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The present study analyzes the offshoring network constructed from the information contained in the Panama Papers, characterizing worldwide regions and countries as well as their intra- and inter-relationships. The Panama Papers 2016 divulgence is the largest leak of offshoring and tax avoidance documentation. The document leak, with a volume content of approximately 2.6 terabytes, involves more than two hundred thousand enterprises in more than two hundred countries. From this information, the offshore connections of individuals and companies are constructed and aggregated using their countries of origin. The top offshore financial regions and countries of the network are identified, and their intra- and inter-relationship are mapped and described. We are able to identify the top countries in the offshoring network and characterize their connectivity structure, discovering the more prominent actors in the worldwide offshoring scenario and their range of influence., Panama Papers; Offshore societies; Tax havens; Geographical networks; Graph Theory; Network Analysis; International Relations; Money; Globalization; Business; Economics

About 30 years ago a very important paper on “Applications of graph theory to enzyme kinetics and protein folding kinetics: steady and non-steady state systems” was published

In recent times the rate at which information is being processed and shared through the internet has tremendously increased. Internet users are in need of systems and tools that will help them manage this information overload. Search engines and recommendation systems have been recently adopted to help solve this problem. The aim of this research is to model a spontaneous research paper recommender system that recommends serendipitous research papers from two large normally mismatched information spaces or domains using BisoNets. Set and graph theory methods were employed to model the problem, whereas text mining methodologies were used to develop nodes and links of the BisoNets. Nodes were constructed from keywords, while links between nodes were established through weighting that was determined from the co-occurrence of corresponding keywords in the same title and domain. Preliminary results from the word clouds indicates that there is no obvious relationship between the two domains. The strongest links in the established information networks can be exploited to display associations that can be discovered between the two matrices. Research paper recommender systems exploit these latent relationships to recommend serendipitous articles when Bisociative Knowledge Discovery techniques and methodologies are utilized appropriately.

Measuring the influence of academic research publication is an meaningful work in academe. In this paper, the co-author and the citation networks are built to calculate the influence of a researcher and a paper in the way of networks separately with the discussion of further applications. At the beginning, the co-author network is built to determine the influence of co-authors. Then, based on the citations among the papers in the database, we build up the citation network with the help of graph theory. Thirdly, the method is implemented with the application of American Airline network analysis. As the final, the analysis of strengths and weaknesses is conducted.

Purpose: This study examined the suitability of using text network analysis (TNA) methodology for topic analysis of academic papers related to nursing. Methods: TNA background theories, software programs, and research processes have been described in this paper. Additionally, the research methodology that applied TNA to the topic analysis of the academic nursing papers was analyzed. Results: As background theories for the study, we explained information theory, word co-occurrence analysis, graph theory, network theory, and social network analysis. The TNA procedure was described as follows: 1) collection of academic articles, 2) text extraction, 3) preprocessing, 4) generation of word co-occurrence matrices, 5) social network analysis, and 6) interpretation and discussion. Conclusion: TNA using author-keywords has several advantages. It can utilize recognized terms such as MeSH headings or terms chosen by professionals, and it saves time and effort. Additionally, the study emphasizes the necessity of developing a sophisticated research design that explores nursing research trends in a multidimensional method by applying TNA methodology.

Asymmetric autocatalysis (Soai reaction) was reported 20 years ago. Since then, this discovery has had an exceptional influence on several branches of natural sciences. In the present paper citations to this milestone article—556 publications of 908 scientists from Google Scholar’s database—are analyzed by graph theoretical and statistical tools. The results enable localization of the most active research groups, their priorities and the identification of the distribution of scientific disciplines influenced by the Soai reaction.

The core of exam management system is how to generate test paper automatically. The existing algorithmic is difficult to simultaneously achieve the requirements with efficient, random, flexible and expansive performance. In this paper, we introduce the maximum flow algorithm of the upper and lower bounds in the graph theory, create a test paper generation model based on constraint conditions, and implement the test paper generation under complex constraints. In addition, to illustrate the success rate and efficiency, the system generated automatically test papers on proposition needs. In turn, it verifies the correctness and rationality of the model. The algorithm proposed in this paper will provide theoretical and technical support for other systems, and it further promotes the development of the exam management system.

