Related papers: Geometry and biological processes
We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current…
Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological…
Humans possess a remarkable capacity to recognize and manipulate abstract structure, which is especially apparent in the domain of geometry. Recent research in cognitive science suggests neural networks do not share this capacity,…
We present and critically discuss five commonly used mathematical models of the meal glucose rate of appearance in humans. Such models are key to simulation of the metabolism in healthy people, people with diabetes, and obese people, and…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
Cell fate decisions emerge as a consequence of a complex set of gene regulatory networks. Models of these networks are known to have more parameters than data can determine. Recent work, inspired by Waddington's metaphor of a landscape, has…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
We present the novel approach to mathematical modeling of information processes in biosystems. It explores the mathematical formalism and methodology of quantum theory, especially quantum measurement theory. This approach is known as {\it…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
In this article we highlight chemotaxis (cellular movement) as a rich source of potential engineering applications and computational models, highlighting current research and possible future work. We first give a brief description of the…
The aim of the paper is to show algorithms for geometrical manipulations on NURBS surfaces. These include generating NURBS surfaces that pass through given points, calculating the minimum distance to a point and include line to surface and…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue…
Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role. We…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
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…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
The article describes the method of using computer-learning tools during the modeling of biological processes in the high school. The author developed web pages for online processing of the results of simulation of the genetic structure of…