相关论文: State space dimensionality in short memory hidden …

We consider average-cost Markov decision processes (MDPs) with Borel state spaces, countable, discrete action spaces, and strictly unbounded one-stage costs. For the minimum pair approach, we introduce a new majorization condition on the…

We present a unified framework for the data-driven construction of stochastic reduced models with state-dependent memory for high-dimensional Hamiltonian systems. The method addresses two key challenges: (\rmnum{1}) accurately modeling…

For statistical inference on an infinite-dimensional Hilbert space $\H $ with no moment conditions we introduce a new class of energy distances on the space of probability measures on $\H$. The proposed distances consist of the integrated…

In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…

The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate…

Stochastic finite-state generators are compressed descriptions of infinite time series. Alternatively, compressed descriptions are given by quantum finite- state generators [K. Wiesner and J. P. Crutchfield, Physica D 237, 1173 (2008)].…

Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…

Von Neumann use 4 assumptions to derive the Hilbert space (HS) formulation of quantum mechanics (QM). Within this theory dispersion free ensembles do not exist. To accommodate a theory of quantum mechanics that allow dispersion free…

The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…

A key question in brain sciences is how to identify time-evolving functional connectivity, such as that obtained from recordings of neuronal activity over time. We wish to explain the observed phenomena in terms of latent states which, in…

One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…

Multistability, the coexistence of multiple stable states, is a cornerstone of nonlinear dynamical systems, governing their equilibrium, tunability, and emergent complexity. Recently, the concept of hidden multistability, where certain…

We consider a pair of correlated processes {Z_n} and {S_n} (two sided), where the former is observable and the later is hidden. The uncertainty in the estimation of Z_n upon its finite past history is H(Z_n|Z_0^{n-1}), and for estimation of…

We study the mechanical unfolding of a simple model protein. The Langevin dynamics results are analyzed using Markov-model methods which allow to describe completely the configurational space of the system. Using transition path theory we…

A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…

A new approach to the theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly small on wide time intervals: the occupation of the virtual…

Peculiarities of multiqubit measurement are for the most part similar to peculiarities of measurement for qudit -- quantum object with finite-dimensional Hilbert space. Three different interpretations of measurement concept are analysed.…

Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…

Hidden Markov Models (HMMs) have become very popular as a computational tool for the analysis of sequential data. They are memoryless machines which transition from one internal state to another, while producing symbols. These symbols…