diagnosis. The severity of clinical symptoms, the causes of B12 deficiency and the treatment goals govern decisions regarding the route and dose of B12 therapy.

The aim of the article is to develop geometrized physics of a vacuum on the basis of two basic postulates: 1) the constancy of the speed of light (more precisely, the speed of propagation of electromagnetic waves) in the vacuum; 2) the ‘vacuum balance condition’ associated with the statement that only mutually opposite formations are born from the vacuum, so that, on average, they completely compensate of the manifestations of each other. The Algebra of signatures is proposed as a mathematical basis for geometrized physics of a vacuum.

Scator set, introduced by Fernández-Guasti and Zaldívar, is endowed with a very peculiar non-distributive product. In this paper we consider the scator space of dimension $1+2$ and the so called fundamental embedding which maps the subset of scators with non-zero scalar component into 4-dimensional space endowed with a natural distributive product. The original definition of the scator product is induced in a straightforward way. Moreove, we propose an extension of the scator product on the whole scator space, including scators with vanishing scalar component.

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

We apply a well known technique of theoretical physics, known as Geometric Algebra or Clifford algebra, to linear electrical circuits with non-sinusoidal voltages and currents. We rederive from the first principles the Geometric Algebra approach to the apparent power decomposition. The important new point consists in a choice of a natural convenient basis in the Clifford vector space which simplifies considerably the presentation. Thus we are able to derive a number of general results which are missing in the former papers. In particular, a natural correspondence with the Current Physical Components approach is shown.

(1) Background: Ectopic pregnancy (EP) is when fertilized ovum implanted outside of uterine cavity. The incidence was 1.5% to 2.0% of all pregnancies [1, 2]. EP decreases fertility ability [3]. This study focused on the pregnancy rate after EP and various parameters influencing pregnancy. (2) Methods: The data was extracted from National Health Insurance Research Database (NHIRD) during 2000-2013. The study group enrolled women with one EP history. Those who did not have EP was put into the control group. Chi-square/Fisher exact test was performed on category variable and t-test was used on continue variables. (3) Results: The EP group had a higher cumulative rate of conceive, 41.55% than control group, 37.14% and 1.16 times higher risk in developing pregnancy (P<0.001). The conceiving rate was lower than the control group in the first 5 years, but higher than the control group in the 10th to 14th years. (4) Conclusions: The fecundability after EP is lower at the beginning, but regained after long term follow.

(1) Background: Sleep disordered breathing represent a growing public health concern, especially among children and adolescents. Full-night polysomnography is considered the gold standard for diagnosing obstructive sleep apnea. Our goals are to identify personal and environmental risk factors for the onset and persistence of sleep respiratory disorders. We also want to investigate the differences in neuropsychological profiles; (2) Methods: This is an observational, retrospective cohort study. We collected information on adenoidectomy or adenotonsillectomy. We reviewed the clinical history and preoperative visits and collected data through a telephone questionnaire. Pediatric Sleep Questionnaire (PSQ) and the Pediatric Quality of Life Inventory (PedsQL) are questionnaires used for screening sleep respiratory disorders in children. The data were statistically analyzed it using SPSS version 22.0 for Windows (SPSS Inc., Chicago, IL); (3) Results: The study involved 138 patients, but only 100 parents participated. A higher percentage of patients with sleep disordered breathing were observed to have mothers who smoked during pregnancy. A smaller proportion of patients with sleep disordered breathing had a habit of using a pacifier. A rise in physical results is associated with a reduction in the PSQ at follow-up (p=0.051). An increase of overall academic achievement is associated with an average decrease in the PSQ at follow-up (p<0.0001). A more significant proportion of patients undergoing adenotonsillectomy were observed to have a history of prematurity and cesarean birth (4) Conclusions: These results provide essential information on the effectiveness and effects of adenotonsillectomy intervention compared to adenoidectomy intervention and the factors associated with SDB in children undergoing these interventions.

In recent years, graph neural networks (GNNs) have become a promising method for analyzing data structured in graph format. By considering connections between entities in a graph, GNNs are able to extract valuable insights. One notable variation of GNN is the graph attention network (GAT), which employs the attention mechanism and has demonstrated promising performance in various applications. However, its ability to incorporate feature information from nodes beyond the immediate neighborhood is limited, leading to degraded performance on heterophilic data. To address this limitation, this thesis proposes a novel attention-based model, namely the Directional Graph Attention Network (DGAT). This model combines the feature-based attention with the global directional information extracted from the graph topology, as inspired by the Directional Graph Network (DGN). A new class of Laplacian matrices is proposed and an existing theoretical result on DGN is extended. This extension bridges a gap in the literature. The experimental results presented in the thesis, based on nine real-world benchmarks and ten synthetic data sets, demonstrate the superiority of the proposed DGAT model compared to the GAT baseline model. Particularly on heterophilic data sets, DGAT showed a notable average increase of approximately 35% in node classification tasks across all heterophilic real-world data sets. In addition, DGAT outperforms GAT by an average margin of around 51% in all ten synthetic data sets with various levels of heterophily

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Background: The effect of COVID-19 infection, versus the indirect effect of the pandemic on body composition remains unclear. This study investigates long-term changes in body composition in COVID–19 survivors compared to a contemporary control group. Method: This is a prospective study involving adults who had a pre-pandemic whole-body DXA scan (DXA#1) performed between 2017 and 2019. Participants were asked to return for a repeat whole-body DXA scan (DXA#2) after the pandemic. Detailed data were collected including medical and COVID history. Inflammation markers and fasting lipids were measured. For those participants who had a COVID-19 infection between the 2 DXAs, DXA#2 was acquired at least one year after COVID-19 infection. Results: Overall, 160 adults were enrolled; 32.5% females, 51.8% non-white, with mean age of 43.2 years. Half (n=80) of the participants had documented COVID infection between their 2 DXA scans (COVID+ group), and the other half never had COVID. COVID-negative participants had an increase in annualized trunk fat (g) [922.5 vs. 159.7; P=0.01], total fat (g) [1564.3 vs. 199.9; P=0.2], and LBM (g) [974.9 vs. -64.5; P=0.0002], when compared to COVID+ group. However, among the COVID+ group, no differences were seen in annualized trunk fat, total fat mass, or LBM between those with PASC and without (p>0.05). Conclusion: During the pandemic, both COVID-19-survivors and COVID-negative groups exhibited increases in weight, and total and trunk fat, likely associated with pandemic-linked lifestyle modifications. However, only COVID-19-survivors had a decline in lean body mass over the same period, regardless of PASC symptoms.