Paper fragment mosaic is one of the applications of Image Mosaic, which plays an important role for Historical Document Re. Based on a series of modeling ideas, we propose a novel method to mosaic strip-type paper fragments In this paper. Firstly, the boundaries are sampled and binarized from paper fragments. Secondly, a matching ratio model is built to calculate the possibility that two fragments are spatial adjacent. Thirdly, the mosaic problem is transformed into a Traveling Salesman Problem (TSP) based on graph theory, and then solved via Linear Programming. In the experiments, a Chinese and an English paper are vertically cut into pieces, each of which is scanned as a picture file. The program coded based on our method can automatically mosaic all the fragments into the complete original paper picture, which proves the effectiveness of our method. Keywords-Image mosaic; Paper mosaic; Traveling salesman problem; Linear programming.

There are so many paper shredder products available in the market, and the decision to select a ‘right shredder’ usually involves a number of criteria. For organizations, complexity arises when the procurement function is to purchase a massive amount of shredders of the same type. This study initiated the idea to use the analytic hierarchy process with graph theory and matrix approach for solving the problem. The proposed model determines the best shredder from a pool of alternatives, given the buyer-side decision-maker’s preference settings. With the expert questionnaire polled and the heterogeneous real data collected, the model is applied to a reduced data set. The size of the decision problem is defined as 8 alternatives are filtered among 26, while the 7 justification attributes considered are fully kept for not losing the experimental meaning. The result shows the effectiveness and applicability of the approach to manage the encountered decision scientifically. As this also implies that not only buyers but also the manufacturers can use this model to analyse ‘something’, it is confident to conduct more future studies. The R script which implements the dynamic programming concept to calculate the assessed index scores for graph theory and matrix approach is perhaps another contribution of this study.

We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the observation of smaller graphs and basic structure of our heuristics. We also explain an evaluation function of each edge for efficient 2-opt local search. Using them, we found the best solutions for several graphs.

The construction of finite-length irregular LDPC codes with low error floors is currently an attractive research problem. In particular, for the binary erasure channel (BEC), the problem is to find the elements of selected irregular LDPC code ensembles with the size of their minimum stopping set being maximized. Due to the lack of analytical solutions to this problem, a simple but powerful heuristic design algorithm, the approximate cycle extrinsic message degree (ACE) constrained design algorithm, has recently been proposed. Building upon the ACE metric associated with a cycle in a code graph, we introduce the ACE spectrum of LDPC codes as a useful tool for evaluation of codes from selected irregular LDPC code ensembles. Using the ACE spectrum, we generalize the ACE constrained design algorithm, making it more flexible and efficient. We justify the ACE spectrum approach through examples and simulation results.

An online-browsing support system for research papers has been developed that extracts technical terms from a paper and presents links to useful pages such as those explaining the terms. A method to further use the extracted technical terms is proposed to recommend papers to a user that are related to the paper he or she is browsing. Specifically, the proposed method generates a bipartite graph consisting of papers retrieved by the extracted technical terms, which are called related papers, and technical terms appearing in these related papers. It then ranks the related papers using the HITS algorithm for analyzing the bipartite graph and recommends top-ranked papers to the user. The proposed method was compared with other recommendation methods in terms of effectiveness in an experiment.

Crumpled sheets of paper tend to exhibit specific and complex structure, which is usually described as ridge network by physicists. Existing literature has showed that it is difficult to automate ridge network detection in crumpled paper because of its complex structure. In this paper, we attempt to develop an automatic detection process in terms of our proposed density criterion. We model the ridge network as a weighted graph, where the nodes indicate the intersections of ridges and the edges are the straightened ridges detected in crumpled paper. We construct the weighted graph by first detecting the nodes and then determining the edge weight using the ridge responses. Next, we formulate a graph density criterion to evaluate the detected ridge network. Finally, we propose an edge linking method to construct the graph by maximizing the proposed density criterion. Our experimental results show that, with the density criterion, our proposed node detection together with the edge line linking method could effectively automate the ridge network detection.

Several models have been proposed to represent conditional executions and dependencies among real-time concurrent tasks for the purpose of schedulability analysis. Among them, task graphs with cyclic recurrent behavior, i.e., those modeled with a single source vertex and a period parameter specifying the minimum amount of time that must elapse between successive activations of the source job, allow for efficient schedulability analysis based on the periodicity of the request and demand bound functions (em rbf and dbf). We leverage results from max-plus algebra to identify a recurrent term in rbf and dbf of general task graph models, even when the execution is neither recurrent nor controlled by a period parameter. As such, the asymptotic complexity of calculating rbf and dbf is independent from the length of the time interval. Experimental results demonstrate significant improvements on the runtime for system schedulability analysis.

