Graph Theory Methods Research Articles

Study on the changes of Structural Covariance Network in post-traumatic stress disorder.

The topological properties of functional brain networks in post-traumatic stress disorder (PTSD) have been thoroughly examined, whereas the topology of structural covariance networks has been researched much less. Based on graph theoretical approaches, we investigated the topological architecture of structural covariance networks among PTSD, trauma-exposed controls (TEC), and healthy controls (HC) by constructing covariance networks driven by inter-regional correlations of cortical thickness. Structural magnetic resonance imaging (sMRI) scans and clinical scales were performed on 27 PTSD, 33 TEC, and 29 HC subjects. Group-level structural covariance networks were established using pearson correlations of cortical thickness between 68 brain areas, and the graph theory method was utilized to study the global and nodal properties. PTSD and HC subjects did not differ at the global level. When PTSD subjects were compared to TEC subjects, they had significantly higher clustering coefficient (p = .014) and local efficiency (p = .031). Nodes having different nodal centralities between groups did not pass the false-discovery rate correction at the node level. According to the structural brain network topological characteristics discovered in this study, PTSD manifests differently compared to the TEC group. In the PTSD group, the SCN keeps the small-world characteristics, but the degree of functional separation is enhanced. The TEC group's reduced small worldness and the tendency for brain network randomization could be signs of trauma recovery.

Intermittent control for synchronization of hybrid multi‐weighted complex networks with reaction‐diffusion effects

In this paper, exponential synchronization for hybrid multi‐weighted complex networks is studied via aperiodically intermittent control. Different from previous work, both Markov jump and reaction‐diffusion effects are simultaneously considered into multi‐weighted complex networks. By employing network split technique, graph theory, and Lyapunov method, several synchronization criteria are derived. These criteria show the effects of multiple weights, Markov jump, and reaction‐diffusion on exponential synchronization. Furthermore, an application to Cohen–Grossberg neural networks is conducted, and the corresponding synchronization criterion is given. Finally, some numerical simulations are presented to show the effectiveness of the obtained theoretical results.

Stability of stochastic delayed semi-Markov jump systems with stochastic mixed impulses: A novel stochastic impulsive differential inequality

In this paper, the pth moment exponential stability of stochastic delayed systems is studied. It is worth mentioning that semi-Markov jump and stochastic mixed impulses are considered simultaneously in the stochastic delayed systems. Besides, a new impulsive differential inequalities with semi-Markov jump and stochastic mixed impulses are established. The method of graph theory, stochastic analysis technique and Lyapunov method are cleverly combined, which contributes to propose stability criteria for stochastic delayed semi-Markov jump systems with stochastic mixed impulses. Finally, the theoretical results are applied to a kind of oscillator systems. The simulation results verify the effectiveness of the theoretical results.

Static and dynamic topological organization of brain functional connectome in acute mild traumatic brain injury.

Prior studies have detected topological changes of brain functional networks in patients with acute mild traumatic brain injury (mTBI). However, the alterations of dynamic topological characteristics in mTBI have been scarcely elucidated. To evaluate static and dynamic functional connectivity topological networks in patients with acute mTBI using resting-state functional magnetic resonance imaging (fMRI). A total of 55 patients with acute mTBI and 55 age-, sex-, and education-matched healthy controls (HCs) were enrolled in this study. All participants underwent resting-state fMRI scans, and data were analyzed using graph-theory methods and a sliding window approach. Post-traumatic cognitive performance and resting-state fMRI data were collected within one week after injury. Static and dynamic functional connectivity patterns were determined by independent component analysis. Spearman's correlation analysis was further performed between fMRI changes and Montreal cognitive assessment (MoCA) scores. Global efficiency was lower (P = 0.02), and local efficiency (P < 0.001) and mean Cp (P < 0.001) were higher in patients with acute mTBI than in HCs. Local efficiency was correlated with visuospatial/executive performance (r = -0.421; P = 0.002) in patients with acute mTBI. Significant differences in nodal efficiency and node degree centrality (P < 0.01) were found between the mTBI and HC groups. For dynamic properties, patients with mTBI showed higher variance (P = 0.016) in global efficiency than HCs. The present study shows that patients with mTBI have abnormal brain functional connectome topology, especially the dynamic graph theory characteristics, which provide new insights into the role of topological network properties in patients with acute mTBI.