The root system plays an irreplaceable role in plant growth. Its improvement can increase crop productivity. However, such system is still mysterious for us. The underlying mechanism has not been fully uncovered. The investigation on proteins related to the root system is an important means to complete this task. In the previous time, lack of root-related proteins makes it impossible to adopt machine learning methods for designing efficient models for the discovery of novel root-related proteins. Recently, a public database on root-related proteins was set up and machine learning methods can be applied in this field. In this study, we proposed a machine learning based model, named Graph-Root, for identification of root-related proteins. The features derived from protein sequences and one network were extracted, where the former features were processed by graph convolutional neural network and multi-head attention, and the later features abstracted the linkage between proteins. These features were fed into the fully connected layer to make prediction. The 5-fold cross-validation and independent tests suggested its good performance. It also outperformed the only one previous model, SVM-Root. Furthermore, the importance of each feature type and component in the proposed model was investigated.

The intense motion of a ship can greatly impacts the comfort of crew members and the safety of the vessel. Therefore, accurately estimating and predicting ship attitudes has become an important issue. This paper introduces the latest development in functional deep learning model called DeepOnet. It takes wave height as input and ship motion as output, using a cause-to-result prediction approach. The modeling data used in this study is sourced from publicly available experimental data from the Iowa Institute of Hydraulic Research. Firstly, parameters system tuning was conducted for the neural network's hyperparameters to determine the appropriate combination of parameters. Secondly, the DeepOnet model for wave height and multi-degree-of-freedom motion was established, and the influence of increasing time steps on prediction accuracy was examined. Finally, a comparison was made between the DeepOnet model and the classical time series model LSTM. It was found that the DeepOnet model had a 10-fold improvement in accuracy for roll and heave attitudes. Moreover, as the forecast duration increased, the advantage of DeepOnet showed a trend of strengthening. As a functional prediction model, DeepOnet provides a new promising tool for very short-term prediction of ship motion.

Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control over the flow of electricity between the source and the load, they are often used passive or active filters. Nevertheless, determining the type of filter and the characteristics of their elements is not a trivial task. In fact, the development of algorithms for calculating the parameters of filters is still an open question. This paper analyzes the use of genetic algorithms to maximize the power factor compensation in non-sinusoidal circuits using passive filters, while concepts of geometric algebra theory are used to represent the flow of power in the circuits. According to the results obtained in different case studies, it can be concluded that the genetic algorithm obtain high quality solutions that could be generalized to similar problems of any dimension.

Recently, many authors have been interested to introduce fuzzy implications over t-norms and t-conorms. In this paper, we introduce (S,N) and residuum fuzzy implication for Dubois t-norm and Hamacher's t-norm. Also, new concepts so-called (T,N) and residual fuzzy co-implication in dual Heyting Algebra are investigated. Some examples as well as application are discussed as well.

The aim of this paper is to show how the mathematical basis is used for a precise treatment of double-entry bookkeeping, which was firstly developed in the nineteenth century by Sir William Rowan Hamilton. This is done by using basic notions of matrix algebra with the roots to the idea of using ordered pairs. We also reveal how the complex numbers and the rationals (fractions) developed in a mainstream of accounting science and became a leading platform for the ongoing processes within the Industry 4.0. The paper concludes with the examples on how accounting operations can be represented by matrix equations with a result of the essential report generating. The author represents a mathematical model of accounting which is independent of the specific existential forms but is capable to undertake the form of any of them and thus has the prospect of being understood and accepted by specialists globally.

For a graph G, let P(G, λ) be its chromatic polynomial. Two graphs G and H are said to be chromatically equivalent if P(G,λ) = P(H,λ). A graph is said to be chromatically unique if no other graph shares its chromatic polynomial. In this paper, chromatic polynomial of the necklace graph N_n, for n ≥ 2 has been determined. It is further shown that N₃ is chromatically unique.

We present a Deep Learning generative model specialized to work with graphs with a regular geometry. It is build on a Variational Autoencoder framework and employs Graph convolutional layers in both encoding and decoding phases. We also introduce a pooling technique (ReNN-Pool), used in the encoder, that allows to downsample graph nodes in a spatially uniform and highly interpretable way. In the decoder, a symmetrical un-pooling technique is used to retrieve the original dimensionality of graphs. Performance of the model are tested on the standard Sprite benchmark dataset, a set of 2D images of video game characters, adequately transforming images data into graphs, and on the more realistic use-case of a dataset of cylindrical-shaped graph data that describe the distributions of the energy deposited by a particle beam in a medium.

Urea cycle disorders (UCDs) are common inborn errors of metabolism, with an incidence of one in 30,000 births. They are caused by deficiencies in any of six enzymes and two carrier proteins, the most common being Ornithine Transcarbamylase Deficiency (OTCD). OTCD results in impairment to excrete nitrogen, causing toxic buildup of ammonia with resultant encephalopathy. Hyperammonemia (HA) induces the conversion of glutamate to glutamine in the brain. Excess glutamine in the brain causes osmotic changes cerebral edema, changes in astrocyte morphology, and cell death. Acute symptoms of HA include vomiting, hyperventilation, seizures, and irritability. Long-term neurological changes include deficits in working memory and executive function. To date, there are no predictors of prognosis of infants with neonatal onset OTCD outside of plasma ammonia level at presentation and duration of hyperammonemic coma. We provide a comprehensive analysis of a 16-year-old male with neonatal onset of OTCD as an example of how brain biomarkers may be useful to monitor disease course and outcome. This male presented at 8 days post natal with plasma ammonia and glutamine of 677 and 4024 micromol/L and had a missense mutation in Exon 4 (p.R129H). Treatment included protein restriction, sodium benzoate, and citrulline, arginine, and iron. He suffered recurrent acute hyperammonemic episodes despite compliance, triggered by infections or catabolic stressors. We discuss the long-term effects of the hyperammonemic episodes by following MRI based disease biomarkers.

The European Union Water Framework Directive (2000/60/EC; WFD) aims to achieve a good ecological and chemical status of all bodies of surface water by 2027. The development of an integrated guidance on surface water chemical monitoring (e.g. WFD Guidance Document No. 7/19) has been transferred into national German law (Ordinance for the Protection of Surface Waters, OGewV). For the majority of compounds, this act requires a monthly sampling frequency to assess the chemical water quality status of a surface water body. To evaluate the representativeness of the sampling strategy under the OGewV, high-frequency online monitoring data is investigated under different sampling scenarios and compared with current, monthly grab sampling strategy. About 23 million data points were analyzed for this study, three chemical parameters (dissolved oxygen, nitrate-nitrogen, chloride concentration) and discharge data were selected from four catchment of different sizes ranging from 51391 km² to 84 km² (Elbe, Vereinigte Mulde, Neiße and two stations at Lockwitzbach). In this paper we proposed short-term online-monitoring (STOM) as a sampling alternative. STOM considers the placement of online sensors over a limited duration and return interval. In general we: (I) compare the results of conventional grab sampling with STOM, (II) investigate the different performance of STOM and grab sampling using discharge data as proxy for analyzing event-mobilized pollutants and (III) investigate the related uncertainties and costs of both sampling methods. Results show, that STOM outperforms grab sampling for parameters where minimum/maximum concentrations are required by law as the probability to catch a single extreme value is higher with STOM. Furthermore, parameters showing a pronounced diurnal pattern, like dissolved oxygen, are also captured considerably better. The performance of STOM showed no substantial improvements for parameters with small concentration variability, as nitrogen-nitrate The analysis of discharge events as a proxy parameter for event-mobilized pollutants proved that the probability of capturing samples during events is significantly increased by STOM.

