Journal articles: 'Network Equilibrium Modeling'

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Zhang, Peng, Hao Yue, Xu Zhang, Chunfu Shao, and Wencan Gao. "Modeling the Equilibrium Road Network Capacity." IEEE Access 7 (2019): 168029–47. http://dx.doi.org/10.1109/access.2019.2946977.

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Ignatenko, O. P. "Game theoretic modeling of AIMD network equilibrium." PROBLEMS IN PROGRAMMING, no. 1 (January 2016): 116–28. http://dx.doi.org/10.15407/pp2016.01.116.

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This paper deals with modeling of network’s dynamic using game theory approach. The process of interaction among players (network users), trying to maximize their payoffs (e.g. throughput) could be analyzed using game-based concepts (Nash equilibrium, Pareto efficiency, evolution stability etc.). In this work we presented the model of TCP network’s dynamic and proved existence and uniqueness of solution, formulated payoff matrix for a network game and found conditions of equilibrium existence depending of loss sensitivity parameter. We consider influence if denial of service attacks on the equilibrium characteristics and illustrate results by simulations.

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Chayjan, R. A., and M. Esna-Ashari. "Modeling of heat and entropy sorption of maize (cv. Sc704): neural network method." Research in Agricultural Engineering 56, No. 2 (2010): 69–76. http://dx.doi.org/10.17221/37/2009-rae.

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Equilibrium moisture content of maize affects its values of dehydration heat and entropy. Precise prediction of heat and entropy with regard to its equilibrium moisture content is a simple and fast method for proper estimation of energy required for dehydration of maize and simulation of dried maize storage. Artificial neural network and thermodynamic equations for computation of maize heat and entropy of sorption were used, as a new method. The artificial neural network method for prediction of the equilibrium moisture content of maize was utilized. The heat of sorption of maize is predicted by a power model. After well training of equilibrium moisture content data sets using the artificial neural network models, predictive power of the model was found to be high (R2 = 0.99). A power regression model was also developed for entropy of sorption. At moisture content above 11% (d.b.) the heat and entropy of sorption of maize decreased smoothly and they were highest at moisture content about 8% (d.b.).

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Hasan, M. K., and K. Nabil A. Safwat. "Comparison of Two Transportation Network Equilibrium Modeling Approaches." Journal of Transportation Engineering 126, no. 1 (2000): 35–40. http://dx.doi.org/10.1061/(asce)0733-947x(2000)126:1(35).

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Jiang, Weijin, Sijian Lv, Yirong Jiang, Jiahui Chen, Fang Ye, and Xiaoliang Liu. "Evolutionary dynamics modeling of symbolic social network structure equilibrium." China Communications 17, no. 10 (2020): 229–40. http://dx.doi.org/10.23919/jcc.2020.10.017.

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Klimenko, Stanislav, Igor Nikitin, Lialia Nikitina, Kira Konich, and Kevin Reinartz. "Numerical modeling of relativistic networks." International Journal of Modern Physics C 28, no. 03 (2017): 1750035. http://dx.doi.org/10.1142/s0129183117500358.

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In this paper, we consider a model of relativistic networks, a topological extension of the model of relativistic particles. Numerical experiments are performed to study thermodynamical properties of the model and their relationship with explicit symmetry of solutions under time reversal. An efficient algorithm is constructed, allowing to generate numerical solutions of high complexity in the given model. The algorithm includes a generator of random topology, an optimal choice of stiffness coefficients for the network and a solver for constrained optimization problem, describing an equilibrium of the network. A system, studied in the given paper, contains about 100 thousands of equations and inequalities. Possible extensions of the algorithm are discussed, necessary for processing of relativistic networks of higher complexity, containing millions of equations.

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Ni, Linglin, Chuqiao Chen, Xiaokun (Cara) Wang, and Xiqun (Michael) Chen. "Modeling network equilibrium of competitive ride-sourcing market with heterogeneous transportation network companies." Transportation Research Part C: Emerging Technologies 130 (September 2021): 103277. http://dx.doi.org/10.1016/j.trc.2021.103277.

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Zhao, Ying, Luis R. De Jesus, Peter Stein, Gregory A. Horrocks, Sarbajit Banerjee, and Bai-Xiang Xu. "Modeling of phase separation across interconnected electrode particles in lithium-ion batteries." RSC Advances 7, no. 65 (2017): 41254–64. http://dx.doi.org/10.1039/c7ra07352f.

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Zhang, Shujuan, Zhen Jin, and Juan Zhang. "The Dynamical Modeling Analysis of the Spreading of Passive Worms in P2P Networks." Discrete Dynamics in Nature and Society 2018 (September 20, 2018): 1–13. http://dx.doi.org/10.1155/2018/1656907.

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Passive worms are prone to spreading through Peer-to-Peer networks, and they pose a great threat to the security of the network. In this paper, considering network heterogeneity and the number of hops a search can reach, we propose a novel mathematical model to study the dynamics of the propagation of passive worms. For the proposed model, the basic reproduction number R0 is derived by employing the existence of the positive equilibrium. And the stabilities of the worm-free equilibrium and positive equilibrium are analyzed. Moreover, we verify the rationality of the model established by comparing the stochastic simulation with the numerical simulation. Finally, we examine the effect of the number of hops on the spread of passive worms and discuss the various immunization strategies. We find that if R0>1, the propagation speed of passive worms is accelerated with the increase of hop count d; if R0<1, the number of infected peers decreases rapidly with the increase of the value of d and drops to zero eventually. Results show that the network topology and the number of hops can affect the spread of passive worms.

