相关论文: Messages on Networks as a Many-Body Problem

The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…

Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models.…

The radiative transfer equation for spectral lines from an extended gas is derived from first principles, treating the gas as a system of many atoms/molecules rather than isolated ones. Line broadening effects are assumed to be dominated by…

We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…

Considered in the paper is the overlaid nature of modern telecommunication networks and expediency of usage the multi-layer graph model for its design. General statement of design problem is given. The design method in general using…

Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…

We consider a number of fundamental statistical and graph problems in the message-passing model, where we have $k$ machines (sites), each holding a piece of data, and the machines want to jointly solve a problem defined on the union of the…

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…

We analyse the flow of information in multiplex networks by means of the communicability function. First, we generalize this measure from its definition from simple graphs to multiplex networks. Then, we study its relevance for the analysis…

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large…

In this paper, we study the consensus problem of multiple agents on a kind of famous graph, Peterson graph. It is an undirected graph with 10 vertices and 15 edges. Each agent randomly walks on this graph and communicates with each other if…

The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over…

In communication networks theory the concepts of networkness and network surplus have recently been defined. Together with transmission and betweenness centrality, they were based on the assumption of equal communication between vertices.…

Multi-agent complex systems comprising populations of decision-making particles, have wide application across the biological, informational and social sciences. We uncover a formal analogy between these systems' time-averaged dynamics and…

We study a simple model of how social behaviors, like trends and opinions, propagate in networks where individuals adopt the trend when they are informed by threshold $T$ neighbors who are adopters. Using a dynamic message-passing…

A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to…

We study the multi-message broadcast problem using abstract MAC layer models of wireless networks. These models capture the key guarantees of existing MAC layers while abstracting away low-level details such as signal propagation and…

We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…

Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…