Related papers: Process Dimension of Classical and Non-Commutative…
We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then employ this ergodic optimization machinery to provide an alternate characterization of unique erogdicity of…
Longitudinal omics data (LOD) analysis is essential for understanding the dynamics of biological processes and disease progression over time. This review explores various statistical and computational approaches for analyzing such data,…
We first introduce and discuss density operator interpretations of quantum theory as a special case of a more general class of interpretations, giving special attention to a version that we call the `atomic version'. We then review some…
A self-organizing joint system classical oscillator + random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness…
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal…
We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…
We consider when there is absolute or unconditional convergence of series of various types of stochastic processes. These processes include differences of averages in ergodic theory and harmonic analysis, like the classical Cesaro average…
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…
Originally inspired by categorical quantum mechanics (Abramsky and Coecke, LiCS'04), the categorical compositional distributional model of natural language meaning of Coecke, Sadrzadeh and Clark provides a conceptually motivated procedure…
A novel approach for analyzing "classical" alternatives to quantum mechanics for explaining the statistical results of an EPRB-like experiment is proposed. This perspective is top-down instead of bottom-up. Rather than beginning with an…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
Various effects in human cognition, often considered `non-classical', have been argued to be most naturally modelled by quantum-like models of decision making. We extend this approach to describe models of cognition and decision-making in…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized…
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…