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Feng, Liping, Lipeng Song, Qingshan Zhao, and Hongbin Wang. "Modeling and Stability Analysis of Worm Propagation in Wireless Sensor Network." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/129598.

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An improved SIRS model considering communication radius and distributed density of nodes is proposed. The proposed model captures both the spatial and temporal dynamics of worms spread process. Using differential dynamical theories, we investigate dynamics of worm propagation to time in wireless sensor networks (WSNs). Reproductive number which determines global dynamics of worm propagation in WSNs is obtained. Equilibriums and their stabilities are also found. If reproductive number is less than one, the infected fraction of the sensor nodes disappears and if the reproduction number is greater than one, the infected fraction asymptotically stabilizes at the endemic equilibrium. Based on the reproduction number, we discuss the threshold of worm propagation about communication radius and distributed density of nodes in WSNs. Finally, numerical simulations verify the correctness of theoretical analysis.

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Singh, Ram, Attiq U. Rehman, Mehedi Masud, et al. "Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network." AIMS Mathematics 7, no. 4 (2022): 5175–98. http://dx.doi.org/10.3934/math.2022289.

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<abstract>In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity $ \mathcal{R}_{0} $ to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely $ (i) $ free equilibrium points, $ (ii) $ absence of stem and progenitor cells, and $ (iii) $ endemic equilibrium points are investigated in this study. The model is first formulated in non-fractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.</abstract>

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Li, Shuping, and Zhen Jin. "Modeling and Analysis of New Products Diffusion on Heterogeneous Networks." Journal of Applied Mathematics 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/940623.

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We present a heterogeneous networks model with the awareness stage and the decision-making stage to explain the process of new products diffusion. If mass media is neglected in the decision-making stage, there is a threshold whether the innovation diffusion is successful or not, or else it is proved that the network model has at least one positive equilibrium. For networks with the power-law degree distribution, numerical simulations confirm analytical results, and also at the same time, by numerical analysis of the influence of the network structure and persuasive advertisements on the density of adopters, we give two different products propagation strategies for two classes of nodes in scale-free networks.

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Liu, Ming, and Yihong Xiao. "Modeling and Analysis of Epidemic Diffusion within Small-World Network." Journal of Applied Mathematics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/841531.

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To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS) model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS) model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.

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Liu, Haoxiang, and David Z. W. Wang. "Modeling and solving discrete network design problem with stochastic user equilibrium." Journal of Advanced Transportation 50, no. 7 (2016): 1295–313. http://dx.doi.org/10.1002/atr.1402.

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Jiang, Jing Long, Yan Zhou, Jing Jing Wang, and Rui Jing Han. "Green Supply Chain Network Equilibrium Model with Genetic Algorithm." Advanced Materials Research 712-715 (June 2013): 3031–37. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.3031.

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In this paper, a new model of oligopolistic competition for green supply chains is developed in the case of single product with the inclusion of environmental concerns. Each firm aims to not only maximize its profit but also minimize its emissions throughout its supply chain. Genetic algorithm is utilized for solving the Nash-Cournot equilibrium without any assumption of continuity and differentiability. With the numerical examples, we not only illustrate the generality of the modeling framework but also how the model can be used in practice to comprehend the effects of changes in the weights.

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Liu, Chunling, Jizi Li, Guo Li, and Xiaogang Cao. "Modeling of Across-Chain Network Dynamic Competition for MNC in Industrial Cluster." International Journal of Advanced Pervasive and Ubiquitous Computing 3, no. 4 (2011): 30–49. http://dx.doi.org/10.4018/japuc.2011100105.

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The huge market and perfect production system in China are attracting more multi-national companies’ interest to invest in China in the form of Foreign Direct Investment (FDI). Therefore, multi-national companies are willing to integrate and optimize global supply chain networks of their own, which enable them to reduce cost and improve market response. As a result, multi-national companies usually embed into local industrial clusters through financial and technological comparative merits to sharpen their competitive edge. This paper considers the across-chain network equilibrium problem involving process of competition and melting between this new global chain and an already existing local chain. The authors model the optimizing behavior of these two chains, derive the equilibrium conditions, and establish the variational inequality formulation, and solve it by using the modified algorithm. Finally, the authors illustrate the model through numerical example and discuss relationships among the price, quantity, technological progress, and satisfaction among two dynamic phases.

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Liu, Bo, Yanqing Cen, and Xianghui Song. "Approximating Dynamic Equilibrium Analysis in Multi-Region Network Based on Macroscopic Fundamental Diagram." Journal of Advanced Transportation 2022 (August 26, 2022): 1–22. http://dx.doi.org/10.1155/2022/2604150.

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Modeling and control of road traffic in large-scale urban networks present considerable challenges. The traffic equilibrium phenomena, with the question of route choice behavior in case of heterogeneous urban networks, has not been thoroughly investigated in parsimonious and classical models due to the limitation, like large network size, spatiotemporal propagation of congestion, and the interaction between driver decisions, etc. In this paper, we propose a bi-level approximating dynamic equilibrium model (BLADEM) for the approximating dynamic equilibrium analysis in multi-region network based on macroscopic fundamental diagram (MFD). The proposed model combines the region-based model and the internal-region model. With the information from region MFD, the region-based model is used to implement the time-dependent regional route choice estimation. Traffic equilibrium condition (dynamic user equilibrium, DUE) is considered in an internal-region model with time-aggregated regional OD demand from the region level. Furthermore, the complexity of the proposed model is derived. Then, the comparative analysis of the algorithm complexity between the proposed model and the DUE model is given. The proposed model is evaluated based on the high-resolution vehicle trajectory data (or connected vehicles trajectory data) from the DiDi platform collected in Chengdu, China with more than 3,000,000 GPS points during a typical workday. The evaluation results show that the proposed model can obtain the approximating traffic dynamics compared with the DUE algorithm. Pleasantly, the improved calculation efficiency is between 21% and 42%. The results indicate the promising potential of using the proposed model to analyze approximating dynamic equilibrium in the multi-region heterogeneous network.

