Mathematical Model Of Network Research Articles

Parametrical synthesis of the complex two-port networks for variants of their inclusion between a source of a signal and a nonlinear part by criterion of maintenance of the set characteristics amplifiers with the general feedback

Introduction: the analysis of known literature shows that the use of various types of matching quadripoles (reactive, resistive, complex, mixed) and a feedback circuit covering a non-linear element makes it possible to increase the area of physical feasibility of given forms of frequency characteristics. The purpose of the work is to increase the area of physical feasibility of given forms of frequency characteristics by optimizing the parameters of matching complex quadripoles and using an additional feedback circuit covering a nonlinear element and a mixed quadripole. Each two-terminal network of such four-terminal networks consists of both resistive and reactive elements. Materials and methods: theory of four-terminal networks, matrix algebra, decomposition method, method of synthesis of microwave control devices, circuit engineering method for analyzing the characteristics of radio devices. Results: Mathematical models of matching complex quadripole networks are obtained in the form of relationships between the elements of their transmission matrix and the dependences of the resistances of their two-terminal circuits on frequency, which are optimal in terms of the criterion for providing specified forms of frequency characteristics. Conclusion: a comparative analysis of the theoretical results (frequency response and phase response of amplifiers) obtained by mathematical modeling in the MathCad system and experimental results obtained by circuit simulation in the OrCad and MicroCap systems shows their satisfactory agreement.

Application of Sensitivity Analysis to Discover Potential Molecular Drug Targets.

Mathematical modeling of signaling pathways and regulatory networks has been supporting experimental research for some time now. Sensitivity analysis, aimed at finding model parameters whose changes yield significantly altered cellular responses, is an important part of modeling work. However, sensitivity methods are often directly transplanted from analysis of technical systems, and thus, they may not serve the purposes of analysis of biological systems. This paper presents a novel sensitivity analysis method that is particularly suited to the task of searching for potential molecular drug targets in signaling pathways. Using two sample models of pathways, p53/Mdm2 regulatory module and IFN--induced JAK/STAT signaling pathway, we show that the method leads to biologically relevant conclusions, identifying processes suitable for targeted pharmacological inhibition, represented by the reduction of kinetic parameter values. That, in turn, facilitates subsequent search for active drug components.

Mathematical, fuzzy logic and artificial neural network modeling of extraction kinetics of essential oil from aerial parts of yarrow (Achillea millefolium L.) using ohmic-assisted hydrodistillation

Mathematical, fuzzy logic and artificial neural network modeling of extraction kinetics of essential oil from aerial parts of yarrow (Achillea millefolium L.) using ohmic-assisted hydrodistillation

New approach to computer-aided learning based on digital library user behavior

The author introduces the mathematical model of recurrent neural network with external memory. It is intended for predicting efficient education trajectory in digital information environments, e. g. digital libraries. The goal of computer-aided learning based on neural networks is to personalize user trajectories. In the study, user behavior is modeled for the more precise personalization in various aspects using recurrent neural networks. The method is designed for two types of recurrent neural networks, i. e. the classic one with sigmoidal activation function and that with LSTM (Long Short-Term Memory). The experiments demonstrated serious advantages of recurrent neural networks over analogous methods in predicting education trajectory. Thus, the proposed model is the more efficient in predictive accuracy (by 15–20% higher than analogous methods). Its prime application area is prediction of optimum user education trajectory in the digital information environment, and digital library, in particul

Mathematical and artificial neural network model in composite electrode assisted electrical discharge coating