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

The exceptional Jordan algebra is the algebra of $3 \times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan’s algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of quantum theory. It has often been suggested that this exceptional algebra could explain physical phenomena not currently explained by the conventional approach, such as values of the fundamental constants of the standard model of particle physics, and their relation to gravitation. We show that this is indeed the case; and this also unravels the connection between general relativity and the weak force. The exceptional Jordan algebra also predicts a new U(1) gravitational interaction which modifies general relativity, and which provides a theoretical basis for understanding the Modified Newtonian Dynamics (MOND).

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

Graph visualization has evolved significantly over time, offering various methods to effectively represent complex data structures. This study introduces a novel force-directed algorithm for 3D data visualization, specifically tailored for commonly used datasets in linked data visualization. Leveraging the power of graph theory and methods, the algorithm aims to address the challenge of creating visually appealing and easily interpretable visualizations, which often necessitate advanced user interaction. By utilizing 3D space and the Unity Engine, the research successfully visualizes data and develops interactive visualizations, overcoming limitations of basic force-directed implementations. The main contribution of presented research is in the force-directed algorithm with springs and controlled placement as a visualization technique that combines the use of springs and attractive forces to stabilize a graph in a 3D environment. The combination of these two techniques also helps prevent the formation of a single large cluster within the graph, enhancing the overall visualization quality.

The Randić index of a graph G is the sum of (dG(u)dG(v))−1/2 over all edges uv of G, where dG(u) denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease Randić index of graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs, and characterize the corresponding extremal graphs.

: Biological networks such as protein interaction networks, gene regulation networks and metabolic pathways are examples of complex networks which are large graphs with small-world and scale-free properties. Analysis of these networks has a profound effect on our understanding the origins of life, health and disease states of organisms, and diagnose diseases to aid the search for remedial processes. In this review, we describe main analysis methods of biological networks using graph theory by first defining main parameters such as clustering coefficient, modularity and centrality. We then survey fundamental graph clustering methods and algorithms followed by the network motif search algorithms with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function carried out by that small network and discovering such a function provides an insight to the overall function of the organism. Lastly, we review network alignment algorithms that achieve to find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor and finding such relationship may help researchers derive ancestral relationships and predict the future evolution of organisms to enable designing new drugs. We conclude by the current challenging areas of biological network analysis using graph theory and parallel processing for high performance analysis

The hybrid bond graph has been studied in depth for scalar bond graphs, but how does this translate to the multi-bond graph? Here, the controlled junction – used to model structural switching such as contact – is extended to the multi-bond case. This is a simple process, assuming that all bonds switch simultaneously (which makes physical sense). A controlled 0-junction is applied to multi-bond graph of a car, which can lose contact with the ground in cornering. Dynamic causality features, but this can be accommodated using an equational submodel in 20-Sim (in a manner similar to that used with scalar bond graphs). The junction is proposed for subsequent work to develop a validated multi-body dynamics car model in cornering.

In the context of cognitive radio, smart city and Internet-of-Things, the need of advanced radio spectrum monitoring becomes crucial. However, surveillance of a wide frequency band without using extremely expensive high sampling rates devices is a challenging task. The recent development of compressed sampling approaches offers a promising solution to these problems. In this context, the Modulated Wideband Converter (MWC), a blind sub-Nyquist sampling system, is probably the most realistic approach and was successfully validated in real-world conditions. The MWC can be realized with existing analog components and there exist calibration methods which are able to integrate the imperfections of the mixers, filters and ADCs, hence allowing its use in real-world. The MWC underlying model is based on signal processing concepts such as filtering, modulation, Fourier series decomposition, oversampling and undersampling, spectrum aliasing, and so on, as well as in-flow data processing. In this paper we develop an MWC model which is entirely based on linear algebra, matrix theory and block processing. We show that this approach has many interests: straightforward translation of mathematical equations into simple and efficient software programming, suppression of some constraints of the initial model, and providing a basis for the development of an extremely fast system calibration method. With a typical MWC acquisition device we obtained a speed up of a factor greater than 20 of the calibration computation time, compared with a previous implementation.

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.

The long-term use of fertilizers and pesticides in conventional cultivation has resulted in a decrease in soil productivity and vegetable yields in greenhouses. However, only a limited number of studies have explored the impacts of organic cultivation on greenhouse soil. Specifically, there is a scarcity of research examining the alterations in soil aggregate mediated organic carbon and microbial communities, which are known to enhance soil productivity. This study investigated the properties of soil aggregates, including the levels of organic carbon fractions, microbial community, and enzyme activity with the three aggregate classes microaggregates (<0.25 mm), small macroaggregates (2-0.25 mm) and large macroaggregates (>2 mm). These investigations were conducted under three different cultivation methods in a greenhouse: conventional cultivation (CC), integrated cultivation (IC), and organic cultivation (OC) in greenhouse. The results showed that (1) OC and IC promoted the formation of small macro-aggregates and enhanced aggregate stability compared to CC, (2) SOC in the three size fractions of OC increased by 98.99%-92.06% compared to CC; EOC increased by 98.47%-117.59%; POC increased by 138.59%-208.70%; MBC increased by 104.71%-230.61%; DOC increased by 21.93%-40.90%, respectively; (3) Organic cultivation significantly increased enzyme activity in all three particle size aggregates and increased the relative abundance of bacteria in micro-aggregates as well as the relative abundance of fungi in small macro-aggregates. Structural equation model (SEM) analysis revealed that organic farming practices fostered the development of smaller macro-aggregates, elevated microbial and enzyme activities within soil aggregates, and facilitated the conversion of soil nutrients and carbon sequestration. consequently, this led to an increase in soil organic carbon content and improved vegetable yield in greenhouse environments. In conclusion, the soil carbon content and vegetable yield are enhanced through long-term organic cultivation in greenhouses, primarily by increasing the proportion of small macro-aggregates.

Management of chronic inflammation and wounds has always been a key issue in the pharmaceutical and healthcare sector. Curcumin (CCM) is an active ingredient extracted from turmeric rhizomes that has antioxidant, anti-inflammatory, and antibacterial activities, thus showing significant effectiveness toward wound healing. However, its shortcomings such as poor water solubility, poor chemical stability and fast metabolic rate limit its bioavailability and long-term use. In this context, hydrogels appear to be a versatile matrix for carrying and stabilizing drugs due to the biomimetic structure, soft porous microarchitecture, and pleasant biomechanical properties. The drug loading/releasing efficiencies can also be controlled by use of highly crystalline and porous metal organic frameworks (MOFs). Here, a flexible hydrogel composed of sodium alginate (SA) matrix and CCM-loaded MOFs was constructed for long-term drug release and antibacterial activity. The morphology and physicochemical properties of composite hydrogels were analyzed by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), ultraviolet visible spectroscopy (UV-Vis), Raman spectroscopy and mechanical property tests. The results showed that the composite hydrogel was highly twistable and bendable to mechanically comply with human skin. The as-prepared hydrogel could capture efficient CCM for slow drug release as well as effective killing of bacteria. Therefore, such composite hydrogel is expected to provide a new management system for chronic wound dressings.