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LEERMAKERS, F. A. M., and E. B. ZHULINA. "SELF-CONSISTENT FIELD MODELING OF THE NEUROFILAMENT NETWORK." Biophysical Reviews and Letters 03, no. 04 (2008): 459–89. http://dx.doi.org/10.1142/s179304800800085x.

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We have investigated, on a self-consistent field level, the equilibrium structure of the neurofilament network formed by the NF -H, NF -M and NF -L proteins, using the one-gradient version of the numerical model of Scheutjens and Fleer. We demonstrate a reticulation of NFs in parallel bundles that occurs due to hydrophobic attractions between apolar aminoacid residues in the terminal parts of the M- and H-tails. We elaborate on the feasibility that the stability of the NF network can be enhanced by specific interactions between the projection domains, possibly induced by accessary proteins. We demonstrate that the phosphorylation of KSP repeats in the M- and H-tails promotes the cross-bridging between the NFs and therefore helps form the NF network.

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Lv, Yu Kun, Shuai Chang, Ze Kun Ge, and Wei Run Lv. "Research on Modeling Method of Thermodynamic Verifying Calculation for Heat-Supply Network." Advanced Materials Research 550-553 (July 2012): 2927–31. http://dx.doi.org/10.4028/www.scientific.net/amr.550-553.2927.

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This paper establishes a model of thermal checking calculation of heat supply network based on graph theory and thermodynamic calculation, by analyzing directly buried installation of thermal network utilizing the heat-transfer mechanism and principle of thermal equilibrium. Take the directly buried heat supply network for instance, in which hot water is as a heat medium. The establishment of the spatial database and attribute database of thermal network based on GIS and Microsoft Access respectively, as well as the thermodynamic calculation of thermal networks based on GIS developed by object oriented programming language VB is done .Thus enables point-and-click query, update on property and thermal calculation functions. Finally, through comparative study on the calculation results and actual operation of the system, we find the relative error of the thermodynamic temperature is less than 10%.

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Liu, Li Hua, Ya Ping Zhang, and Yu Wei. "Modeling and Simulation of Bus Priority Oriented Urban Road Network Elastic Equilibrium." Advanced Engineering Forum 5 (July 2012): 150–54. http://dx.doi.org/10.4028/www.scientific.net/aef.5.150.

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As the poor applicability of rail transit and elevated road limited by economy, population and many other factors, the waste of road resources caused by bus lane, maximizing application of available road resources and bus facilities, reducing the environmental pollution is the critical issue faced by current situation of urban transportation development in China. Guided by Bus Priority Oriented, utilized comprehensive techniques, such as ABC classification, bi-level programming model, sensitivity analysis, this paper constructed a theoretical frame of elastic equilibrium based on system optimization. Taking time and environment as optimized objectives, This paper established the Bi-Level multiobjective programming model based on travel time, and programmed with MATLAB for the calculation. Finally, the case study is illustrated. the software VISSIM was adopted to realize the simulation of the volume before and after the implementation of elastic plan in urban areas of PingDingshan. The simulation results showed the validity and feasibility of the modeling and simulation of Bus Priority Oriented urban road network elastic equilibrium.

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Yao, Jian, Ilan Adler, and Shmuel S. Oren. "Modeling and Computing Two-Settlement Oligopolistic Equilibrium in a Congested Electricity Network." Operations Research 56, no. 1 (2008): 34–47. http://dx.doi.org/10.1287/opre.1070.0416.

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Moghadam, M., and S. Asgharzadeh. "On the application of artificial neural network for modeling liquid-liquid equilibrium." Journal of Molecular Liquids 220 (August 2016): 339–45. http://dx.doi.org/10.1016/j.molliq.2016.04.098.

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Zhang, Junlin, and Hai Yang. "Modeling route choice inertia in network equilibrium with heterogeneous prevailing choice sets." Transportation Research Part C: Emerging Technologies 57 (August 2015): 42–54. http://dx.doi.org/10.1016/j.trc.2015.06.005.

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Faúndez, Claudio A., Felipe A. Quiero, and José O. Valderrama. "Phase equilibrium modeling in ethanol+congener mixtures using an artificial neural network." Fluid Phase Equilibria 292, no. 1-2 (2010): 29–35. http://dx.doi.org/10.1016/j.fluid.2010.01.001.

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Lu, Chung-Cheng, and Hani S. Mahmassani. "Modeling User Responses to Pricing." Transportation Research Record: Journal of the Transportation Research Board 2085, no. 1 (2008): 124–35. http://dx.doi.org/10.3141/2085-14.

