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Designing homogeneous networks is considered one typical strategy for solving the problem of strength and toughness conflict of polymer network materials. Experimentalists have proposed the hypothesis of obtaining a structurally homogeneous hydrogel by crosslinking tetra-armed polymers, whose homogeneity was claimed to be verified by scattering characterization and other methods. Nevertheless, it is highly desirable to further evaluate this issue from other perspectives. In this study, a coarse-grained molecular dynamics simulation coupled with a stochastic reaction model is applied to reveal the topological structure of a polymer network synthesized by tetra-armed monomers as precursors. Two different scenarios, distinguished by whether internal cross-linking is allowed, are considered. We introduce the Dijkstra algorithm from graph theory to precisely characterize the network structure. The microscopic features of the network structure, e.g., loop size, dispersity, and size distribution, are obtained via the Dijkstra algorithm. By comparing the two reaction scenarios, Scenario II exhibits an overall more idealized structure. Our results demonstrate the feasibility of the Dijkstra algorithm for precisely characterizing the polymer network structure. We expect this work will provide a new insight for the evaluation and description of gel networks and further help to reveal the dynamic process of network formation. [ABSTRACT FROM AUTHOR]

Biomolecular condensates formed by multicomponent phase separation play crucial roles in diverse cellular processes. Accurate assessment of individual-molecule contributions to condensate formation and precise characterization of their spatial organization within condensates are crucial for understanding the underlying mechanism of phase separation. Using molecular dynamics simulations and graph theoretical analysis, we demonstrated quantitatively the significant roles of cation-π and π–π interactions mediated by aromatic residues and arginine in the formation of condensates in polypeptide systems. Our findings reveal temperature and chain length-dependent alterations in condensate network parameters, such as the number of condensate network layers, and changes in aggregation and connectivity. Notably, we observe a transition between assortativity and disassortativity in the condensate network. Moreover, polypeptides W, Y, F, and R consistently promote condensate formation, while the contributions of other charged and two polar polypeptides (Q and N) to condensate formation depend on temperature and chain length. Furthermore, polyadenosine and polyguanosine can establish stable connections with aromatic and R polypeptides, resulting in the reduced involvement of K, E, D, Q, and N in phase separation. Overall, this study provides a distinctive, precise, and quantitative approach to characterize the multicomponent phase separation. [ABSTRACT FROM AUTHOR]

Modeling the dynamics of glassy systems has been challenging in physics for several decades. Recent studies have shown the efficacy of Graph Neural Networks (GNNs) in capturing particle dynamics from the graph structure of glassy systems. However, current GNN methods do not take the dynamic patterns established by neighboring particles explicitly into account. In contrast to these approaches, this paper introduces a novel dynamical parameter termed "smoothness" based on the theory of graph signal processing, which explores the dynamic patterns from a graph perspective. Present graph-based approaches encode structural features without considering smoothness constraints, leading to a weakened correlation between structure and dynamics, particularly on short timescales. To address this limitation, we propose a Geometry-enhanced Graph Neural Network (Geo-GNN) to learn the smoothness of dynamics. Results demonstrate that our method outperforms state-of-the-art baselines in predicting glassy dynamics. Ablation studies validate the effectiveness of each proposed component in capturing smoothness within dynamics. These findings contribute to a deeper understanding of the interplay between glassy dynamics and static structure. [ABSTRACT FROM AUTHOR]

In this paper, we present a new module to predict the potential surface reconstruction configurations of given surface structures in the framework of our machine learning and graph theory assisted universal structure searcher. In addition to random structures generated with specific lattice symmetry, we made full use of bulk materials to obtain a better distribution of population energy, namely, randomly appending atoms to a surface cleaved from bulk structures or moving/removing some of the atoms on the surface, which is inspired by natural surface reconstruction processes. In addition, we borrowed ideas from cluster predictions to spread structures better between different compositions, considering that surface models of different atom numbers usually have some building blocks in common. To validate this newly developed module, we tested it with studies on the surface reconstructions of Si (100), Si (111), and 4H–SiC (1 1 ̄ 02) − c (2 × 2) , respectively. We successfully gave the known ground states, as well as a new SiC surface model, in an extremely Si-rich environment. [ABSTRACT FROM AUTHOR]

Summary: The wireless sensor network‐assisted Internet of Things convergence has diverse applications. In most applications, the sensors are battery‐powered, and it is necessary to use the energy judiciously to extend their functional duration effectively. Mobile sinks‐based data collection is used to extend the lifespan of these networks. However, providing a scalable and effective solution with consideration for multicriteria factors of quality of service and lifetime maximization is still a challenge. This work addresses this problem with a hybrid wireless sensor network with long‐term evolution‐assisted architecture. The issue of maximizing lifetime and providing multifactor quality of service is solved as a two‐stage optimization problem involving clustering and data collection path scheduling. Hybrid meta‐heuristics is used to solve the clustering optimization problem. Minimal Steiner tree‐based graph theory is applied to schedule the data collection path for sinks. Unlike existing works, the lifetime maximization without QoS degradation is addressed by hybridizing multiple approaches of multicriteria optimal clustering, optimal path scheduling, and network adaptive traffic class‐based data scheduling. This hybridization extends the network's lifespan and improves the QoS regarding packet transmission within the proposed solution. Through simulation analysis, the introduced approach yields a noteworthy increase of at least 6% and reduces packet delivery delay by 26% compared with existing methodologies. [ABSTRACT FROM AUTHOR]

