Related papers: Estimation of Mutation Rates from Fluctuation Expe…
We consider a fractional version of the classical nonlinear birth process of which the Yule--Furry model is a particular case. Fractionality is obtained by replacing the first order time derivative in the difference-differential equations…
The origin of the erraticity behaviour observed recently in the experiment is studied in some detail. The negative-binomial distribution is used to fit the experimental multiplicity distribution. It is shown that, with the multiplicity…
We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B $\to$ 2A reaction. We…
The microscopic probability distribution function of the Sherrington-Kirkpatrick (SK) model of spin glasses is calculated explicitly as a function of time by a high-temperature expansion. The resulting formula to the third order of the…
The dissipation function for a system is defined as the natural logarithm of the ratio between probabilities of a trajectory and its time-reversed trajectory, and its probability distribution follows a well-known relation called the…
In this paper, we consider the Langevin equation from an unusual point of view, that is as an archetype for a dissipative system driven out of equilibrium by an external excitation. Using path integral method, we compute exactly the…
Many models in natural language processing define probabilistic distributions over linguistic structures. We argue that (1) the quality of a model' s posterior distribution can and should be directly evaluated, as to whether probabilities…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
The detailed fluctuation theorem implies symmetry in the generating function of entropy production probability. The integral fluctuation theorem directly follows from this symmetry and the normalization of the probability. In this paper, we…
Given a permutation statistic $s : S_n \to \mathbb{R}$, define the mean statistic $\bar{s}$ as the statistic which computes the mean of $s$ over conjugacy classes. We describe a way to calculate the expected value of $s$ on a product of $t$…
This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - <x>)$ is computed exactly and shown to satisfy a central limit theorem as $N \to \infty$. For the…
We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…
Considering voting rules based on evaluation inputs rather than preference rankings modifies the paradigm of probabilistic studies of voting procedures. This article proposes several simulation models for generating evaluation-based voting…
Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by $\theta \in…
In this paper, we propose some representations of a generalized linear birth process called fractional Yule process (fYp). We also derive the probability distributions of the random birth and sojourn times. The inter-birth time distribution…
An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time-evolutions of…
This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…