This study developed a support system that can retrieve papers by using the paper-relationship diagrams (PRDs) that express the relationships among papers. The system has the following functions: (1) users can see various relationships among papers by visualizing of PRDs; and (2) the visualization patterns can be changed dynamically by users own point of view. To implement the dynamic and safe visualization of the PRDs, the authors formalized user requirements for visualization as a set of constraints on the graph drawing problem, and developed an algorithm that visualizes the PRDs based on the graph drawing problem. By the implementation of the dynamic and safe visualization of the PRDs, users can see various relationships among papers by changing their own point of view.

WCFA (Web service interface control flow automata) is enhanced by allowing pre/post-conditions for certain Web service invocations to be declared. The formal definition of WCFA is given. Global behaviors of web service compositions (described by a set of WCFA) are captured by ARG (abstract reachability graph), in which each control point is equipped with a state formula and a call stack. The algorithm for constructing ARG uses a path-sensitive analysis to compute the state formulas. Pre/post-conditions are verified during the construction, where unreachable states are detected and pruned. Assertions can be made at nodes of ARG to express both safety properties and call stack inspection properties. Then a SAT solver is used to check whether the assertions are logical consequences of the state formulas(or/and call stacks).

Maintaining line of sight to a moving object or person over long distances is critical in many applications, e.g., mobile communications, security, surveillance. Determining the best places to position (or build) technologies is difficult because even small changes in the location can greatly affect the so-called viewshed, which is the collection of land areas within line of sight of a given observer. The need for multiple sensors or towers further complicates this problem, as they often need to work cooperatively to achieve the best possible coverage. This study proposes a novel approach that consists of two separate inventions: 1) Introduction of a meaningful measure of quality for coverage to compare competing configurations; and 2) Optimization of that well-defined objective function to find the best suitable sensor parameters for practical applications. Preliminary results suggest unprecedented performance on a wide range of real terrains.

It is proved that the coordination sequence of the graph obtained from a crystal is of quasi-polynomial type, as had been postulated by Grosse-Kunstleve et al. [Acta Cryst. (1996), A52, 879–889] in their study of coordination sequences of zeolites., The coordination sequence of a graph measures how many vertices the graph has at each distance from a fixed vertex and is a generalization of the coordination number. Here it is proved that the coordination sequence of the graph obtained from a crystal is of quasi-polynomial type, as had been postulated by Grosse-Kunstleve et al. [Acta Cryst. (1996), A52, 879–889].

Supplemental Digital Content is Available in the Text. Hub topology is altered in fibromyalgia, and disruption of the excitatory tone within the insula influences hub status and is associated with clinical pain intensity., A critical component of brain network architecture is a robust hub structure, wherein hub regions facilitate efficient information integration by occupying highly connected and functionally central roles in the network. Across a wide range of neurological disorders, hub brain regions seem to be disrupted, and the character of this disruption can yield insights into the pathophysiology of these disorders. We applied a brain network–based approach to examine hub topology in fibromyalgia, a chronic pain condition with prominent central nervous system involvement. Resting state functional magnetic resonance imaging data from 40 fibromyalgia patients and 46 healthy volunteers, and a small validation cohort of 11 fibromyalgia patients, were analyzed using graph theoretical techniques to model connections between 264 brain regions. In fibromyalgia, the anterior insulae functioned as hubs and were members of the rich club, a highly interconnected nexus of hubs. In fibromyalgia, rich-club membership varied with the intensity of clinical pain: the posterior insula, primary somatosensory, and motor cortices belonged to the rich club only in patients with the highest pain intensity. Furthermore, the eigenvector centrality (a measure of how connected a region is to other highly connected regions) of the posterior insula positively correlated with clinical pain and mediated the relationship between glutamate + glutamine (assessed by proton magnetic resonance spectroscopy) within this structure and the patient's clinical pain report. Together, these findings reveal altered hub topology in fibromyalgia and demonstrate, for the first time to our knowledge, a neurochemical basis for altered hub strength and its relationship to the perception of pain.

It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. This paper is a position paper defining the problem and announcing our intention to launch an open effort to define this standard., Comment: 2 pages, IEEE HPEC 2013