Model of knowledge representation in the system of information support for decision making

Objectives. The problem of mathematical modeling of the knowledge in the information support system for decision-making is being solved. The approach is based on the formalization of semantic relations in the language. The formalization of such relations provides an adequate representation of knowledge and serves as a theoretical basis for the algorithmization of user interaction with the system.When solving the problem of knowledge modeling, three main goals are pursued: the construction of a mathematical model of semantic relations, the study of the properties of marginal syntagmas and the construction of algorithms for the formation of a dictionary of syntagmatic structures.Methods. Methods of set theory, graph theory and mathematical linguistics are used.Results. A mathematical model of knowledge representation in the information decision support system has been developed. The concepts of semantic relations in the language are formalized and the properties of marginal syntagmas are investigated. The proven properties of such structures provide the algorithmization of information processes in the system under consideration.Conclusion. As an implementation of the model proposed in the article, algorithms for creating dictionaries of syntagmas and syntagmatic structures have been developed. When forming a set of syntagmas, the assertions about proved in the article marginal syntagmas are used. A set of syntagmatic structures is built taking into account their typology. Syntagmatic structures in the dictionary acquire the status of communicative fragment, i.e. stable phrases to synthesize the information system language.

Trans_Proc

A reconfigurable transform processor is proposed and implemented here. Firstly, a brief study of processors implementing different transformations is presented. We have categorized the transform processor as the one which can implement a number of linear transforms using reconfigurability. The theoretical suitability regarding the architecture of the processor is proved by graph theory method. Then the complete architecture of the overall processor and the processing element is presented and implemented using VHDL. The complete instruction set suitable to the processor is designed. The instructions are mapped to the sequence of control signals. Generating sequence of control signals for every type of instructions would finally create a hardwired control unit for the processor which was also presented. Next the processor is fed with data to simulate it. A three-phase simulation is carried out to prove the correctness of the design. Finally the same processor with a data bus width of 32 to 512 is implemented and compared in terms of speed and size.

The structural brain network topology of episodic memory.

Episodic memory is supported by a distributed network of brain regions, and this complex network of regions does not operate in isolation. To date, neuroscience research in this area has typically focused on the activation levels in specific regions or pairwise connectivity between such regions. However, research has yet to investigate how the complex interactions of structural brain networks influence episodic memory abilities. We applied graph theory methods to diffusion-based anatomical networks in order to examine the structural architecture of the medial temporal lobe needed to support effective episodic memory functioning. We examined the relationship between performance on tests of verbal and non-verbal episodic memory with node strength, which indexes how well connected a brain region is in the network. Findings mapped onto the Posterior Medial memory system, subserved by the parahippocampal cortex and overlapped with findings of previous studies of episodic memory employing different methodologies. This expands our current understanding by providing independent evidence for the importance of identified regions and suggesting the particular manner in which these regions support episodic memory.

Large-Scale Exploration of Whole-Brain Structural Connectivity in Anorexia Nervosa: Alterations in the Connectivity of Frontal and Subcortical Networks

BackgroundAnorexia nervosa (AN) is characterized by disturbances in cognition and behavior surrounding eating and weight. The severity of AN combined with the absence of localized brain abnormalities suggests distributed, systemic underpinnings that may be identified using diffusion-weighted magnetic resonance imaging and tractography to reconstruct white matter pathways. MethodsDiffusion-weighted magnetic resonance imaging data acquired from female patients with AN (n= 147) and female healthy control (HC) participants (n = 119), ages 12 to 40 years, were combined across 5 studies. Probabilistic tractography was completed, and full-cortex connectomes describing streamline counts between 84 brain regions were generated and harmonized. Graph theory methods were used to describe alterations in network organization in AN. The network-based statistic tested between-group differences in brain subnetwork connectivity. The metrics strength and efficiency indexed the connectivity of brain regions (network nodes) and were compared between groups using multiple linear regression. ResultsIndividuals with AN, relative to HC peers, had reduced connectivity in a network comprising subcortical regions and greater connectivity between frontal cortical regions (p < .05, familywise error corrected). Node-based analyses indicated reduced connectivity of the left hippocampus in patients relative to HC peers (p < .05, permutation corrected). Severity of illness, assessed by body mass index, was associated with subcortical connectivity (p < .05, uncorrected). ConclusionsAnalyses identified reduced structural connectivity of subcortical networks and regions, and stronger cortical network connectivity, among individuals with AN relative to HC peers. These findings are consistent with alterations in feeding, emotion, and executive control circuits in AN, and may direct hypothesis-driven research into mechanisms of persistent restrictive eating behavior.