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In a previous contribution, the authors showed how to incorporate user heterogeneity in determining equilibrium route choices in a network in response to pricing. Presented here is a generalization of that framework to incorporate joint consideration of route and departure time as well as heterogeneity in a wider range of behavioral characteristics. A multicriterion simultaneous route and departure time user equilibrium (MSRDUE) model is presented, along with a simulation-based algorithm intended for practical network applications. The model explicitly considers heterogeneous users with different values of time (VOTs) and values of (early or late) schedule delay (VOESDs or VOLSDs) in their joint choice of departure times and paths characterized by a set of trip attributes that include travel time, out-of-pocket cost, and schedule delay cost. The problem is formulated as an infinite-dimensional variational inequality problem and solved by a column generation-based algorithmic framework that embeds (a) an extreme nondominated alternative-finding algorithm to obtain the VOT, VOESD, and VOLSD breakpoints that define multiple user classes and the associated least trip cost (joint departure time and path) alternative for each user class; (b) a traffic simulator to capture traffic flow dynamics and determine travel costs experienced; and (c) a path-swapping multiclass alternative flow-updating scheme to solve the restricted multiclass SRDUE problem defined by a subset of feasible alternatives. Application to an actual network illustrates the properties of the algorithm and underscores the importance of capturing user heterogeneity and temporal shifts in the appraisal of dynamic pricing schemes.

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Blocher, Jordan, and Frederick C. Harris. "An Equilibrium Analysis of a Secondary Mobile Data-Share Market." Information 12, no. 11 (2021): 434. http://dx.doi.org/10.3390/info12110434.

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Internet service providers are offering shared data plans where multiple users may buy and sell their overage data in a secondary market managed by the ISP. We propose a game-theoretic approach to a software-defined network for modeling this wireless data exchange market: a fully connected, non-cooperative network. We identify and define the rules for the underlying progressive second price (PSP) auction for the respective network and market structure. We allow for a single degree of statistical freedom—the reserve price—and show that the secondary data exchange market allows for greater flexibility in the acquisition decision making of mechanism design. We have designed a framework to optimize the strategy space using the elasticity of supply and demand. Wireless users are modeled as a distribution of buyers and sellers with normal incentives. Our derivation of a buyer-response strategy for wireless users based on second price market dynamics leads us to prove the existence of a balanced pricing scheme. We examine shifts in the market price function and prove that our network upholds the desired properties for optimization with respect to software-defined networks and prove the existence of a Nash equilibrium in the overlying non-cooperative game.

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Marin, Andrea. "PRODUCT-FORM IN G-NETWORKS." Probability in the Engineering and Informational Sciences 30, no. 3 (2016): 345–60. http://dx.doi.org/10.1017/s0269964816000048.

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The introduction of the class of queueing networks called G-networks by Gelenbe has been a breakthrough in the field of stochastic modeling since it has largely expanded the class of models which are analytically or numerically tractable. From a theoretical point of view, the introduction of the G-networks has lead to very important considerations: first, a product-form queueing network may have non-linear traffic equations; secondly, we can have a product-form equilibrium distribution even if the customer routing is defined in such a way that more than two queues can change their states at the same time epoch. In this work, we review some of the classes of product-forms introduced for the analysis of the G-networks with special attention to these two aspects. We propose a methodology that, coherently with the product-form result, allows for a modular analysis of the G-queues to derive the equilibrium distribution of the network.

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Feng, Liping, Hongbin Wang, Qi Han, Qingshan Zhao, and Lipeng Song. "Modeling Peer-to-Peer Botnet on Scale-Free Network." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/212478.

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Peer-to-peer (P2P) botnets have emerged as one of the serious threats to Internet security. To prevent effectively P2P botnet, in this paper, a mathematical model which combines the scale-free trait of Internet with the formation of P2P botnet is presented. Explicit mathematical analysis demonstrates that the model has a globally stable endemic equilibrium when infection rate is greater than a critical value. Meanwhile, we find that, in scale-free network, the critical value is very little. Hence, it is unrealistic to completely dispel the P2P botnet. Numerical simulations show that one can take effective countermeasures to reduce the scale of P2P botnet or delay its outbreak. Our findings can provide meaningful instruction to network security management.

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Robson, Edward, and Vinayak V. Dixit. "Constructing a Database for Computable General Equilibrium Modeling of Sydney, Australia, Transport Network." Transportation Research Record: Journal of the Transportation Research Board 2606, no. 1 (2017): 54–62. http://dx.doi.org/10.3141/2606-07.

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In the search for benefits to justify transport projects, economic appraisals have increasingly incorporated the valuation of impacts to the wider economy. Computable general equilibrium (CGE) models provide a framework to estimate these impacts by simulating the interactions of urban economies and transport networks. In CGE models, households and firms are represented by microeconomic behavioral functions, and markets adjust according to prices. As markets both inside and outside the transport network are taken into account, a wide variety of measures that can assist in economic appraisals can be extracted. However, urban CGE models are computationally burdensome and require detailed, spatially disaggregate data. This paper discusses the methodology used to develop a database, including an input–output table, for the calibration of an urban CGE model for Sydney, Australia. Official and publicly available data sources were manipulated by using a number of mathematical and statistical techniques to compile a table for 249 regions and 20 sectors across Sydney. Issues, such as determining the appropriate level of aggregation, generating incomplete data, and managing conflicting data, that other input–output table developers may encounter when constructing multiregional tables were addressed in the study. The table entries themselves were mapped and explored, as they provide a useful study of the spatial economy of Sydney. Future work will focus on streamlining the construction of input–output tables and incorporating new data sources.

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Cats, Oded, and Jens West. "Learning and Adaptation in Dynamic Transit Assignment Models for Congested Networks." Transportation Research Record: Journal of the Transportation Research Board 2674, no. 1 (2020): 113–24. http://dx.doi.org/10.1177/0361198119900138.

