Graph Theory Methods Research Articles

Brain network construction and analysis for patients with mild cognitive impairment and Alzheimer's disease based on a highly-available nodes approach.

IntroductionUsing brain network and graph theory methods to analyze the Alzheimer's disease (AD) and mild cognitive impairment (MCI) abnormal brain function is more and more popular. Plenty of potential methods have been proposed, but the representative signal of each brain region in these methods remains poor performance.MethodsWe propose a highly‐available nodes approach for constructing brain network of patients with MCI and AD. With resting‐state functional magnetic resonance imaging (rs‐fMRI) data of 84 AD subjects, 81 MCI subjects, and 82 normal control (NC) subjects from the Alzheimer's Disease Neuroimaging Initiative Database, we construct connected weighted brain networks based on the different sparsity and minimum spanning tree. Support Vector Machine of Radial Basis Function kernel was selected as classifier.ResultsAccuracies of 74.09% and 77.58% in classification of MCI and AD from NC, respectively. We also performed a hub node analysis and found 18 significant brain regions were identified as hub nodes.ConclusionsThe findings of this study provide insights for helping understanding the progress of the AD. The proposed method highlights the effectively representative time series of brain regions of rs‐fMRI data for construction and topology analysis brain network.

A Fast Terminal Matching Method for Interference Coordination Based on Wavelet Transform and Graph Theory in Ultra-Dense Multi-Cell Scenarios

The intensive deployment of cells in a wireless communication system may significantly increase the network capacity, but it may cause more complex and severe inter-cell interference. In order to effectively coordinate the interference, terminals in different cells are matched with the purpose of avoiding severe interference, called terminal matching, and a fast method is proposed in this article for multi-cell scenarios. By constructing a fully weighted graph of all the base stations with interferences as the weights, the minimum spanning tree method in graph theory is used to identify the coordination relationship among all the cells, and multiple coordination pairs can be obtained. For each coordination pair, terminal matching is modeled as a two-dimensional assignment problem between the coefficients after wavelet decomposition and Hungarian algorithm is applied to obtain their optimal match. Wavelet transform is used to extract the scale transformation coefficients describing the terminal features in each single cell, so that the optimization process can be accelerated because the amount of these coefficients is dramatically reduced after several layers of wavelet decomposition. The minimum Hamilton path method in graph theory is used to rank the terminals in each cell based on their key features, so that the coefficients lose as minimum useful information as possible during wavelet decomposition. Simulation results show that the performance of the proposed method reaches approximately the optimal matching obtained by traversing all the coordination possibilities among all the cells. Compared with the simulated annealing algorithm, the performance loss in terms of system spectral efficiency is only about 2%, but the proposed method requires only less than one thousandth of its computational time.

Методика обоснования тестовых информационно -технических воздействий, обеспечивающих рациональную полноту аудита защищенности объекта критической информационной инфраструктуры

Relevance. Security issues of information systems in critical infrastructure objects become important now. However, current tasks of information security audit of critical infrastructure objects are mainly limited to checking them for compliance with requirements of standards and documents. With this approach to the audit, security of these objects from real attacks by hackers remains unclear. Therefore, objects are subjected to a testing procedure, namely, penetration testing, in order to objectively verify their security. An analysis of publications in this area shows that there is not mathematical approaches to selection of test cyber attacks for penetration testing set. The goals of the paper is to form the selection method of test cyber attacks that ensure the rational completeness of the security audit of a critical information infrastructure object. Research methods. Methods of probability theory and mathematical statistics, methods of graph theory and set theory are used in the paper to achieve the research goals. Results. The Select Method of test cyber attacks for security audit of a critical information infrastructure object with rational completeness is presented in the paper. This method formalizes the selection process in the form of a two-stage procedure. At the first stage, based on the topological model of the object testing, a set of testing paths is formed, and these paths are ordered by the degree of weight increase. The path weight is the efficiency/cost indicator that takes in account the test resource for realized of a test cyber attack, the vulnerability of an object element, and the level of damage caused to the element by this test cyber attack. At the second stage of the method, from an ordered set of test paths are selected of such, which would ensure the maximization of the whole absolute cost of the detected damage, within the limits on the resource making of test cyber attacks. It is using of this method in audit practice will allow us to justify the most effective test cyber attacks according to the “efficiency/cost” criterion, as well as to form test sets that will ensure the rational completeness of the audit of the critical infrastructure object.

Graph theory in paediatric epilepsy: A systematic review.