Background: Alzheimer's disease (AD) and frontotemporal dementia (FTD) are the two most common neurodegenerative dementias, presenting with similar clinical features that challenge accurate diagnosis. Despite extensive research, the underlying pathophysiological mechanisms remain unclear, and effective treatments are limited. This study aims to investigate the alterations in brain network connectivity associated with AD and FTD to enhance our understanding of their pathophysiology and establish a scientific foundation for their diagnosis and treatment. Methods: We analyzed preprocessed electroencephalogram (EEG) data from the OpenNeuro public dataset, comprising 36 patients with AD, 23 patients with FTD, and 29 healthy controls (HC). Participants were in a resting state with eyes closed. We estimated the average functional connectivity using the Phase Lag Index (PLI) for lower frequencies (delta and theta) and the Amplitude Envelope Correlation with leakage correction (AEC-c) for higher frequencies (alpha, beta, and gamma). Graph theory was applied to calculate topological parameters, including mean node degree, clustering coefficient, characteristic path length, global and local efficiency. A permutation test was then utilized to assess changes in brain network connectivity in AD and FTD based on these parameters. Results: Both AD and FTD patients showed increased mean PLI values in the theta frequency band, along with increases in average node degree, clustering coefficient, global efficiency, and local efficiency. Conversely, mean AEC-c values in the alpha frequency band were notably diminished, which was accompanied by decreases average node degree, clustering coefficient, global efficiency, and local efficiency. Furthermore, AD patients in the occipital region showed an increase in theta band node degree and decreased alpha band clustering coefficient and local efficiency, a pattern not observed in FTD. Conclusions: Our findings reveal distinct abnormalities in the functional network topology and connectivity in AD and FTD, which may contribute to a better understanding of the pathophysiological mechanisms of these diseases. Specifically, patients with AD demonstrated a more widespread change in functional connectivity, while those with FTD retained connectivity in the occipital lobe. These observations could provide valuable insights for developing electrophysiological markers to differentiate between the two diseases. [ABSTRACT FROM AUTHOR]

A total coloring of a graph G is an assignment of colors to all the elements (vertices and edges) of the graph in such a way that no two adjacent or incident elements receive the same color. The total chromatic number of G, denoted by χzz(G), is the minimum number of colors needed for a total coloring of G. The Total Coloring Conjecture (TCC) proposed independently by Behzad and Vizing claims that, Δ(G) + 1 ≤ χ"(G) ≤ Δ(G) + 2, where Δ(G) is the maximum degree of G. The lower bound is sharp and the upper bound remains to be proved. In this paper, we prove the TCC for certain classes of lexicographic and deleted lexicographic products of graphs. Also, we obtained the lower bound for certain classes of these products. [ABSTRACT FROM AUTHOR]

Domination in graphs and coloring of graphs are two main areas of investigation in graph theory. Power domination is a variant of domination in graphs introduced in the study of the problem of monitoring an electric power system. Based on the notions of power domination and coloring of a graph, the concept of power dominator coloring of a graph was introduced. The minimum number of colors required for power dominator coloring of a graph G is called the power dominator chromatic number χpd(G) of G, which has been computed for some classes of graphs. Here we compute the power dominator chromatic number for splitting graphs of certain classes of graphs. [ABSTRACT FROM AUTHOR]

The harmonic polynomial was defined in order to understand better the harmonic topological index. Here, we obtain several properties of this polynomial, and we prove that several properties of a graph can be deduced from its harmonic polynomial. Also, we prove that graphs with the same harmonic polynomial share many properties although they are not necessarily isomorphic. [ABSTRACT FROM AUTHOR]

The main aim of the paper is to give the crossing number of the join product G* + Dn for the graph G* isomorphic to 4-regular graph on six vertices except for two distinct edges with no common vertex such that two remaining vertices are still adjacent, and where Dn consists of n isolated vertices. The proofs are done with possibility of an existence of a separating cycle in some particular drawing of the investigated graph G* and also with the help of well-known exact values for crossing numbers of join products of two subgraphs Hk of G* with discrete graphs. [ABSTRACT FROM AUTHOR]

We extend the notion of balance from the realm of signed and gain graphs to conjugate skew gain graphs which are skew gain graphs where the labels on the oriented edges get conjugated when we reverse the orientation. We characterize the balance in a conjugate skew gain graph in several ways especially by dealing with its adjacency matrix and the g -Laplacian matrix. We also deal with the concept of anti-balance in conjugate skew gain graphs. [ABSTRACT FROM AUTHOR]

A triangular tile latching system consists of a set Σ of equilateral triangular tiles with at least one latchable side and an attachment rule which permits two tiles to get latched along a latchable side. In this paper we determine the language generated by a triangular tile latching system in terms of planar graphs. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a connected graph with the vertex-set V and the edgeset E. The subdivision graph S(G) of the graph G is obtained from G by adding a vertex in the middle of every edge of G. In this paper, we investigate some properties of the graphs S (G) and L(S (G)), where L(S (G)) is the line graph of S (G). We will see that S (G) and L(S (G)) inherit some properties of G. For instance, we show that if G Cn, then Aut(G) = Aut(L(S(G))) (as abstract groups), where Cn is the cycle of order n. [ABSTRACT FROM AUTHOR]

Given a graph G = (V, E), a function f: V → {0, 1, 2, 3, 4} is a triple Roman dominating function (TRDF) of G, for each vertex v ∈ V, (i) if f (v) = 0, then v must have either one neighbour in V4, or either two neighbours in V2 ∪ V3 (one neighbour in V3) or either three neighbours in V2, (ii) if f (v) = 1, then v must have either one neighbour in V3 ∪ V4 or either two neighbours in V2, and if f (v) = 2, then v must have one neighbour in V2 ∪ V3 ∪ V4. The triple Roman domination number of G is the minimum weight of an TRDF f of G, where the weight of f is v V f (v). The triple Roman domination problem is to compute the triple Roman domination number of a given graph. In this paper, we study the triple Roman domination problem. We show that the problem is NP-complete for the star convex bipartite and the comb convex bipartite graphs and is APX-complete for graphs of degree at most 4. We propose a linear-time algorithm for computing the triple Roman domination number of proper interval graphs. We also give an (2H (Δ(G) + 1) - 1)-approximation algorithm for solving the problem for any graph G, where Δ(G) is the maximum degree of G and H (d) denotes the first d terms of the harmonic series. In addition, we prove that for any ε > 0 there is no (1/4 - ε) ln |V |-approximation polynomial-time algorithm for solving the problem on bipartite and split graphs, unless NP ⊆ DTIME (|V |O(log log |V |)). [ABSTRACT FROM AUTHOR]

