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Among the properties describing the behavior of centrality measures with respect to network modifications, score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target with respect to the remaining nodes. It is known (Boldi and Vigna Intern Math 10:222–262, 2014, Boldi et al. Netw Sci 5(4):529–550, 2017) that score and rank monotonicity hold in directed graphs for almost all the classical centrality measures. In undirected graphs one expects that the corresponding properties hold when adding a new edge—in this case, both endpoints of the new edge should enjoy the increase in score/rank. However, recent results (Boldi et al. in Netw Sci 11(3):1–23, 2023) have shown that this is not true: for many centrality measures, it is possible to find situations in which adding an edge reduces the rank of one of its two endpoints. In this paper we introduce a weaker property for undirected networks, semi-monotonicity, in which just one of the two endpoints of a new edge is required to enjoy score or rank monotonicity. We show that this property is satisfied by closeness centrality, by a large class of distance-based centralities, and (somehow surprisingly) by betweenness centrality. In the last two cases, we prove in fact a stronger property, basin dominance, which is of independent interest. [ABSTRACT FROM AUTHOR]

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the implementation of a sequence of activities designed to convey to future teachers the importance of systematically solving problems that involve searching for or constructing different cases. Specifically, participants are provided with the three pieces of the Brügner's tangram and assigned the task of identifying all possible convex polygons that can be constructed. Moreover, they are required to elucidate the methodological approach underpinning their exploratory process, with an emphasis on establishing relationships between the polygons. Graphs are introduced as one of the possible approaches for modelling the problem, offering a graphical representation that aids in the systematic search for solutions. This paper describes different activities involving the Brügner's tangram which has demonstrated its adaptability as an instructional resource. The teaching sequence adheres to the five-phase structure proposed within the framework of the van Hiele model, which is also part of the course. [ABSTRACT FROM AUTHOR]

We initiate the investigation of the parameterized complexity of Diameter and Connectivity in the streaming paradigm. On the positive end, we show that knowing a vertex cover of size k allows for algorithms in the Adjacency List (AL) streaming model whose number of passes is constant and memory is O (log n) for any fixed k. Underlying these algorithms is a method to execute a breadth-first search in O (k) passes and O (k log n) bits of memory. On the negative end, we show that many other parameters lead to lower bounds in the AL model, where Ω (n / p) bits of memory is needed for any p-pass algorithm even for constant parameter values. In particular, this holds for graphs with a known modulator (deletion set) of constant size to a graph that has no induced subgraph isomorphic to a fixed graph H, for most H. For some cases, we can also show one-pass, Ω (n log n) bits of memory lower bounds. We also prove a much stronger Ω (n 2 / p) lower bound for Diameter on bipartite graphs. Finally, using the insights we developed into streaming parameterized graph exploration algorithms, we show a new streaming kernelization algorithm for computing a vertex cover of size k. This yields a kernel of 2k vertices (with O (k 2) edges) produced as a stream in poly (k) passes and only O (k log n) bits of memory. [ABSTRACT FROM AUTHOR]

This survey article presents a comprehensive and conceptual overview of anomaly detection (AD) using dynamic graphs. We focus on existing graph-based AD techniques and their applications to dynamic networks. The contributions of this survey article include the following: (i) a comparative study of existing surveys on AD; (ii) a Dynamic Graph-based anomaly detection (DGAD) review framework in which approaches for detecting anomalies in dynamic graphs are grouped based on traditional machine learning models, matrix transformations, probabilistic approaches, and deep learning approaches; (iii) a discussion of graphically representing both discrete and dynamic networks; and (iv) a discussion of the advantages of graph-based techniques for capturing the relational structure and complex interactions in dynamic graph data. Finally, this work identifies the potential challenges and future directions for detecting anomalies in dynamic networks. This DGAD survey approach aims to provide a valuable resource for researchers and practitioners by summarizing the strengths and limitations of each approach, highlighting current research trends, and identifying open challenges. In doing so, it can guide future research efforts and promote advancements in AD in dynamic graphs. [ABSTRACT FROM AUTHOR]

We consider a stochastic matching model with a general compatibility graph, as introduced in Mairesse and Moyal (J Appl Probab 53(4):1064–1077, 2016). We prove that most common matching policies (including fcfm, priorities and random) satisfy a particular sub-additive property, which we exploit to show in many cases, the coupling-from-the-past to the steady state, using a backwards scheme à la Loynes. We then use these results to explicitly construct perfect bi-infinite matchings, and to build a perfect simulation algorithm in the case where the buffer of the system is finite. [ABSTRACT FROM AUTHOR]