Graph theoretical studies have been designed to investigate network topologies during life. Network science and graph theory methods may contribute to a better understanding of brain function, both normal and abnormal, throughout developmental stages. The degree to which childhood epilepsies exert a significant effect on brain network organisation and cognition remains unclear. The hypothesis suggests that the formation of abnormal networks associated with epileptogenesis early in life causes a disruption in normal brain network development and cognition, reflecting abnormalities in later life. Neurological diseases with onset during critical stages of brain maturation, including childhood epilepsy, may threaten this orderly neurodevelopmental process. According to the hypothesis that the formation of abnormal networks associated with epileptogenesis in early life causes a disruption in normal brain network development, it is then mandatory to perform a proper examination of children with new-onset epilepsy early in the disease course and a deep study of their brain network organisation over time. In regards, graph theoretical analysis could add more information. In order to facilitate further development of graph theory in childhood, we performed a systematic review to describe its application in functional dynamic connectivity using electroencephalographic (EEG) analysis, focussing on paediatric epilepsy.

The main aspects of creating a system of data mining on the status of patients with Parkinson’s disease

This article describes an approach to the collection and preprocessing of data received from mobile phones for the purpose of their further processing by data mining methods, in particular using neural networks. This is a comprehensive work that was carried out using graph theory methods; parallel computing, set theory, databases, fuzzy logic methods and neural networks, mobile application design methods. The most important results of this work, which are presented in this article, are developed methods for accelerating data processing in relational and NoSQL databases, the architecture of a system for monitoring the status of patients with Parkinson’s disease using mobile technologies; modules for a mobile phone for collecting patient status data; and modules based on neural networks for classifying the status of patients with Parkinson’s disease.

Интеллектуальная система помощи туристу: IT-сервис создания персонального туристического маршрута по КБР

The aim of the study is to develop an automated system for generating tourist routes in the Kabardino-Balkarian Republic using modern information technologies. The article is devoted to a comprehensive analysis of the use of IT technologies in tourism, as well as the systematization of electronic data on the recreational complex of the CBD. The subject of the study is the IT-system of tourist assistance. To build routes between sights, graph theory methods are used, and an expert system is used to select the optimal route at the request of the user. This paper considers ways to generate up-to-date information for comfortable tourism based on open electronic resources. The scientific novelty of the study is the development of an intelligent tourist assistance system in the region, as well as a mobile application with similar capabilities. As a result of the study, conclusions will be obtained that allow to develop an IT service for creating a personal tourist route along the CBD, which will meet modern requirements and exceed existing analogues.

Моделирование APT-атак, эксплуатирующих уязвимость Zerologon

Purpose: the need to assess the effectiveness of the security systems for significant objects of critical information infrastructure determines the need to develop simple and adequate mathematical models of computer attacks. The use of mathematical modeling methods in the design of security system of significant object allows without significant cost and impact on the functioning of the object to justify the requirements to the system as a whole or its individual parts. The purpose of the present paper is to develop a model of the process of multistage targeted computer attack that exploits the Zerologon vulnerability, based on the representation of the attack by a Markov random process with discrete states and continuous time. Methods: methods of Markov process theory, probability theory, computational mathematics and graph theory are used in the model to formalize the attack. Novelty: application of methods of computational mathematics for functional analysis of the results of Kolmogorov’s system of equations allows to solve the problem of maximizing the time of stable operation of critical information infrastructure during computer attacks against it, using the known methods of analysis of continuous functions. Result: formulated a general statement of the problem of modeling the process of a multistage targeted computer attack using a system of Kolmogorov equations, describing the probabilities of being in conflict states of the security system with the intruder. By the Adams method implemented in Mathcad environment, numerical solutions depending on time were obtained. We introduce a security system performance index as a ratio of probability of triggering the security system and blocking intruder’s actions during the attack to the probability of successful completion of the attack. We give an example of research of computer attack realization in a typical information infrastructure, including a corporate network with domain architecture and an automated control system of some technological process. 1 For the considered example defined the optimal values of time parameters of security system. When implementing protective measures with reasonable probabilistic-time characteristics proved an increase in time of stable operation of critical information infrastructure from 11 to 189 hours.

