Related papers: Model simplification and loss of irreversibility

Effectively learning from sequential data is a longstanding goal of Artificial Intelligence, especially in the case of long sequences. From the dawn of Machine Learning, several researchers have pursued algorithms and architectures capable…

For a class of irreducible Markov chains with an infinitely countable set of states, we establish a new verifiable necessary and sufficient condition for recurrence and transience. We show that if one of the basic assumptions is not…

For the canonical two-state model of transcription, we derive exact analytic expressions for the entropy production rate of transcription at steady state, and assess detailed balance breaking in transcription. Our analytics allow us to…

We study the transient response of a colloidal bead which is released from different heights and allowed to relax in the potential well of an optical trap. Depending on the initial potential energy, the system's time evolution shows…

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available.…

The objective of this work is to show that adiabatic processes can be very similar to isothermal ones. First, we show that the criteria for the compatibility of linear-response theory with the Second Law of Thermodynamics for thermally…

This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countable state space. That is, the discrete components of the…

This paper mainly discusses the diffusion on complex networks with time-varying couplings. We propose a model to describe the adaptive diffusion process of local topological and dynamical information, and find that the Barabasi-Albert…

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two…

We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the…

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus let down a curtain on a possible formulation of a principle of…

We propose Markov two-components processes (M2CP) as a probabilistic model of asynchronous systems based on the trace semantics for concurrency. Considering an asynchronous system distributed over two sites, we introduce concepts and tools…

We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…

Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…

Population dynamics are often subject to random independent changes in the environment. For the two strategy stochastic replicator dynamic, we assume that stochastic changes in the environment replace the payoffs and variance. This is…

We discuss problems posed by the quantitative study of time inhomogeneous Markov chains. The two main notions for our purpose are merging and stability. Merging (also called weak ergodicity) occurs when the chain asymptotically forgets…

Switched systems are capable of modeling processes with underlying dynamics that may change abruptly over time. To achieve accurate modeling in practice, one may need a large number of modes, but this may in turn increase the model…

We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method proposed by Takahashi, Fujii, Hino and Hayakawa [1]. This method…