The NP method was used to elucidate the contributions of vehicles and coal combustion to seasonal and long-term atmospheric PM-bound Pyr and 1-NP concentrations in Kanazawa, Kitakyushu, Shenyang, and Shanghai in the Western Pacific region from 1997 to 2021. Among the four cities, Kanazawa demonstrated the lowest Pyr concentration. The contribution of vehicles to Pyr before and after 2010 were 35% and 5%, respectively. The 1-NP concentration reduced by a factor of more than 1/10. These changes can be attributed to the emission control from vehicles. Kitakyushu revealed the second lowest Pyr and the lowest 1-NP concentrations. Coal combustion was found to be the main contributor to Pyr, while its contribution to 1-NP increased from 9% to 19%. The large contribution of coal combustion is attributed to iron manufactures. Shenyang demonstrated the highest atmospheric Pyr concentration with its largest seasonal change. Vehicles are the largest contributors to 1-NP. However, coal combustion, including winter coal heating, contributed 97% or more to Pyr and more than 14% to 1-NP. Shanghai revealed the second highest Pyr and 1-NP concentrations, but the former was substantially lower than in Shenyang. Coal combustion was the major contributor, but the contribution of vehicles to Pyr was larger before 2010 similar to Kanazawa.

Direct and indirect effects after mine operations cease must ideally be subject to perpetual monitoring routines in order to detect possible risks or avoid adverse effects on the surrounding ecosystems at an early stage. In this contribution, mining subsidence lakes created inside the nature reserve Kirchheller Heide and Hilsfeld Forest are subjected to analysis for a long-term monitoring scheme. For this purpose, we employ high-resolution unmanned aerial system (UAS)-based multispectral and thermal mapping tools to provide a fast, non-invasive and multitemporal environmental monitoring method. Specifically, we propose to monitor vegetation evolution through multispectral analysis, biotypes identification using machine learning algorithms, and water surface extent detection, together with their thermal behavior. The aim of this contribution is to present the proposed workflow and first results to establish a baseline for future analyses and subsequent surveys for longterm multi-temporal monitoring

Here we present a fast and highly scalable community structure preserving network module detection that recursively integrates graph sparsification and clustering. Our algorithm, called SparseClust, participated in the most recent DREAM community challenge on disease module identification, an open competition to comprehensively assess module identification methods across a wide range of biological networks.

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.

The statistical analysis of impact of the top 50 solar flares of X-class (1997-2023) on the global seismic activity, as well as on the earthquake preparation zones located in illuminated part of the globe and in the area of 5000 km radius around the subsolar point was carried out. It is shown by a method of epoch superposition that for all cases the increase of seismicity is observed, especially in the region around the subsolar point (up to 38%) during 10 days after the solar flare in comparison with preceding 10 days. The case study of aftershock sequence of strong M=9.1 earthquake (Su-matra-Andaman Islands, 26.12.2004) after the solar flare of X7.2 class (20.01.2005) demonstrated that the number of aftershocks with magnitude M≥2.5 increases more than 20 times after the solar flare with a delay of 7 days. For the case of the Darfield earthquake (M=7.1, 04.09.2010, New Zealand) it was shown that strong solar flares of class X and M probably triggered two strong aftershocks (M>6) with the same delay of 6 days on the Port Hills fault, which is the most sensitive to external electromagnetic impact from point of view of the fault electrical conductivity and orientation. Based on the obtained results the possible application of natural electromagnetic triggering of earthquakes is discussed for a short-term earthquake prediction using confidently recorded strong external electromagnetic triggering impacts on the specific earthquake preparation zones, as well as ionospheric perturbations due to aerosol emission from the earthquake sources recorded by satellites.

For disciplines like biological science, security, and the medical field, link prediction is a popular research area. To demonstrate the link prediction many methods have been proposed. Some of them that have been demonstrated through this review paper are TransE, Complex, DistMult, and DensE models. Each model defines link prediction with different perceptions. We argue that the practical performance potential of these methods, having similar parameter values, using the fine-tuning technique to evaluate their reliability and reproducibility of results. We describe those methods and experiments; provide theoretical proofs and experimental examples, demonstrating how current link prediction methods work in such settings. We use the standard evaluation metrics for testing the model's ability.

Graph neural networks (GNNs) build on the success of deep learning models by extending them for use in graph spaces. Transfer learning has proven extremely successful for traditional deep learning problems: resulting in faster training and improved performance. Despite the increasing interest in GNNs and their use cases, there is little research on their transferability. This research demonstrates that transfer learning is effective with GNNs, and describes how source tasks and the choice of GNN impact the ability to learn generalisable knowledge. We perform experiments using real-world and synthetic data within the contexts of node classification and graph classification. To this end, we also provide a general methodology for transfer learning experimentation and present a novel algorithm for generating synthetic graph classification tasks. We compare the performance of GCN, GraphSAGE and GIN across both the synthetic and real-world datasets. Our results demonstrate empirically that GNNs with inductive operations yield statistically significantly improved transfer. Further we show that similarity in community structure between source and target tasks support statistically significant improvements in transfer over and above the use of only the node attributes.

Lie algebra plays an important role in the study of singularity theory and other field of sciences. Finding numerous invariants linked with isolated singularities is always a main interest in the classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo \cite{HYZ10} have been found a new class of Lie algebra \texorpdfstring{ $ \mathcal{L}_ k (V)$}{LG}, \texorpdfstring{$k\geq 1$}{LG} i.e., Der ($M_{k}(V), M_{k}(V)$) and purposed a conjecture over its dimension $\delta_{k}(V)$ for $k\geq0$. Later they proved it true for $k$ up to $k=1,2,3,4,5$. In this work, the main concern is whether it's true for a higher value of $k$. According to this, we calculate first, the dimension of Lie algebra \texorpdfstring{$\mathcal{L}_ k (V)$}{LG} for $k=6$ and then compute the upper estimate conjecture of fewnomial isolated singularities. Along with, we also justify the inequality conjecture: \texorpdfstring{$\delta_{k+1}(V) < \delta_{k}(V)$}{LG} for $k=6$. Our calculated results are innovative and a new addition to the study of singularity theory.

The Process Algebra model has been shown to provide an alternative mathematical framework for non-relativistic quantum mechanics (NRQM). It reproduces the wave functions of non-relativistic quantum mechanics to a high degree of accuracy. It posits a fundamental level of finite, discrete events upon which the usual entities of NRQM supervene. It has been suggested that the Process Algebra model provides a true completion of NRQM, free of divergences and paradoxes, with causally local information propagation, contextuality and realism. Arguments in support of these claims have been mathematical. Missing has been an ontology of this fundamental level from which the formalism naturally emerges. In this paper it is argued that information and information flow provides this ontology. Higher level constructs such as energy, momentum, mass, spacetime, are all emergent from this fundamental level.