The present paper is studied the mathematical and artificial neural network (ANN) model in electrical discharge deposition of magnesium alloy. Surface coating is covering the workpiece surface with desired coating materials to improve the surface properties. Electrical discharge coating (EDC) is an electro thermal process, used for creating hard coating over the workpiece. In this present study, magnesium alloy is deposited using WC-Cu composite electrode by EDC. RSM is used to develop design matrix for carrying out EDC experiments. Compaction load, discharge current and pulse on time are controlled, whereas material deposition rate (MDR) and surface roughness (SR) are measured as response. The objective of this investigation is to predict the MDR and SR using neural network technique. ANN model developed by back propagation algorithm is proposed in this study for predicting the responses. ANOVA is conducted to identify the dominating parameter, which significantly affects the responses. Correlation coefficient between the ANN and RSM is 0.99, which is close to the unity for ANN. It was revealed that the prediction of proposed ANN was found to be excellent to the RSM model. MDR increased with increasing discharge current and pulse on time. SR decreased with increasing compaction load.

Modern Energy Optimization Approach for Efficient Data Communication in IoT-Based Wireless Sensor Networks

Many researchers are drawn to mobile wireless sensor networks (WSN) and the Internet of Things (IoT) because of the significant challenges of power consumption and network connectivity. A technique that takes into consideration the characteristics such as network probability, the identified region of individual nodes, and the radius of the whole identified region is presented in this article. Free-space propagation is carried out in the region of interest. This approach assures network connection, long-term communication sustainability, and maximum energy efficiency. It was discovered that a mathematical network model can be built using the probability theory. It has been possible to examine and evaluate the changes in sensor nodes as a function of distance from the detection region using this approach. As a result, a correlation has been established between a network’s communication radius and the identified region. Additionally, a novel method has been developed to reduce energy consumption and sustain connectivity through boosting the connectivity feature. Notably, IoT-based WSN architectures require more energy optimization than any other network, because they have resource-limited nodes. Also, a simulation plot of the proposed approach’s mathematical network scheme is shown to show if it works. The proposed method consumes much less energy averagely 40% compared to the existing methods, which are LEACH, ZTR, and DSR when the radius is 100.

Validation-based model selection for 13C metabolic flux analysis with uncertain measurement errors.

Accurate measurements of metabolic fluxes in living cells are central to metabolism research and metabolic engineering. The gold standard method is model-based metabolic flux analysis (MFA), where fluxes are estimated indirectly from mass isotopomer data with the use of a mathematical model of the metabolic network. A critical step in MFA is model selection: choosing what compartments, metabolites, and reactions to include in the metabolic network model. Model selection is often done informally during the modelling process, based on the same data that is used for model fitting (estimation data). This can lead to either overly complex models (overfitting) or too simple ones (underfitting), in both cases resulting in poor flux estimates. Here, we propose a method for model selection based on independent validation data. We demonstrate in simulation studies that this method consistently chooses the correct model in a way that is independent on errors in measurement uncertainty. This independence is beneficial, since estimating the true magnitude of these errors can be difficult. In contrast, commonly used model selection methods based on the χ2-test choose different model structures depending on the believed measurement uncertainty; this can lead to errors in flux estimates, especially when the magnitude of the error is substantially off. We present a new approach for quantification of prediction uncertainty of mass isotopomer distributions in other labelling experiments, to check for problems with too much or too little novelty in the validation data. Finally, in an isotope tracing study on human mammary epithelial cells, the validation-based model selection method identified pyruvate carboxylase as a key model component. Our results argue that validation-based model selection should be an integral part of MFA model development.

Zoning Study on the Influence of Sluice Operation on Flood Drainage of Plain River Network

