Related papers: Structural classification of continuous time Marko…
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov transition operators provide explicit,…
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…
In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…
Certain chemical reaction networks (CRNs) when modeled as a deterministic dynamical system taken with mass-action kinetics have the property of reaction network detailed balance (RNDB) which is achieved by imposing network-related…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Can the direction of time and the causal structure of space-time be inferred from operational principles? Causal models and tensor networks offer complementary perspectives: the former encodes cause-effect relations via directed graphs,…
Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…
We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be…
This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can…
Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is…
In a temporal network causal paths are characterized by the fact that links from a source to a target must respect the chronological order. In this article we study the causal paths structure in temporal networks of human face to face…
Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix $P$ can be approximated by…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion,…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
Many neural systems display cascading behavior characterized by uninterrupted sequences of neuronal firing. This gap precludes an understanding of how variations in network structure manifest in neural dynamics and either support or impinge…
Multiple works regarding convergence analysis of Markov chains have led to spectral gap decomposition formulas of the form \[ \mathrm{Gap}(S) \geq c_0 \left[\inf_z \mathrm{Gap}(Q_z)\right] \mathrm{Gap}(\bar{S}), \] where $c_0$ is a…
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability,…