An Adaptive and Bounded Controller for Formation Control of Multi-Agent Systems with Communication Break

Aiming at maneuvering, input saturation, and communication interference in the controller design for formation control multi-agent systems, a novel nonlinear bounded controller is proposed. Based on coordinates transformation, reference information is processed, and nonlinear effects of maneuvering are analyzed. Then a nonlinear controller is established with graph theory, consensus algorithm, and Lyapunov method, which guarantee the stability of the controller. For input saturation avoidance, adaptive parameters are put forward with the Lyapunov function. Considering the communication breaks, various conditions of the sensing graph are discussed for stable formation control, and a dynamic programming regulator is proposed for unknown position reference needed for formation keeping. Comparison with the traditional consensus method is provided in numerical simulation to verify the stability and feasibility of the proposed strategy.

Bipartite leader-following synchronization of fractional-order delayed multilayer signed networks by adaptive and impulsive controllers

This article addresses the problem of bipartite leader-following synchronization of fractional-order delayed multilayer signed networks. It is worth emphasizing that fractional dynamics and multiple connections between nodes with multiple time delays are considered into signed networks. In our main results, adaptive control (continuous control) and impulsive control (discontinuous control) are both designed to reach the bipartite leader-following synchronization of the underlying networks. In addition, a Halanay inequality of fractional version is established. With the help of it, by using signed graph theory and Lyapunov method, some bipartite synchronization criteria are derived under the Lyapunov-type theorems and coefficients-type theorems. Then, as an application of theoretical results, the bipartite leader-following synchronization of fractional-order coupled Chua’s circuits modeled on delayed multilayer signed networks is considered. Finally, two numerical examples are exhibited to exemplify the usefulness and feasibility of the theoretical results.

Abnormal Dynamic Functional Connectivity in Patients With End-Stage Renal Disease.

Dynamic functional connectivity (FC) analysis can capture time-varying properties of connectivity; however, studies focusing on dynamic FC in patients with end-stage renal disease (ESRD) are very limited. This is the first study to explore the dynamic aspects of whole-brain FC and topological properties in ESRD patients. Resting-state functional magnetic resonance imaging data were acquired from 100 ESRD patients [50 hemodialysis (HD) patients and 50 non-dialysis patients] and 64 healthy controls (HCs). Independent component analysis, a sliding-window approach and graph-theory methods were used to study the dynamic FC properties. The intrinsic brain FC were clustered into four configuration states. Compared with HCs, both patient groups spent longer time in State 3, in which decreased FC between subnetworks of the default mode network (DMN) and between the dorsal DMN and language network was observed in these patients, and a further reduction in FC between the DMN subnetworks was found in HD patients compared to non-dialysis patients. The number of transitions and the variability of global and local efficiency progressively decreased from that in HCs to that of non-dialysis patients to that of HD patients. The completion time of Trail Making Test A and Trail Making Test B positively correlated with the mean dwell time of State 3 and negatively correlated with the number of transitions in ESRD patients. Our findings suggest impaired functional flexibility of network connections and state-specific FC disruptions in patients with ESRD, which may underlie their cognitive deficits. HD may have an adverse effect on time-varying FC.

The Optimal and Economic Planning of a Power System Based on the Microgrid Concept with a Modified Seagull Optimization Algorithm Integrating Renewable Resources

In the past, planning to develop an electricity generation capacity supply of consumable load, an acceptable level of reliability, and minimum cost has played significant roles. Due to technological development in energy and the support of energy policymakers to make the most of these clean and cheap resources, a significant amount of research has been conducted to make the most of such energy. Constraints such as low capacity, output power uncertainty, and sustainability problems have made using distributed energy sources costly and complex. Theoretically, capacity development planning in a power system is part of macro-energy planning. It is generally based on specific development policies in each country’s national interest. In addition to being economical, the purpose of this planning was to find the best capacity development plan commensurate with the amount of consumption so that the development plan does not go beyond the permissible limits of reliability, environmental issues, and other constraints. On the other hand, due to the considerable growth of divided production, especially energy sources, it is essential to use microgrids. Accordingly, in this research study, in the process of solving the problem of planning and providing load growth by the distributed generation units to maximize reliability and minimize investment costs, the creation of smaller networks was investigated. To optimize zoning, the weighted graph theory method, in which the weight of the edges is the apparent power passing through the lines, was adopted. In addition, reactive power reliability was included in the calculations to improve the economic aspects. Probabilistic modeling for the presence of renewable resources was employed to bring the model to reality. Since the above problem is very complex, a Seagull-based algorithm and chaos theory were utilized to solve this matter. Finally, the suggested method for the sample system is discussed in different scenarios, indicating an improvement in the system’s performance. According to the numerical results, the NSGA, SPEA, and MOPSO have mean values of 68.3%, 50.2%, and 48.3%, which are covered by the proposed optimization algorithm.

Network representation and analysis of energy coupling mechanisms in cellular metabolism by a graph-theoretical approach.

Mechanisms coupling the chemical reactions of oxidation and ATP synthesis in cellular metabolism by the fundamental biological process of oxidative phosphorylation (OX PHOS) in mitochondria provide > 90% of the energy requirements in living organisms. Mathematical graph theory methods have been extensively used to characterize various metabolic, regulatory, and disease networks in biology. However, networks of energy coupling mechanisms in OX PHOS have not been represented and analyzed previously by these approaches. Here, the problem of biological energy coupling is translated into a graph-theoretical framework, and all possible coupling schemes between oxidation and ATP synthesis are represented as graphs connecting these processes by various intermediates or states. The problem is shown to be transformed into the hard problem of finding a Hamiltonian tour in the networks of possible constituent mechanisms, given the constraints of a cyclical nature of operation of enzymes and biological molecular machines. Accessible mathematical proofs of three theorems that guarantee sufficient conditions for the existence of a Hamiltonian cycle in simple graphs are provided. The results of the general theorems are applied to the set of possible coupling mechanisms in OX PHOS and shown to (1) unequivocally differentiate between the major theories and mechanisms of energy coupling, (2) greatly reduce the possibilities for detailed consideration, and (3) deduce the biologically selected mechanism using additional constraints from the cumulative experimental record. Finally, an algorithm is constructed to implement the graph-theoretical procedure. In summary, the enormous power and generality of mathematical theorems and approaches in graph theory are shown to help solve a fundamental problem in biology.

A piecewise probabilistic harmonic power flow approach in unbalanced residential distribution systems

With the improvement of living standards and economic growth, the electricity consumption of Chinese residents is increasing year by year. Due to the existence of many nonlinear devices in residential loads, a large number of time-varying harmonic currents are randomly injected into the residential distribution system (RDS), which makes it difficult for a single deterministic harmonic power flow (HPF) method to evaluate the probabilistic and time-varying harmonics of residential loads. In this paper, a piecewise probabilistic HPF method is proposed to evaluate the harmonic emission level. First, a piecewise probabilistic harmonic coupled model (HCM) is used to analyze the harmonic generated by residential loads, which can demonstrate the probabilistic and time-varying harmonic characteristics. Second, based on the HCM, a decoupled approach combing the graph theory and current injection method is established to calculate the HPF with residential loads. Third, based on the HCM and HPF calculation method, a field theory is used to evaluate the probabilistic harmonics of an unbalanced RDS. Field measurement results in different residential areas and simulation results in IEEE-13, 123, and 8500 test systems verify the accuracy, validity, and efficiency of the proposed model and calculation methods.

