相关论文: Markov bases for two-way subtable sum problems

We derive formulae for the number of set-valued standard tableaux of two-rowed shapes, keeping track of the total number of entries, the number of entries in the first row, and the number of entries in the second row. Key in the proofs is a…

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via…

In this paper, we formally introduce the concept of a row-sum matrix over an arbitrary group $G$. When $G$ is cyclic, these types of matrices have been widely used to build uniform 2-factorizations of small Cayley graphs (or, Cayley…

Dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive…

We study symmetric nonnegative forms and their relationship with symmetric sums of squares. For a fixed number of variables $n$ and degree $2d$, symmetric nonnegative forms and symmetric sums of squares form closed, convex cones in the…

Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…

Let $n \geq 1$ be a squarefree integer, and let $M$, $A$ be two groups of order $n$. Using our previous results on the enumeration of Hopf-Galois structures on Galois extensions of fields of squarefree degree, we determine the number of…

This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their…

In this paper we continue our study, begun in part I, of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of three or four squares of primes. We correct a serious…

Degree-based graph construction is an ubiquitous problem in network modeling, ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive…

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…

A monoid $M$ is said to be surjunctive if every injective cellular automaton with finite alphabet over $M$ is surjective. We show that monoid algebras of surjunctive monoids are stably finite. In other words, given any field $K$ and any…

In this manuscript we study properties of multidimensional shifts. More precisely, we study the necessary and sufficient conditions for a shift to be sofic, i.e. the boundary between sofic shifts and effective ones. To this end, we use…

Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…

Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…

Recent work has discussed the importance of multiplicative closure for the Markov models used in phylogenetics. For continuous-time Markov chains, a sufficient condition for multiplicative closure of a model class is ensured by demanding…

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…

We consider a polling system with two queues, where a single server is attending the queues in a cyclic order and requires non-zero switching times to switch between the queues. Our aim is to identify a fairly general and comprehensive…

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they…

Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…