The drainage of river network in Yaobei plain is of great significance to the social and economic development of Yuyao and Ningbo. Linhai Pujiang gate and Taojia Road gate are two important gates for drainage of the river network in Yaobei plain. With the different time of opening the gate for dispatching, the water level reduction values of different towns, streets and communities in the river network are different. If the water level decline in the river network area is classified according to a certain way, the impact degree and impact range of sluice drainage on river network drainage can be studied, so as to classify and partition the impact of drainage according to the degree of impact, township streets can formulate different drainage countermeasures. Therefore, it is of great significance to study the impact of gate operation on river network drainage. In order to fully study the flood drainage function of the sea gate of Yaobei plain river network, based on the preliminary establishment and verification of the plane two-dimensional mathematical model of Yuyao plain river network, this paper calculates the changes of water level and velocity in different areas of towns and streets of Yuyao river network with time and region after the flood drainage operation of the gate for 7 hours under different conditions, according to the range of water level drop of 0.05m and different numerical ranges, this paper classifies the influence areas of large gate drainage on Yaobei river network drainage, and obtains seven partitions of the influence of large gate dispatching on Yaobei river network drainage. According to this partition, the regional river network drainage countermeasures are preliminarily analyzed, which provides a reference basis for the drainage decision-making of township streets.

IoT platform for failure management in water transmission systems

In aging water supply systems, many components have exceeded their service life. Consequently, tools are needed to efficiently manage the failures in these systems. This work describes the development and implementation of a web tool for the management of breakdowns in water transmission networks. The proposed tool, called wAIter, consists of a network of wireless water pressure sensors that send real-time data to an IoT platform. The core of the platform consists of a rule-based decision algorithm, which detects and classifies failures based on the recorded pressure values and then sends an alert to repair them. In addition, wAIter uses the mathematical model of the hydraulic network to estimate the maximum repair time without causing supply interruptions. This information is key in the decision-making process to repair breakdowns and facilitate repair work management. Finally, the results of the implementation in a real water transmission network are presented.

Network Reconstruction and Modelling Made Reproducible with moped.

Mathematical modeling of metabolic networks is a powerful approach to investigate the underlying principles of metabolism and growth. Such approaches include, among others, differential-equation-based modeling of metabolic systems, constraint-based modeling and metabolic network expansion of metabolic networks. Most of these methods are well established and are implemented in numerous software packages, but these are scattered between different programming languages, packages and syntaxes. This complicates establishing straight forward pipelines integrating model construction and simulation. We present a Python package moped that serves as an integrative hub for reproducible construction, modification, curation and analysis of metabolic models. moped supports draft reconstruction of models directly from genome/proteome sequences and pathway/genome databases utilizing GPR annotations, providing a completely reproducible model construction and curation process within executable Python scripts. Alternatively, existing models published in SBML format can be easily imported. Models are represented as Python objects, for which a wide spectrum of easy-to-use modification and analysis methods exist. The model structure can be manually altered by adding, removing or modifying reactions, and gap-filling reactions can be found and inspected. This greatly supports the development of draft models, as well as the curation and testing of models. Moreover, moped provides several analysis methods, in particular including the calculation of biosynthetic capacities using metabolic network expansion. The integration with other Python-based tools is facilitated through various model export options. For example, a model can be directly converted into a CobraPy object for constraint-based analyses. moped is a fully documented and expandable Python package. We demonstrate the capability to serve as a hub for integrating reproducible model construction and curation, database import, metabolic network expansion and export for constraint-based analyses.

Combinatorial topology and geometry of fracture networks.

A map is proposed from the space of planar surface fracture networks to a four-parameter mathematical space, summarizing the average topological connectivity and geometrical properties of a network idealized as a convex polygonal mesh. The four parameters are identified as the average number of nodes and edges, the angular defect with respect to regular polygons, and the isoperimetric ratio. The map serves as a low-dimensional signature of the fracture network and is visually presented as a pair of three-dimensional graphs. A systematic study is made of a wide collection of real crack networks for various materials, collected from different sources. To identify the characteristics of the real materials, several well-known mathematical models of convex polygonal networks are presented and worked out. These geometric models may correspond to different physical fracturing processes. The proposed map is shown to be discriminative, and the points corresponding to materials of similar properties are found to form closely spaced groups in the parameter space. Results for the real and simulated systems are compared in an attempt to identify crack networks of unknown materials.