Let tp (G) denote the number of paths in a graph G and let f: E → Z+ be an edge labeling of G. The weight of a path P is the sum of the labels assigned to the edges of P. If the set of weights of the paths in G is {1, 2, 3,..., tp (G)}, then f is called a Leech labeling of G and a graph which admits a Leech labeling is called a Leech graph. In this paper, we prove that the complete bipartite graphs K2, n and K3, n are not Leech graphs and determine the maximum possible value that can be given to an edge in the Leech labeling of a cycle. [ABSTRACT FROM AUTHOR]

A k -CEC graph is a graph G which has connected domination number Yc(G) = k and Yc(G+uv) < k for every uv ∈ E(G). A k-CVC graph G is a 2-connected graph with γc(G) = k and γc(G - v) < k for any v ∈ V (G). A graph is said to be maximal k-CVC if it is both k-CEC and k-CVC. Let δ, κ, and α be the minimum degree, connectivity, and independence number of G, respectively. In this work, we prove that for a maximal 3-CVC graph, if α = κ, then κ = δ. We additionally consider the class of maximal 3-CVC graphs with α < κ and κ < δ, and prove that every 3-connected maximal 3-CVC graph when κ < δ is Hamiltonian connected. [ABSTRACT FROM AUTHOR]

A coloring C = (V1,...,Vk) of G partitions the vertex set V (G) into independent sets Vi which are said to be color classes with respect to the coloring C. A vertex v is said to have a dominator (dom) color class in C if there is color class Vi such that v is adjacent to all the vertices of Vi and v is said to have an anti-dominator (anti-dom) color class in C if there is color class Vj such that v is not adjacent to any vertex of Vj. Dominator coloring of G is a coloring C of G such that every vertex has a dom color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G, denoted by χd(G). Global Dominator coloring of G is a coloring C of G such that every vertex has a dom color class and an anti-dom color class. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number of G, denoted by χgd(G). In this paper, we give a counterexample for the conjecture posed in [I. Sahul Hamid, M.Rajeswari, Global dominator coloring of graphs, Discuss. Math. Graph Theory 39 (2019), 325-339] that for a graph G, if Xgd(G) = 2χd(G), then G is a complete multipartite graph. We deduce upper and lower bound for the global dominator chromatic number of Mycielskian of the graph G in terms of dominator chromatic number of G. [ABSTRACT FROM AUTHOR]

We investigate natural Turán problems for mixed graphs, generalizations of graphs where edges can be either directed or undirected. We study a natural Turán density coefficient that measures how large a fraction of directed edges an F -free mixed graph can have; we establish an analogue of the Erdős-Stone-Simonovits theorem and give a variational characterization of the Turán density coefficient of any mixed graph (along with an associated extremal F -free family). This characterization enables us to highlight an important divergence between classical extremal numbers and the Turán density coefficient. We show that Turán density coefficients can be irrational, but are always algebraic; for every positive integer k , we construct a family of mixed graphs whose Turán density coefficient has algebraic degree k. [ABSTRACT FROM AUTHOR]

The decision to treat children with benign epilepsy with centrotemporal spikes (BECTS) using antiseizure medications (ASM) is controversial. Our goal is to compare the effect of ASM treatment on the alteration of electroencephalographic (EEG) functional connectivity and power across four frequency bands in children with BECTS. Children with BECTS with two-year follow-up were retrospectively divided into ASM versus non-ASM groups. The network properties of the EEGs as based on network-based statistic and graph theory were evaluated by the following indices: global efficiency, clustering coefficient, betweenness centrality, and nodal strength in four frequency bands (delta, theta, alpha, and beta). EEG power including absolute power (AP) and relative power (RP) was analyzed in four frequency bands. In children with BECTS with ASM treatment, there was no significant change in EEG connectivity across all bands before and after two years of ASM. In children with BECTS without ASM treatment, there was a significant increase of global efficiency, clustering coefficient, and nodal strength but not the betweenness centrality in the delta band after two years of follow-up. A decrease in AP in the delta and theta bands and a decrease in RP in the theta band were found in the ASM group after two years of treatment. Our results suggest that ASM may play a role in modulating the development of increasing overall brain connectivity and in downregulating overt synaptic activity, but not intrinsic focal connectivity, in the early years of BECTS. The changes in the EEG power indicate that ASM significantly normalized slow-wave band power. [ABSTRACT FROM AUTHOR]

Strongly regular graphs (SRGs) provide a fertile area of exploration in algebraic combinatorics, integrating techniques in graph theory, linear algebra, group theory, finite fields, finite geometry, and number theory. Of particular interest are those SRGs with a large automorphism group. If an automorphism group acts regularly (sharply transitively) on the vertices of the graph, then we may identify the graph with a subset of the group, a partial difference set (PDS), which allows us to apply techniques from group theory to examine the graph. Much of the work over the past four decades has concentrated on abelian PDSs using the powerful techniques of character theory. However, little work has been done on nonabelian PDSs. In this paper we point out the existence of genuinely nonabelian PDSs, that is, PDSs for parameter sets where a nonabelian group is the only possible regular automorphism group. We include methods for demonstrating that abelian PDSs are not possible for a particular set of parameters or for a particular SRG. Four infinite families of genuinely nonabelian PDSs are described, two of which—one arising from triangular graphs and one arising from Krein covers of complete graphs constructed by Godsil—are new. We also include a new nonabelian PDS found by computer search and present some possible future directions of research. [ABSTRACT FROM AUTHOR]

