Related papers: A Notion of Entropy for Stochastic Processes on Ma…

This paper concerns discrete-time occupancy processes on a finite graph. Our results can be formulated in two theorems, which are stated for vertex processes, but also applied to edge process (e.g., dynamic random graphs). The first theorem…

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

Many learning algorithms can be represented as Markov processes, and understanding their generalization error is a central topic in learning theory. For specific continuous-time noisy algorithms, a prominent analysis technique relies on…

The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…

Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…

The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…

We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. Burdzy and Pal in their paper proposed a continuous version of graphical models --…

Entropy is a classical measure to quantify the amount of information or complexity of a system. Various entropy-based measures such as functional and spectral entropies have been proposed in brain network analysis. However, they are less…

We derive new discrete event simulation algorithms for marked time point processes. The main idea is to couple a special structure, namely the associated local independence graph, as defined by Didelez arXiv:0710.5874, with the activity…

Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…

We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…

We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a version of Hofbauer's Markov diagram, (ii) the…

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…

A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…

Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…

The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

At the nanoscale, random effects govern not only the dynamics of a physical system but may also affect its observation. This work introduces a novel paradigm for coarse graining that eschews the assignment of a unique coarse-grained…