Accurately detecting anomalies in microservice systems is crucial to avoid system failures and economic losses for users. Existing approaches detect anomalies by extracting sequential information from single-modal data, such as metrics or logs. However, they do not clearly analyze the temporal and spatial dependencies of each data type and ignore the correlation between different types of data, which can lead to a significant number of false positives. In this paper, we propose a novel Microservice system Anomaly Detection method via Multi-modal data and Multi-feature extraction (MADMM), which performs a joint analysis of metrics and logs from a spatial and temporal perspective. Specifically, we firstly construct separate feature graphs for metrics and logs in each time window. A graph convolution network is then utilized to capture the spatial correlation among different metrics, while a graph attention network is employed to analyze the contextual relationships among different log events. Then, we design a Cross-Modal Attention-based Gate Recurrent Unit (CMA-GRU) to capture the intricate temporal dependencies of each modal data and facilitate fulfilling cross-modal interactions. Finally, we introduce multi-grained contrastive learning methods to learn robust cross-modal features from both inter- and intra-modality aspects. Experimental results on real-world datasets demonstrate that MADMM outperforms existing baseline methods and exhibits better robustness. [ABSTRACT FROM AUTHOR]

One of the main challenges in molecular science is to model a chemical complex and predict its thermochemical properties. Various researchers have developed a number of hypothetical techniques in this regard, and one of them is focused on the topological indices. A topological index is a number associated with a molecule's structural graph that is considered to be capable of predicting certain chemical and physical properties of molecules. Degree-based topological indices are one of the groups of topological indices that are crucial in chemical graph theory. Shannon's entropy is a fundamental factor of a subclass of topological indices that measures the structural information of the graphs. In this study, we examine the entropy based on topological indices such as the first and second Zagreb indices, the general Randić index, the harmonic and sum-connectivity index of Hanoi graph. Moreover, we determine a number of multiplicative invariants, and different polynomials for Hanoi graphs with graphical illustrations. [ABSTRACT FROM AUTHOR]

Compartmental models of disease spread have been well studied on networks built according to the Configuration Model, i.e., where the degree distribution of individual nodes is specified, but where connections are made randomly. Dynamics of spread on such "first order" networks were shown to be profoundly different compared to epidemics under the traditional mass action assumption. Assortativity, i.e., the preferential mixing of nodes according to degree, is a second order property that is thought to impact epidemic trajectory. We first show how assortative mixing can come about from individual preferences to connect with others of lower or higher degree, and propose an algorithm for constructing such a network. We then investigate via simulation how this network structure favors or inhibits diffusion processes, such as the spread of an infectious disease. [ABSTRACT FROM AUTHOR]

Anosov diffeomorphisms are an important class of dynamical systems with many peculiar properties. Ever since they were introduced in the sixties, it has been an open question which manifolds can admit such diffeomorphisms, where tori of dimension greater than or equal to two are the typical examples. It is conjectured that the only manifolds supporting an Anosov diffeomorphism are finitely covered by a nilmanifold, a type of manifold closely related to rational nilpotent Lie algebras. In this paper, we study the existence of Anosov diffeomorphisms for a large class of these nilpotent Lie algebras, namely the ones that can be realized as a rational form in a Lie algebra associated to a graph. From a given simple undirected graph, one can construct a complex c-step nilpotent Lie algebra, which in general contains different non-isomorphic rational forms, as described by the authors in previous work. We determine precisely which forms correspond to a nilmanifold admitting an Anosov diffeomorphism, leading to the first class of complex nilpotent Lie algebras having several non-isomorphic rational forms and for which all the ones that are Anosov are described. In doing so, we put a new perspective on certain classifications in low dimensions and correct a false result in the literature. [ABSTRACT FROM AUTHOR]

