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Tracking a Markov-Modulated Stationary Degree Distribution of a Dynamic Random Graph

Maziyar Hamdi, Vikram Krishnamurthy, George Yin
2014 IEEE Transactions on Information Theory  
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according  ...  Second, a stochastic approximation algorithm is presented to track empirical degree distribution as it evolves over time.  ...  A class of stochastic approximation algorithms are used to track the expected degree distribution of such Markov-modulated dynamic graphs. A. Why Analyze the Degree Distribution?  ... 
doi:10.1109/tit.2014.2346183 fatcat:htwyf4ffyreqphlkhvmh52iqqm

Tracking the Empirical Distribution of a Markov-modulated Duplication-Deletion Random Graph [article]

Maziyar Hamdi, Vikram Krishnamurthy, George Yin
2013 arXiv   pre-print
The paper comprises of 2 results. First, motivated by social network applications, we analyze the asymptotic behavior of the degree distribution of the Markov-modulated random graph.  ...  This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according  ...  ESTIMATING (TRACKING) THE DEGREE DISTRIBUTION OF THE FIXED SIZE MARKOV-MODULATED DUPLICATION-DELETION RANDOM GRAPH In Sec.II, a degree distribution analysis is provided for the fixed size Markov-modulated  ... 
arXiv:1303.0050v1 fatcat:bct27m7z5je23ptekctj4iipfm

Interactive Sensing and Decision Making in Social Networks

Vikram Krishnamurthy
2014 Foundations and Trends® in Signal Processing  
Research in this area involves the interaction of dynamic random graphs, socio-economic analysis, and statistical inference algorithms.  ...  This monograph provides a survey, tutorial development, and discussion of four highly stylized examples: social learning for interactive sensing; tracking the degree distribution of social networks; sensing  ...  We further show that the stationary degree distribution of Markov-modulated duplication-deletion random graphs depends on the dynamics of such graphs and, thus, on the state of nature.  ... 
doi:10.1561/2000000048 fatcat:5hr4ebohczhrlolw4whenlicj4

Location Update Accuracy in Human Tracking system using Zigbee modules [article]

B. Amutha, M.Ponnavaikko
2009 arXiv   pre-print
A location and tracking system becomes very important to our future world of pervasive computing.  ...  We present a system level approach to localizing and tracking Human and blind users on a basis of different sources of location information [GPS plus Zigbee].  ...  Random Walks A Random Walk on connected, undirected, non-bipartite Graph G can be modeled as a Markov Chain Mg, where the vertices of the Graph, V(G), are represented by the location states of the Markov  ... 
arXiv:0912.1019v1 fatcat:2cyk7x67xjbijd2ccemcllhk6q

Using higher-order Markov models to reveal flow-based communities in networks

Vsevolod Salnikov, Michael T. Schaub, Renaud Lambiotte
2016 Scientific Reports  
Markov processes have been the prevailing paradigm to model such a network-based dynamics, for instance in the form of random walks or other types of diffusions.  ...  Importantly, simple Markov models lack memory in their dynamics, an assumption often not realistic in practice.  ...  This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimismtion), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State  ... 
doi:10.1038/srep23194 pmid:27029508 pmcid:PMC4814833 fatcat:lxnghqgr4rhsxep2rxboaty56e

Memory in network flows and its effects on spreading dynamics and community detection

Martin Rosvall, Alcides V. Esquivel, Andrea Lancichinetti, Jevin D. West, Renaud Lambiotte
2014 Nature Communications  
This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it ignores a potentially important feature of the dynamics: where flow moves to may  ...  For example, capturing dynamics with a second-order Markov model allows us to reveal actual travel patterns in air traffic and to uncover multidisciplinary journals in scientific communication.  ...  Edler, A. Eklöf, D. Kolp, C. Poletto and D. Vilhena for many discussions. M.R. was supported by the Swedish Research Council grant 2012-3729.  ... 
doi:10.1038/ncomms5630 pmid:25109694 fatcat:jls4nzjikbd77kyqbpaia5w6vy

Markov Chain Methods for Analyzing Urban Networks

D. Volchenkov, P. Blanchard
2008 Journal of statistical physics  
Being defined on the dual graph representations of transport networks random walks describe the equilibrium configurations of not random commodity flows on primary graphs.  ...  Random walks embed graphs into Euclidean space in which distances and angles acquire a clear statistical interpretation.  ...  Acknowledgement The work has been supported by the Volkswagen Foundation (Germany) in the framework of the project: "Network formation rules, random set graphs and generalized epidemic processes" (Contract  ... 
doi:10.1007/s10955-008-9591-2 fatcat:vbqaawjvirdyxpndv4a4dy3g6e

Topological Analysis of Tokyo Metropolitan Railway System [chapter]

