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Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…
This paper presents a systematic mapping study on the model-driven engineering of safety and security concerns in systems. Integrated modeling and development of both safety and security concerns is an emerging field of research. Our…
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…
From interacting cellular components to networks of neurons and neural systems, interconnected units comprise a fundamental organizing principle of the nervous system. Understanding how their patterns of connections and interactions give…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…
Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine with the aim to replace a look-up table approach. The NN training process presents an…
This limited review is intended as an introduction to the fast growing subject of mathematical modelling of cell metabolism and its biochemical pathways, and more precisely on pathways linked to apoptosis of cancerous cells. Some basic…
Diffusion models, which leverage stochastic processes to capture complex data distributions effectively, have shown their performance as generative models, achieving notable success in image-related tasks through iterative denoising…
Single particle models are sufficient for many topics in introductory physics courses, but become misleading when applied to situations involving changes in internal energy. This paper merges two parallel attempts to reform the teaching of…
Embedded distributed inference of Neural Networks has emerged as a promising approach for deploying machine-learning models on resource-constrained devices in an efficient and scalable manner. The inference task is distributed across a…
This article presents a survey of work on lifted graphical models. We review a general form for a lifted graphical model, a par-factor graph, and show how a number of existing statistical relational representations map to this formalism. We…
Numerical association rule mining is a widely used variant of the association rule mining technique, and it has been extensively used in discovering patterns and relationships in numerical data. Initially, researchers and scientists…
In this review, we highlight recent developments in the application of machine learning for molecular modeling and simulation. After giving a brief overview of the foundations, components, and workflow of a typical supervised learning…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
Stochastic networks represent very important subject of research because they have been found in almost all branches of modern science, including also sociology and economy. We provide a information theory point of view, mostly based on its…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…