In molecular biology, constructing a genome based on substantially many reads from multitudes of deoxyribonucleic acid (DNA) strings has become an insurmountable task; one which has been continuously addressed by the introduction of various assembly algorithms based on three steps called the overlap-layout-consensus strategy. In the overlap step, the De Bruijn graph is one of many graphs that illustrate the data of all the assembly algorithms. In this article, by using definitions and methods of mathematical induction, some properties of the De Bruijn graph of one time and two times non-sequential repetition of patterns in a DNA string are presented. Examples of these De Bruijn graphs are also given. From there, a generalisation of said properties for m times non-sequential pattern repetition in a DNA string is acquired by means of mathematical induction, as well. The theoretical work in this research is invaluable to develop algorithms that increase the computational efficiency of assembly algorithms. [ABSTRACT FROM AUTHOR]

Clique counts are crucial in applications like detecting communities in social networks and recurring patterns in bioinformatics. Counting k-cliques—a fully connected subgraph with k nodes, where each node has a direct, mutual, and symmetric relationship with every other node—becomes computationally challenging for larger k due to combinatorial explosion, especially in large, dense graphs. Existing exact methods have difficulties beyond k = 10, especially on large datasets, while sampling-based approaches often involve trade-offs in terms of accuracy, resource utilization, and efficiency. This difficulty becomes more pronounced in dense graphs as the number of potential k-cliques grows exponentially. We present Boundary-driven approximations of k-cliques (BDAC), a novel algorithm that approximates k-clique counts without using recursive procedures or sampling methods. BDAC offers both lower and upper bounds for k-cliques at local (per-vertex) and global levels, making it ideal for large, dense graphs. Unlike other approaches, BDAC's complexity remains unaffected by the value of k. We demonstrate its effectiveness by comparing it with leading algorithms across various datasets, focusing on k values ranging from 8 to 50. [ABSTRACT FROM AUTHOR]

High-order structures have been recognised as suitable models for systems going beyond the binary relationships for which graph models are appropriate. Despite their importance and surge in research on these structures, their random cases have been only recently become subjects of interest. One of these high-order structures is the chemical hypergraph, which relates couples of subsets (hypervertices) of an arbitrary number of vertices. Here we develop the Erdős–Rényi model for chemical hypergraphs, which corresponds to the random realisation of edges of the complete chemical hypergraph. A particular feature of random chemical hypergraphs is that the ratio between their expected number of edges and their expected degree or size is 3/2 for large number of vertices. We highlight the suitability of chemical hypergraphs for modelling large collections of chemical reactions and the importance of random chemical hypergraphs to analyse the unfolding of chemistry. [ABSTRACT FROM AUTHOR]

Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to recognize a continuous function from its graph. To help mitigate this problem, these visuals can be used alongside the definitions in analysis courses, and in calculus courses where the same definitions are used. The content is arranged into a series of pictures accompanied by questions, with suggestions for the instructor on how to guide students in their learning. The design allows students to make their own discoveries and connections. The investigations crescendo to a surprising fact: that almost all continuous functions are differentiable nowhere! [ABSTRACT FROM AUTHOR]

Understanding graphs in the dynamics of market (DM) is a challenge to learners; its teaching demands a specific kind of teacher’s knowledge. This study aims to examine the topic-specific pedagogical content knowledge (TSPCK) of experienced economics teachers in teaching graphs in DM to enhance learners’ understanding of the topic. It reports using a qualitative approach underpinned by the TSPCK framework for teaching specific topics developed by Mavhunga. Data were collected through classroom observations and analyzed thematically using a case study of two economics teachers. The study revealed that adopting a step-by-step approach and the use of worked graphical examples promote an understanding of graphs in DM. It also established that active learning is preferable to the predominant chalk-and-talk (lecture) method of teaching graphs in DM. The study proposed a Dynamics of Market Graphical Framework (DMG-Framework) to enable teachers, particularly pre-service teachers in lesson delivery, to enhance learners’ understanding of graphs in DM. The result of this study will broaden the international view in the teaching of graphs in DM. [ABSTRACT FROM AUTHOR]

The frustum model simulates network evolution by extending cliques, which represent highly interacting groups in social networks. In each time-step, new vertices are added adjacent to existing cliques of prescribed order. The model exhibits several features of social networks, such as densification, short distances, bad spectral expansion, and high local clustering. [ABSTRACT FROM AUTHOR]

