Related papers: Geometry and biological processes
In this paper we survey recent work on the use of statistical model checking techniques for biological applications. We begin with an overview of the basic modelling techniques for biochemical reactions and their corresponding stochastic…
In this paper we present a preliminary study for designing interactive systems that are sensible to human emotions based on the body movements. To do so, we first review the literature on the various approaches for defining and…
The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
In this paper, we investigate a mathematical modeling of biochemical processes which makes it possible to determine the adaptation of a biosystem to open environmental conditions.
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
Measurement in biological systems became a subject of concern as a consequence of numerous reports on limited reproducibility of experimental results. To reveal origins of this inconsistency, we have examined general features of biological…
Geometric quantization procedures go usually through an extension of the original theory (pre-quantization) and a subsequent reduction (selection of the physical states). In this context we describe a full geometrical mechanism which…
This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
Graphical modelling has a long history in statistics as a tool for the analysis of multivariate data, starting from Wright's path analysis and Gibbs' applications to statistical physics at the beginning of the last century. In its modern…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology.