Mathematical Model Of Network Research Articles

Genetic algorithm as a tool for modeling calculations of electric power systems

Evolutionary modeling is one of the areas of artificial intelligence, which essence is the computational processes interpretation and the final forms of integral computational algorithms construction from their existence, variability and development the points of view in natural systems. All evolutionary modeling methods are of an optimization nature due to the basic use of the theory of natural selection principles. One of the most common methods of evolutionary modeling is the genetic algorithm (GA). It is the method of adaptive search for solutions based on the principles of the evolution and the natural selection with the preservation of biological terminology in a simplified form theories. Its essence is to determine the most fit individual (solution) by the value of its fitness function during evolution, considering the analysis of the heredity influences and the external environment. Despite the biological terminology, genetical algorithms are a universal computational tool that can be used to solve a wide range of complex problems, including the electric power industry. The authors considered the issue of the genetic algorithm use in the framework of calculating the steady state of the electrical network (SS EN), since the mathematical electrical network model is a system of high-order nonlinear equations, where all the restrictions imposed by the physical properties of the object under consideration are taken into account. Its solution is a rather laborious optimization problem, due to the operating electrical networks complexity. The correct solution of this system is the most critical stage in the calculation of the SS EN. It is the reason for importance and urgency of the search for SS EN calculating optimal methods task. This paper presents the development results of an analytical apparatus that made it possible to search for a solution to the problem of calculating electrical networks steady-state modes using the genetic algorithm based on special software.

Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.

Improving the Methods of Assessing the Socio-Economic Potential of the Regions of the Republic of Uzbekistan on the Basis of Intellectual Mathematical Models

The article examines the investment potential of the territories of the Republic of Uzbekistan and the issues and investment distribution problems in them. Also, in the article predictions were made using programs of mathematical models of artificial neural networks in the analysis of distributions process problems,and the results were determined by comparing the results with trend and panel methods. Sustainable territorial socio-economic development is determined by general laws of country socio-economic development, the share of export products in the total output of the region, depending on the composition of the gross regional product, in key sectors of the economy is determined by features such as competitive product, scientific potential, population income. Therefore, the problems that arise in ensuring the socio-economic development of the region in modern conditions will have their own regional characteristics.Addressing the territorial socio-economic development problems require strengthening the regulatory role of the state in determining regional economic policy, governance, the development of effective systems, tools and methods of state regulation. Sustainable territorial socio-economic development also depends on the self-sufficiency level of resources and effective budget finance, credit, tax and price policies.

Braiding Braak and Braak: Staging patterns and model selection in network neurodegeneration.

A hallmark of Alzheimer’s disease is the aggregation of insoluble amyloid-beta plaques and tau protein neurofibrillary tangles. A key histopathological observation is that tau protein aggregates follow a structured progression pattern through the brain. Mathematical network models of prion-like propagation have the ability to capture such patterns, but a number of factors impact the observed staging result, thus introducing questions regarding model selection. Here, we introduce a novel approach, based on braid diagrams, for studying the structured progression of a marker evolving on a network. We apply this approach to a six-stage ‘Braak pattern’ of tau proteins, in Alzheimer’s disease, motivated by a recent observation that seed-competent tau precedes tau aggregation. We show that the different modeling choices, from the model parameters to the connectome resolution, play a significant role in the landscape of observable staging patterns. Our approach provides a systematic way to approach model selection for network propagation of neurodegenerative diseases that ensures both reproducibility and optimal parameter fitting.

Mathematical modelling of SigE regulatory network reveals new insights into bistability of mycobacterial stress response

BackgroundThe ability to rapidly adapt to adverse environmental conditions represents the key of success of many pathogens and, in particular, of Mycobacterium tuberculosis. Upon exposition to heat shock, antibiotics or other sources of stress, appropriate responses in terms of genes transcription and proteins activity are activated leading part of a genetically identical bacterial population to express a different phenotype, namely to develop persistence. When the stress response network is mathematically described by an ordinary differential equations model, development of persistence in the bacterial population is associated with bistability of the model, since different emerging phenotypes are represented by different stable steady states.ResultsIn this work, we develop a mathematical model of SigE stress response network that incorporates interactions not considered in mathematical models currently available in the literature. We provide, through involved analytical computations, accurate approximations of the system’s nullclines, and exploit the obtained expressions to determine, in a reliable though computationally efficient way, the number of equilibrium points of the system.ConclusionsTheoretical analysis and perturbation experiments point out the crucial role played by the degradation pathway involving RseA, the anti-sigma factor of SigE, for coexistence of two stable equilibria and the emergence of bistability. Our results also indicate that a fine control on RseA concentration is a necessary requirement in order for the system to exhibit bistability.

Vibro-Fluidized Bed Drying of Pumpkin Seeds: Assessment of Mathematical and Artificial Neural Network Models for Drying Kinetics

Pumpkin seeds were dried in a vibro-fluidized bed dryer (VFBD) at different temperatures at optimized vibration intensity of 4.26 and 4 m/s air velocity. The drying characteristics were mapped employing semiempirical models and Artificial Neural Network (ANN). Prediction of drying behavior of pumpkin seeds was done using semiempirical models, of which, one was preferred as it indicated the best statistical indicators. Two-term model showed the best fit of data with R2 − 0.999, and lowest χ2 − 1.03 × 10−4 and MSE 7.55 × 10−5. A feedforward backpropagation ANN model was trained by the Levenberg–Marquardt training algorithm using a TANSIGMOID activation function with 2-10-2 topology. Performance assessment of ANN showed better prediction of drying behavior with R2 = 0.9967 and MSE = 5.21 × 10−5 for moisture content, and R2 = 0.9963 and MSE = 2.42 × 10−5 for moisture ratio than mathematical models. In general, the prediction of drying kinetics and other drying parameters was more precise in the ANN technique as compared to semiempirical models. The diffusion coefficient, Biot number, and hm increased from 1.12 × 10−9 ± 3.62 × 10−10 to 1.98 × 10−9 ± 4.61 × 10−10 m2/s, 0.51 ± 0.01 to 0.60 ± 0.01, and 1.49 × 10−7 ± 4.89 × 10−8 to 3.10 × 10−7 ± 7.13 × 10−8 m/s, respectively, as temperature elevated from 40 to 60°C. Arrhenius’s equation was used to the obtain the activation energy of 32.71 ± 1.05 kJ/mol.

Research and practice on optimal design method of the oilfield water injection system pipeline network

The efficiency of oilfield water injection system is generally low and energy consumption is high. With the deepening of oilfield exploitation, the water cut of the oilfield is increasing, the power consumption of the water injection system is increasing year by year, the oilfield exploitation cost is increasing, and energy conservation and consumption reduction are very important. In order to improve oilfield water injection efficiency and reduce water injection energy loss, this paper puts forward the pipe network optimization design method of partial pressure water injection, establishes the mathematical model of partial pressure water injection pipe network and throttling loss calculation model, compiles the calculation software of partial pressure water injection mathematical model, optimizes the partial pressure interval, calculates the partial pressure points, effectively reduces the energy loss of water injection system and improves the efficiency of water injection system.

Identification of sources with abnormal radon exhalation rates based on radon concentrations in underground environments

When there is poor ventilation or an irregular radon exhalation rate in an underground environment, it is necessary to judge whether the radon concentration is abnormal. To protect personal safety and health from radon gas, it is necessary to track the location of an abnormal radon source and measure its release rate to formulate emergency control and eradication measures. However, in an underground environment, it is impossible to fully monitor the radon concentration at every location, and as a result, blind spots are present, making it difficult to obtain timely early warnings in the event of an abnormal radon exhalation rate. Based on the distribution of radon concentration in an underground environment, this research establishes a theoretical mathematical model of an underground ventilation network containing radon. We combined particle swarm optimization with the long short-term memory (PSO-LSTM) method, which uses part of a time series signal of monitored radon concentrations to track the location of an abnormal radon source and determine an abnormal radon exhalation rate. Performing experiments of theoretical examples and actual underground ventilation environment examples, we prove the necessity of optimizing the monitoring position of the angle-connected ventilation network. The results show that the PSO-LSTM model based on radon concentration monitoring can process time series signals. Its accuracy and decision coefficient greater that is than 0.9 indicate the reliability of the model and method.