This paper focuses on the migration pathways (MP) of individuals from a rural population in the Philippines. The succession of migrations undertaken by an individual and the role of previous migration(s) in subsequent migration have received relatively little attention in migration studies. The present paper fills this knowledge gap by identifying MP types and exploring links between migrations from a life course perspective. It develops a methodological framework based on sequence and graph analysis. Based on research conducted in Bohol (Philippines) using field data, the two methods are jointly used to reveal the diversity of MP. We focused on migrations done between the ages of 15 and 30. Typical MP were identified using hierarchical clustering. Socioeconomic data collected during surveys were used to characterise the types of MP (e.g., gender, education and age). Sequence analysis revealed six types of MP: some are common across the Philippines (e.g., the circular migration towards Mindanao until the 1970s), while others are specific to the area (e.g., permanent migration toward other places in Bohol). Graphs offer alternative representations of MP that allow to consider the shape of both individual and collective MP. The approach developed here is reproducible, easy to implement and contributes to a better understanding of the complexity of migration by looking at the migrants' histories. [ABSTRACT FROM AUTHOR]

We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an algebraic semantics in the style of Meseguer and Montanari, in terms of free coloured props, and allows the following unification: for P a Petri net, the Segal space of P-processes is shown to be the free coloured prop-in-groupoids on P. There is also an unfolding semantics à la Winskel, which bypasses the classical symmetry problems: with the new formalism, every Petri net admits a universal unfolding, which in turn has associated an event structure and a Scott domain. Since everything is encoded with explicit sets, Petri nets and their processes have elements. In particular, individual-token semantics is native. (Collectivetoken semantics emerges from rather drastic quotient constructions à la Best–Devillers, involving taking π0 of the groupoids of states [ABSTRACT FROM AUTHOR]

Copyright of Econometrics / Ekonometria is the property of Sciendo and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A regular unranked tree folding consists of a regular unranked tree language and a folding operation that merges (i.e., folds) selected nodes of a tree to form a graph; the combination is a formal device for representing graph languages. If, in the process of folding, the order among edges is discarded so that the result is an unordered graph, then two applications of a fold operation are enough to make the associated parsing problem NP-complete. However, if the order is kept, then the problem is solvable in non-uniform polynomial time. In this paper, we address the remaining case, where only one fold operation is applied, but the order among the edges is discarded. We show that, under these conditions, the problem is solvable in non-uniform polynomial time. [ABSTRACT FROM AUTHOR]

We raise the question of the realizability of permutation modules in the context of Kahn’s realizability problem for abstract groups and the G-Moore space problem. Specifically, given a finite group G, we consider a collection { M i } i = 1 n of finitely generated Z G -modules that admit a submodule decomposition on which G acts by permuting the summands. Then we prove the existence of connected finite spaces X that realize each M i as its i-th homology, G as its group of self-homotopy equivalences E (X) , and the action of G on each M i as the action of E (X) on H i (X ; Z) . [ABSTRACT FROM AUTHOR]

We present PyGenStability, a general-use Python software package that provides a suite of analysis and visualization tools for unsupervised multiscale community detection in graphs. PyGenStability finds optimized partitions of a graph at different levels of resolution by maximizing the generalized Markov Stability quality function with the Louvain or Leiden algorithm. The package includes automatic detection of robust graph partitions and allows the flexibility to choose quality functions for weighted undirected, directed, and signed graphs and to include other user-defined quality functions. [ABSTRACT FROM AUTHOR]

This study aims to examine pre-service teachers’(PTs’) understandings of graphs and how their understandings about graphs have transformed into instructional practices as they participated in a lesson study. It was employed case study and three PTs participated. They initially viewed graphs as instruments for organizing and representing data. As the lesson study progressed, they began to view graphs as instruments to answer statistical questions. This fundamental transformation in their understanding resulted in a change in how they designed and implemented their lesson plans. They designed tasks around a statistical question and made connections with this question while deciding the type of graph and interpreting the graph. In addition, they anticipated students’ possible conceptions. Hence, for these PTs, understanding the function graphs as instruments to answer statistical questions can be considered as a key development understanding (KDU), which was built on multiple experiences of designing, implementing and evaluating lessons. [ABSTRACT FROM AUTHOR]

Whole-genome alignment (WGA) is a critical process in comparative genomics, facilitating the detection of genetic variants and aiding our understanding of evolution. This paper offers a detailed overview and categorization of WGA techniques, encompassing suffix tree-based, hash-based, anchor-based, and graph-based methods. It elaborates on the algorithmic properties of these tools, focusing on performance and methodological aspects. This paper underscores the latest progress in WGA, emphasizing the increasing capacity to manage the growing intricacy and volume of genomic data. However, the field still grapples with computational and biological hurdles affecting the precision and speed of WGA. We explore these challenges and potential future solutions. This paper aims to provide a comprehensive resource for researchers, deepening our understanding of WGA tools and their applications, constraints, and prospects. [ABSTRACT FROM AUTHOR]

We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces. [ABSTRACT FROM AUTHOR]

A model of a system of wireless power transfer (WPT) pads is developed, where each WPT pad is modeled as a node and the coupling between pads is modeled as graph edges. This modeling approach is generalized to admit primary, secondary, and booster coils, where power can flow among the pads and a pad can fill multiple roles. An excitation in one pad induces voltage and current in all neighboring pads, causing each pad to act as both a booster coil and either a transmitter or a receiver. Power flow through the entire system can be modeled with the graph structure; the power flow can then be optimized by alternating the phases of the WPT excitations to maximize power transfer. An example is shown where exploiting the graph-based WPT system modeling increases total energy transfer by 25% compared to another method. This increase occurs without altering the geometry of the pads or the magnitude of the pad excitations. [ABSTRACT FROM AUTHOR]

Summary: Killer immunoglobulin‐like receptor (KIR) and KIR‐ligand (KIRL) interactions play an important role in natural killer cell‐mediated effects after haematopoietic stem cell transplantation (HCT). Previous work has shown that accounting for known KIR–KIRL interactions may identify donors with optimal NK cell‐mediated alloreactivity in the adult transplant setting. Paediatric acute leukaemia patients were retrospectively analysed, and KIR‐KIRL combinations and maximal inhibitory KIR ligand (IM‐KIR) scores were determined. Clinical outcomes were examined using a series of graphs depicting clinical events and endpoints. The graph methodology demonstrated that prognostic variables significant in the occurrence of specific clinical endpoints remained significant for relevant downstream events. KIR‐KIRL combinations were significantly predictive for reduced grade 3–4 aGVHD likelihood, in patients transplanted with increased inhibitory KIR gene content and IM‐KIR = 5 scores. Improvements were also observed in associated outcomes for both ALL and AML patients, including relapse‐free survival, GRFS and overall survival. This study demonstrates that NK cell KIR HLA interactions may be relevant to the paediatric acute leukaemia transplant setting. Reduction in aGVHD suggests KIR effects may extend beyond NK cells. Moving forward clinical trials utilizing donors with a higher iKIR should be considered for URD HCT in paediatric recipients with acute leukaemia to optimize clinical outcomes. [ABSTRACT FROM AUTHOR]

We introduce a graph associated with any stable map defined from the connected sum # n (S 1 × S 2) of n copies of the product S 1 × S 2 to the Euclidean 3-space. This graph has a weight on each vertex and a pair of weights on each edge, and its properties provide a necessary and sufficient condition to be the graph of a stable map defined from # n (S 1 × S 2) to the Euclidean 3-space. [ABSTRACT FROM AUTHOR]

A cocomparability graph is a graph whose complement admits a transitive orientation. An interval graph is the intersection graph of a family of intervals on the real line. In this paper we investigate the relationships between interval and cocomparability graphs. This study is motivated by recent results (Corneil et al., SIAM J. Comput. 42(3):792–807, 2013; Dusart et al., SIAM J. Comput. 50(3):1148–1153, 2021; Dusart and Habib, Discret. Appl. Math. 216:149–161, 2017) that show that for some problems, the algorithm used on interval graphs can also be used with small modifications on cocomparability graphs. Many of these algorithms are based on graph searches that preserve cocomparability orderings. First we propose a characterization of cocomparability graphs via a lattice structure on the set of their maximal cliques. Using this characterization we can prove that every maximal interval subgraph of a cocomparability graph G is also a maximal chordal subgraph of G. Although the size of this lattice of maximal cliques can be exponential in the size of the graph, it can be used as a framework to design and prove algorithms on cocomparability graphs. In particular we show that a new graph search, namely Local Maximal Neighborhood Search (LocalMNS) leads to an algorithm to find in linear time a maximal interval subgraph of a cocomparability graph which improves on the current state of knowledge. Although computing all simplicial vertices is known to be equivalent to the recognition of triangle-free graphs or boolean multiplication, see (Krastch and Spinrad, SIAM J. Comput. 36(2):310–325, 2007; Coudert and Ducoffe, SIAM J. Discrete Math. 32(1):682–694, 2018), we will show that our structural insights in cocomparability graphs together with the definition of a new graph search, allow us to achieve linear time on this class of graphs. [ABSTRACT FROM AUTHOR]

Many deep learning works on financial time-series forecasting focus on predicting future prices/returns of individual assets with numerical price-related information for trading, and hence propose models designed for univariate, single-task, and/or unimodal settings. Forecasting for investment and risk management involves multiple tasks in multivariate settings: forecasts of expected returns and risks of assets in portfolios, and correlations between these assets. As different sources/types of time-series influence future returns, risks, and correlations of assets in different ways, it is also important to capture time-series from different modalities. Hence, this article addresses financial time-series forecasting for investment and risk management in a multivariate, multitask, and multimodal setting. Financial time-series forecasting, however, is challenging due to the low signal-to-noise ratios typical in financial time-series, and as intra-series and inter-series relationships of assets evolve across time. To address these challenges, our proposed Temporal Implicit Multimodal Network (TIME) model learns implicit inter-series relationship networks between assets from multimodal financial time-series at multiple time-steps adaptively. TIME then uses dynamic network and temporal encoding modules to jointly capture such evolving relationships, multimodal financial time-series, and temporal representations. Our experiments show that TIME outperforms other state-of-the-art models on multiple forecasting tasks and investment and risk management applications. [ABSTRACT FROM AUTHOR]

The article considers the application of the analysis method using graph theory to determine critical points in the air networks of Ukraine, Turkey and Moldova. The goal is to identify critical points in the above-mentioned aerial networks. The reason is the probability of resuming air traffic between Ukraine and neighboring countries (with the exception of the Russian Federation). The data on the network is obtained from collections of aeronautical information. Modeling was performed in the Python software environment using libraries for processing and visualizing the received data. The main criteria used to determine the criticality of a radio navigation point are Betweenness centrality and Closeness centrality. In addition, the collection and comparison of statistical data on the number of routes and radio navigation points in each of the studied countries will be performed. The obtained data are useful, because it will give an opportunity to compare the results with those obtained during the study of the Ukrainian network and for air navigation service providers to improve the existing network. [ABSTRACT FROM AUTHOR]

Hiking trails are a basic type of tourist infrastructure, which, on the one hand, make areas available for tourist traffic, and on the other hand, can contribute to the protection of the natural environment (if they are well designed and maintained). Owing to the variety of performed functions, their designation is determined by several factors: natural, technical, economic, social. Networks of trails change constantly. The aim of this article is to determine exactly what factors influence transformations within the hiking trail networks and what is their significance. To this end, three study areas in the Sudetes were analysed: one on the Polish side of the Sudetes–the Table (Stołowe) Mountains, and two on the Czech side–the rock town near the village of Sloup v Čechách and the central part of Zlatohorská vrchovina. An analysis of changes in the shape of the networks over time was carried out, as well as surveys of institutions that were responsible for or influenced these transformations. These areas are characterised by a significant level of changes in the trail network. Among the factors influencing these changes, the tourist attractiveness of the area, the resilience of the environment, the intensity of tourism traffic, the environmental transformations associated with it, the history of tourism development and land ownership changes should be considered the most important. At each stage of forming networks, the key factor should be tourists' needs, including the desire to escape the urbanised environment. For this reason, trails should avoid roads with artificial (hard) surfaces and heavy automobile traffic. [ABSTRACT FROM AUTHOR]

The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently the class of graphs in which all associated symmetric matrices possess the Strong Spectral Property (denoted G SSP ) were studied, and along these lines we aim to study properties of graphs that exhibit a so-called barbell partition. Such a partition is a known impediment to membership in the class G SSP . In particular we consider the existence of barbell partitions under various standard and useful graph operations. We do so by considering both the preservation of an already present barbell partition after performing said graph operations as well as barbell partitions which are introduced under certain graph operations. The specific graph operations we consider are the addition and removal of vertices and edges, the duplication of vertices, as well as the Cartesian products, tensor products, strong products, corona products, joins, and vertex sums of two graphs. We also identify a correspondence between barbell partitions and graph substructures called forts, using this correspondence to further connect the study of zero forcing and the Strong Spectral Property. [ABSTRACT FROM AUTHOR]

