Related papers: Markov Capacity for Factor Codes with an Unambiguo…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…
A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent…
Suitable reachability conditions can make two different fixed point semantics of a transition system coincide. For instance, the total and partial expected reward semantics on Markov chains (MCs) coincide whenever the MC at hand is almost…
This paper studies several aspects of symbolic factors of $\mathcal{S}$-adic subshifts of finite alphabet rank. First, we address a problem raised in [DDPM20] about the topological rank of symbolic factors of $\mathcal{S}$-adic subshifts…
Markov networks are probabilistic graphical models that employ undirected graphs to depict conditional independence relationships among variables. Our focus lies in constraint-based structure learning, which entails learning the undirected…
A new sufficient condition is proposed in the problem of Central Limit Theorem in the array scheme for non-homogeneous Markov Chains.
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
We study the communication over Finite State Channels (FSCs), where the encoder and the decoder can control the availability or the quality of the noise-free feedback. Specifically, the instantaneous feedback is a function of an action…
We propose a definition of graph subshifts of finite type that can be seen as extending both the notions of subshifts of finite type from classical symbolic dynamics and finitely presented groups from combinatorial group theory. These are…
Motivated by physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law $Y =A X$, where $X$ and $Y$ are the input and output matrices,…
In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.
For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.
A recent result by Kardo\v{s}, M\'a\v{c}ajov\'a and Zerafa [J. Comb. Theory, Ser. B. 160 (2023) 1--14] related to the famous Berge-Fulkerson conjecture implies that given an arbitrary set of odd pairwise edge-disjoint cycles, say $\mathcal…
We prove that the criterion for Markov equivalence provided by Zhao et al. (2005) may involve a set of features of a graph that is exponential in the number of vertices.
We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors and factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique…
A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…
The $k$-th power of a graph $G$ is the graph whose vertex set is $V(G)^k$, where two distinct $k$-tuples are adjacent iff they are equal or adjacent in $G$ in each coordinate. The Shannon capacity of $G$, $c(G)$, is…