Graph Theory Methods Research Articles

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.

The 2MASS redshift survey galaxy group catalogue derived from a graph-theory based friends-of-friends algorithm

ABSTRACT We present the galaxy group catalogue for the recently completed 2MASS Redshift Survey (2MRS; Macri et al. 2019) which consists of 44 572 redshifts, including 1041 new measurements for galaxies mostly located within the Zone of Avoidance. The galaxy group catalogue is generated by using a novel, graph-theory based, modified version of the friends-of-friends algorithm. Several graph-theory examples are presented throughout this paper, including a new method for identifying substructures within groups. The results and graph-theory methods have been thoroughly interrogated against previous 2MRS group catalogues and a Theoretical Astrophysical Observatory (TAO) mock by making use of cutting-edge visualization techniques including immersive facilities, a digital planetarium, and virtual reality. This has resulted in a stable and robust catalogue with on-sky positions and line-of-sight distances within 0.5 and 2 Mpc, respectively, and has recovered all major groups and clusters. The final catalogue consists of 3022 groups, resulting in the most complete ‘whole-sky’ galaxy group catalogue to date. We determine the 3D positions of these groups, as well as their luminosity and comoving distances, observed and corrected number of members, richness metric, velocity dispersion, and estimates of R200 and M200. We present three additional data products, i.e. the 2MRS galaxies found in groups, a catalogue of subgroups, and a catalogue of 687 new group candidates with no counterparts in previous 2MRS-based analyses.

Functional Organization of Brain Network in Peripheral Neural Anastomosis Rats after Electroacupuncture: An ICA and Connectome Analysis

Acupuncture is a mild therapy in rehabilitation practice of peripheral nerve injury. Previous studies confirmed the deep participation of brain plasticity in the process of functional restoration. The therapeutic effect of acupuncture is also believed to be closely associated with brain plasticity, especially in the hypothalamus and limbic system. But the fuzzy neural mechanism somehow limits the application or improvement of this therapy. There is little information about the effect of acupuncture on topological properties of brain networks. Instead of functional segregation approach, we utilized graph theory method to analyze the large-scale and distributed properties of information processing. We first established rat model of sciatic nerve injury and performed rehabilitation therapy of electroacupuncture for 120 days. Meanwhile, we used independent component analysis to extract seven sub-networks from the whole brain. Then measurements of graph theory were calculated in each sub-network as well as the whole brain network. We found no significant difference of any measurement in whole brain network among intervention group, model group and normal group. But the assortativity, hierarchy, small-world properties of sub-network displayed significant differences among three groups. It induces changes of neural plasticity in several sub-networks instead of whole brain network. We attributed the changes to the enhancement of the short-term compensatory adaptation and the reduction of the long-term overacting regional information transmission. The present study may shed light on the vague distinction of large-scale property of brain networks after electroacupuncture, which leads to a better understanding of this ancient traditional Chinese therapy.

On the Boundary of Incidence Energy and Its Extremum Structure of Tricycle Graphs

With the wide application of graph theory in circuit layout, signal flow chart and power system, more and more attention has been paid to the network topology analysis method of graph theory. In this paper, we construct a graph transformation which can reflect the monotonicity of coefficients and reduce the number of graphs. A sharp lower bound for incidence energy in the tricyclic graphs is given and all the extremal structures are characterized. The most interesting things that we find two different classes tricyclic graphs have the same signless Laplacian characteristic polynomials and one of the extremal graphs beyond all expectations

Structure Description of Liquid 1,3-Propanediol and Ethylene Glycol by Graph Theory and Percolation Methods

Structure Description of Liquid 1,3-Propanediol and Ethylene Glycol by Graph Theory and Percolation Methods

Inner synchronisation of stochastic impulsive multi-links coupled systems via discrete-time state observations control

In this paper, the inner synchronisation of stochastic impulsive coupled systems with multi-links (SISM) is investigated. The feedback control based on discrete-time state observations, impulsive effects and multiple links are added to stochastic coupled systems simultaneously for the first time. Instead of the mean-square exponential synchronisation, the pth () moment exponential synchronisation is studied. A main theorem is proposed by average impulsive interval approach, graph theory and Lyapunov method to ensure the pth moment exponential synchronisation of SISM. Additionally, we apply the theoretical results to stochastic impulsive Rössler-like circuits with multi-links, which is the first attempt. Finally, a numerical example is provided to illustrate the effectiveness of the developed results.

A graph theory approach to analyze birth defect associations.

Birth defects are prenatal morphological or functional anomalies. Associations among them are studied to identify their etiopathogenesis. The graph theory methods allow analyzing relationships among a complete set of anomalies. A graph consists of nodes which represent the entities (birth defects in the present work), and edges that join nodes indicating the relationships among them. The aim of the present study was to validate the graph theory methods to study birth defect associations. All birth defects monitoring records from the Estudio Colaborativo Latino Americano de Malformaciones Congénitas gathered between 1967 and 2017 were used. From around 5 million live and stillborn infants, 170,430 had one or more birth defects. Volume-adjusted Chi-Square was used to determine the association strength between two birth defects and to weight the graph edges. The complete birth defect graph showed a Log-Normal degree distribution and its characteristics differed from random, scale-free and small-world graphs. The graph comprised 118 nodes and 550 edges. Birth defects with the highest centrality values were nonspecific codes such as Other upper limb anomalies. After partition, the graph yielded 12 groups; most of them were recognizable and included conditions such as VATER and OEIS associations, and Patau syndrome. Our findings validate the graph theory methods to study birth defect associations. This method may contribute to identify underlying etiopathogeneses as well as to improve coding systems.