Let G = (V, E~) be a graph, with vertex set V and edge set E. An independent dominating set S of G is a subset of V with the property that every vertex in V -- S is adjacent to some vertex in S and no two vertices within S are adjacent. The number of vertices in a minimum independent dominating set in the graph G is called the independent domination number i(G} of G. In this article, the independent domination number of graphs obtained through vertex switching have been computed with appropriate illustration. [ABSTRACT FROM AUTHOR]

In the last two decades, we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs into vector‐based representations that preserve the most essential structural properties of graphs. For this purpose, a large number of graph embedding methods have been proposed in the literature. Most of them produce general‐purpose embeddings suitable for a variety of applications such as node clustering, node classification, graph visualization and link prediction. In this article, we propose two novel graph embedding algorithms based on random walks that are specifically designed for the node classification problem. Random walk sampling strategies of the proposed algorithms have been designed to pay special attention to hubs–high‐degree nodes that have the most critical role for the overall connectedness in large‐scale graphs. The proposed methods are experimentally evaluated by analyzing the classification performance of three classification algorithms trained on embeddings of real‐world networks. The obtained results indicate that our methods considerably improve the predictive power of examined classifiers compared with currently the most popular random walk method for generating general‐purpose graph embeddings (node2vec). [ABSTRACT FROM AUTHOR]

In this paper, we will construct a few types of graphs based on the ideal-annihilator, right-ideal-annihilator, left-ideal-annihilator for a KU-algebras. We will also study some graph invariants, such as connectivity, regularity, and planarity for these graphs. [ABSTRACT FROM AUTHOR]

In this paper, we study the connection between the odd cycles of a finite, simple graph G and the symbolic powers of its edge ideal. When the odd cycles of G are disjoint, we give a decomposition of the symbolic powers of the edge ideal based on the number and size of the odd cycles of G. This shows that the symbolic powers of the edge ideal are completely dependent on the odd cycles of G. [ABSTRACT FROM AUTHOR]

This article deals with the inverse obnoxious center location problem on general networks in which the edge lengths are modified at the minimum overall cost with respect to given modification bounds such that a predetermined facility point becomes an obnoxious center location under the modified edge lengths on the perturbed network. Exact combinatorial algorithms with linear time complexities are developed for obtaining the optimal solutions of the problem under the weighted Chebyshev, bottleneck-type Hamming and sum-type Hamming cost norms. [ABSTRACT FROM AUTHOR]

We show that every countable cograph has either one or infinitely many siblings. This answers, very partially, a conjecture of Thomass'e. The main tools are the notion of well quasi-ordering and the correspondence between cographs and some labelled ordered trees. [ABSTRACT FROM AUTHOR]

Copyright of Operations Research Transactions / Yunchouxue Xuebao is the property of Editorial office of Operations Research Transactions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Topic modeling aims to discover latent themes in collections of text documents. It has various applications across fields such as sociology, opinion analysis, and media studies. In such areas, it is essential to have easily interpretable, diverse, and coherent topics. An efficient topic modeling technique should accurately identify flat and hierarchical topics, especially useful in disciplines where topics can be logically arranged into a tree format. In this paper, we propose Community Topic, a novel algorithm that exploits word co-occurrence networks to mine communities and produces topics. We also evaluate the proposed approach using several metrics and compare it with usual baselines, confirming its good performances. Community Topic enables quick identification of flat topics and topic hierarchy, facilitating the on-demand exploration of sub- and super-topics. It also obtains good results on datasets in different languages. [ABSTRACT FROM AUTHOR]

Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers, tablets, and mobile phones. There are six items; for each, students are to view a video animation of a dynamic situation (e.g., a toy car moving along a square track), declare their understanding of the situation, select a Cartesian graph to represent a relationship between given attributes in the situation, and enter text to explain their graph choice. To theorize students' graph reasoning, we draw on Thompson's theory of quantitative reasoning, which explains students' conceptions of attributes as being possible to measure. To code students' written responses, we appeal to Johnson and colleagues' graph reasoning framework, which distinguishes students' quantitative reasoning about one or more attributes capable of varying (Covariation, Variation) from students' reasoning about observable elements in a situation (Motion, Iconic). Quantitizing those qualitative codes, we examine connections between the latent variables of students' graph reasoning and graph selection. Using structural equation modeling, we report a significant finding: Students' graph reasoning explains 40% of the variance in their graph selection (standardized regression weight is 0.64, p < 0.001). Furthermore, our results demonstrate that students' quantitative forms of graph reasoning (i.e., variational and covariational reasoning) influence the accuracy of their graph selection. [ABSTRACT FROM AUTHOR]

