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Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can…
Astrophysical foreground substraction is crucial to retrieve the cosmic microwave background (CMB) polarization out of the observed data. Recent efforts have been carried out towards the development of a minimally informed component…
Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured,…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
Current clinical decision-making in oncology relies on averages of large patient populations to both assess tumor status and treatment outcomes. However, cancers exhibit an inherent evolving heterogeneity that requires an individual…
We introduce a novel way to combine boosting with Gaussian process and mixed effects models. This allows for relaxing, first, the zero or linearity assumption for the prior mean function in Gaussian process and grouped random effects models…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
We develop a mathematical model for dynamic simulation of an alkaline electrolyzer plant. The plant includes the stack, a water recirculation system and hydrogen storage with compressor. We model each component of the system with mass and…
In the previous paper of this series [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Physical Review B, submitted] we detailed a procedure--epsilon-machine spectral reconstruction--to discover and analyze patterns and disorder in…
We introduce three stochastic cooperative models for particle deposition and evaporation relevant to ionic self-assembly of nanoparticles with applications in surface fabrication and nanomedicine. We present a method for mapping a…
This document outlines the development of numerous new theoretical approaches to model associating fluids. For a detailed abstract please see page ii.
Allosteric interactions occur when binding at one part of a complex affects the interactions at another part. Allostery offers a high degree of control in multi-species processes, and these interactions play a crucial role in many…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
Recent advancement in machine learning algorithms reaches a point where medical devices can be equipped with artificial intelligence (AI) models for diagnostic support and routine automation in clinical settings. In medicine and healthcare,…
Within the current uncertainties in the treatment of the coupling between pulsation and convection, limiting amplitude, nonlinear, convective models appear the only viable approach for providing theoretical predictions about the intrinsic…
We make a very large realisation of a Gaussian white noise field, called PANPHASIA, public by releasing software that computes this field. Panphasia is designed specifically for setting up Gaussian initial conditions for cosmological…
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…
We study the steady states of a system of cross-diffusion equations arising from the modeling of chemotaxis with local sensing, where the motility is a decreasing function of the concentration of the chemical. In order to capture the many…
Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…