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Spatial transcriptomics (ST) is a novel technology that enables the observation of gene expression at the resolution of individual spots within pathological tissues. ST quantifies the expression of tens of thousands of genes in a tissue…
Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the…
We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes: Gene A and Gene B which synthesize the TFs and the target gene proteins respectively. We show through analytic…
Stochasticity plays important roles in molecular networks when molecular concentrations are in the range of $0.1 \mu$M to $10 n$M (about 100 to 10 copies in a cell). The chemical master equation provides a fundamental framework for studying…
Gene expression has a stochastic component owing to the single molecule nature of the gene and the small number of copies of individual DNA binding proteins in the cell. We show how the statistics of such systems can be mapped on to quantum…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
We address the problem of approximating the moments of the solution, $\boldsymbol{X}(t)$, of an It\^o stochastic differential equation (SDE) with drift and a diffusion terms over a time-grid $t_0, t_1, \ldots, t_n$. In particular, we assume…
We propose a probabilistic model for interpreting gene expression levels that are observed through single-cell RNA sequencing. In the model, each cell has a low-dimensional latent representation. Additional latent variables account for…
We present a numerical algorithm that allows the approximation of optimal controls for stochastic reaction-diffusion equations with additive noise by first reducing the problem to controls of feedback form and then approximating the…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: $G_0W_0$, $G_0W_0^tc$, and…
Phenomenon of stochastic separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. In high-dimensional datasets under broad assumptions each point can be…
Estimation and inference in dynamic discrete choice models often relies on approximation to lower the computational burden of dynamic programming. Unfortunately, the use of approximation can impart substantial bias in estimation and results…
Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…
In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes the lower bound of its marginalized log-likelihood. Then,…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
Stochastic resetting, the procedure of stopping and re-initializing random processes, has recently emerged as a powerful tool for accelerating processes ranging from queuing systems to molecular simulations. However, its usefulness is…