Related papers: High-Order Correlation Functions of Binary Multi-S…
Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key r\^ole in their development, while the self-adjointness of associated operators together with the use of…
We report on simultaneous recordings from cells in all layers of visual cortex and models developed to capture the higher order structure of population spiking activity. Specifically, we use Ising, Restricted Boltzmann Machine (RBM) and…
Neurons in the central nervous system communicate with each other with the help of series of Action Potentials, or spike trains. Various studies have shown that neurons encode information in different features of spike trains, such as the…
The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to…
In this article almost semi-continuous processes with stationary independent increments on a finite irreducible Markov chain are considered. For these processes the components of matrix factorization identity are concretely defined. On the…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states.…
Markov processes are widely used in modeling random phenomena/problems. However, they may not be adequate in some cases where more general processes are needed. The conditionally Markov (CM) process is a generalization of the Markov process…
We study the class structure of finite-alphabet Markov chains with arbitrary memory length. To capture the structural constraints induced by prohibited transitions, we introduce the skeleton of a higher-order transition kernel, defined as a…
Learning the undirected graph structure of a Markov network from data is a problem that has received a lot of attention during the last few decades. As a result of the general applicability of the model class, a myriad of methods have been…
Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear…
We establish Bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) Markov chains. These inequalities achieve sharp variance proxies and encompass the classical Bernstein inequality for…
We present an integral formula for a special correlation function of the isotropic spin-1/2 antiferromagnetic Heisenberg chain. The correlation function describes the probability for the occurrence of a string of consecutive up-spins as a…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
There is a scalability gap between probabilistic and non-probabilistic verification. Probabilistic model checking tools are based either on explicit engines or on (Multi-Terminal) Binary Decision Diagrams. These structures are complemented…
There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
We study the statistical properties of Ising spin chains with finite (although arbitrary large) range of interaction between the elements. We examine mesoscopic subsystems (fragments of an Ising chain) with the lengths comparable with the…
We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove identities of combinatorial significance relating to…