Related papers: A Statistical Mechanical Load Balancer for the Web
We consider the edge-triangle model (or Strauss model), and focus on the asymptotic behavior of the triangle density when the size of the graph increases to infinity. This random graph belongs to the class of exponential random graphs,…
In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with…
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific…
In the study of small and large networks it is customary to perform a simple random walk, where the random walker jumps from one node to one of its neighbours with uniform probability. The properties of this random walk are intimately…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
Adding dynamic bonds in polymer networks enables reprocessing and recycling; however the full impact of reversible bonds on dynamic network mechanics remains unclear. We build model dynamic networks and observe substantial deviations from…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
We consider the following dynamic load-balancing process: given an underlying graph $G$ with $n$ nodes, in each step $t\geq 0$, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks…
Stochastic blockmodels are generative network models where the vertices are separated into discrete groups, and the probability of an edge existing between two vertices is determined solely by their group membership. In this paper, we…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
Statistical fragment emission from excited nuclear systems is studied within the framework of a schematic Fermi-gas model combined with Weisskopf's detailed balance approach. The formalism considers thermal expansion of finite nuclear…
Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states : the principle is to maximize the Shannon entropy…
This chapter provides a comprehensive and self-contained discussion of the most recent developments of information theory of networks. Maximum entropy models of networks are the least biased ensembles enforcing a set of constraints and are…
A theory to predict the steady state position of a dissipative, flow-controlled system, as defined by a control volume, is developed based on the Maximum Entropy (MaxEnt) principle of Jaynes, involving minimisation of a generalised free…