Related papers: Simplifying Biochemical Models With Intermediate S…

In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Unfortunately, this model is unable to generate realistic market…

A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…

Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…

The far-reaching consequences of ecological interactions in the dynamics of biological communities remain an intriguing subject. For decades, competition has been a cornerstone in ecological processes, but mounting evidence shows that…

A modeling formalism is proposed for the description and study of living and life-like systems. It provides an abstract conceptual model framework for real life and evolution of biological organisms. It is proposed, that this model…

Computation of biological processes creates great promise for everyday life and great challenges for physical scientists. Simulations of molecular dynamics appeal to biologists as a natural extension of structural biology. Once biologists…

Many scientific models are composed of multiple discrete components, and scientists often make heuristic decisions about which components to include. Bayesian inference provides a mathematical framework for systematically selecting model…

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…

In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a…

The interpretability of machine learning, particularly for deep neural networks, is crucial for decision making in real-world applications. One approach is replacing the un-interpretable machine learning model with a surrogate model, which…

Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates…

Signal processing traditionally relies on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and additional domain knowledge. Simple…

Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…

Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to…

Finite mixtures of matrix normal distributions are a powerful tool for classifying three-way data in unsupervised problems. The distribution of each component is assumed to be a matrix variate normal density. The mixture model can be…

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…

Gene-gene interactions are often regarded as playing significant roles in influencing variabilities of complex traits. Although much research has been devoted to this area, to date a comprehensive statistical model that addresses the…

Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…

It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…

Biological systems are governed by coupled interactions between intracellular metabolism and bioreactor operation that span multiple time scales. Constraint-based metabolic models are widely used to describe intracellular metabolism, but…