Next-generation cancer and oncology research needs to take full advantage of the multi-modal structured, or graph, information, with the graph datatypes ranging from molecular structures to spatially resolved imaging and digital pathology to biological networks to knowledge graphs. Graph Neural Networks (GNNs) efficiently combine the graph structure representations with the high predictive performance of deep learning, especially on the large multi-modal datasets. In this review article, we survey the landscape of recent (2020-present) GNN applications in the context of cancer and oncology research, and delineate six currently predominant research areas. Subsequently, we identify the most promising directions for future research. We compare GNNs with graphical models and "non-structured" deep learning, and devise the guidelines for cancer and oncology researchers or physician-scientists asking the question of whether they should adopt the GNN methodology in their research pipelines.

Graphs are largely used in computer science to model relations, or associations, among entities the compose complex systems. More recently, they found a broad field of application in bioinformatics and medical informatics supporting modelling, analysis of many systems. The applications span from representing interactions among molecules within cells, to model the functions of the brains. In order to support research, algorithms from graph theory that are able to extract knowledge from network should be coupled to efficient visualisation techniques. Although the importance of such topic, we retain that many challenges should be faced in the futures, such as automated pathway and network layout to better match biologists’ needs, the developing of a standard able to give more and better choices to represent nodes, edges finally, the developing of automated mechanism able to improve the network navigation methods that help users manage large and complex networks with the goal to improve the usability.

This paper presents the Advanced Syntactic-Graph Convolutional Model (ASGCM), a pioneering approach in Aspect-Based Sentiment Analysis (ABSA) that integrates syntactic dependency features within a graph convolution framework. ASGCM stands out for its novel use of dependency edge encoding and tag-based graph convolutions, providing a fine-grained analysis of sentiments associated with specific aspects in text. This model meticulously captures the intricacies of syntactic structures, thereby offering enhanced precision in sentiment analysis. Notably, ASGCM incorporates a dual-layer graph convolution system: one layer processes syntactic dependencies (edges), while the other interprets semantic roles (tags), ensuring a comprehensive understanding of both structural and contextual elements in text. We rigorously tested ASGCM on multiple datasets, including both English and Chinese languages, and our findings reveal a significant improvement in sentiment classification accuracy compared to existing models. The versatility of ASGCM makes it a robust tool for diverse linguistic environments, setting a new standard for ABSA methodologies.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved by machines, which still poses challenges in natural language processing and computer vision. Significant progress promotes existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to the poor effect of the theorem prediction and affect the accuracy in problem solving. In this paper, the formal language graph is constructed by the extracted formal language set and used to theorem prediction by graph convolutional network. So as to better extract the relationship set of diagram elements, an improved diagram parser was proposed. The test results indicate that the improved method has good results in solving the problem with interpretability geometry.

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.

Many parameters and complex boundaries are involved in the spatial arrangement of an under-ground powerhouse for a hydropower station, which requires reference to many relevant cases and specifications. However, in practical applications, retrieving relevant cases or specifications is difficult, and there is a lack of knowledge of cascading logic among design parameters. For this question, a targeted knowledge graph based on knowledge graph management technology is established to support subsequent applications. This paper proposes a new concept of con-structing a knowledge graph for building information modeling (BIM) underground power-houses of hydropower stations. Firstly, the ontology skeleton of hydropower station spatial ar-rangement design, which represents the knowledge organization structure of the knowledge graph, is reconstructed by carefully analyzing the requirements for intelligent modeling of un-derground powerhouses. A large amount of unstructured data is identified based on optical character recognition (OCR) technology and is divided into words to extract correlation knowledge based on THULAC. In the next step, the knowledge triad of the spatial arrangement of the underground powerhouse is extracted based on ChatGPT and stored in a Neo4j knowledge base to build a knowledge graph. Finally, the knowledge graph is serviced to realize the query of knowledge and parameter recommendation to assist the digital intelligent design of spatial arrangement of an underground powerhouse of pumped storage hydropower stations.

The accurate prediction of molecular properties such as lipophilicity and aqueous solubility are of great importance and pose challenges in several stages of the drug discovery pipeline. Machine learning methods like graph-based neural networks (GNNs) have shown exceptionally good performance in predicting these properties. In this work, we introduce a novel GNN architecture, called directed edge graph isomorphism network (D-GIN). It is composed of two distinct sub-architectures (D-MPNN, GIN) and achieves an improvement in accuracy over its sub-architectures employing various learning, and featurization strategies. We argue that combining models with different key aspects help make graph neural networks deeper and simultaneously increase their predictive power. Furthermore, we address current limitations in assessment of deep-learning models, namely, comparison of single training run performance metrics, and offer a more robust solution.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

：Non-Euclidean data, such as social networks, and citation relationships between documents, has node information and structural information. Graph Convolutional Network(GCN) can automatically learn node features and association information between nodes. The core ideology of the graph convolutional network is to aggregate node information by using edge information, thereby generating a new node feature. In the process of updating node features, there are two core influencing factors. One is the number of neighboring nodes of the central node, the other is the contribution of the neighboring nodes to the central node. Due to the previous GCN methods not simultaneously considering the numbers and different contributions of neighboring nodes to the central node, we design the Adaptive Attention Mechanism(AAM). To further enhance the representational capability of the model, we utilize Multi-Head Graph Convolution(MHGC). Finally, we adopt cross-entropy(CE) loss function to describe the difference between the predicted results of node categories and the ground truth (GT). Combined with backpropagation, this ultimately achieves accurate node classification. Based on AAM, MHGC and CE, we contrive the novel Graph Adaptive Attention Network (GAAN). Experiments show that the classification accuracy has achieved outstanding performances on Cora, Citeseer and Pubmed datasets.

This report gives a comprehensive summary of two problems about graph convolutional networks (GCNs): over-smoothing and heterophily challenges, and outlines future directions to explore.

The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

The focus of our study was the changes in the composition of semi-natural dry grasslands in Hungary. Since these valuable habitats were created with the help of humans, their preservation also requires regular treatment. Our mowing experiment aimed to investigate the suppression of the native Calamagrostis epigejos L. Roth. In Hungary, in the Cserhát Mountains, eight permanent plots were mowed twice a year. The vegetation was sampled annually between 2001 and 2011. The effects of mowing were investigated with repeated measures analysis of variance (ANOVA). After 10 years, the C. epigejos cover of the mowed plots decreased significantly, from the initial average of 62.38 to 7.50%. Surprisingly, we also experienced a similar decrease in the control plots. Regular treatment also had a positive effect on the number of species and diversity. Species richness increased continuously in both treatment types, which indicates the combined effect of vegetation succession and treatment. The biomass growth of other Poaceae and Fabaceae species, which are important from a grassland management perspective, was also facilitated by mowing. Our results suggest that long-term in situ experiments and continuous botanical studies are needed to establish a reliable utilization of grasslands.