Debugging procedure of the replica class errors in the production knowledge bases

The problem of detecting errors in the production knowledge bases of knowledge - oriented information systems that arise at the stage of formation of the knowledge base by experts is considered. It was determined that such errors related to the conflicting opinions of experts and/or limited (imperfect) description of the subject area. There was analyzed approaches for their debugging. Ways to improve existing approaches for debugging static replica errors was shown. Possible ways of applying the obtained solutions to debug errors "contradiction", "redundancy", "incompleteness" was shown. Solutions for expanding the formalized definition of static error of the production network, considering the requirements for the accuracy of information was suggested. The issues of the influence of errors of the “replica” class on the results of derivation according to the rules of the production knowledge base was considered. The possibility of applying the methods of graph theory to solve the problem of error reduction of the "replica" class is proved. An algorithmic structure for detecting and debugging errors of this class has been developed. It allows, in contrast to existing solutions, to detect duplicate vertices at each rank of the graph to which the production knowledge base is reduced. Software implementation for detection and debugging of static errors of incomplete, partial, and complete duplication was developed, using recursion, which allows to reduce the requirements for preparing an array of input data for processing. The obtained solutions meet the requirements of DSTU ISO / IEC 9126, DSTU ISO / IEC 14598 and consider the requirements of the series of standards Software Quality Requirements and Evaluation as the values of the vertices of the graph of the event tree. During problem solving process specifics of the LMS operation are considered, first of all formalizing possibilities in the various aspects of knowledge (aletic, dissociative, causal, diontic) and ensuring a given level of efficiency in finding solutions.

Linear transformations of tropical matrices preserving the cyclicity index

Abstract We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open to characterize those.

Study on classification and identification of depressed patients and healthy people among adolescents based on optimization of brain characteristics of network

To enhance the accuracy of computer-aided diagnosis of adolescent depression based on electroencephalogram signals, this study collected signals of 32 female adolescents (16 depressed and 16 healthy, age: 16.3 ± 1.3) with eyes colsed for 4 min in a resting state. First, based on the phase synchronization between the signals, the phase-locked value (PLV) method was used to calculate brain functional connectivity in the θ and α frequency bands, respectively. Then based on the graph theory method, the network parameters, such as strength of the weighted network, average characteristic path length, and average clustering coefficient, were calculated separately ( P < 0.05). Next, using the relationship between multiple thresholds and network parameters, the area under the curve (AUC) of each network parameter was extracted as new features ( P < 0.05). Finally, support vector machine (SVM) was used to classify the two groups with the network parameters and their AUC as features. The study results show that with strength, average characteristic path length, and average clustering coefficient as features, the classification accuracy in the θ band is increased from 69% to 71%, 66% to 77%, and 50% to 68%, respectively. In the α band, the accuracy is increased from 72% to 79%, 69% to 82%, and 65% to 75%, respectively. And from overall view, when AUC of network parameters was used as a feature in the α band, the classification accuracy is improved compared to the network parameter feature. In the θ band, only the AUC of average clustering coefficient was applied to classification, and the accuracy is improved by 17.6%. The study proved that based on graph theory, the method of feature optimization of brain function network could provide some theoretical support for the computer-aided diagnosis of adolescent depression.

Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects

Abstract This paper investigates the robust exponential stability (RES) issue for fractional-order coupled quaternion-valued neural networks (FCQNNs) with parametric uncertainties and impulsive effects. According to the rules of quaternion algebra and its properties, a new fractional-order inequality is built, which greatly generalizes the existing fractional-order inequality in the real domain. On the basis of quaternion inequality technique, newly established inequality, together with algebraic graph theory and iterative method, several criteria for easy verification are presented, which depend on not only impulsive gain and maximum impulsive interval but also the scale of the controlled vertices. Furthermore, the convergence rate of the considered FCQNN is also estimated. Finally, numerical results are given to substantiate our theoretical criteria.

Brain Resilience: The Effect of White Matter Disease on Brain Networks in Cognitively Normal Older Adults

Brain pathologies are increasingly understood to confer mobility risk, but the malleability of functional brain networks may be a mechanism for mobility reserve. In particular, white matter hyperintensities (WMH) are strongly associated with mobility and alter functional network connectivity. To assess the potential role of brain networks as a mechanism of mobility reserve, 116 participants with MRI from the Brain Networks and Mobility Function (B-NET) were categorized into 4 groups based on median splits of SPPB scores and WMH burden: Expected Healthy (EH: low WMH, SPPB>10, N=45), Expected Impaired (EI: high WMH, SPPB10, N=24), Unexpected Impaired (EI: low WMH, SPPB<10, N=10) and Unexpected Unhealthy (UH: low WMH, SPPB<10, N=37). Functional brain networks were calculated using graph theory methods and white matter hyperintensities were quantified with the Lesion Segmentation Toolbox (LST) in SPM12. Somatomotor cortex community structure (SMC-CS) was similar between UH and EH with both having higher consistency than EI and UI. However, UH displayed a unique increase in second-order connections between the motor cortex and the anterior cingulate. It is possible that this increase in connections is a signal of higher reserve or resilience in UH participants and may indicate a mechanism of compensation in regards to mobility function and advanced WMH burden. These data suggest functional brain networks may be a mechanism for mobility resilience in older adults at mobility risk due to WMH burden.