A new module, Guided Ligand Replacement (GLR), has been developed in Phenix to increase the ease and success rate of ligand placement when prior protein-ligand complexes are available., The process of iterative structure-based drug design involves the X-ray crystal structure determination of upwards of 100 ligands with the same general scaffold (i.e. chemotype) complexed with very similar, if not identical, protein targets. In conjunction with insights from computational models and assays, this collection of crystal structures is analyzed to improve potency, to achieve better selectivity and to reduce liabilities such as absorption, distribution, metabolism, excretion and toxicology. Current methods for modeling ligands into electron-density maps typically do not utilize information on how similar ligands bound in related structures. Even if the electron density is of sufficient quality and resolution to allow de novo placement, the process can take considerable time as the size, complexity and torsional degrees of freedom of the ligands increase. A new module, Guided Ligand Replacement (GLR), was developed in Phenix to increase the ease and success rate of ligand placement when prior protein–ligand complexes are available. At the heart of GLR is an algorithm based on graph theory that associates atoms in the target ligand with analogous atoms in the reference ligand. Based on this correspondence, a set of coordinates is generated for the target ligand. GLR is especially useful in two situations: (i) modeling a series of large, flexible, complicated or macrocyclic ligands in successive structures and (ii) modeling ligands as part of a refinement pipeline that can automatically select a reference structure. Even in those cases for which no reference structure is available, if there are multiple copies of the bound ligand per asymmetric unit GLR offers an efficient way to complete the model after the first ligand has been placed. In all of these applications, GLR leverages prior knowledge from earlier structures to facilitate ligand placement in the current structure.

In this paper, a bipartite scientific collaboration network is constructed to identify the vital researchers in a scientific research group. There are two kinds of vertices in the network, where one kind of vertices represent the researchers and the other ones illustrate the papers. The edges are connected to the vertices which belong to two different classes. Through the bipartite network, a model is developed to evaluate the researcher's importance within the research group by introducing four indices. Such indices are relative ranking value, professional title, paper quality and co-author importance, respectively. Accordingly, two algorithms are developed, one is to compute the impact probability between papers and researchers, and the other one aims to calculate the cooperation probability between researchers. Evaluation results show the proposed model works well by comparing with other evaluating indices.

We introduce a metric in graph search and demonstrate its application for segmenting retinal optical coherence tomography (OCT) images of macular pathology. Our proposed “adjusted mean arc length” (AMAL) metric is an adaptation of the lowest mean arc length search technique for automated OCT segmentation. We compare this method to Dijkstra’s shortest path algorithm, which we utilized previously in our popular graph theory and dynamic programming segmentation technique. As an illustrative example, we show that AMAL-based length-adaptive segmentation outperforms the shortest path in delineating the retina/vitreous boundary of patients with full-thickness macular holes when compared with expert manual grading.

Motivation: While protein secondary structure is well understood, representing the repetitive nature of tertiary packing in proteins remains difficult. We have developed a construct called the relative packing group (RPG) that applies the clique concept from graph theory as a natural basis for defining the packing motifs in proteins. An RPG is defined as a clique of residues, where every member contacts all others as determined by the Delaunay tessellation. Geometrically similar RPGs define a regular element of tertiary structure or tertiary motif (TerMo). This intuitive construct provides a simple approach to characterize general repetitive elements of tertiary structure. Results: A dataset of over 4 million tetrahedral RPGs was clustered using different criteria to characterize the various aspects of regular tertiary structure in TerMos. Grouping this data within the SCOP classification levels of Family, Superfamily, Fold, Class and PDB showed that similar packing is shared across different folds. Classification of RPGs based on residue sequence locality reveals topological preferences according to protein sizes and secondary structure. We find that larger proteins favor RPGs with three local residues packed against a non-local residue. Classifying by secondary structure, helices prefer mostly local residues, sheets favor at least two local residues, while turns and coil populate with more local residues. To depict these TerMos, we have developed 2 complementary and intuitive representations: (i) Dirichlet process mixture density estimation of the torsion angle distributions and (ii) kernel density estimation of the Cartesian coordinate distribution. The TerMo library and representations software are available upon request. Contact: jtsai@pacific.edu Supplementary information: Supplementary data are available at Bioinformatics online.

We present a new, first-of-its-kind, fully automated computational tool MOTIF-EM for identifying regions or domains or motifs in cryoEM maps of large macromolecular assemblies (such as chaperonins, viruses, etc.) that remain conformationally conserved. As a by-product, regions in structures that are not conserved are revealed: this can indicate local molecular flexibility related to biological activity. MOTIF-EM takes cryoEM volumetric maps as inputs. The technique used by MOTIF-EM to detect conserved sub-structures is inspired by a recent breakthrough in 2D object recognition. The technique works by constructing rotationally invariant, low-dimensional representations of local regions in the input cryoEM maps. Correspondences are established between the reduced representations (by comparing them using a simple metric) across the input maps. The correspondences are clustered using hash tables and graph theory is used to retrieve conserved structural domains or motifs. MOTIF-EM has been used to extract conserved domains occurring in large macromolecular assembly maps, including as those of viruses P22 and epsilon 15, Ribosome 70S, GroEL, that remain structurally conserved in different functional states. Our method can also been used to build atomic models for some maps. We also used MOTIF-EM to identify the conserved folds shared among dsDNA bacteriophages HK97, Epsilon 15, and ô29, though they have low-sequence similarity. Contact: mitul@cs.stanford.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Graph mining algorithms that seek to find interesting structure in a graph are compelling for many reasons but may not lead to useful information learned from the data. This position paper explores the current graph mining approaches and suggests why certain algorithms may provide misleading information whereas others may be just what is needed. In particular, algorithms that ignore the rich set of node and edge properties that are prevalent in many real-world graphs are in danger of finding results based on the wrong information.