The proposed method deals with the problem of data privacy and sharing when processing personal mobility tracking data. Previous methods concentrate on producing highly detailed data on short-term and restricted areas, e.g. for autonomous driving scenarios. Another possibility consists of city-wide scales and beyond, that are used to predict general traffic flows. The presented approach takes the tracked mobility behavior of individuals to create coherent new mobility data that reflects the long-term mobility behavior of the person, guaranteeing location persistency and sound embedding within the point-of-interest structure of the observed area. After an analysis and clustering step with the original data, the area is distributed into a geospatial grid structure (H3 is used here), and the neighborhood relationships between the grids are interpreted as a graph. A feed-forward-autoencoder and a graph encoding-decoding network generate a latent space representation of the area. The original clustered data is associated with their respective H3 grids. With a greedy algorithm approach and concerning privacy strategies, new combinations of grids are top-level patterns for individual mobility behavior. Concrete locations are found and connected within the grids based on the original data. The described method is then applied to a study with 1000 participants from the city of Munich in Germany, and the results are described, showing the application of the approach in generating synthetic data, enabling further research on individual mobility behavior and patterns. The result is a sharable dataset on the same abstraction level as the input data, which makes it interesting, particularly for machine learning applications.

The real-time Railway Traffic Management Problem (rtRTMP) is discussed in the field of railway transportation. In this paper, rtRTMP is considered for planning shunting routes based on the use of routing methods on a spatial-temporal graph. An approach and algorithm of Spatial-Temporal Graph formation for rail yard transportation network is proposed. The idea is to construct an undirected loop-free Double Vertex Graph for determining optimal shunting routes consisting of several half-runs for several trains shunting under draw-out tracks capacity constraints. Experimental results on the rail yard simulation model are presented.

The graph model enables a broad range of analysis, thus graph processing is an invaluable tool in data analytics. At the heart of every graph processing system lies a concurrent graph data structure that stores the graph. Such a data structure needs to be highly efficient for both graph algorithms and queries. Due to the continuous evolution, the sparsity, and the scale-free nature of real-world graphs, graph processing systems face the challenge of providing an appropriate graph data structure that enables both fast analytical workloads and low-memory fast graph mutations. Existing graph structures offer a hard tradeoff between read-only performance, update friendliness, and memory consumption upon updates. In this paper, we introduce CSR++, a new graph data structure that removes these tradeoffs and enables both fast read-only analytics and quick and memory-friendly mutations. CSR++ combines ideas from CSR, the fastest read-only data structure, and adjacency lists to achieve the best of both worlds. We compare CSR++ to CSR, adjacency lists from the Boost Graph Library, as well as state-of-the-art update-friendly graph structures: LLAMA, STINGER, GraphOne, and Teseo. In our evaluation, which is based on popular graph processing algorithms executed over real-world graphs, we show that CSR++ remains close to CSR in read-only concurrent performance (within 10% on average), while significantly outperforming CSR (by an order of magnitude) and LLAMA (by almost 2×) with frequent updates. We also show that both CSR++’s update throughput and analytics performance exceed that of several state-of-the-art graph structures, while maintaining low memory consumption when the workload includes updates.

It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.

This study introduces a comparative analysis of two deep learning (multilayer perceptron neural networks (MLP-NN) and the long short term memory networks (LSTMN)) models for transit travel time prediction. The two models were trained and tested using one-year worth of data for a bus route in Blacksburg, Virginia. In this study, the travel time was predicted between each two successive stations to all the model to be extended to include bus dwell times. Additionally, two additional models were developed for each category (MLP of LSTM): one for only segments including controlled intersections (controlled segments) and another for segments with no control devices along them (uncontrolled segments). The results show that the LSTM models outperform the MLP models with a RMSE of 17.69 sec compared to 18.81 sec. When splitting the data into controlled and uncontrolled segments, the RMSE values reduced to 17.33 sec for the controlled segments and 4.28 sec for the uncontrolled segments when applying the LSTM model. Whereas, the RMSE values were 19.39 sec for the controlled segments and 4.67 sec for the uncontrolled segments when applying the MLP model. These results demonstrate that the uncertainty in traffic conditions introduced by traffic control devices has a significant impact on travel time predictions. Nonetheless, the results demonstrate that the LSTMN is a promising tool that can has the ability to account for the temporal correlation within the data. The developed models are also promising tools for reasonable travel time predictions in transit applications.

Objective: The long-term care insurance (LTCI) system was introduced in 2000 to provide financial support for long-term care services to older adults. What is known on this topic report focuses on a comparative analysis of how the LTCI system has affected older people in Japan. Methods: We obtained data from the literature about the LTCI system, compared and analysed the collected articles, and concluded. Results: The LTCI system has improved access to long-term care services, with more older adults receiving care than before the system’s implementation. This service has improved the quality of life for many elderly individuals who require assistance with daily activities. Furthermore, the LTCI system has alleviated the financial burden of long-term care services since the insurance covers a large portion of the costs. It has made older adults maintain their independence and dignity, as they can afford the necessary care without relying solely on their savings or burdening their families. Conclusions: Japan’s LTCI system has positively impacted older adults by improving access to long-term care services and alleviating financial burdens. However, challenges such as increasing demand and variations in service quality need to be addressed to ensure the system effectively supports older people in Japan.

The study introduces a novel method to identify potential citation manipulation in academic papers using perturbations of a deep embedding model, incorporating Graph Masked Autoencoders. This approach integrates textual information with graph connectivity evidence, resulting in a more sophisticated model of citation distribution. By training a deep network using partial data and reconstructing masked connections, the method leverages the inherent characteristics of central connections under network perturbations. Quantitative evaluations demonstrate its remarkable ability to pinpoint trustworthy citations in the analyzed data and raise concerns about potentially unreliable references due to potential manipulation.

Due to the inclusion of both the principles and divination methods, the study of Yijing (Yijing) becomes more complex. The complex data types, diverse semantic relationships, and unclear influencing mechanisms in Yijing pose challenges to its scientific research. Knowledge graph, as an advanced way of organizing knowledge, can provide technical support in exploring the hidden connections and knowledge structure within text resources. This paper proposes a method of constructing a Yijing knowledge graph based on Neo4j. By analyzing the concepts, entities, and various related relationships in Yijing, the method discusses the basic architecture, data model, and implementation steps of constructing the Yijing knowledge graph. It also extracts, integrates, and structures the Yijing knowledge, allowing for inquiries, associations, and reasoning about the knowledge and its various elements. By adopting a top-down approach, the paper reconstructs the fundamental knowledge system of the Yijing, including yin-yang, the five elements, generation and restriction, 64 hexagrams, and six lines(yao). It establishes a knowledge graph pattern layer and a data layer that encompass concepts, attributes, and relationships. With the technical support of the Neo4j platform, the visualization and retrieval of Yijing knowledge are realized, providing new ideas and methods for studying the mechanisms of the Yijing. The proposed method of constructing a Yijing knowledge graph can be expanded to other types of ancient scripture knowledge graph research and can be applied to the field of digital humanities, promoting in-depth cross-disciplinary research and integration.