We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems. The input to the Weighted Diverse Bases problem consists of a matroid M , a weight function ω : E (M) → N , and integers k ≥ 1 , d ≥ 1 . The task is to decide if there is a collection of k bases B 1 , ⋯ , B k of M such that the weight of the symmetric difference of any pair of these bases is at least d . The input to the Weighted Diverse Common Independent Sets problem consists of two matroids M 1 , M 2 defined on the same ground set E , a weight function ω : E → N , and integers k ≥ 1 , d ≥ 1 . The task is to decide if there is a collection of k common independent sets I 1 , ⋯ , I k of M 1 and M 2 such that the weight of the symmetric difference of any pair of these sets is at least d . The input to the Diverse Perfect Matchings problem consists of a graph G and integers k ≥ 1 , d ≥ 1 . The task is to decide if G contains k perfect matchings M 1 , ⋯ , M k such that the symmetric difference of any two of these matchings is at least d . We show that none of these problems can be solved in polynomial time unless P = NP . We derive fixed-parameter tractable ( FPT ) algorithms for all three problems with (k , d) as the parameter, and present a p o l y (k , d) -sized kernel for Weighted Diverse Bases. [ABSTRACT FROM AUTHOR]

Graph representation learning has been a very active research area in recent years. The goal of graph representation learning is to generate graph representation vectors that capture the structure and features of large graphs accurately. This is especially important because the quality of the graph representation vectors will affect the performance of these vectors in downstream tasks such as node classification, link prediction and anomaly detection. Many techniques have been proposed for generating effective graph representation vectors, which generally fall into two categories: traditional graph embedding methods and graph neural network (GNN)–based methods. These methods can be applied to both static and dynamic graphs. A static graph is a single fixed graph, whereas a dynamic graph evolves over time and its nodes and edges can be added or deleted from the graph. In this survey, we review the graph-embedding methods in both traditional and GNN-based categories for both static and dynamic graphs and include the recent papers published until the time of submission. In addition, we summarize a number of limitations of GNNs and the proposed solutions to these limitations. Such a summary has not been provided in previous surveys. Finally, we explore some open and ongoing research directions for future work. [ABSTRACT FROM AUTHOR]

Complex networking analysis is a powerful technique for understanding both complex networks and big graphs in ubiquitous computing. Particularly, there are several novel metrics, such as k-clique and k-core are proposed in order to study the relative importance of nodes in complex networks. Among of those metrics, k-core analysis is an effective approach for simplifying graphical structure. However, the relation between k and the scale of networks is not explored in most existing literature. Toward this end, this paper formulate a new research problem, θ -Iceberg Core decomposition in graphs, which is able to incorporate a parameter θ ( 0 < θ ≤ 1 ) used for relaxing the output of k-cores. Further, we propose a formal concept analysis based approach for θ -Iceberg Core decomposition. The proposed approach and its conclusions can provide theoretical basis and guidance for the potential applications of θ -Iceberg Core analysis in complex networks. [ABSTRACT FROM AUTHOR]

Analysis of the physical-chemical characteristics of chemical structures requires the incorporation of topological indices into account. A structure-based approach that concentrates antiviral treatment on the main protease of the SARS-COV-2 virus. One degree-based measure that is a little comparable to the Zagreb index and Lanzhou index. This paper analyzed the effectiveness of the chemical compounds pyroxene, amphibole, detour-saturated plants, and several antiviral medications listed for the Lanzhou index. The obtained results demonstrate a significant relationship between the Lanzhou index under investigation and the physicochemical features of potential antiviral medications. The Lanzhou index for antioxidant drugs for M polynomial is enumerated. [ABSTRACT FROM AUTHOR]

The binary number system is the basic number representation in computing. We can encode natural numbers with finite 0-1 sequences. The representation of natural numbers is based on this system. However, this poses problems and is technically not perfect. Several attempts have been made to handle integers (signed numbers). We mention only two: the balanced triple number system and the number system with base − 2 . Our paper introduces new possibilities. We also shed light on the graph theoretical background of the new number systems. [ABSTRACT FROM AUTHOR]