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This paper presents a research study focused on uncovering the hidden population distribution from the viewpoint of a variational non-Bayesian approach. It asserts that if the hidden probability density function (PDF) has continuous partial…
We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times that is generated by a…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
In this work, we present the logistic branching Brownian motion with selection (Log-BBM), a modification of the N-BBM defined by Groisman et. al (2020), in which birth and competition events are decoupled to allow for a variable population…
In this paper, we use a biorthogonal approach (Appell system) to construct and characterize the spaces of test and generalized functions associated to the fractional Poisson measure $\pi_{\lambda,\beta}$, that is, a probability measure in…
Methods used to infer nuclear parameters from neutron count statistics fall into two categories depending on whether they use moments or count number probabilities. As probabilities are in general more difficult to calculate, we are…
This paper introduces a general class of Replicator-Mutator equations on a multi-dimensional fitness space. We establish a novel probabilistic representation of weak solutions of the equation by using the theory of Fockker-Planck-Kolmogorov…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
Using convex Grothendieck fibrations, we characterize the von Neumann entropy as a functor from finite-dimensional non-commutative probability spaces and state-preserving *-homomorphisms to real numbers. Our axioms reproduce those of Baez,…
There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…
It is known that solutions of Richardson equations can be represented as stationary points of the "energy" of classical free charges on the plane. We suggest to consider "probabilities" of the system of charges to occupy certain states in…
The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MPB equations with the self Green's function as the self…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
Particle number fluctuations $N(t)$, measured in virtual observation boxes of an image or a simulation, offer a way to quantify particle dynamics when particle tracking is impractical, such as in high-density systems. While traditionally…
The analytical probability distribution of finite systems obeying Bose-Einstein statistics in one, two, and three dimensions are investigated by using a canonical ensemble approach. Starting from the canonical partition function of the…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
We initiate a study of the following problem: Given a continuous domain $\Omega$ along with its convex hull $\mathcal{K}$, a point $A \in \mathcal{K}$ and a prior measure $\mu$ on $\Omega$, find the probability density over $\Omega$ whose…
We study the least-energy way to reshape a probability distribution when motion is constrained to a horizontal bundle, that is, optimal transport and distribution steering in sub-Riemannian geometry, motivated by density control over…