This research uses the computing of conceptual distance to measure information content in Wikipedia categories. The proposed metric, generality, relates information content to conceptual distance by determining the ratio of information a concept provides to others compared to the information it receives. The DIS-C algorithm calculates generality values for each concept, considering each relationship's conceptual distance and distance weight. The findings of this study were compared to current methods in the field and found to be comparable to results obtained using the WordNet corpus. This method offers a new approach to measuring information content applied to any relationship or topology in conceptualization.

Existing Knowledge Graph (KG) models for commonsense question answering present two challenges: (i) existing methods retrieved entities related to questions from the knowledge graph, which may extract noise and irrelevant nodes, and (ii) lack of interaction representation between questions and graph entities. However, current methods mainly focus on retrieving relevant entities with some noisy and irrelevant nodes. In this paper, we propose a novel Retrieval-augmented Knowledge Graph (RAKG) model, which solves the above issues through two key innovations. First, we leverage the density matrix to make the model reason along the corrected knowledge path and extract an enhanced knowledge graph subgraph. Second, we fuse representations of questions and graph entities through a bidirectional attention strategy, in which two representations fuse and update by Graph Convolutional Network (GCN). To evaluate the performance of our method, we conduct experiments on two widely-used benchmark datasets CommonsenseQA and OpenBookQA. The case study gives insight into findings that the augmented subgraph provides reasoning along the corrected knowledge path for question answering.

List-only entity linking is the task of mapping ambiguous mentions in texts to target entities in a group of entity lists. Different from traditional entity linking task, which leverages rich semantic relatedness in knowledge bases to improve linking accuracy, list-only entity linking can merely take advantage of co-occurrences information in entity lists. State-of-the-art work utilizes co-occurrences information to enrich entity descriptions, which are further used to calculate local compatibility between mentions and entities to determine results. Nonetheless, entity coherence is also deemed to play an important part in entity linking, which is yet currently neglected. In this work, in addition to local compatibility, we take into account global coherence among entities. Specifically, we propose to harness co-occurrences in entity lists for mining both explicit and implicit entity relations. The relations are then integrated into an entity graph, on which Personalized PageRank is incorporated to compute entity coherence. The final results are derived by combining local mention-entity similarity and global entity coherence. The experimental studies validate the superiority of our method. Our proposal not only improves the performance of list-only entity linking, but also opens up the bridge between list-only entity linking and conventional entity linking solutions.

The growth rate in academic and scientific publications increased very fast. Researchers must choose a good representative and significant literature in publications, which has become challenging worldwide. Usually, the paper citation number indicates this paper's potential influence and importance. However, this standard metric of citation numbers cannot be used as a measurement to judge the popularity and significance of the recently published papers. To address this challenge, this paper presents an effective prediction method called FutureCite to predict the future citation level of research articles. FutureCite combines machine learning with text and graph mining techniques, leveraging their abilities in classification, datasets in-depth analysis, and feature extraction. FutureCite aims to predict future citation levels of research articles applying a multilabel classification approach. FutureCite can extract significant semantic features and capture the interconnection relationships found in scientific articles during feature extraction using textual content, citation networks, and metadata as feature resources. Our goal is to contribute to the advancement of substantial effective approaches impacting the citation counts in scientific publications by enhancing the precision of future citations. We conducted several experiments using a comprehensive publication dataset to evaluate our method and determine the impact of using a variety of machine learning algorithms. FutureCite demonstrated its robustness and efficiency and showed promising results based on different evaluation metrics. Using the FutureCite model has significant implications in improving the researchers' ability to determine targeted literature for their research and better understand the potential impact of research publications.

In recent years, there has been significant growth in the ubiquity and popularity of three dimensional(3D) point clouds, with an increasing focus on the classification of 3D point clouds. To extract richer features from point clouds, many researchers have turned their attention to various point set regions and channels within irregular point clouds. However, this approach has limited capability in attending to crucial regions of interest in 3D point clouds and may overlook valuable information from neighboring features during feature aggregation. Therefore, this paper proposes a novel 3D point cloud classification method based on global attention and adaptive graph convolution. The method consists of two main branches: the first branch com-putes attention masks for each point, while the second branch employs adaptive graph convolu-tion to extract global features from the point set. It dynamically learns features based on point interactions, generating adaptive kernels to effectively and precisely capture diverse relationships among points from different semantic parts. Experimental results demonstrate that the proposed model achieves 93.8% in overall accuracy and 90.8% in average accuracy on the ModeNet40 dataset.

An important indicator of human-related pollution in watersheds is dissolved oxygen (DO). The DO is highly dependent on both space and time characteristics of the watershed and is directly linked to eutrophication, which impairs the development of both the aquatic fauna and flora, also negatively impacting the water quality. Aspiring to reach a more accurate and precise forecasting approach to predict levels of DO, the present work proposes new graph-based and transformer-based deep learning models. The models were trained and validated for the Credit River Watershed, and the results were compared with both benchmarking and literature-found approaches. The proposed Graph Neural Network Sample and Aggregate (GNN-SAGE) model was the best-performing approach, reaching coefficient of determination (R2) and Root Mean Squared Error (RMSE) values of 97% and 0.34 ppm, respectively. The findings from the Shapley additive explanations (SHAP) indicated that the GNN-SAGE benefited from spatiotemporal information from the surrounding stations, improving the model’s results, and that temperature is a major input attribute for determining future DO levels. The results established that the proposed GNN-SAGE model stands as a state-of-the-art solution for DO forecasting, with potential for real-time water quality applications.

Convolutional neural networks (CNN) have attracted much attention as a commonly used method for hyperspectral image (HSI) classification in recent years, however, CNNs can only be applied to Euclidean data and have limitations in dealing with relationships due to the limitations of local feature extraction. However, each pixel of a hyperspectral image contains a set of spectral bands that are correlated and interact with each other, and the methods used to process Euclidean data cannot effectively obtain these correlations. In contrast, the graph convolutional network (GCN) can be used in non-Euclidean data, but usually leads to oversmoothing and ignoring local detail features due to the need for superpixel segmentation processing to reduce computational effort. To overcome the above problems, we constructed a network a fusion network based on GCN and CNN, which contains two branches: a graph convolutional network based on superpixel segmentation and a convolutional network with added attention mechanism. The graph convolu-tional branch can extract the structural features and capture the relationships between the nodes, and the convolutional branch can extract the detailed features in the local fine region. Owing to the fact that the features extracted from the two branches are different, the classification performance can be improved by fusing the complementary features extracted from the two branches. To vali-date the proposed algorithm, experiments were conducted on three widely used datasets, namely Indian Pines, Pavia University, and Salinas, and the overall accuracy of 98.78% was obtained in the Indian Pines dataset, and the overall accuracy of 98.99% and 98.69% was obtained in the other two datasets. The results showed that the proposed fusion network can obtain richer features and achieve high classification accuracy.