Using graph theory to detect ageing and Alzheimer’s disease‐ related changes in the structure of cognitive networks

AbstractBackgroundIn accordance with the physiological networks which underlie it, human cognition is characterised by both segregation and interdependence of a number of cognitive domains. Cognition itself, therefore, constitutes a network, the organisation of which may be quantifiable using methods of graph theory. The present study aimed to exploit graph theory methods to assess changes in cognitive profiles throughout healthy ageing and further interrogate how such profiles may differ in the presence of pathology.MethodA comprehensive neuropsychological test battery was performed in 6 participant groups; 3 groups of healthy adults split into the age ranges 18‐39 (N 75), 40‐64 (N 75) and 65 and over (N 70) and 3 patient groups including adults with amnestic mild cognitive impairment (MCI, N 75), non‐amnestic MCI (N 31) and Alzheimer’s type dementia (N 60). Partial correlations were performed on standardised scores between 16 cognitive tests. A binarised adjacency matrix was then created for each group in which significant correlations (p &lt;.05) were retained as the connections or edges and each cognitive test represented a node. Network analysis measures were then applied to each matrix using the Brain Connectivity Toolbox.ResultNetwork wide clustering and local efficiency of nodes showed an increase between the stages of normal ageing and this was considerably exacerbated by the presence of disease. Conversely, average betweenness centrality first showed an increase between the young and middle‐aged groups but was reduced compared to middle‐aged in the healthy older group. This reduction appeared to be again exacerbated within patients. These findings were particularly apparent between patients and healthy adults in tests of memory function.ConclusionWhile whole network approaches have become a staple of functional neuroimaging, such techniques have rarely been applied to the structure of cognition itself. Here, it has been demonstrated that the organisation of our cognitive networks is influenced not only by the ageing process but is further significantly altered by the presence of disease. Further investigation in this area may provide a novel approach for quantifying the effects of disease on cognitive function and could contribute to the development of sophisticated diagnostic tools in the future.

A Method of Descriptions for Graph Labelings

Labeling the graph is the most essential method in graph theory, we develop a rule for some graph labeling instead of labeling functions of a graph elements which arrives the same result as in the graph labeling. Labeling is an allottment of digits to the vertex (dots) or edge (lines) or the two under certain conditions, most popular labeling method trace their origin called functions (labeling). Labeled graphs provide mathematical models called mathematical functions f : G → X. The graph labeling of a graph variables are used in various area such as resolutions in the subfield of matrix theory and cryptography to mention a few. Here we develop a rule graph labeling and it is very useful in the field of coding theory.

Analysis of morphological changes of rural settlement patterns after World War II in the metropolitan area of Łódź using a graph theory based method

Abstract This research concerns the complex problem of morphological transformations of villages in the intra-urban area (i.e. settlements incorporated into acity), as well as the suburban area, using the example of the metropolitan area of Łódź, Poland. The main aim of the research was to analyse the diversity of selected rural settlements and their spatial changes after World War II.. The study was based on preserved historical maps and today’s plans. An analysis of morphological changes of selected villages was conducted using graph theory methods. It was noticed that the graph development index should depend on the relative number of edges in relation to the number of nodes and the number of graph cycles, which express the degree of complexity of a settlement unit. Three main groups of villages, characterised by different scales of morphological transformations, were distinguished as a result of the study. Settlement units with orthomorphic transformations, where all spatial modifications were mainly additive and the initial layouts have been preserved almost completely, represent the first group of villages. The second group is composed of units with semi-metamorphic transformations, where the spatial reorganization was significant, but not total. The third group includes villages with metamorphic changes, where the initial layouts have been totallytransformed.

Altered Brain Structural Networks in Patients with Brain Arteriovenous Malformations Located in Broca's Area.