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The distribution of passenger demand over the transit network is forecasted using transit assignment models which conventionally assume that passenger loads satisfy network equilibrium conditions. The approach taken in this study is to model transit path choice as a within-day dynamic process influenced by network state variation and real-time information. The iterative network loading process leading to steady-state conditions is performed by means of day-to-day learning implemented in an agent-based simulation model. We explicitly account for adaptation and learning in relation to service uncertainty, on-board crowding and information provision in the context of congested transit networks. This study thus combines the underlying assignment principles that govern transit assignment models and the disaggregate demand modeling enabled by agent-based simulation modeling. The model is applied to a toy network for illustration purposes, followed by a demonstration for the rapid transit network of Stockholm, Sweden. A full-scale application of the proposed model shows the day-to-day travel time and crowding development for different levels of network saturation and when deploying different levels of information availability.

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Avramidis, Stavros, and Lazaros Iliadis. "Wood-water sorption isotherm prediction with artificial neural networks: A preliminary study." Holzforschung 59, no. 3 (2005): 336–41. http://dx.doi.org/10.1515/hf.2005.055.

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Abstract This is a preliminary study that proposes an original prototype artificial neural network to be used in addition to the two classic sorption isotherm modeling methods, Hailwood-Horrobin (HH) and Guggenheim-Anderson-deBoer (GAB), in predicting the equilibrium moisture content in wood at three different temperatures (30, 45 and 60°C) for softwood (lodgepole pine) sapwood and heartwood specimens. Contrary to the HH and GAB equations, which use physical data for modeling, the predictive power of the artificial neural network is based on both physical and chemical data for the specific wood types. The results prove the potential efficient use of neural networks in predicting moisture content based not only on the ambient conditions, but also on taking into consideration the chemical composition of wood.

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Gupta, Churni, Necibe Tuncer, and Maia Martcheva. "A network immuno-epidemiological model of HIV and opioid epidemics." Mathematical Biosciences and Engineering 20, no. 2 (2022): 4040–68. http://dx.doi.org/10.3934/mbe.2023189.

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<abstract>In this paper, we introduce a novel multi-scale network model of two epidemics: HIV infection and opioid addiction. The HIV infection dynamics is modeled on a complex network. We determine the basic reproduction number of HIV infection, $ \mathcal{R}_{v} $, and the basic reproduction number of opioid addiction, $ \mathcal{R}_{u} $. We show that the model has a unique disease-free equilibrium which is locally asymptotically stable when both $ \mathcal{R}_{u} $ and $ \mathcal{R}_{v} $ are less than one. If $ \mathcal{R}_{u} &gt; 1 $ or $ \mathcal{R}_{v} &gt; 1 $, then the disease-free equilibrium is unstable and there exists a unique semi-trivial equilibrium corresponding to each disease. The unique opioid only equilibrium exist when the basic reproduction number of opioid addiction is greater than one and it is locally asymptotically stable when the invasion number of HIV infection, $ \mathcal{R}^{1}_{v_i} $ is less than one. Similarly, the unique HIV only equilibrium exist when the basic reproduction number of HIV is greater than one and it is locally asymptotically stable when the invasion number of opioid addiction, $ \mathcal{R}^{2}_{u_i} $ is less than one. Existence and stability of co-existence equilibria remains an open problem. We performed numerical simulations to better understand the impact of three epidemiologically important parameters that are at the intersection of two epidemics: $ q_v $ the likelihood of an opioid user being infected with HIV, $ q_u $ the likelihood of an HIV-infected individual becoming addicted to opioids, and $ \delta $ recovery from opioid addiction. Simulations suggest that as the recovery from opioid use increases, the prevalence of co-affected individuals, those who are addicted to opioids and are infected with HIV, increase significantly. We demonstrate that the dependence of the co-affected population on $ q_u $ and $ q_v $ are not monotone.</abstract>

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Zhang, Hong, Shigen Shen, Qiying Cao, Xiaojun Wu, and Shaofeng Liu. "Modeling and analyzing malware diffusion in wireless sensor networks based on cellular automaton." International Journal of Distributed Sensor Networks 16, no. 11 (2020): 155014772097294. http://dx.doi.org/10.1177/1550147720972944.

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Wireless sensor networks, as a multi-hop self-organized network system formed by wireless communication, are vulnerable to malware diffusion by breaking the data confidentiality and service availability, owing to their low configuration and weak defense mechanism. To reveal the rules of malware diffusion in the really deployed wireless sensor networks, we propose a model called Malware Diffusion Based on Cellular Automaton to describe the dynamics of malware diffusion based on cellular automaton. According to the model, we first analyze and obtain the differential equations, which can reflect the various state dynamics of sensor nodes with cellular automaton. Then, we attain the equilibrium points of the model Malware Diffusion Based on Cellular Automaton to determine the threshold for whether malware will diffuse or die out in wireless sensor networks. Furthermore, we compute the basic regeneration number of the model Malware Diffusion Based on Cellular Automaton using the next-generation matrix and prove the stability of the equilibrium points. Finally, via experimental simulation, we verify the effectiveness of the model Malware Diffusion Based on Cellular Automaton, which can provide administrators with the theoretical guidance on suppressing malware diffusion in wireless sensor networks.

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Ozbay, Kaan, Aleek Datta, and Pushkin Kachroo. "Application of Stochastic Learning Automata for Modeling Departure Time and Route Choice Behavior." Transportation Research Record: Journal of the Transportation Research Board 1807, no. 1 (2002): 154–62. http://dx.doi.org/10.3141/1807-19.

