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We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of…
This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the…
Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions involving three or more components of a network system. Most of these methods are defined only in the time domain and rely…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…
Small nonequelibrium systems driven by an external periodic protocol can be described by Markov processes with time-periodic transition rates. In general, current fluctuations in such small systems are large and may play a crucial role. We…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined…
The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate.…
In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from…
Markov processes are shown to be consistent with metastable states seen in pulsar phenomena, including intensity nulling, pulse-shape mode changes, subpulse drift rates, spindown rates, and X-ray emission, based on the typically broad and…
We present a novel characterization of slow variables for continuous Markov processes that provably preserve the slow timescales. These slow variables are known as reaction coordinates in molecular dynamical applications, where they play a…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the…
Discrete time crystals are novel phases of matter that break the discrete time translational symmetry of a periodically driven system. In this work, we propose a classical system of weakly-nonlinear parametrically-driven coupled oscillators…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
We consider a finite state discrete time process X. Without loss of generality the finite state space can be identified with the set of unit vectors {e1, e2, . . . , eN} with ei = (0, . . . , 0, 1, 0, . . . , 0)0 2 RN. For a Markov chain…
We consider the problem of finding the transition rates of a continuous-time homogeneous Markov chain under the empirical condition that the state changes at most once during a time interval of unit length. It is proven that this…