The widely acknowledged detrimental impact of early adversity on child development has driven efforts to understand the underlying mechanisms that may mediate these effects within the developing brain. Recent efforts have begun to move beyond associating adversity with the morphology of individual brain regions towards determining if and how adversity might shape their interconnectivity. However, whether adversity effects a global shift in the organisation of whole‐brain networks remains unclear. In this study, we assessed this possibility using parental questionnaire and diffusion imaging data from The Avon Longitudinal Study of Parents and Children (ALSPAC, N = 913), a prospective longitudinal study spanning more than 20 years. We tested whether a wide range of adversities—including experiences of abuse, domestic violence, physical and emotional cruelty, poverty, neglect, and parental separation—measured by questionnaire within the first seven years of life were significantly associated with the tractography‐derived connectome in young adulthood. We tested this across multiple measures of organisation and using a computational model that simulated the wiring economy of the brain. We found no significant relationships between early exposure to any form of adversity and the global organisation of the structural connectome in young adulthood. We did detect local differences in the medial prefrontal cortex, as well as an association between weaker brain wiring constraints and greater externalising behaviour in adolescence. Our results indicate that further efforts are necessary to delimit the magnitude and functional implications of adversity‐related differences in connectomic organization. Research Highlights: Diverse prospective measures of the early‐life environment do not predict the organisation of the DTI tractography‐derived connectome in young adulthoodWiring economy of the connectome is weakly associated with externalising in adolescence, but not internalising or cognitive abilityFurther work is needed to establish the scope and significance of global adversity‐related differences in the structural connectome [ABSTRACT FROM AUTHOR]

This paper proposes a novel method that integrates a tailored spectral graph metric and economic aspects within a coupled bi-objective optimization framework for the simultaneous pipe sizing and partitioning of water distribution networks (WDNs). Besides minimum pressure head and topological WDN connectivity, the telescopic diameter distribution criterion is applied through a new algorithm in the sizing phase to help the optimization converge towards sound engineering solutions. The application of the proposed method to a synthetic layout and a real Italian case study proves the superiority of the solutions obtained with the novel method from hydraulic and managerial/operational viewpoints in comparison with those obtained with a traditional decoupled method (separate pipe sizing and partitioning) in terms of i) compliance with service pressure constraints and ii) ease of management following WDN partitioning into district metered areas (DMAs). [ABSTRACT FROM AUTHOR]

The concept of functional localization within the brain and the associated risk of resecting these areas during removal of infiltrating tumors, such as diffuse gliomas, are well established in neurosurgery. Global efficiency (GE) is a graph theory concept that can be used to simulate connectome disruption following tumor resection. Structural connectivity graphs were created from diffusion tractography obtained from the brains of 80 healthy adults. These graphs were then used to simulate parcellation resection in every gross anatomical region of the cerebrum by identifying every possible combination of adjacent nodes in a graph and then measuring the drop in GE following nodal deletion. Progressive removal of brain parcellations led to patterns of GE decline that were reasonably predictable but had inter-subject differences. Additionally, as expected, there were deletion of some nodes that were worse than others. However, in each lobe examined in every subject, some deletion combinations were worse for GE than removing a greater number of nodes in a different region of the brain. Among certain patients, patterns of common nodes which exhibited worst GE upon removal were identified as "connectotypes". Given some evidence in the literature linking GE to certain aspects of neuro-cognitive abilities, investigating these connectotypes could potentially mitigate the impact of brain surgery on cognition. [ABSTRACT FROM AUTHOR]

Spectral clustering, as an algorithm based on graph theory and spectral theory, has shown excellent performance in the classification tasks of hyperspectral images in recent years. Although better results have been achieved, some challenges still exist. The inclusion of a priori information can increase the performance of spectral clustering algorithms; however, in practice, it is often unable to meet the demand for a priori information; at the same time, spectral clustering for the quality of the similarity matrix is demanding, and some of the current algorithms are to improve the similarity matrix from the aspect of data planning, and ultimately for the label feature matrices are diluted. In response to the above problems, this paper proposes a self-supervised spectral clustering with spectral embedding (SESSC). The algorithm obtains a low-dimensional representation of the data through spectral embedding, which can simplify clustering while preserving feature information; then uses the similarity matrix about the data and the guidance of the sample constraint information to obtain a new similarity matrix in order to further refine the structural graph, and the result can feed back and optimize the label feature matrix and the low-dimensional representation of the data. Additionally, we introduce a fractional theory in the update of the sample variable matrix, which assures the integrity and validity of the information in the update. Experimental results show that the proposed algorithm has better performance in hyperspectral image classification than existing spectral clustering algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the triangle width problem, which generalizes the classic two-machine flexible job-shop problem (FJSP) with tooling constraints. This new problem can be studied from three different angles: scheduling, matrix visualization, and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to establish the N P -Hardness and polynomiality of several of its subcases. This problem allows us to find more elegant (and probably shorter) proofs for several combinatorial problems in our analysis setting. Our study provides an elegant generalization of Johnson's argument for the two-machine flow shop. It also shows the relation between the question: "Is a matrix triangular?" and the "k-visit of a graph". [ABSTRACT FROM AUTHOR]

The normalized distance Laplacian of a graph G is defined as D L (G) = T (G) − 1 / 2 (T (G) − D (G)) T (G) − 1 / 2 where D (G) is the matrix with pairwise distances between vertices and T (G) is the diagonal transmission matrix. In this project, we study the minimum and maximum spectral radii associated with this matrix, and the structures of the graphs that achieve these values. In particular, we prove a conjecture of Reinhart that the complete graph is the unique graph with minimum spectral radius, and we give several partial results towards a second conjecture of Reinhart regarding which graph has the maximum spectral radius. [ABSTRACT FROM AUTHOR]