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Stochastic learning automata (SLA) theory is used to model the learning behavior of commuters within the context of the combined departure time route choice (CDTRC) problem. The SLA model uses a reinforcement scheme to model the learning behavior of drivers. A multiaction linear reward-ϵ-penalty reinforcement scheme was introduced to model the learning behavior of travelers based on past departure time choice and route choice. A traffic simulation was developed to test the model. The results of the simulation are intended to show that drivers learn the best CDTRC option, and the network achieves user equilibrium in the long run. Results indicate that the developed SLA model accurately portrays the learning behavior of drivers, while the network satisfies user equilibrium conditions.

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Kitthamkesorn, Songyot, Anthony Chen, Xiangdong Xu, and Seungkyu Ryu. "Modeling Mode and Route Similarities in Network Equilibrium Problem with Go-Green Modes." Networks and Spatial Economics 16, no. 1 (2013): 33–60. http://dx.doi.org/10.1007/s11067-013-9201-y.

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Joekar-Niasar, Vahid, and S. Majid Hassanizadeh. "Effect of fluids properties on non-equilibrium capillarity effects: Dynamic pore-network modeling." International Journal of Multiphase Flow 37, no. 2 (2011): 198–214. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2010.09.007.

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S. R., Mugunthan. "Wireless Rechargeable Sensor Network Fault Modeling and Stability Analysis." March 2021 3, no. 1 (2021): 47–54. http://dx.doi.org/10.36548/jscp.2021.1.006.

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Wide attention has been acquired by the field of wireless rechargeable sensor networks (WRSNs ) across the globe due to its rapid developments. Addressing the security issues in the WRSNs is a crucial task. The process of reinfection, charging and removal in WRSN is performed with a low-energy infected susceptible epidemic model presented in this paper. A basic reproductive value is attained after which the epidemic equilibrium and disease-free points of global and local stabilities are simulated and analyzed. Relationship between the reproductive value and rate of charging as well as the stability is a unique characteristic exhibited by the proposed model observed from the simulations. The WRSN and malware are built with ideal attack-defense strategies. When the reproductive value is not equal to one, the accumulated cost and non-optimal control group are compared in the sensor node evolution and the optimal strategies are validated and verified.

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Lu, Chengqiang, Qi Liu, Chao Wang, Zhenya Huang, Peize Lin, and Lixin He. "Molecular Property Prediction: A Multilevel Quantum Interactions Modeling Perspective." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1052–60. http://dx.doi.org/10.1609/aaai.v33i01.33011052.

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Predicting molecular properties (e.g., atomization energy) is an essential issue in quantum chemistry, which could speed up much research progress, such as drug designing and substance discovery. Traditional studies based on density functional theory (DFT) in physics are proved to be time-consuming for predicting large number of molecules. Recently, the machine learning methods, which consider much rule-based information, have also shown potentials for this issue. However, the complex inherent quantum interactions of molecules are still largely underexplored by existing solutions. In this paper, we propose a generalizable and transferable Multilevel Graph Convolutional neural Network (MGCN) for molecular property prediction. Specifically, we represent each molecule as a graph to preserve its internal structure. Moreover, the well-designed hierarchical graph neural network directly extracts features from the conformation and spatial information followed by the multilevel interactions. As a consequence, the multilevel overall representations can be utilized to make the prediction. Extensive experiments on both datasets of equilibrium and off-equilibrium molecules demonstrate the effectiveness of our model. Furthermore, the detailed results also prove that MGCN is generalizable and transferable for the prediction.

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Ma, Wei, and Zhen (Sean) Qian. "A Generalized Single-Level Formulation for Origin–Destination Estimation under Stochastic User Equilibrium." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 48 (2018): 58–68. http://dx.doi.org/10.1177/0361198118782041.

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Origin–destination (OD) demand is an indispensable component for modeling transportation networks, and the prevailing approach to estimating OD demand using traffic data is through bi-level optimization. A bi-level optimization approach considering equilibrium constraints is computationally challenging for large-scale networks, which prevents the OD estimation (ODE) being scalable. To solve for ODE in large-scale networks, this paper develops a generalized single-level formulation for ODE incorporating stochastic user equilibrium (SUE) constraints. Two single-level ODE models are specifically discussed and tested. One employs a SUE based on the satisfaction function, and the other is based on the Logit model. Analytical properties of the new formulation are analyzed. The estimation methods are proven to be unbiased. Gradient-based algorithms are proposed to solve for this formulation. Numerical experiments are conducted on a small network and a large network, along with sensitivity analysis on sensor locations, historical OD information and measurement error. Results indicate that the new single-level formulation, in conjunction with the proposed solution algorithms, can achieve accuracy comparable with the bi-level formulation, while being much more computationally efficient for large networks.

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Gorelova, D. Yu. "Methodological approaches to determination of stability coefficient in network organization structures." Herald of the Ural State University of Railway Transport, no. 2 (2020): 110–19. http://dx.doi.org/10.20291/2079-0392-2020-2-110-119.