Navigation methodology for vehicle city route optimal choice

Relevance. The study is a fundamentally new approach to such an extremely important problem as the congestions in large cities. The solution of this global problem is a step in the realization of a smart city concept. Goal. The aim of the study is to create basic elements of technology that can stabilize urban traffic and bring it to a qualitatively new state. To achieve this goal, the following tasks have been formulated: – to create a model of a city transport network in the form of an oriented weighted non-planar multigraph with dynamically loaded arcs; – to activate a city electronic map in the Traffic Management Centre (TMC) which allows tracking each vehicle; – to navigate the time-optimal routes for all those vehicles that request the route; – to implement the work of the software algorithm in real time with constant updating of the route of each tracked vehicle. That will allow monitoring changes in city traffic in real time and making adjustments to the route of each vehicle. Research methods. The research is based on the use of mechanisms for modeling and working with various networks – the graph theory and the A-star algorithm. The latter traces the route on the graph (transport network) between two selected positions of the vehicle graph theory – origin and destination. The heuristic A-star algorithm – a powerful computational method of graph theory has been used in the study. This makes it possible to synchronize vehicles flows and therefore provides a qualitatively new level to the control of urban traffic. The results. The problem of traffic load registration for the city transport network essential for navigating a vehicle route in metropolis has been solved. Traffic data of the real transport network have been reproduced on the city electronic map. Each vehicle received a unique marker consisting of an origin-destination pair and can be tracked on the map. Since each vehicle is under control of the Traffic Management Center (TMC), it is possible to track it along the optimal route, taking an urban traffic dynamic into account. Support is provided via the General Packet Radio Service (GPRS) channel, which allows each driver to receive instructions as to an optimal travel path. Conclusions. The study has proposed a working software module that navigates a time-optimized route on the graph that represents the model of the real transport city network.

METHOD FOR DETERMINING THE SEQUENCE OF REACTIONS TO PREDICT THE CONSEQUENCES OF TECHNOGENIC POLLUTION

To predict the negative consequences of man-made pollution with harmful substances, a method for determining possible ways of chemical reactions taking into account the chemical and thermodynamic properties of a given set of components, the theoretical foundations of chemical stoichiometry and thermodynamics, patterns of influence of thermodynamic parameters on the direction of chemical reactions. In this regard, chemical objects were presented in the form of multidimensional vectors, taking into account thermodynamic parameters, for the calculation of which used the methods of chemical thermodynamics. The generation of chemical reactions was carried out using the methods of mathematical statistics and combinatorics, and to determine the sequences of chemical reactions, the methods of graph theory. It is proposed to write a chemical compound as the sum of basis vectors, which allowed to represent compounds and interactions between them in n-dimensional space and to determine possible chemical interactions with the help of the main principles of work with integer vector space. Three conditions for the possibility of chemical interaction by this method are clarified and the values of enthalpy and Gibbs energy of each reaction are introduced, which are determined by the values of the corresponding potentials for each of the compounds. For the convenience of the image and further calculations, the element-enthalpy and element-gibs spaces were used separately. An algorithm for this method is created and tested, features for different boundary conditions of its use are studied, its efficiency on real chemical reaction systems is checked. An algorithm for determining the possibilities of chemical reactions in multicomponent systems to determine their man-made load on the environment is proposed.

Abnormal dynamic functional connectivity in first-episode, drug-naïve adolescents with major depressive disorder.

Previous neuroimaging studies have identified disrupted large-scale functional brain networks in major depressive disorder (MDD); however, most of them focused on adult patients and were based on static functional connectivity (FC). Thus, we aimed to investigate the patterns of change in dynamic FC in depressed adolescents. Resting-state functional magnetic resonance imaging data were acquired from 60 first-episode, drug-naïve adolescents with MDD and 60 matched healthy controls (HCs). Then, the dynamic FC properties were analyzed using a sliding windows approach, k-means clustering, and graph theory methods. The intrinsic brain FC were clustered into two configuration states-a more frequent and relatively sparsely connected State 1 and a less frequent and more strongly interconnected State 2. Compared with HCs, depressed adolescents had higher reoccurrence fraction and dwell time in State 1, and lower reoccurrence fraction and dwell time in State 2, and higher total number of transitions between the two states. Depressed adolescents showed decreased FC within the default mode network (DMN) and between the DMN and other networks in State 1. Additionally, the MDD group showed higher variances in the global and local efficiency. Furthermore, the duration of illness was positively correlated with the number of state transitions, and the 17-item Hamilton Depression Rating Scale score was positively correlated with the mean dwell time in State 1. This study demonstrated abnormal dynamic FC in depressed adolescents, which provided new insights into the pathophysiological mechanisms of adolescent-onset depression.