Neural Network Multistage Method for The Forecasting Electrical Insulating Materials Characteristics

The solution to the problem of non-destructive monitoring of thermal processes in insulating materials is shown. The main configuration parameters of the artificial neural network are determined. A mathematical model and architecture of a neural network for the forecasting thermal fluctuation processes are developed. The architecture of a neural network with a consistently distributed structure is synthesized. A forecasting technique is proposed and functions are obtained for assessing the long-term permissible heating values of the cable current-carrying core insulating material. Temperature monitoring will allow to monitor both the condition and the throughput of the lines.

Optimization of Pipe Network Simulation Algorithm for Tree-Shaped Water Injection System in Large-Scale Oilfield

As intelligence technology develops, there is a higher requirement for computing speed and accuracy of water injection system simulation. In this paper, aiming at the tree-shaped water injection pipe network system of large-scale oilfields, based on the energy equation for calculating the pressure drop [Formula: see text] of pipe section, a mathematical model of the pipeline unit and the node unit is established, and finally, a mathematical model of pipe network for the entire water injection system is established; then, the improved iterative algorithm is used to solve the simulation model of water injection system. In this way, we determine the boundary calculation conditions, take the water injection station as reference node, and use the maximum pressure of water injection well as the initial value of the reference node for calculation, which reduces the number of iterations in model calculation; by comparing the simulation results of different iteration steps, 0.01 is selected as the iteration step size due to its higher calculation accuracy; and the calculation process has also been optimized. The process of solving the characteristic matrix [Formula: see text] is combined with the process of calculating the pressure drop [Formula: see text] of pipe section, and placed outside the algorithm loop, thereby shortening the calculation time of a single cycle and reducing the calculation amount of the algorithm. The application cases show that the proposed optimization algorithm for water injection system pipe network simulation can be used as an effective method to improve the solution speed and calculation accuracy of the simulation algorithm of tree-shaped water injection system in large-scale oilfields.

Dynamic hypergraphs of renewal processes in mobile networks.

The characteristics of random geometric hypergraphs are studied as mathematical models of scalable wireless computer networks. An efficient algorithm for finding cliques in geometric graphs, constructing hypergraphs from geometric configurations has been developed. The types of hyper-edges in hypergraphs generated by a scalable configuration have been identified. The influence of random failures of nodes of computer networks and their restorations on the dynamics of hypergraphs of networks is considered. The analysis of the dynamics of the number of active nodes depending on the type of probability distributions of uptime and recovery time is carried out. The dependences of the mathematical expectation of the number of hyper-edges of certain types in the geometric hypergraph of a wireless computer network on the network operation time, on the radii of zones of reliable reception / transmission of a signal, on the ratio of the parameters of local recovery processes are obtained. The presentation of the results is accompanied by charts.

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks.

Mathematical models of biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can be tested by means of targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring in rule-based modeling. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration, or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel "black-box" deterministic simulator that effectively realizes both a fine-grained and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely, the Dormand-Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855×, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.

Using Infinite-server Resource Queue with Splitting of Requests for Modeling Two-channel Data Transmission

New Radio Access Technology 3GPP New Radio has become the fundamental wireless technology in the fifth-generation networks, which allows us to achieve high data rates due to the ability to work in the millimeter-wave band. But the key feature and the main problem of 5G New Radio networks is that people themselves, cars, buildings, etc. are signal blockers, while the base stations of the fourth generation networks have widescreen broadcasting and such small obstacles do not cause loss of connection. Service providers and mobile operators are already testing the proposed technology. In this connection, the scientific community has the task of analyzing the performance of these systems and increasing it in the future. Currently, there are known studies of “basic” mathematical models of such networks. By this term, we mean models built in the simplest possible assumptions. However, due to the justified necessity of introducing new technology into the daily lives of subscribers, service providers pose the scientific community with the task of analyzing the effectiveness of the most appropriate mathematical models. For example, a technology of splitting transmitted data into two streams using as 5G and both 4G transmission technologies is considered now by 3GPP Project Coordination Group. The paper is devoted to such a problem. We consider a mathematical model of the message transmitting with the implementation of the splitting function in the communication networks of New Radio technology in the form of a resource queueing system with a renewal arrival process and non-exponential service. For this problem, an approximation of a stationary two-dimensional probability distribution of the number of occupied resources in parallel service units is obtained. It is shown that this approximation coincides with the Gaussian distribution, and its area of applicability is shown.

Determination of 3D pore network structure of freeze-dried maltodextrin

This article describes and discusses the determination of the pore network structure from X-ray microcomputed tomography images of freeze-dried maltodextrin based on image processing. Maltodextrin is used because of its relevance for research and pharmaceutical applications. Image processing is based on conventional methods for image filtering and binarization, which are specifically the Gaussian filter, anisotropic diffusion filter, and Otsu thresholding as well as adaptive thresholding. It is shown, that the combination of the different image processing methods has only a minor impact on the final results of the estimated porosity. More critical is the segmentation of the overall void space into individual pores using the watershed algorithm, especially if the markers of the Euclidean distance map are not accurately defined. Oversegmentation of the void space into too many small pores was obviated by the use of a Gaussian smoothing filter on the Euclidean distance map. The approximation of the structure by spherical or cylindrical geometrical objects was addressed in further discussions as an essential step for the determination of the mathematical pore network model. It was found that the choice of the specific geometrical object has a major impact on the final pore size distribution of the generated pore networks. For the case of maltodextrin, with long and narrow pores, the approximation by segmented cylinders, replacing the individual pore subvolumes, yields the best agreement. The computed pore network structures are further investigated in regard of the correlation of vapor transport regimes and structure variation. It is shown that the small differences obtained from the various combinations of image processing and network reconstruction methods have a negligible impact if temperature and pressure are low (T = −18 °C, P = 10 Pa) and constant.

Suppression of chaotic bursting synchronization in clustered scale-free networks by an external feedback signal.

Oscillatory activities in the brain, detected by electroencephalograms, have identified synchronization patterns. These synchronized activities in neurons are related to cognitive processes. Additionally, experimental research studies on neuronal rhythms have shown synchronous oscillations in brain disorders. Mathematical modeling of networks has been used to mimic these neuronal synchronizations. Actually, networks with scale-free properties were identified in some regions of the cortex. In this work, to investigate these brain synchronizations, we focus on neuronal synchronization in a network with coupled scale-free networks. The networks are connected according to a topological organization in the structural cortical regions of the human brain. The neuronal dynamic is given by the Rulkov model, which is a two-dimensional iterated map. The Rulkov neuron can generate quiescence, tonic spiking, and bursting. Depending on the parameters, we identify synchronous behavior among the neurons in the clustered networks. In this work, we aim to suppress the neuronal burst synchronization by the application of an external perturbation as a function of the mean-field of membrane potential. We found that the method we used to suppress synchronization presents better results when compared to the time-delayed feedback method when applied to the same model of the neuronal network.

Model order reduction for gas and energy networks

To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms.For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network models.

