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Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…
We investigate the evidence/flexibility (i.e., "Occam") paradigm and demonstrate the theoretical and empirical consistency of Bayesian evidence for the task of determining an appropriate generative model for network data. This model…
We present an asymptotic analysis of a stochastic two-compartmental cell division system with regulatory mechanisms inspired by Getto et al. (2013). The hematopoietic system is modeled as a two-compartment system, where the first…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
First-principles-based modelings have been extremely successful in providing crucial insights and predictions for complex biological functions and phenomena. However, they can be hard to build and expensive to simulate for complex living…
The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…
Hybrid neural ordinary differential equations (neural ODEs) integrate mechanistic models with neural ODEs, offering strong inductive bias and flexibility, and are particularly advantageous in data-scarce healthcare settings. However,…
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…
The day we understand the time evolution of subcellular elements at a level of detail comparable to physical systems governed by Newton's laws of motion seems far away. Even so, quantitative approaches to cellular dynamics add to our…
Dynamical systems in the life sciences are often composed of complex mixtures of overlapping behavioral regimes. Cellular subpopulations may shift from cycling to equilibrium dynamics or branch towards different developmental fates. The…
Regression-based decoding of continuous movements is essential for human-machine interfaces (HMIs), such as prosthetic control. This study explores a feature-based approach to encoding Surface Electromyography (sEMG) signals, focusing on…
Grid cells in the medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space. These cells are learned after birth and are thought to support spatial navigation but also more abstract…
Galactic systems are inherently multiphase, and understanding the roles and interactions of the various phases is key towards a more complete picture of galaxy formation and evolution. For instance, these interactions play a pivotal role in…
Understanding cell fate selection remains a central challenge in developmental biology. We present a class of simple yet biologically-motivated mathematical models for cell differentiation that generically generate oscillations and hence…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
This paper is concerned with the robustness of the sustained oscillations predicted by an epidemic ODE model defined on contact networks. The model incorporates the spread of awareness among individuals and, moreover, a small inflow of…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
Hybrid models composing mechanistic ODE-based dynamics with flexible and expressive neural network components have grown rapidly in popularity, especially in scientific domains where such ODE-based modeling offers important interpretability…
Stochastic dynamic models have been extensively used for the description of processes with uncertainties arising in the operations research, behavioral sciences, and many other application areas. A large class of the problems from these…