Related papers: Interpretation and approximation tools for big, de…

In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows…

Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…

To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…

In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…

More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…

Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible…

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the…

We investigate the capacity of transformers to learn algorithms involving their context while solely being trained using next token prediction. We set up Markov chains with random transition matrices and we train transformers to predict the…

Stochastic models of reaction networks are becoming increasingly important in Systems Biology. In these models, the dynamics is generally represented by a continuous-time Markov chain whose states denote the copy-numbers of the constituent…

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…

Continual incorporation of new knowledge is essential for the long-term evolution of large language models (LLMs). Existing approaches typically rely on parameter-update algorithms to mitigate catastrophic forgetting, yet they suffer from…

Most successful applications of deep learning involve similar training and test conditions. However, tasks such as biological sequence design involve searching for sequences that improve desirable properties beyond previously known values,…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…

Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…

Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…