Related papers: Ultrametric Diffusion, Rugged Energy Landscapes an…

From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and…

The expansion of global production networks has raised many important questions about the interdependence among countries and how future changes in the world economy are likely to affect the countries' positioning in global value chains. We…

We introduce a unified operator-theoretic framework for analyzing mixing times of finite-state ergodic Markov chains that applies to both reversible and non-reversible dynamics. The central object in our analysis is the projected transition…

Ultametrics are an important class of distances used in applications such as phylogenetics, clustering and classification theory. Ultrametrics are essentially distances that can be represented by an edge-weighted rooted tree so that all of…

An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…

A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in…

In this work, we study the effects of finite buffers on the throughput and delay of line networks with erasure links. We identify the calculation of performance parameters such as throughput and delay to be equivalent to determining the…

The geometric structure of an optimization landscape is argued to be fundamentally important to support the success of deep neural network learning. A direct computation of the landscape beyond two layers is hard. Therefore, to capture the…

This paper studies a generic model for cooperative cognitive radio networks where the secondary user is equipped with a finite relay queue as well as a finite battery queue. Our prime objective is to characterize the stable throughput…

By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are…

Relying on an exact time evolution scheme, we identify a novel transient energy transfer phe- nomenon in an exactly-solvable quantum microscopic model consisting of a three-level system coupled to two non-Markovian zero-temperature bosonic…

Current concepts of neural networks have emerged over two centuries of progress beginning with the neural doctrine to the idea of neural cell assemblies. Presently the model of neural networks involves distributed neural circuits of nodes,…

In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…

Many applications in networked control require intermittent access of a controller to a system, as in event-triggered systems or information constrained control applications. Motivated by such applications and extending previous work on…

In this paper, we study the dynamics of epidemic processes taking place in temporal and adaptive networks. Building on the activity-driven network model, we propose an adaptive model of epidemic processes, where the network topology…

Filtration, flow in narrow channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. If the blockage is temporary, which means that after a finite time the channel…

We introduce the concept of a Markov influence system (MIS) and analyze its dynamics. An MIS models a random walk in a graph whose edges and transition probabilities change endogenously as a function of the current distribution. This…

According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture…

Inspired by biological swimming and flying with distributed sensing, we propose a data-driven approach for load estimation that relies on complex networks. We exploit sparse, real-time pressure inputs, combined with pre-trained transition…

Finite-state Markov models are widely used for modeling wireless channels affected by a variety of non-idealities, ranging from shadowing to interference. In an industrial environment, the derivation of a Markov model based on the wireless…