Mathematical simulation of heat transfer in nonaccessible channels of heat supply system network

High values of standard heat losses in the heating networks of central heat supply systems indicate an opportunity to increase their energy efficiency. Сurrently available mathematical models of heat networks are described in the scientific studies of Polovnikov V.Yu., Kuznetsov G.V., Tarasevich E.I. But they do not solve the problem of assessing changes of the thermal networks state when energy-saving measures are used. The purpose of the study is to determine the permissible heat perception of the device collector for utilization of heat losses in the heating main channel. The study is based on the development and research of mathematical models of heat exchange processes in the heat supply network. A mathematical modeling method is chosen to search for acceptable operating modes of this device. The method can help to determine properly changes in the operation of the heat network. A descriptive mathematical model with distributed parameters based on differential equations with partial derivatives is used in modeling heat transfer processes in the heat network. The model is implemented using the finite element method. The authors propose a device for the utilization of heat losses in the heating channel. The authors have developed mathematical models of heat transfer processes in heat networks of underground trench laying in nonaccessible channels in a traditional design with the use of a heat-reflecting screen and combined action of the network and the device for the utilization of heat losses in the heat channel. Based on the comparison of the calculation results, the permissible heat perception value of the device collector for the utilization of heat losses has been determined. It equals to 90 % of the initial thermal losses. Mathematical models have been verified by comparing the results obtained and the experimental data with an error of less than 6 %. The developed mathematical models allow us to study the influence of heat perception of the device collector and the heat-reflecting screen on the operating mode of the heat network. It can be used to determine the geometric parameters of the collector of the device.

Astrocytes mediate analogous memory in a multi-layer neuron–astrocyte network

Modeling the neuronal processes underlying short-term working memory remains the focus of many theoretical studies in neuroscience. In this paper, we propose a mathematical model of a spiking neural network (SNN) which simulates the way a fragment of information is maintained as a robust activity pattern for several seconds and the way it completely disappears if no other stimuli are fed to the system. Such short-term memory traces are preserved due to the activation of astrocytes accompanying the SNN. The astrocytes exhibit calcium transients at a time scale of seconds. These transients further modulate the efficiency of synaptic transmission and, hence, the firing rate of neighboring neurons at diverse timescales through gliotransmitter release. We demonstrate how such transients continuously encode frequencies of neuronal discharges and provide robust short-term storage of analogous information. This kind of short-term memory can store relevant information for seconds and then completely forget it to avoid overlapping with forthcoming patterns. The SNN is inter-connected with the astrocytic layer by local inter-cellular diffusive connections. The astrocytes are activated only when the neighboring neurons fire synchronously, e.g., when an information pattern is loaded. For illustration, we took grayscale photographs of people’s faces where the shades of gray correspond to the level of applied current which stimulates the neurons. The astrocyte feedback modulates (facilitates) synaptic transmission by varying the frequency of neuronal firing. We show how arbitrary patterns can be loaded, then stored for a certain interval of time, and retrieved if the appropriate clue pattern is applied to the input.

Psychological Health Assessment Model of Enterprise Employees Based on DNN Technology

All enterprises gradually recognise the importance of employees’ healthy psychology to business activities in order to improve their own economic level and occupy a certain leading position in the economic market. The main factors affecting employees’ psychological health are used as input samples in this paper, and a network model of enterprise employees’ psychological health prediction based on DNN is developed. To form a specific set, the psychological health indicators are separated from the complex test items. The key influencing factors in psychological health assessment are chosen as input vectors, and the DNN algorithm’s output results are obtained, analysed, and compared. Following sample training, the artificial NN’s error between predicted and measured values is only 3.55 percent, achieving the desired effect. The DNN principle is used in this paper to create a mathematical prediction network model based on an analysis of psychological factors affecting employees in businesses. The calculation of the final result of the prediction system is simple and flexible when the parameters of the NN are changed, and the network model’s prediction efficiency and accuracy are greatly improved.