With the rapid development of the Internet industry, the problem of information overload has arisen due to the abundance of information available online. Recommendation algorithms, as the core of recommendation systems, have been attracting much attention and are a hot topic of research for many experts and scholars. The classical recommendation algorithms are mainly divided into three major categories: collaborative filtering recommendation algorithms, content-based recommendation algorithms, and hybrid-based recommendation algorithms. Although these algorithms are widely used in various fields, with the proliferation of information, these traditional recommendation algorithms are no longer able to meet the needs of the times. To address this issue, recommendation systems have been developed to provide users with personalized and relevant information or products. Despite the wide use of recommendation algorithms, such as collaborative filtering, content-based filtering, and hybrid approaches, traditional recommendation algorithms have limitations and are no longer suitable for meeting the demands of the times. This paper proposes a new recommendation algorithm, SFRRG, that fuses structure and feature information in graph neural networks to improve the performance of the recommendation system in rating prediction. The effectiveness of the proposed algorithm is demonstrated through experiments on various data sets and compared with existing recommendation algorithms.

The chemical graph theory is a subfield of mathematical chemistry which applies classic graph theory to chemical entities and phenomena. Chemical graphs are main data structures to represent chemical structures in cheminformatics. Computable properties of graphs lay the foundation for (quantitative) structure activity and structure property predictions - a core discipline of cheminformatics. It has a historic relevance for natural sciences, such as chemistry, biochemistry and biology, and is in the heart of modern disciplines, such as cheminformatics and bioinformatics. This review first covers the history of chemical graph theory, then provides an overview of its various techniques and applications for CASE, and finally summarises modern tools using chemical graph theory for CASE.

This article aims to solve the problem of robust supervision of a reverse osmosis desalination system (RO-DS) with two models, external model and bond graph model. The structure of an industrial system from the point of view of the external model operates according to several modes of operation (degraded and normal). For this external model, we cannot locate the faults since we are talking about a global operation of the system. The possible solution for the development of research was to use the multidisciplinary model called bond graph. This model by its graphic nature and using a unified language makes it possible to model the industrial system element by element from where it helps the user not only to detect the faults but also to locate them when they appear in the system. The results suggest that the use of the bond graph model for alarm 02 is a reverse osmosis error (RO1); these phenomena are readable on the bond graph model and can be quantified by equations. The equation of the model of this reverse osmosis (RO1) is found in the residual equations (r5, r6 and r7), so that these residues will be sensitive to this rupture. The possible solution during research development was to use the bond graph model to supplement information with physical knowledge and to locate faults. This article also describes the operating safety (by minimizing false alarms and non-detections as well as delays in fault detection) of the desalination system by using the bond graph model described in Linear Fractional Transformation (LFT) form for enable it to manage the robust supervision of a desalination system. An approach based on (LFT-BG) is developed to monitor tank leakage (Cu) and reverse osmosis (RO1 and RO2) faults or valve level (V1 and V2) closures and membrane clogging reverse osmosis (Rm1 and Rm2) that can occur in the reverse osmosis desalination system (RO-DS).

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the groups $F_4$ and $E_6$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for quarks and charged leptons. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ and $E_6$ symmetry. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

In this paper, we establish the necessary and sufficient conditions for solving a dual split quaternion matrix equation AXB=C, and present the general solution expression when solvability is achieved. As an application, we delve into the necessary and sufficient condition for the existence of Hermitian solution to this equation by using a newly defined real representation method. Furthermore, we obtain the solutions for the dual split quaternion matrix equations AX=C and XB=C. Finally, we provide a numerical example to demonstrate the findings of this paper.

With recent advancements in network technology and spread of Internet, use of social network services and Internet of Things devices has flourished, leading to a continuous generation of large volumes of graph stream data, where changes, such as additions or deletions of vertices and edges occur over time. Additionally, owing to the need for efficient use of storage space and security requirements, graph stream data compression has become essential in various applications. Even though various studies on graph compression methods have been conducted, most of them do not fully reflect the dynamic characteristics of graph streams and complexity of large graphs. In this paper, we propose a compression scheme using provenance data to efficiently process and analyze large graph stream data. It obtains provenance data by analyzing graph stream data and builds a pattern dictionary based on this to perform dictionary-based compression. By improving the existing dictionary-based graph compression methods, it enables more efficient dictionary management through tracking pattern changes and evaluating their importance using provenance. Furthermore, it considers the relationships among sub-patterns using an FP-tree and performs pattern dictionary management that updates pattern scores based on time. Our experiments show that the proposed scheme outperforms existing graph compression methods in key performance metrics, such as compression rate and processing time.

Human action recognition (HAR) based on skeleton data is a challenging yet important technique because of its wide range of applications in many fields, including patient monitoring, security surveillance, and observing human-machine interactions. Many algorithms that attempt to distinguish between many types of activities have been proposed. However, most practical applications require highly accurate detection of specific types of activities. In this study, a novel and highly accurate spatiotemporal graph autoencoder network for HAR based on skeleton data is proposed. Furthermore, an extensive study was conducted using different modalities. For this purpose, a spatiotemporal graph autoencoder that automatically learns spatial as well as temporal patterns from human skeleton datasets was built. The powerful graph convolutional network named GA-GCN, developed in this study, notably outperforms most of the existing state-of-the-art methods based on two common datasets, namely NTU RGB+D and NTU RGB+D 120 . On the first dataset, we achieved an accuracy of 92.3% and 96.7% based on the cross-subject and cross-view evaluations, respectively. On the other more challenging dataset (i.e. NTU RGB+D 120), GA-GCN achieved 88.8% and 90.4% based on the cross-subject and cross-set evaluation, respectively.

In the realm of autonomous vehicle environment perception, the primary objective of point cloud target detection is to swiftly and accurately identify three-dimensional objects from point cloud data. To meet this requirement, the prevalent network architecture employed in the industry is the voxel-based PointPillars model. Nonetheless, this model faces challenges in maintaining detection accuracy when objects are obscured or diminutive in size. In response to this issue, we introduce AGPNet, a novel model that seamlessly integrates four key modules: Data Augmentation, Dynamic Graph CNN, Pillar Feature Net, and Detection Head (SSD). The Data Augmentation module enhances the adaptability of point cloud data to complex and ever-changing real-world environments. The Dynamic Graph CNN module endows the network structure with geometric features, which encapsulate not only the point itself but also its adjacent points. The Pillar Feature Net module translates three-dimensional point cloud data into pseudo-image data through the utilization of voxels. Subsequently, the Detection Head (SSD) module leverages this pseudo-image data to conduct target detection of three-dimensional objects. Our experiments, conducted on the KITTI dataset, demonstrate that our proposed method boosts object detection accuracy by 6-7 percentage points compared to the PointPillars model, while maintaining similar detection times.