Topological indices (TIs) have rich applications in various biological contexts, particularly in therapeutic strategies for cancer. Predicting the performance of compounds in the treatment of cancer is one such application, wherein TIs offer insights into the molecular structures and related properties of compounds. By examining, various compounds exhibit different degree-based TIs, analysts can pinpoint the treatments that are most efficient for specific types of cancer. This paper specifically delves into the topological indices (TIs) implementations in forecasting the biological and physical attributes of innovative compounds utilized in addressing cancer through therapeutic interventions. The analysis being conducted to derivatives of sulfonamides, namely, 4-[(2,4-dichlorophenylsulfonamido) methyl]cyclohexanecarboxylic acid (1), ethyl 4-[(naphthalene-2-sulfonamido) methyl]cyclohexanecarboxylate (2), ethyl 4-[(2,5-dichlorophenylsulfonamido) methyl]cyclohexanecarboxylate (3), 4-[(naphthalene-2-sulfonamido) methyl]cyclohexane-1-carboxylic acid (4) and (2S)-3-methyl-2-(naphthalene-1-sulfonamido)-butanoic acid (5), is performed by utilizing edge partitioning for the computation of degree-based graph descriptors. Subsequently, a linear regression-based model is established to forecast characteristics, like, melting point and formula weight in a quantitative structure-property relationship. The outcomes emphasize the effectiveness or capability of topological indices as a valuable asset for inventing and creating of compounds within the realm of cancer therapy. [ABSTRACT FROM AUTHOR]

A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical descriptors in algebraic form. The Quantitative Structure-Property Relationship study makes use of Modified Polynomials (M-Polynomials) as a mathematical tool. M-Polynomials used to create connections between a material's various properties and its structural characteristics. In this study, we calculated several modified polynomials and gave a polynomial description of the magnesium iodide structure. Particularly, we computed first, second and modified Zagreb indices based M-polynomials. Randić index, and inverse Randić indices based M-polynomials are also computed in this work. [ABSTRACT FROM AUTHOR]

Binary liquid systems serve as valuable prototypes for comprehending biologically and chemically relevant properties of hydrogen bonds, revealing both noteworthy patterns and anomalies in their behaviour. Aniline, acetone and their binary mixtures with other liquids are used in various industrial processes, drug design, and as cleaning agents. This study is a molecular dynamics exploration of aniline and acetone binary mixture, over a concentration range of 9 : 1–1 : 9 for each component. The investigation includes employing techniques such as radial distribution function (RDF), coordination number calculation, hydrogen bond statistics, and graph theoretical analysis (GTA) through the NetworkX module in python, cluster analysis, Voronoi entropy calculation, interaction energy calculation and FTIR spectroscopy for all concentrations studied. The results uncover a compelling trend: a decrease in the number of hydrogen bonds as the concentration of acetone increases. Additionally, increased acetone concentration correlates positively with the breakdown of larger and more complex hydrogen‐bonded structures, indicating the formation of small hydrogen‐bond structures. [ABSTRACT FROM AUTHOR]

Background and Objective: Spinal muscular atrophy (SMA) is one of the most common monogenic neuromuscular diseases, and the pathogenesis mechanisms, especially the brain network topological properties, remain unknown. This study aimed to use individual‐level morphological brain network analysis to explore the brain neural network mechanisms in SMA. Methods: Individual‐level gray matter (GM) networks were constructed by estimating the interregional similarity of GM volume distribution using both Kullback–Leibler divergence‐based similarity (KLDs) and Jesen‐Shannon divergence‐based similarity (JSDs) measurements based on Automated Anatomical Labeling 116 and Hammersmith 83 atlases for 38 individuals with SMA types 2 and 3 and 38 age‐ and sex‐matched healthy controls (HCs). The topological properties were analyzed by the graph theory approach and compared between groups by a nonparametric permutation test. Additionally, correlation analysis was used to assess the associations between altered topological metrics and clinical characteristics. Results: Compared with HCs, although global network topology remained preserved in individuals with SMA, brain regions with altered nodal properties mainly involved the right olfactory gyrus, right insula, bilateral parahippocampal gyrus, right amygdala, right thalamus, left superior temporal gyrus, left cerebellar lobule IV–V, bilateral cerebellar lobule VI, right cerebellar lobule VII, and vermis VII and IX. Further correlation analysis showed that the nodal degree of the right cerebellar lobule VII was positively correlated with the disease duration, and the right amygdala was negatively correlated with the Hammersmith Functional Motor Scale Expanded (HFMSE) scores. Conclusions: Our findings demonstrated that topological reorganization may prioritize global properties over nodal properties, and disrupted topological properties in the cortical–limbic‐cerebellum circuit in SMA may help to further understand the network pathogenesis underlying SMA. [ABSTRACT FROM AUTHOR]

Multiple pathways and outcomes are common in evolutionary sequences for biological and other environmental systems due to nonlinear complexity, historical contingency, and disturbances. From any starting point, multiple evolutionary pathways are possible. From an endpoint or observed state, multiple possibilities exist for the sequence of events that created it. However, for any observed historical sequence—e.g., ecological or soil chronosequences, stratigraphic records, or lineages—only one historical sequence actually occurred. Here, a measure of the embedded complexity of historical sequences based on algebraic graph theory is introduced. Sequences are represented as system states S(t), such that S(t − 1) ≠ S(t) ≠ S(t + 1). Each sequence of N states contains nested subgraph sequences of length 2, 3, ..., N − 1. The embedded complexity index (which can also be interpreted in terms of embedded information) compares the complexity (based on the spectral radius λ1) of the entire sequence to the cumulative complexity of the constituent subsequences. The spectral radius is closely linked to graph entropy, so the index also reflects information in the sequence. The analysis is also applied to ecological state-and-transition models (STM), which represent observed transitions, along with information on their causes or triggers. As historical sequences are lengthened (by the passage of time and additional transitions or by improved resolutions or new observations of historical changes), the overall complexity asymptotically approaches λ1 = 2, while the embedded complexity increases as N2.6. Four case studies are presented, representing coastal benthic community shifts determined from biostratigraphy, ecological succession on glacial forelands, vegetation community changes in longleaf pine woodlands, and habitat changes in a delta. [ABSTRACT FROM AUTHOR]