Intelligent Control Systems in Urban Planning Conflicts: Social Media Users’ Perception

The relevance of this study is determined by the need to develop technologies for effective urban systems management and resolution of urban planning conflicts. The paper presents an algorithm for analyzing urban planning conflicts. The material for the study was data from social networks, microblogging, blogs, instant messaging, forums, reviews, video hosting services, thematic portals, online media, print media and TV related to the construction of the North-Eastern Chord (NEC) in Moscow (RF). To analyze the content of social media, a multimodal approach was used. The paper presents the results of research on the development of methods and approaches for constructing mathematical and neural network models for analyzing the social media users’ perceptions based on their digital footprints. Artificial neural networks, differential equations, and mathematical statistics were involved in building the models. Differential equations of dynamic systems were based on observations enabled by machine learning. Mathematical models were developed to quickly detect, prevent, and address conflicts in urban planning in order to manage urban systems efficiently. In combination with mathematical and neural network model the developed approaches, made it possible to draw a conclusion about the tense situation around the construction of the NEC, identify complaints of residents to constructors and city authorities, and propose recommendations to resolve and prevent conflicts. Research data could be of use in solving similar problems in sociology, ecology, and economics.

An effective fault management scheme and comprehensive double line‐frequency ripple propagation analysis for MVDC networks

This paper proposes an effective fault management scheme for medium-voltage direct current (MVDC) networks, which includes a virtual-impedance-based fault current limiter (VI-FCL) on the DC side and a positive-negative-sequence (PNS) control scheme on the AC side. Depending on the fault current value, different protection strategies are adopted, which include either isolating the fault by opening circuit breakers or riding through the fault with the proposed VI-FCL. It is known that unbalanced grid voltage can be found in conventional AC distribution feeders due to unbalanced loading conditions among three phases. The unbalanced grid voltage could induce double line-frequency (2ω) ripples on both DC voltage and current, which could thereby trigger protection malfunction in the DC sub-sections. Therefore, the PNS control scheme is used to eliminate the 2ω ripples of both DC voltages and currents caused by unbalanced AC voltages. Furthermore, a detailed 2ω mathematical model of the MVDC network under unbalanced AC voltage condition is derived to investigate how the 2ω ripple propagates across the network. A voltage source converter based multi-terminal MVDC network is built to test DC faults with different fault currents, unbalanced AC voltages, and different control schemes. The test results verify both the proposed fault management scheme and the 2ω ripple propagation analysis.

Research on Factors Affecting Power Flow of Direct Current Grid Considering Different Control Modes

Direct Current grid technology based on flexible Direct Current transmission is one of the key means to solve large-scale grid integration and consumption of new energy. The flexible Direct Current transmission technology developed in recent years has superior control performance, strong flexibility, and independent control of active power. And reactive power, can be connected to the weak Alternating Current system. This article derives the power flow equation of the Direct Current transmission network by establishing a mathematical model of the Direct Current transmission network and combining different system-level control strategies in the Direct Current transmission network. The Newton-Raphson method is used to solve the power flow distribution of the Direct Current network when the master-slave control and droop control are adopted. The influence of the two control methods on the power flow distribution of the Direct Current network is compared through a calculation example.

Comprehensive Methods of Evaluation of Distance Learning System Functioning

Given recent events, training during quarantine can only take place remotely. To ensure quality training, communication must be seamless. To do this, the network must function smoothly. The solution to this problem is functionally stable networks that allow uninterrupted transmission of information due to redundancy. An important issue is the definition of redundancy. To solve this problem, the article considers the method of synthesis of the structure of the distance learning system. The method of synthesis of network structure used for providing distance learning by the criterion of maximum functional stability on the basis of the introduction of correcting communication lines is offered. With this method, you can develop tools for self-recovery of distributed software, taking into account the characteristics of disparate computer resources through the use of redundancy. This will allow you to develop functionally stable software systems, significantly reduce the recovery time of such systems after or in the event of possible failures. To increase the efficiency of the developed method, the mathematical model of the hyper network based on two hypergraphs was improved, which allows taking into account different requirements for the quality of the network.