Применение сверточных нейронных сетей для распознавания диабетической ретинопатии на цифровых изображениях

The aim of the research. Training of a convolutional neural network for recognition of diabetic retinopathy in digital images of the ocular fundus. Material and methods. A set of digital images from the Kaggle open-access digital repository was used. The set included 12,498 scans of the ocular fundus: 4,584 scans included signs of diabetic retinopathy while 7,914 images did not have such signs. The images with signs of diabetic retinopathy were additionally subdivided according to the disease stages. Building of mathematical models for the convolutional neural network was performed in the PyCharm programming environment using the Python programming language. Results. The maximum accuracy achieved during training of the mathematical model of the convolutional neural network for classification into 5 classes (absence of diabetic retinopathy signs and 4 stages in presence of such signs) was only 57.4 % [56.9; 57.9]. Training of the mathematical model of the convolutional neural network for binary classification (presence of retinopathy at any stage or its absence) lead to 80.7 % accuracy [79.9; 81.2] in recognition of diabetic retinopathy on digital images of the eye retina. Conclusion. A trained convolutional neural network model for binary classification provides for a sufficient degree of accuracy in classification and recognition of presence of diabetic retinopathy in digital images of the eye retina. Therefore, this model may be applied for screening of diabetic retinopathy if integrated with medical information systems or relevant medical equipment.

Limited visibility graphs and modeling obstacles to network interaction

The problems of constructing mathematical and simulation models of wireless computer and sensor networks deployed in areas of terrain containing numerous obstacles that prevent the propagation of a high-frequency radio signal are considered. Graphs of limited visibility are proposed as a mathematical model of the network structure. An algorithm for generating simulation models of terrain areas is presented. The characteristics of the terrain are introduced: the coefficient of the obstacle shape, the effective area, the length of the free path, methods for their calculation are proposed. The influence of the shape factor on the connectivity of a limited visibility graph is shown. The dependences of the effective area and length of the free path from the rank and number of obstacles in the region are obtained.

Электротепловые переходные процессы в сети с высокотемпературным сверхпроводящим трансформатором с функцией токоограничения

The results of a study of thermal and electromagnetic transients in an electric power system containing a high-temperature superconducting (HTS) transformer with a current limiting function are presented. For carrying out the research work, an experimental HTS transformer sample with windings made of Y1Bа2Cu3O7 superconductor and with liquid nitrogen at an operating temperature of 77 K serving as dielectric medium was developed. It has been demonstrated, taking the experimental sample as an example, that transformers with HTS windings can be used to limit short-circuit currents in electrical systems. By using the developed mathematical model of a three-phase single-machine network containing an HTS transformer, it became possible to perform an in-depth analysis of electromagnetic transients in the current limiting mode and to study the thermal and electrodynamic effects produced by the short-circuit current in varying the short-circuit fault kind (single-phase, two-phase and three-phase short-circuit faults) and the type of connected load (active, active-inductive, and active-capacitive) on the current limiting degree. It has been determined that significant heat flows arise at the current limitation moment, which also should be limited. A positive effect of HTS transformers on the electric power system operating modes is shown. The obtained results of theoretical and experimental studies of HTS transformers prove a high efficiency of their current limiting function.

УПРАВЛЕНИЕ СИСТЕМОЙ ФИРМЕННОГО СЕРВИСА АВТОМОБИЛЕЙ ПРИ ВНЕДРЕНИИ РЕЦИКЛИНГА ДЕФЕКТНЫХ ДЕТАЛЕЙ

The increase in the environmental burden from the modern technosphere against the background of increased consumption has actualized the task of expanding the “reuse” concept. An analysis of studies on reverse logistics systems revealed the limitations of existing approaches: consideration of only end-of-life vehicles and poor consideration of the stochastic nature of the processes occurring in the system. In this regard, we have compiled mathematical model of a branded reverse logistics network. It considers income from the sale of repairable defective units that are formed when a vehicle is sent to a service center for repair. On its basis, we have developed a simulation model of a service center, in which the storage and restoration of defective parts is organized. This model can be used as a decision-making tool to manage branded service systems when automotive manufacturers introduce recycling.