Takeshi Ozeki
2012 Infrastructure Design, Signalling and Security in Railway  
The initial condition is a random distribution of node probability amplitude. SPM with medium 0.1   leads to the dominant mode as the stationary state of the rosary network.  ...  The degree distribution is illustrated in Fig.2 .1(c) (the "degree" denotes the number of links of a node).  ...  On the other hand, the family networks with 3 M  show quicker transition to the stationary state corresponding to the dominant mode, as shown in the second row of Table A.1.  ... 
doi:10.5772/36509 fatcat:mpjc476ctna3xli5z2mezlmsuu

Online Markov decision processes with Kullback-Leibler control cost [article]

Peng Guan and Maxim Raginsky and Rebecca Willett
2014 arXiv   pre-print
A number of new results on Markov decision processes with KL control cost are also obtained.  ...  the state costs) under mild regularity conditions is presented, along with a demonstration of the performance of the proposed strategy on a simulated target tracking problem.  ...  In this example, the state space X is the vertex set of an undirected graph, and the passive dynamics P * specifies some default random walk on this graph.  ... 
arXiv:1401.3198v1 fatcat:bbct44wmeba3dmz3fxdmfl2aua

Reinforcement Learning: Stochastic Approximation Algorithms for Markov Decision Processes [article]

Vikram Krishnamurthy
2015 arXiv   pre-print
This article presents a short and concise description of stochastic approximation algorithms in reinforcement learning of Markov decision processes.  ...  The algorithms can also be used as a suboptimal method for partially observed Markov decision processes.  ...  Let π θ (i, a) denote the stationary distribution of the Markov process z k .  ... 
arXiv:1512.07669v1 fatcat:75gl33u3b5fclbmb7jmg3qlagi

A random walker's view of networks whose growth it shapes [article]

Robert J. H. Ross and Charlotte Strandkvist and Walter Fontana
2019 arXiv   pre-print
We study a simple model in which the growth of a network is determined by the location of one or more random walkers.  ...  Modulating the extent to which the location of node attachment is determined by the walker as opposed to random selection is akin to scaling the speed of the walker and generates new limiting behavior.  ...  WING DYNAMICS ADMITS A STATIONARY DEGREE DISTRIBUTION By a stationary degree distribution p(k) we mean that lim N (t)→∞ n(k, t) N (t) → p(k, t) = p(k) constant in t, (S2) where n(k, t) is the number of  ... 
arXiv:1811.09611v2 fatcat:ikr5zawoenhqlpb4aacffebyxa

State aggregations in Markov chains and block models of networks [article]

Mauro Faccin, Michael T. Schaub, Jean-Charles Delvenne
2020 arXiv   pre-print
likelihood landscape of this popular generative network model from a dynamical lens.  ...  We further highlight how we can uncover coherent, long-range dynamical modules for which considering a time-scale T >> 1 is essential, using synthetic flows and real-world ocean currents, where we are  ...  to a degree distribution).  ... 
arXiv:2005.00337v1 fatcat:5uhsviw2i5dinon45urj7amp2m

Hidden Markov processes

Y. Ephraim, N. Merhav
2002 IEEE Transactions on Information Theory  
An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel.  ...  An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented.  ...  They also thank Randal Douc, Catherine Matias, Éric Moulines, and Tobias Rydén for making available preprints of their most recent work.  ... 
doi:10.1109/tit.2002.1003838 fatcat:6r7stou5ijgi7kjs6tifsyghfm

2015 Index IEEE Transactions on Automatic Control Vol. 60

2015 IEEE Transactions on Automatic Control  
., +, TAC Feb. 2015 570-575 Fastest Mixing Reversible Markov Chains on Graphs With Degree Propor- tional Stationary Distributions.  ...  Hildebrand, R., +, TAC July 2015 1731-1744 Fastest Mixing Reversible Markov Chains on Graphs With Degree Propor- tional Stationary Distributions.  ...  Quality of experience  ... 
doi:10.1109/tac.2015.2512305 fatcat:5gut6qeomfh73fwfvehzujbr5q

Exploratory search during directed navigation in C. elegans and Drosophila larva

Mason Klein, Sergei V Krivov, Anggie J Ferrer, Linjiao Luo, Aravinthan DT Samuel, Martin Karplus
2017 eLife  
How does directed navigation in a gradient modulate random exploration either parallel or orthogonal to the gradient?  ...  We find that the statistics of random exploration in any direction are little affected by directed movement along a stimulus gradient.  ...  The stationary, steady state probability distribution P st is computed as the solution of equation P st i ¼ P j P ij ðDtÞP st j .  ... 
doi:10.7554/elife.30503 pmid:29083306 pmcid:PMC5662291 fatcat:ljqogafkxvbpvf3lp5ehqnbcri
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