A dominating set of a graph is a subset of vertices such that every vertex not in the subset has at least one neighbor within the subset. The corresponding optimization problem is known to be NP-hard. It is proved to be beneficial to separate the solution process in two stages. First, one can apply a fast greedy algorithm to obtain an initial dominating set and then use an iterative procedure to purify (reduce) the size of this dominating set. In this work, we develop the purification stage and propose new purification algorithms. The purification procedures that we present here outperform, in practice, the earlier known purification procedure. We have tested our algorithms for over 1300 benchmark problem instances. Compared to the estimations due to known upper bounds, the obtained solutions are about seven times better. Remarkably, for the 500 benchmark instances for which the optimum is known, the optimal solutions are obtained for 46.33% of the tested instances, whereas the average error for the remaining instances is about 1.01. [ABSTRACT FROM AUTHOR]

Background This article introduces a novel index aimed at uncovering specific brain connectivity patterns associated with Alzheimer's disease (AD), defined according to neuropsychological patterns. Methods Electroencephalographic (EEG) recordings of 370 people, including 170 healthy subjects and 200 mild-AD patients, were acquired in different clinical centres using different acquisition equipment by harmonising acquisition settings. The study employed a new derived Small World (SW) index, SWcomb, that serves as a comprehensive metric designed to integrate the seven SW parameters, computed across the typical EEG frequency bands. The objective is to create a unified index that effectively distinguishes individuals with a neuropsychological pattern compatible with AD from healthy ones. Results Results showed that the healthy group exhibited the lowest SWcomb values, while the AD group displayed the highest SWcomb ones. Conclusions These findings suggest that SWcomb index represents an easy-to-perform, low-cost, widely available and non-invasive biomarker for distinguishing between healthy individuals and AD patients. [ABSTRACT FROM AUTHOR]

Graph theory is widely used today in many fields, including mathematical chemistry. In this area, numerous topological indices have been studied. Topological indices are used to define the topology of a molecular graph and relate it to various relevant properties. The most commonly used topological indices are degree-based and distance-based indices. This article examines the Gutman index, which holds great significance in chemistry. The Gutman index is a well-known topological index that simultaneously uses both degree and distance. These graphs are important because they enable the study of the properties of a graph under different transformations. It has been extensively studied in the literature and finds numerous applications in chemistry, physics, and other fields. Transformation graphs are graphs that are used to model molecular structures, physical networks, and algorithms in fields such as chemistry, computer science and physics. Original graph's symmetry, connectivity and other structural features can be revealed through these transformations. This article focuses on studying the Gutman index of some transformation graphs to provide a new topological index that can be used to examine their properties, and general formulas have been obtained. [ABSTRACT FROM AUTHOR]

This paper considers the secure distributed control consensus problem of linear multi‐agent systems (MASs) under switching topologies, subject to intermittent sequential scaling attacks, which was compelled to scaling factor, attack frequency, duration and cooperative‐competitive networks. First, the scenario of a fixed topology is considered, and a novel control protocol combined with a logarithmic quantizer and relative state measurements of neighbouring agents is discussed. The sighed graph is utilized to characterize the communication topology determined by the information flow directions and captured by the graph Laplacian matrix. After that, sufficient conditions for effectiveness of the developed control methods in guiding the MASs to secure bipartite leader‐following consensus are constructed. Second, the scenario of switching topologies is considered, and it is derived that the secure bipartite consensus will be achieved if the designed state feedback control protocol with the scaling factor, the attack duration, attack frequency and switching signal are selected properly. At last, to prove the effectiveness of the designed controllers, a simulation example depended on the real‐word actual military is introduced. [ABSTRACT FROM AUTHOR]

• Multiple sclerosis can lead to various functional alterations of sensorimotor brain networks. • The value of resting-state EEG or dynamic EEG during a motor tastk to assess motor impaiment in multiple sclerosis was reviewed. • EEG biomarkers could be used to develop future neuromodulation therapy of disease-related motor disorders in multiple sclerosis. Electroencephalography (EEG) can highlight significant changes in spontaneous electrical activity of the brain produced by altered brain network connectivity linked to inflammatory demyelinating lesions and neuronal loss occurring in multiple sclerosis (MS). In this review, we describe the main EEG findings reported in the literature to characterize motor network alteration in term of local activity or functional connectivity changes in patients with MS (pwMS). A comprehensive literature search was conducted to include articles with quantitative analyses of resting-state EEG recordings (spectrograms or advanced methods for assessing spatial and temporal dynamics, such as coherence, theory of graphs, recurrent quantification, microstates) or dynamic EEG recordings during a motor task, with or without connectivity analyses. In this systematic review, we identified 26 original articles using EEG in the evaluation of MS-related motor disorders. Various resting or dynamic EEG parameters could serve as diagnostic biomarkers of motor control impairment to differentiate pwMS from healthy subjects or be related to a specific clinical condition (fatigue) or neuroradiological aspects (lesion load). We highlight some key EEG patterns in pwMS at rest and during movement, both suggesting an alteration or disruption of brain connectivity, more specifically involving sensorimotor networks. Some of these EEG biomarkers of motor disturbance could be used to design future therapeutic strategies in MS based on neuromodulation approaches, or to predict the effects of motor training and rehabilitation in pwMS. [ABSTRACT FROM AUTHOR]

The ranking of nodes in a network according to their centrality or ''importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread. [ABSTRACT FROM AUTHOR]

Paley graphs form a nice link between the distribution of quadratic residues and graph theory. These graphs possess remarkable properties which make them useful in several branches of mathematics. Classically, for each prime number p we can construct the corresponding Paley graph using quadratic and non-quadratic residues modulo p. Therefore, Paley graphs are naturally associated with the Legendre symbol at p which is a quadratic Dirichlet character of conductor p. In this article, we introduce the generalized Paley graphs. These are graphs that are associated with a general quadratic Dirichlet character. We will then provide some of their basic properties. In particular, we describe their spectrum explicitly. We then use those generalized Paley graphs to construct some new families of Ramanujan graphs. Finally, using special values of L-functions, we provide an effective upper bound for their Cheeger number. As a by-product of our approach, we settle a question raised in [Cramer et al.: The isoperimetric and Kazhdan constants associated to a Paley graph, Involve 9 (2016), 293–306] about the size of this upper bound. [ABSTRACT FROM AUTHOR]

