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We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…
We consider a class of stochastic gradient optimization schemes. Assuming that the objective function is strongly convex, we prove weak error estimates which are uniform in time for the error between the solution of the numerical scheme,…
Adaptation mechanism of cells on the basis of stochastic gene expression and epigenetic modification is proposed. From marginally stable states generated by epigenetic modification, a gene expression pattern that achieves greater cell…
In this work, we study a protein synthesis degradation process by defining a general mathematical model. Using generating function technique we present a method that allows exact calculation of joint probability distribution of protein…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
While the analytical solution for the marginal distribution of a stochastic chemical reaction network has been extensively studied, its joint distribution, i.e. the solution of a high-dimensional chemical master equation, has received much…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…
We provide the first stochastic convergence rates for a family of adaptive quadrature rules used to normalize the posterior distribution in Bayesian models. Our results apply to the uniform relative error in the approximate posterior…
Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells…
In the stochastic formulation of chemical kinetics, the stationary moments of the population count of species can be described via a set of linear equations. However, except for some specific cases such as systems with linear reaction…
It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with…
Expectation propagation (EP) is a deterministic approximation algorithm that is often used to perform approximate Bayesian parameter learning. EP approximates the full intractable posterior distribution through a set of local approximations…
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists' ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate…
Over the last several decades it has been increasingly recognized that stochastic processes play a central role in transcription. Though many stochastic effects have been explained, the source of transcriptional bursting (one of the most…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
Stochastic process discovery is concerned with deriving a model capable of reproducing the stochastic character of observed executions of a given process, stored in a log. This leads to an optimisation problem in which the model's parameter…
Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…
Compartmentalised biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyse…
Diffusion models have shown a great ability at bridging the performance gap between predictive and generative approaches for speech enhancement. We have shown that they may even outperform their predictive counterparts for non-additive…