This work introduces an information-theoretic lower bound on the number of fundamental cycles for bipartite graphs of low-density parity-check (LDPC) code ensembles. This information-theoretic bound is expressed in terms of the achievable gap to capacity when the transmission of the code ensemble takes place over a memoryless binary-input output-symmetric (MBIOS) channel. The bound shows quantitatively the necessity of cycles in bipartite graphs which represent good LDPC code ensembles. More explicitly, it shows that the number of fundamental cycles should grow at least like log 1/e where e designates the gap in rate to capacity, hence, it is unbounded as the gap to capacity vanishes. For the derivation of this bound, a new information-theoretic lower bound on the average right degree, which also behaves like log 1/e, is derived. The interested reader is referred to the full paper version [9].

We give graph-theoretic formalization of origami, the art of paper folding. Starting from the abstract origami system, we model origami construction as are write sequence of abstract origami's. To reason about the entire origami construction for the computational purposes, we define a labeled hypergraph for origami and give the abstraction of origami fold as a set of algebraic graph rewrite rules. We give detailed description of the fold operation in terms of graph rewriting. The graph-theoretic formalism enables us to reason in two separate domains of discourse, i.e. pure combinatoric domain and geometrical domain R2.

In recent years, the peer-to-peer paradigm has gained momentum in several application areas: file-sharing and VoIP applications have been able to attract millions of end users, while large-scale distributed computing frameworks, including the Grid, have proven their ability of attacking large scientific problems. We believe, however, that the potential of the P2P approach has not been completely exploited yet. The goal of this position paper is to propose another scientific area where the P2P cooperation paradigm could be profitably adopted: network analysis, i.e. the mathematical characterization of the main graph-theoretic properties of a large-scale network. We discuss the potential issues that must be confronted with when a decentralized approach to network analysisis taken, and we propose a preliminary research plan.

With modern optical imaging methods, it is possible to map structural and functional connectivity. Optical imaging studies that aim to describe large-scale neural connectivity often need to handle large and complex datasets. In order to interpret these datasets, new methods for analyzing structural and functional connectivity are being developed. Recently, network analysis, based on graph theory, has been used to describe and quantify brain connectivity in both experimental and clinical studies. We outline how to apply regional, functional network analysis to mesoscale optical imaging using voltage-sensitive-dye imaging and channelrhodopsin-2 stimulation in a mouse model. We include links to sample datasets and an analysis script. The analyses we employ can be applied to other types of fluorescence wide-field imaging, including genetically encoded calcium indicators, to assess network properties. We discuss the benefits and limitations of using network analysis for interpreting optical imaging data and define network properties that may be used to compare across preparations or other manipulations such as animal models of disease.

This short paper uses grid graphs and other concepts from elementary graph theory to enumerate the number of words contained in a crossword puzzle.

SUMMARY OF COMMUNICATIONS stone with dropstone on the roche moutonnee from Salto,to cross-bedded and “convoluted” sandstone beds in theriver channel, toward NW. They are interpreted as proxi-mal and distal glacial facies respectively, associated withan advance and retreat of the glacier.Those rocks are overlain by an extensive andthick shale (pellitic) section that may representthe deposit of a marine transgressive post-glacialepisode. Dropstones in the shale denote presenceof icebergs and permanence of glacial influence dur-ing sedimentation. — ( December 14, 2001 ). ∗ Supported by FAPESP 00/6039-6.**E-mail: jbviviani@aol.com MULTIDISCIPLINARY THEMES Alcides N. Sial and Valderez P. Ferreira(Organizers) EFFICIENT ALGORITHMS FOR PACKING BOXESINTO CONTAINER Sostenes L. S. Lins Departamento de Matematica, CCEN, Universidade Federalde Pernambuco, Recife, PE, Brazil. The problem of packing boxes into bigger boxes(containers) is a practical problem which, by its economi-cal significance, deserves a serious and inspired scientificapproach. From a strictly mathematical point of view, itis an incredibly challenging problem which badly needsgood heuristics to solve it. We have been involved in try-ing to find such heuristics since 1997. These heuristicsuse new concepts in graph theory (the tets), in data struc-ture (the phormas), and used some classical algorithms astopological sorting and the coding of combinatorial ob-jects to approach real world packing problems. A distin-guished feature of our approach is the visual treatment ofthe spatial packing: we produce a sequence of homoge-neous increments (a loading plan) in the packings whichmakes it easy to visualize and to actually produce the so-lutions found.We have produced a set of effective heuristics fordealing with real world box packing problems: we permitvarious types of boxes, various types of containers, de-mand requirements on the boxes and the information onwhichboxtypescanchangeitsverticaldirection. Theim-plementation of our heuristics produces very good pack-ings as compared with non-scientific ones: typically weput 7% to 12% more boxes. The full paper related to thesematters is scheduled to be published this year (2002) inthe European Journal of Operations Research.A computer package named ExpedPlex is under de-velopment, where the pertinent algorithms are being effi-ciently implemented. — (

