Related papers: An energy function and its application to the peri…
An irreversible $k$-threshold process (also a $k$-neighbor bootstrap percolation) is a dynamic process on a graph where vertices change color from white to black if they have at least $k$ black neighbors. An irreversible $k$-conversion set…
We investigate kinetic energy properties of an irrotational deep-water Stokes wave. By introducing a conformal hodograph transform, we perform complex analysis in the new variables, and show that the existence of the streamline time-period…
A graph $G$ is a $k$-leaf power if there exists a tree $T$ whose leaf set is $V(G)$, and such that $uv \in E(G)$ if and only if the distance between $u$ and $v$ in $T$ is at most $k$. The graph classes of $k$-leaf powers have several…
If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if…
We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform…
We give a bound for the graph energy with given maximal degree in terms of the second and fourth moments of a graph. In the case in which the graph is $d$-regular we obtain the bound that is given in Van Dam, E. et al. (2014). through…
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion…
We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and…
We provide a method to deduce the preferences governing the restructuring dynamics of a network from the observed rewiring of the edges. Our approach is applicable for systems in which the preferences can be formulated in terms of a…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…
We employ the recently developed framework of the energetics of stochastic processes (called `stochastic energetics'), to re-analyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find…
We propose a simple density functional expression for the upper bound of the kinetic energy for electronic systems. Such a functional is valid in the limit of slowly varying density, its validity outside this regime is discussed by making a…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
We consider the height of random k-trees and k-Apollonian networks. These random graphs are not really trees, but instead have a tree-like structure. The height will be the maximum distance of a vertex from the root. We show that w.h.p. the…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
The adaptation rule for Vector Quantization algorithms, and consequently the convergence of the generated sequence, depends on the existence and properties of a function called the energy function, defined on a topological manifold. Our aim…
We propose two classes of dynamic versions of the classical Erd\H{o}s-R\'enyi graph: one in which the transition rates are governed by an external regime process, and one in which the transition rates are periodically resampled. For both…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…