Focal brain lesions, such as stroke and tumors, can lead to remote structural alterations across the whole-brain networks. Brain arteriovenous malformations (AVMs), usually presumed to be congenital, often result in tissue degeneration and functional displacement of the perifocal areas, but it remains unclear whether AVMs may produce long-range effects upon the whole-brain white matter organization. In this study, we used diffusion tensor imaging and graph theory methods to investigate the alterations of brain structural networks in 14 patients with AVMs in the presumed Broca's area, compared to 27 normal controls. Weighted brain structural networks were constructed based on deterministic tractography. We compared the topological properties and network connectivity between patients and normal controls. Functional magnetic resonance imaging revealed contralateral reorganization of Broca's area in five (35.7%) patients. Compared to normal controls, the patients exhibited preserved small-worldness of brain structural networks. However, AVM patients exhibited significantly decreased global efficiency (p = 0.004) and clustering coefficient (p = 0.014), along with decreased corresponding nodal properties in some remote brain regions (p < 0.05, family-wise error corrected). Furthermore, structural connectivity was reduced in the right perisylvian regions but enhanced in the perifocal areas (p < 0.05). The vulnerability of the left supramarginal gyrus was significantly increased (p = 0.039, corrected), and the bilateral putamina were added as hubs in the AVM patients. These alterations provide evidence for the long-range effects of AVMs on brain white matter networks. Our preliminary findings contribute extra insights into the understanding of brain plasticity and pathological state in patients with AVMs.

Graph fractal dimension and the structure of fractal networks.

Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

Exponential Stability of Fractional-Order Complex Multi-Links Networks With Aperiodically Intermittent Control.

In this article, the exponential stability problem for fractional-order complex multi-links networks with aperiodically intermittent control is considered. Using the graph theory and Lyapunov method, two theorems, including a Lyapunov-type theorem and a coefficient-type theorem, are given to ensure the exponential stability of the underlying networks. The theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative. To be specific, the larger control gain, the higher the exponential convergence rate. Meanwhile, when aperiodically intermittent control degenerates into periodically intermittent control, a corollary is also provided to ensure the exponential stability of the underlying networks. Furthermore, to show the practicality of theoretical results, as an application, the exponential stability of fractional-order multi-links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established. Finally, the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example.

Comparison between hamming method and modified path matrix approach to identify isomorphism in PGTs

Structural Synthesis and Analysis plays a major role in identifying the Isomorphism and Symmetry of a Planetary Gear Train (PGT). In synthesis process, detection of isomorphism in PGTs with given number of links and Degree of Freedom (DOF) is essential. One gear pair and one turning pair will be added to the existing link to generate next level PGT. One isomorphic PGT is selected at random to generate higher link PGTs. Graph theory and matrix methods are used by different kinematicians to identify the symmetry and isomorphism in PGTs. Every method has its own merits and demerits. In this paper a comparison was made between the Hamming number technique and Modified Path Matrix (MPM) approach. For easy analysis, PGTs are converted in to graphs and matrices are extracted from these graphs. In this paper isomorphism is checked by using Adjacency matrix and Modified path Matrix. 4-link and 6-link PGTs were considered for analysis in both the methods and compared the results. It is observed that Hamming Number approach is simple and feasible method among the two to identify the symmetry and isomorphism in PGTs.

Economic Integration Stages Clarification of the Countries in Electricity Trade

The article analyzes regional energy cooperation in sub-regions of Asia with a detailed study of South Asia and the CIS. The aim is to develop the theory of energy markets integration by adding an element of mutual trade to it. The study is based on statistics data of electricity exports by sub-regions of Eurasia based on the information of bilateral exports. The level of regional economic integration was estimated by the “export share” indicator, as well as by graph theory methods. Four out of nine countries in the South Asian region are not yet included in energy trade. This fact does not allow to speak about the success of the efforts undertaken by international organizations in the subregion as a whole. The results of the network analysis show that the relations between the countries of the region are fragmented, the problem of South Asian countries integration in the field of electricity trade is far from a solution. In the CIS, only 10% of electricity is traded within the region. There are two clusters of countries in the subregion. The countries of the larger cluster are connected through trade with the rest of the world. The countries of the second cluster — Kazakhstan, Tajikistan, Kyrgyzstan and Uzbekistan — are interconnected, but not with Russia, being the beneficiaries of the Central Asian Regional Economic Cooperation Program. Thus, the prevailing architecture of regional ties may indicate small integration created by the efforts of an international organization in the region. The CIS region meets the description of the energy markets' integration level as being between “interconnection” and “shallow”. To characterize the integration level, we recommend examining the graph connectivity, centrality indicators, and the number and size of clusters. Russia's efforts in the area of electricity trade in Asia are examined in four aspects. Development assistance is inadequate, and membership in the Asian Development Bank is likely to become a pressing issue. Cooperation with the CIS countries leaves aside two countries of the post-Soviet space, it is not able to attract four more countries of Central Asia to cooperate. Cooperation within the EAEU is insufficient for Belarus and Armenia, therefore, the creation of a single electric energy market by 2025 is an urgent task.