Enhancement of reliability is critical in designing and planning of distribution systems that operate efficiently and with minimal interruption to customer loads, because they use various types of resources and technologies to meet energy demand such as distributed generation (DG). DG is expected to play an enhanced role in emerging power systems. One of the major issues in the planning stage for future distribution systems is the optimal design of multiple micro-grids (MMGs) in distribution systems. This paper describes a novel method for clustering a traditional passive distribution system into a cluster of Multiple Micro Grids (MMGs). Clustering a traditional distribution system into MMGs provides numerous merits for costumers and distribution system operators, including a local control strategy to minimise interaction between various MGs, local reactive power compensation to prevent fault propagation, minimise power losses, and ultimately improving system reliability. In each MG area, DGs and reactive power resources are deployed to reach the acceptable level of reliability. The proposed clustering procedure is based on a weighted graph partitioning approach, with the weights representing the apparent power of the lines. Various reliability tests were performed in order to determine the best location for DG penetration in the distribution system. The passive distribution system becomes an active system after DG penetration. As a result, planners must investigate the influence of DG on distribution system reliability. The aim of this paper is to investigate the impact of DG on distribution system reliability. The results on the test distribution system demonstrate the proposed method’s performance and effectiveness.

Different from the typical topology derivation of power electronics converters (PECs) depending on manual effort, this paper aims to explore a programmable method based on graph theory for multi-port dc-dc converters with reduced switches. By mathematically modelling converters with graph theory and transforming their working criterions into the corresponding graph constraints, the topology derivation can be automatically and conveniently solved with the aid of computer program. In the paper, principle of the proposed graph theory based programmable method is firstly introduced in detail. Then, it is employed to derive multi-port dc-dc converters with reduced switches and a diversity of new topologies are simultaneously excavated, among which a favorable one is selected to be theoretically introduced and experimentally verified. The proposed method remains relatively simple with the increasing number of ports, as the graph constraints of working criterions are almost the same for different number of ports. More importantly, because PECs can be essentially regarded as graphs with different components and their connecting relationships, the proposed method is applicable for many various converters.

In this paper, the asynchronous event-triggered control mechanism (AETCM) is introduced to the set stabilization problem of k-valued logical control networks (KVLCNs). Under the proposed AETCM, each node of the system updates its event-triggered instants independently. In this case, how to coordinate the behaviors of various nodes is a challenge for us. As to this paper, we firstly transform the set stabilization problem of KVLCNs into the shortest path problem in graph theory and then construct a weighted directed hypergraph. Next, an improved heap-optimized Dijkstra algorithm is designed for the optimal asynchronous event-triggered controller. Furthermore, we study set stabilization of KVLCNs with time delays. In terms of applications, how to flexibly adapt AETCM to specific models is a difficult problem. In this paper, as applications, consensus of finite-field networks (FFNs) with arbitrary communication delays and synchronization of KVLCNs are investigated. Finally, two numerical examples are shown to illustrate the effectiveness of the proposed algorithms.

This paper is concerned with the stabilization of complex-valued stochastic coupled systems possessing multiple time delays and regime-switching jump diffusion (RSJD) via periodically intermittent control. Moreover, most of the existing results about RSJD are considered in real-valued cases, which is extended to complex-valued cases in this paper. Combining the Lyapunov method with the graph theory, some sufficient conditions can be obtained, which reflect that the realization of stability is related to stochastic disturbance strength, coupling strength and control rate. Additionally, the theoretical results are applied to complex-valued stochastic coupled oscillators with multiple time delays and RSJD. In the end, some simulation results are presented to demonstrate the validity and availability of the theoretical results.