Integrative system biology and mathematical modeling of genetic networks identifies shared biomarkers for obesity and diabetes.

Obesity and type 2 and diabetes mellitus (T2D) are two dual epidemics whose shared genetic pathological mechanisms are still far from being fully understood. Therefore, this study is aimed at discovering key genes, molecular mechanisms, and new drug targets for obesity and T2D by analyzing the genome wide gene expression data with different computational biology approaches. In this study, the RNA-sequencing data of isolated primary human adipocytes from individuals who are lean, obese, and T2D was analyzed by an integrated framework consisting of gene expression, protein interaction network (PIN), tissue specificity, and druggability approaches. Our findings show a total of 1932 unique differentially expressed genes (DEGs) across the diabetes versus obese group comparison (p≤0.05). The PIN analysis of these 1932 DEGs identified 190 high centrality network (HCN) genes, which were annotated against 3367 GO terms and functional pathways, like response to insulin signaling, phosphorylation, lipid metabolism, glucose metabolism, etc. (p≤0.05). By applying additional PIN and topological parameters to 190 HCN genes, we further mapped 25 high confidence genes, functionally connected with diabetes and obesity traits. Interestingly, ERBB2, FN1, FYN, HSPA1A, HBA1, and ITGB1 genes were found to be tractable by small chemicals, antibodies, and/or enzyme molecules. In conclusion, our study highlights the potential of computational biology methods in correlating expression data to topological parameters, functional relationships, and druggability characteristics of the candidate genes involved in complex metabolic disorders with a common etiological basis.

МЕТОДИ РОБОТИ КОМАНДИРА ТА ШТАБУ ВІЙСЬКОВОЇ ЧАСТИНИ НАЦІОНАЛЬНОЇ ГВАРДІЇ УКРАЇНИ ТА ЇХ ФОРМАЛІЗАЦІЯ

The governing bodies of the military units of the National Guard of Ukraine objectively or subjectively take into account the system of basic methods of military-scientific knowledge in the performance of combat missions during daily service, emergencies and martial law. According to the authors, there are the following scientific methods-approaches: historical, logical, qualitative, quantitative, natural, model, systemic, conceptual, individual and collective work, complex, program-target, sequential and parallel work; methods-techniques: analysis and synthesis, comparison and analogy, generalization, abstraction, induction and deduction, intuition, prediction of modeling of combat options, forecasting of options, planning, research of combat, briefing, assessment of the situation on the elements of design service and combat operations of the guard and its elements, deception of the enemy, concealment of the plan of service and combat operations of the guard, operational and tactical analysis, qualitative and quantitative justification and military experiment. When formalizing the methods of work of the commander and staff of the military unit of the National Guard of Ukraine, it is advisable to distinguish the following forms: depiction of methods of work in the state space (work schedule); depiction of methods of work by reducing tasks to subtasks (algorithm or program of logical-analytical activity); comprehensive depiction of methods of work (network schedule or mathematical network model to support decision-making or design of combat operations of the guard); depiction of methods of work of combat operations of the commander and staff in the form of theorems, artificial intelligence. New methods of work of combat operations of the guard (first of all, operational level) in the operations of the security and defense sector of the state, can be put into practice after their scientific and theoretical justification. Such a substantiation is currently the subject of a separate research work with the participation of the authors of this article. In the future, these methods may form the basis of a system of basic methods of work of the commander and staff of the military unit during the preparation and conduct of combat operations of the National Guard of Ukraine. In practice, the approach to determining the methods of work of the commander and staff can be implemented during exercises and during their preparation in order to justify the simultaneous or sequential performance of combat (operational) tasks of the guard by appointment, concentration or dispersal of guards, etc.