Objective: Focal to bilateral tonic–clonic seizures (FBTCS) represent a challenging subtype of focal temporal lobe epilepsy (TLE) in terms of both severity and treatment response. Most studies have focused on regional brain analysis that is agnostic to the distribution of white matter (WM) pathways associated with a node. We implemented a more selective, edge‐wise approach that allowed for identification of the individual connections unique to FBTCS. Methods: T1‐weighted and diffusion‐weighted images were obtained from 22 patients with solely focal seizures (FS), 43 FBTCS patients, and 65 age/sex‐matched healthy participants (HPs), yielding streamline (STR) connectome matrices. We used diffusion tensor‐derived STRs in an edge‐wise approach to determine specific structural connectivity changes associated with seizure generalization in FBTCS compared to matched FS and HPs. Graph theory metrics were computed on both node‐ and edge‐based connectivity matrices. Results: Edge‐wise analyses demonstrated that all significantly abnormal cross‐hemispheric connections belonged to the FBTCS group. Abnormal connections associated with FBTCS were mostly housed in the contralateral hemisphere, with graph metric values generally decreased compared to HPs. In FBTCS, the contralateral amygdala showed selective decreases in the structural connection pathways to the contralateral frontal lobe. Abnormal connections in TLE involved the amygdala, with the ipsilateral side showing increases and the contralateral decreases. All the FS findings indicated higher graph metrics for connections involving the ipsilateral amygdala. Data also showed that some FBTCS connectivity effects are moderated by aging, recent seizure frequency, and longer illness duration. Significance: Data showed that not all STR pathways are equally affected by the seizure propagation of FBTCS. We demonstrated two key biases, one indicating a large role for the amygdala in the propagation of seizures, the other pointing to the prominent role of cross‐hemispheric and contralateral hemisphere connections in FBTCS. We demonstrated topographic reorganization in FBTCS, pointing to the specific WM tracts involved. [ABSTRACT FROM AUTHOR]

PROFESSIONAL MUSICIANS HAVE BEEN TEACHING/ learning/interpreting Western classical tonal music for longer than atonal music. This may be reflected in their brain plasticity and playing efficiency. To test this idea, EEG connectivity networks (EEG-CNs) of expert cellists at rest and during real and imagined musical interpretation of tonal and atonal excerpts were analyzed. Graphs and connectomes were constructed as models of EEG-CNs, using functional connectivity measurements of EEG phase synchronization in different frequency bands. Tonal and atonal interpretation resulted in a global desynchronization/dysconnectivity versus resting--irrespective of frequency bands--particularly during imagined-interpretation. During the latter, the normalized local information-transfer efficiency (NLE) of graph-EEG-CN's small-world structure at rest increased significantly during both tonal and atonal interpretation, and more significantly during atonalinterpretation. Regional results from the graphs/connectomes supported previous findings, but only certain EEG frequency bands. During imagined-interpretation, the number of disconnected regions and subnetworks, as well as regions with higher NLE, were greater in atonal-interpretation than in tonal-interpretation for delta/theta/gamma-EEG-CNs. The opposite was true during real-interpretation, specifically limited to alpha-EEG-CN. Our EEG-CN experimental paradigm revealed perceptual differences in musicians' brains during tonal and atonal interpretations, particularly during imagined-interpretation, potentially due to differences in cognitive roots and brain plasticity for tonal and atonal music, which may affect the musicians' interpretation. [ABSTRACT FROM AUTHOR]

With the emerging era of E‐commerce and online shopping, people are also in a habit to receive default product recommendations on the web pages that they access. Google is already providing such suggestions. Till now recommendations were made only based on previous sentiments or feedback or ratings, but this research has improved the product recommendation method by including one more parameter for the same. This article represents two parameters for making predictions of product allocation to a new customer. These parameters are ratings given by the existing users for that particular product and the region to which the new customer belongs. Following these parameters, a prediction model and an algorithm, Improved_Collab_Similarity, have been implemented. The dataset has been developed where India as a country along with all its States has been considered for products which are popular for their creation based on regional and ancient skills of the people belonging to that area. Results for the mentioned prediction model have been discussed in this article where generally precision increases with the increase in a number of products but at some points, it does not increase when a smaller number of that product was purchased by the customers. [ABSTRACT FROM AUTHOR]

The concept of rainbow connection was introduced by Chartrand et al. in 2008. The k -rainbow index, which is a generalization of rainbow connection number was also introduced by Chartrand et al. in 2010. These two new graph-parameters are defined for all edge-colored graphs. Krivelevich and Yuster in 2010 naturally introduced the rainbow vertex-connection number which is defined on vertex-colored graphs. As a natural counterpart of the k -rainbow index and a generalization of rainbow vertex-connection number, Mao introduced the concept of k -vertex-rainbow index in 2016. Nowadays they have become new and active subjects in graph theory. In this survey we attempt to bring together most of the basic and new results that dealt with the k -rainbow index and k -vertex-rainbow index. [ABSTRACT FROM AUTHOR]

The evaluation of cognitive functions interactions has become increasingly implemented in the cognition exploration. In the present study, we propose to examine the organization of the cognitive network in healthy participants through the analysis of behavioral performances in several cognitive domains. Specifically, we aim to explore cognitive interactions profiles, in terms of cognitive network, and as a function of participants' handedness. To this end, we proposed several behavioral tasks evaluating language, memory, executive functions, and social cognition performances in 175 young healthy right-handed and left-handed participants and we analyzed cognitive scores, from a network perspective, using graph theory. Our results highlight the existence of intricate interactions between cognitive functions both within and beyond the same cognitive domain. Language functions are interrelated with executive functions and memory in healthy cognitive functioning and assume a central role in the cognitive network. Interestingly, for similar high performance, our findings unveiled differential organizations within the cognitive network between right-handed and left-handed participants, with variations observed both at a global and nodal level. This original integrative network approach to the study of cognition provides new insights into cognitive interactions and modulations. It allows a more global understanding and consideration of cognitive functioning, from which complex behaviors emerge. [ABSTRACT FROM AUTHOR]

Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide (InP) via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide (InP) . [ABSTRACT FROM AUTHOR]

This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. In contrast to existing synchronization network models, the current study considers both internal time‐varying delays and coupling time‐varying delays. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a new inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. To demonstrate the effectiveness of the present approach, simulation results are illustrated. In this paper, we consider the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. Different from the existing synchronization of the networks model, we take the internal time‐varying delays and the coupling time‐varying delays into account. By analyzing the two factors (i.e. time‐varying delays and uncertainties) on the synchronization performance of stochastic uncertain complex dynamic networks, a novel inverse optimal adaptive control is proposed. The analysis tool developed in this paper is based on Lyapunov technique, algebraic graph theory and inverse optimality, which does not need to solve Hamilton‐Jacobi‐Bellman equation. Some sufficient conditions are established for the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. [ABSTRACT FROM AUTHOR]

Under the envisioned smart grid paradigm, there is an increasing demand for a fast, accurate, and efficient power flow solution for distribution system operation and control. Various solution techniques have been proposed, each with its own unique formulation, solution methodology, advantages, and drawbacks. Motivated by challenges associated with the integration of renewable distributed energy resources and electric vehicles into distribution systems and further by the speed and convergence limitations of existing tools, this paper presents a novel graph‐based power flow solution for smart grid's real‐time operation and control, named Flow‐AugmentationPF algorithm. The proposed method formulates a power flow problem as a network‐flow problem and solves it by using a maximum‐flow algorithm, inspired by the push‐relabel max‐flow technique. The performance of the proposed algorithm is tested and validated using several benchmark networks of different sizes, topologies, and parameters and compared against the most commonly used solution techniques and commercial software packages, namely PSS/E and PSCAD. The proposed formulation is simple, accurate, fast, yet computationally efficient, as it is based on matrix‐vector multiplication, and is also scalable, considering the formulation works as a graph‐based method, which, inherently, allows for parallel computation for added computational speed. [ABSTRACT FROM AUTHOR]

Given a connected graph G = (V , E) , with n ≔ | V | vertices and m ≔ | E | edges, a cut can be represented as a bipartition { S , S ¯ } of the vertices or as the set of those edges in E having one endpoint in S and the other in S ¯ , denoted by δ G (S , S ¯). A cut is minimal, or also called bond , if and only if the two induced subgraphs obtained by removing the edges in the cut are both connected. When the bond separates two given vertices s and t , we talk about s , t - bond. In this work, we consider the problems of listing all the bonds and listing all the s , t -bonds in a graph. These fundamental problems find application in many research areas, such as, beyond graph theory, network reliability, bioinformatics, and chemistry. The state-of-the-art algorithm exploits binary partition to output each s , t -bond in O (m) per bond, being thus classified as an O (m) -delay algorithm. Here we present two new algorithms to address these problems. The first one implements a slightly different branching strategy than the state of the art, though achieving the same complexity. Anyway, we can improve it by relying on dynamic data structures and amortized analysis, obtaining an algorithm that outputs a new bond in O ˜ (n). By assuming only the two bond-shores are output for every bond, this is the first output-linear algorithm listing bonds. In case we commit to explicitly providing the entire edge-set of every bond, the delay becomes O ˜ (n) + | δ G (S , S ¯) |. • We study the problem of listing all minimal cuts (or bonds) in a graph. • We exploit a different branching strategy than Tsukiyama et al. (1980). • We provide a first algorithm having the same complexity as Tsukiyama et al. (1980). • We rely on dynamic data structures and amortized analysis to improve our approach. • We propose the first O ˜ (n) -delay algorithm to list all bonds in a graph. [ABSTRACT FROM AUTHOR]

Collaborative crowdsensing is a team collaboration model that harnesses the intelligence of a large network of participants, primarily applied in areas such as intelligent computing, federated learning, and blockchain. Unlike traditional crowdsensing, user recruitment in collaborative crowdsensing not only considers the individual capabilities of users but also emphasizes their collaborative abilities. In this context, this paper takes a unique approach by modeling user interactions as a graph, transforming the recruitment challenge into a graph theory problem. The methodology employs an enhanced Prim algorithm to identify optimal team members by finding the maximum spanning tree within the user interaction graph. After the recruitment, the collaborative crowdsensing explored in this paper presents a challenge of unfair incentives due to users engaging in free-riding behavior. To address these challenges, the paper introduces the MR-SVIM mechanism. Initially, the process begins with a Gaussian mixture model predicting the quality of users' tasks, combined with historical reputation values to calculate their direct reputation. Subsequently, to assess users' significance within the team, aggregation functions and the improved PageRank algorithm are employed for local and global influence evaluation, respectively. Indirect reputation is determined based on users' importance and similarity with interacting peers. Considering the comprehensive reputation value derived from the combined assessment of direct and indirect reputations, and integrating the collaborative capabilities among users, we have formulated a feature function for contribution. This function is applied within an enhanced Shapley value method to assess the relative contributions of each user, achieving a more equitable distribution of earnings. Finally, experiments conducted on real datasets validate the fairness of this mechanism. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fixed-time synchronization of time-varying coupled competitive neural networks with impulsive effects. Synchronizing impulses and desynchronizing impulses are each taken into account. The innovative pure power-law control is designed in this paper to avoid vibratory behaviors, which is more straightforward and effective than the common design including the linear and power-law terms. Note that the key difficulty is determining how to ensure fixed-time synchronization and estimate the settling time in an impulsive sense since the impulsive influences may lead to the discontinuity of the states. However, the theoretical framework of fixed-time synchronization under desynchronizing impulses has not been constructed much in the existing literature, which deeply motivated us to contribute to this analysis. By using the average impulsive intervals method, graph theory, and the Lyapunov method, two cases of the settling time along with the fixed-time synchronization criteria regarding the synchronizing and desynchronizing impulses are given. Lastly, a numerical example is provided to show the viability and accuracy of the discovered theoretical results. [ABSTRACT FROM AUTHOR]