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results

PurposeThe purpose of this paper is to develop a framework for the safety performance measurement of belt conveyor systems.Design/methodology/approachA structural methodology of graph theory and matrix approach is used for developing a framework for safety performance measurement of belt conveyor systems.FindingsThe development of a framework for safety performance measurement of belt conveyor systems is essential for ensuring plant safety. For this, safety performance factors, including design and operating contextual factors of belt conveyor systems, are identified. The factors along with their interrelations are modeled using digraph. An equivalent matrix of the digraph provided safety performance function (SPF) of belt conveyor systems, leading to the development of a safety performance index (SPI).Practical implicationsThe developed framework will enable the designers for evaluating and comparing alternative designs of conveyor systems from the safety viewpoint. The plant operators can make inferences from the SPI to identify the weak contextual factors in the plant and develop action plans for its mitigation.Originality/valueThe paper is novel and employs graph theory and matrix approach for safety performance measurement. The methodology helps in the quantitative evaluation of the safety performance of belt conveyor systems.

Network science is a widely studied subject and graph theory has a major role in it. This paper studies connectivity status of vertices in a fuzzy graph. This paper adopt connectivity status to build up the status sequence related to a fuzzy graph. Results on connectivity status and status sequence of different structures are obtained. On the basis of connectivity status, vertices of a fuzzy graph can be classified into connectivity status enhancing vertices, connectivity status reducing vertices and connectivity status neutral vertices. Connectivity status analysis of vertices is also carried out. Algorithms related to these concepts are provided and an application related to bandwidth allocation problem in networking is proposed.

This paper is concerned with the almost sure exponential synchronization of a multilayer network which is set up on a non-strongly connected digraph that can be classified into several layers by Tarjan’s algorithm. Note that, in the multilayer network, white-noise-based time-varying coupling and drift term coupling are proposed to simulate two kinds of coexisting distinguishable interactions between vertices. We develop a normal analytical framework for studying synchronization of the multilayer network. Firstly, via aperiodically intermittent pinning noises, synchronization of vertices situated on the first layer is achieved in the layered network. Secondly, under the impact of the white-noise-based time-varying coupling in diffusion term, synchronization of the vertices located in other layer networks is developed with the support of synchronization for the pinned vertices. Employing Lyapunov method, graph theory and stochastic analysis technique, a criterion of almost sure global exponential synchronization is obtained. By adopting the concepts of average noise control rate and average noise control period proposed recently, we lessen the conservativeness of the conditions restricted on aperiodically intermittent noise control to optimize our results. Furthermore, an application to a class of Chua’s circuits is exhibited in detail. In the end, we provide a numerical example to verify the validity of the theoretical results.

The Graceful Tree Conjecture stated by Rosa in the mid 1960s says that every tree can be gracefully labelled. It is one of the best known open problems in Graph Theory. The conjecture has caused a great interest in the study of gracefulness of simple graphs and has led to many new contributions to the list of graceful graphs. However, it has to be acknowledged that not much is known about the structure of graceful graphs after 55 years. Our paper adds an infinite family of classes of graceful graphs to the list of known simple graceful graphs. We introduce classes of \(k\)-enriched fan graphs \(kF_n\) for all integers \(k, n\ge 2\) and we prove that these graphs are graceful. Moreover, we provide characterizations of the \(k\)-enriched fan graphs \(kF_n\) among all simple graphs via Sheppard's labelling sequences introduced in the 1970s, as well as via labelling relations and graph chessboards. These last approaches are new tools for the study of graceful graphs introduced by Haviar and Ivaska in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a nice visualization of graceful labellings. We close our paper with an open problem concerning another infinite family of extended fan graphs.

Graph theory is a branch of mathematics that allows for the characterization of complex networks, and has rapidly grown in popularity in network neuroscience in recent years. Researchers have begun to use graph theory to describe the brain networks of individuals with brain tumors to shed light on disrupted networks. This systematic review summarizes the current literature on graph theoretical analysis of magnetic resonance imaging data in the brain tumor population with particular attention paid to treatment effects and other clinical factors. Included papers were published through June 24th, 2020. Searches were conducted on Pubmed, PsycInfo, and Web of Science using the search terms (graph theory OR graph analysis) AND (brain tumor OR brain tumour OR brain neoplasm) AND (MRI OR EEG OR MEG). Studies were eligible for inclusion if they: evaluated participants with a primary brain tumor, used graph theoretical analyses on structural or functional MRI data, MEG, or EEG, were in English, and were an empirical research study. Seventeen papers met criteria for inclusion. Results suggest alterations in network properties are often found in people with brain tumors, although the directions of differences are inconsistent and few studies reported effect sizes. The most consistent finding suggests increased network segregation. Changes are most prominent with more intense treatment, in hub regions, and with factors such as faster tumor growth. The use of graph theory to study brain tumor patients is in its infancy, though some conclusions can be drawn. Future studies should focus on treatment factors, changes over time, and correlations with functional outcomes to better identify those in need of early intervention.