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The article focuses on theoretical approaches of modeling of network organization structures. Advantages and disadvantages of network organization structures are given. Network nodes are shown in modeling as graphs and connecting lines as its ribs. Issues of organization networks stability from the model viewpoint were analyzed. Main requirements to geometry configuration of organization networks are stated which must correspond to a practical goal, i.e.: stability, reliability, feasibility or profitability. The term «geometrical stability» was examined and conditions for its achievement. The concept of integrated assessment of network organization structure stability is presented. A set of mathematical features is proposed for construction a mathematical model of organization network stability, divided into two groups of coefficients (geometrical and economic), reflecting the framework of the network structure under study as a geometrical object. A number of coefficients is deduced and studied, which makes it possible to evaluate the organization network on a wider and deeper scale. Concepts of quantitative and structural stability are studied. A principle of equilibrium for the network organization structure as a social and economic system is formulated. Their distinctive feature is found out. Underlying ideas of development of the integrated indicator of stability and methods to determine network organization structure of major company management were grounded. New approaches to calculation of the integrated indicator of network organization structure stability are suggested.

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O’Mahony, Margaret M., Kieran J. Kirwan, and Sean McGrath. "Modeling the Internalization of External Costs of Transport." Transportation Research Record: Journal of the Transportation Research Board 1576, no. 1 (1997): 93–98. http://dx.doi.org/10.3141/1576-12.

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Increases in traffic congestion and pollution levels in urban areas in Europe have resulted in the need to develop reliable and transferable methods of assessing the environmental and social effects of transport pricing and other regulatory policies. To achieve this, it is necessary to quantify the marginal social costs of transport as a function of travel demand and then to obtain the optimum marginal social cost by maximization of utility subject to budget constraints. The work conducted by Trinity College, Dublin, on a project (TRENEN) funded by the European Union JOULE II Non-Nuclear Energy Program is described. The project involved the development and calibration of an optimization model, the TRENEN model, based on welfare economics to address fundamental issues relating to the external costs of transport. The determination of the optimum function type used to represent the transport demand–delay relationship (which was obtained using an existing four-stage network model) for input to the TRENEN model is described. The TRENEN model is quite different from network modeling in that it is fundamentally macrolevel in its approach and works in an economic framework rather than at a traffic network level. Also discussed is a calibration of the TRENEN model for Dublin, the capital city of Ireland. Dublin currently experiences high levels of traffic congestion, particularly in the morning peak period, resulting from a heavy demand for car travel and the poor level of service associated with public transport. The possibility of using the TRENEN model, which addresses the issue of “social equilibrium” at a macrolevel, in conjunction with the more traditional “network equilibrium” approach used by traditional four-stage microsimulation modeling techniques, is discussed.

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Chou, Porchiung Ben, Michael A. Ehrlich, and Ronald Sverdlove. "Efficiency, stability, and government regulation of risk-sharing financial networks." Managerial Finance 45, no. 6 (2019): 760–80. http://dx.doi.org/10.1108/mf-06-2018-0287.

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Purpose By applying models of social and economic networks to financial institutions, the purpose of this paper is to address the issues of how policy makers can promote financial network stability and social efficiency. Design/methodology/approach The authors characterize the decentralized network formation of financial institutions in three stages through which institutions choose to become member banks connected to a central bank, bank-holding company subsidiaries or non-banks. Financial institutions choose one of the three roles in an endogenous process by considering the effects of sharing shocks among the members of the network. In the model, there is a social-welfare-maximizing government regulator at the center of the network. Findings The authors show that the stable equilibrium network is not always the efficient network, so the central authority must use policy instruments to ensure that the stable equilibrium network is as close as possible to the efficient network. Research limitations/implications To obtain the theoretical results, the authors make assumptions about the utility function and risk aversion of a financial institution, as well as about the costs of network formation. These assumptions might need to be relaxed to bring the model closer to real-world institutions. Practical implications The results suggest that regulators must try to set their policy variables to make the efficient network as close as possible to the stable network. Originality/value The contribution is to incorporate concepts from social network theory into the modeling of financial networks. The results may be of use to regulators in maintaining the stability of the financial system.

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Hsieh, Chih-Sheng, Lung-Fei Lee, and Vincent Boucher. "Specification and estimation of network formation and network interaction models with the exponential probability distribution." Quantitative Economics 11, no. 4 (2020): 1349–90. http://dx.doi.org/10.3982/qe944.

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We model network formation and interactions under a unified framework by considering that individuals anticipate the effect of network structure on the utility of network interactions when choosing links. There are two advantages of this modeling approach: first, we can evaluate whether network interactions drive friendship formation or not. Second, we can control for the friendship selection bias on estimated interaction effects. We provide microfoundations of this statistical model based on the subgame perfect equilibrium of a two‐stage game and propose a Bayesian MCMC approach for estimating the model. We apply the model to study American high school students' friendship networks using the Add Health dataset. From two interaction variables, GPA and smoking frequency, we find that the utility of interactions in academic learning is important for friendship formation, whereas the utility of interactions in smoking is not. However, both GPA and smoking frequency are subject to significant peer effects.

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Zhang, Jie, Zhiying Zhang, and Yuehui Liu. "Impact of Interest Rate Risk on Supply Chain Network under Bank Credit and Trade Credit Financing." Mathematical Problems in Engineering 2021 (December 8, 2021): 1–12. http://dx.doi.org/10.1155/2021/4718912.