GPU-accelerated N-1 static security analysis based on fine-grained parallelism HELM

With the increment of scale of power system, the accuracy and efficiency requirements of N-1 static security analysis (SSA) keep increasing. In order to satisfy these requirements, this paper proposed a GPU-accelerated N-1 SSA method to reduce computation burden and ensure the accuracy of alternating current power flow (ACPF) and connectivity test simultaneously. First, in the algorithm, ACPF is performed by holomorphic embedding load flow method (HELM). The construction and solution of sparse linear system both adopts fine-grained parallelism. According to the mathematical lemma of combining linear equations, this paper performs fine-grained parallelism Padé approximation of HELM. Second, considering the high time complexity of the original search-based algorithm and adjacency matrix method which is not suitable for sparse graph, this paper proposes a GPU-accelerated Union Set algorithm. Its main advantage is lower time complexity compared to other graph theory methods. And most importantly, it is very suitable for parallelization. Shared memory can be used in this algorithm well. Therefore, it is not complicated to perform a block-level parallelism in GPU-accelerated Union Set. Finally, the overall framework of GPU-accelerated N-1 SSA method is shown in this paper. It has been tested on large-scale power systems of up to 2869 buses. The computation results are compared with MATPOWER and the execution times are compared with other mainstream method to show the improvement in performance.

Dynamics of the Brain Functional Network Associated With Subjective Cognitive Decline and Its Relationship to Apolipoprotein E €4 Alleles.

The aim of our study was to explore the dynamic functional alterations in the brain in patients with subjective cognitive decline (SCD) and their relationship to apolipoprotein E (APOE) €4 alleles. In total, 95 SCD patients and 49 healthy controls (HC) underwent resting-state functional magnetic resonance imaging (rs-fMRI). Then, the mean time series of 90 cortical or subcortical regions were extracted based on anatomical automatic labeling (AAL) atlas from the preprocessed rs-fMRI data. The static functional connectome (SFC) and dynamic functional connectome (DFC) were constructed and compared using graph theory methods and leading eigenvector dynamics analysis (LEiDA), respectively. The SCD group displayed a shorter lifetime (p = 0.003, false discovery rate corrected) and lower probability (p = 0.009, false discovery rate corrected) than the HC group in a characteristic dynamic functional network mainly involving the bilateral insular and temporal neocortex. No significant differences in the SFC were detected between the two groups. Moreover, the lower probability in the SCD group was found to be negatively correlated with the number of APOE ε4 alleles (r = −0.225, p = 0.041) in a partial correlation analysis with years of education as a covariate. Our results suggest that the DFC may be a more sensitive parameter than the SFC and can be used as a potential biomarker for the early detection of SCD.

On optimization of the mixed charging infrastructure of electric buses for urban routes

Objectives. When transition from a fleet of diesel buses to a fleet of electric buses, it is important to optimize the charging infrastructure, which combines the slow-charging technologies at the depot overnight and fast recharging at the terminals of the routes. The purpose of the study is to create models and methods for developing the cost-effective solutions for selecting this type of charging infrastructure for a fleet of electric buses serving the city route system, taking into account a number of specific conditions. The operation of the fleet and charging infrastructure is modeled both for the depot at night and for the terminal stops in the most representative period of the day, characterized by the highest intensity of passenger traffic and maximum power consumption.Methods. Methods of set theory, graph theory and linear approximation are used.Results. A mathematical model has been developed for the problem of optimizing a mixed-type charging infrastructure for an electric bus fleet. The total daily cost of charging stations, degradation of electric bus batteries and consumed electricity was chosen as the objective function. The model is formulated as a mixed integer linear programming problem.Conclusion. To solve the formulated problem, standard solvers like IBM ILOG CPLEX can be used. The solution of the problem lies in the choice of durations and schedules for charging electric buses at low-capacity charging stations in the depot at night and at high-capacity charging stations of terminal stops in a given range of peak hours.