A Moore (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and outdegree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r, z, k) for mixed graphs. When the order of G is close to M(r, z, k) vertices, we refer to it as an almost Moore graph. The first part of this paper is a survey about known Moore (and almost Moore) general mixed graphs that turn out to be Cayley graphs. Then, in the second part of the paper, we give new results on the bipartite case. First, we show that Moore bipartite mixed graphs with diameter three are distance-regular, and their spectra are fully characterized. In particular, an infinity family of Moore bipartite (1, z, 3)-mixed graphs is presented, which are Cayley graphs of semidirect products of groups. Our study is based on the line digraph technique, and on some results about when the line digraph of a Cayley digraph is again a Cayley digraph. This research has been partially supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RBI00.

There have been many recent fears of severe house-price decreases in some provinces in China causing a nationwide collapse of the housing market. Therefore, this paper aims to clarify the linkage structure of China's housing market and its risk contagion routes. Given monthly data of provincial housing and stock-market capital returns from 2001M01 to 2019M12, on the basis of graph theory, this paper first explores the linkage structure of provincial housing markets. Relying on the linkage structure, this paper then simulates the effect of unexpected negative shocks from the stock market on the probabilities of a housing-market collapse based on the epidemic model. The results show that (i) consistently with practical evidence, the probability of housing-market collapse is relatively high in the southwest of China and (ii) reducing housing-market linkage, such as through a blocking mechanism, to prevent collapse is helpful.

$$Q$$ -neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real-life problems. Graph theory has now become a major branch of applied mathematics, and it is generally regarded as a branch of combinatorics. In this research paper, we introduce the concept of $$Q$$ -neutrosophic soft graphs (Q- $${\mathcal{N}\mathcal{S}}Gs$$ ) that are made by combining $$Q$$ -neutrosophic soft sets with graphs and describe different methods of their construction. A $$Q$$ -neutrosophic soft graphs model is very much efficient for such real word problems which can construct more precise, flexible, and comparable system as compared to the classical, fuzzy and neutrosophic graph models. In this paper, we first define the concept of $$Q$$ -neutrosophic soft graph (Q- $${\mathcal{N}\mathcal{S}}G$$ ). In this paper we introduce the concept of $$Q$$ - $${\mathcal{N}\mathcal{S}}G$$ , strong Q- $${\mathcal{N}\mathcal{S}}G$$ , union and intersection of Q- $${\mathcal{N}\mathcal{S}}G$$ . The new concept is called Q- $${\mathcal{N}\mathcal{S}}G$$ multicriteria decision-making method (Q- $${\mathcal{N}\mathcal{S}}GMCDM$$ for short). Finally, we describe the utility of the $$Q$$ -neutrosophic soft graph and its applications in communication network and decision-making problem.

The computation of the optimal path is one of the critical problems in graph theory. It has been utilized in various practical ranges of real world applications including image processing, file carving and classification problem. Numerous techniques have been proposed in finding optimal path solutions including using ant colony optimization (ACO). This is a nature-inspired metaheuristic algorithm, which is inspired by the foraging behavior of ants in nature. Thus, this paper study the improvement made by many researchers on ACO in finding optimal path solution. Finally, this paper also identifies the recent trends and explores potential future research directions in file carving.

Recently, the intelligent traffic control system and its uncertainty analysis are considered one of the hot spots for utilizing the available techniques. It became more essential when the automatic car, electric vehicle, and other smart cars have introduced the transportation. To control the traffic accident and smooth road services an intelligent traffic control system required. It will be also useful in decreasing the time, reaction time, and efficiency of traffic. However, the problem arises while characterization of true, false or uncertain regions of traffic flow and its future approximation. To deal with this issue some available mathematical technique for traffic flow using rough set, fuzzy rough set, and its extension with the neutrosophic set is discussed in this paper. Some of the papers related to graphical visualization of traffic flow is also discussed for further improvement. The rough set theory can be useful for dealing the uncertain, incomplete, and indeterminate data set. Hence, the hybridization of the neutrosophic set and rough can be considered one of the efficient tools for intelligent traffic control and its approximation via automatic red, green and yellow lights. This paper tried to provide an overview of each available technique to solve the traffic problem. It is hoped that the proposed study will be helpful for several researchers working on traffic flow, traffic accident diagnosis, and its hybridization as future research