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The purpose of this study is to propose a methodology that reflects the impact of interest rate risk on firms in supply chain network under bank financing and trade credit and further describe how trade credit improves the impact of interest rate risk on supply chain network through a financial flow equilibrium. A mean-variance framework and a network equilibrium analysis are integrated to provide a modeling framework. The model allows for the investigation of how bank credit financing (BCF) and trade credit financing (TCF) affect the payment strategy and financial flow of interconnected firms in supply chain networks and how they are affected by interest rate risks. The optimal behavior of manufacturers and retailers is described through variational inequality. We construct a supply chain network equilibrium model and derive qualitative properties of the solution and the function that becomes assimilated to the variational inequality problem. Additionally, variational inequality is solved using the modified projection method. This study extends the research on the impact of interest rate risk on the decision in supply chain network of firms. While other studies focus on the game between banks and firms, only a few authors have made attempts to examine the game between one manufacturer and one retailer in supply chain. An effective trade credit strategy is obtained by balancing cash and credit transactions. Through the case study, we learn how to balance the capital flow effectively to improve the negative impact of interest rate risk on supply chain.

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Samuilik, Inna, and Felix Sadyrbaev. "On trajectories of a system modeling evolution of genetic networks." Mathematical Biosciences and Engineering 20, no. 2 (2022): 2232–42. http://dx.doi.org/10.3934/mbe.2023104.

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<abstract> A system of ordinary differential equations is considered, which arises in the modeling of genetic networks and artificial neural networks. Any point in phase space corresponds to a state of a network. Trajectories, which start at some initial point, represent future states. Any trajectory tends to an attractor, which can be a stable equilibrium, limit cycle or something else. It is of practical importance to answer the question of whether a trajectory exists which connects two points, or two regions of phase space. Some classical results in the theory of boundary value problems can provide an answer. Some problems cannot be answered and require the elaboration of new approaches. We consider both the classical approach and specific tasks which are related to the features of the system and the modeling object. </abstract>

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Muthuvel, Somasundaram, Sivakumar Rajagopal, and Shamala K. Subramaniam. "Analysis of Security Issues in Wireless Body Area Networks in Heterogeneous Networks." Sensors 22, no. 19 (2022): 7588. http://dx.doi.org/10.3390/s22197588.

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Body Area Network (BAN) is one of the most important techniques for observing patient health in real time and identifying and analyzing diseases. For effective implementation of this technology in practice and to benefit from it, there are some key issues which are to be addressed, and among those issues, security is highly critical. WBAN will have to operate in a cooperative networking model of multiple networks such as those of homogeneous networks, for the purpose of performance and reliability, or those of heterogeneous networks, for the purpose of data transfer and processing from application point of view, with the other networks such as the networks of hospitals, clinics, medical experts, etc. and the patient himself/herself, who may be moving from one network to another. This paper brings out the issues related to security in WBAN in separate networks as well as in multiple networks. For WBAN working in a separate network, the IEEE 802.15.6 standard is considered. For WBANs working in multiple networks, especially heterogeneous networks, the security issues are considered. Considering the advancements of artificial intelligence (AI), the paper describes how AI is addressing some challenges faced by WBAN. The paper describes possible approaches which can be taken to address these issues by modeling a security mechanism using various artificial intelligence techniques. The paper proposes game theory with Stackelberg security equilibrium (GTSSE) for modeling security in heterogeneous networks in WBAN and describes the experiments conducted by the authors and the results proving the suitability of the modeling using GTSSE.

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Liu, Xiaoyang, Chao Liu, and Xiaoping Zeng. "Online Social Network Emergency Public Event Information Propagation and Nonlinear Mathematical Modeling." Complexity 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/5857372.

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Emergency public event arises everyday on social network. The information propagation of emergency public event (favorable and harmful) is researched. The dynamics of a susceptible-infected-susceptible and susceptible-infected-removed epidemic models incorporated with information propagation of emergency public event are studied. In particular, we investigate the propagation model and the infection spreading pattern using nonlinear dynamic method and results obtained through extensive numerical simulations. We further generalize the model for any arbitrary number of infective network nodes to mimic existing scenarios in online social network. The simulation results reveal that the inclusion of multiple infective node achieved stability and equilibrium in the proposed information propagation model.

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Canen, Nathan, Jacob Schwartz, and Kyungchul Song. "Estimating local interactions among many agents who observe their neighbors." Quantitative Economics 11, no. 3 (2020): 917–56. http://dx.doi.org/10.3982/qe923.

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In various economic environments, people observe other people with whom they strategically interact. We can model such information‐sharing relations as an information network, and the strategic interactions as a game on the network. When any two agents in the network are connected either directly or indirectly in a large network, empirical modeling using an equilibrium approach can be cumbersome, since the testable implications from an equilibrium generally involve all the players of the game, whereas a researcher's data set may contain only a fraction of these players in practice. This paper develops a tractable empirical model of linear interactions where each agent, after observing part of his neighbors' types, not knowing the full information network, uses best responses that are linear in his and other players' types that he observes, based on simple beliefs about the other players' strategies. We provide conditions on information networks and beliefs such that the best responses take an explicit form with multiple intuitive features. Furthermore, the best responses reveal how local payoff interdependence among agents is translated into local stochastic dependence of their actions, allowing the econometrician to perform asymptotic inference without having to observe all the players in the game or having to know the precise sampling process.

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L.Pandharipande, S., and Yogesh Moharkar. "Artificial Neural Network Modeling of Equilibrium Relationship for Partially Miscible Liquid-Liquid Ternary System." International Journal of Computer Applications 52, no. 8 (2012): 1–5. http://dx.doi.org/10.5120/8219-1641.

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Argatov, Ivan, and Vitaly Kocherbitov. "A note on artificial neural network modeling of vapor-liquid equilibrium in multicomponent mixtures." Fluid Phase Equilibria 502 (December 2019): 112282. http://dx.doi.org/10.1016/j.fluid.2019.112282.

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Journal articles on the topic 'Network Equilibrium Modeling'

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