O biológii, matematike a výpočtoch - rozhovor s A. Lindenmayerom
O teorii katastrof
Observers for Canonic Models of Neural Oscillators
We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar...
On Chemotaxis Models with Cell Population Interactions
This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are discussed and...
On classification with missing data using rough-neuro-fuzzy systems
The paper presents a new approach to fuzzy classification in the case of missing data. Rough-fuzzy sets are incorporated into logical type neuro-fuzzy structures and a rough-neuro-fuzzy classifier is derived. Theorems which allow determining the structure of the rough-neuro-fuzzy classifier are given. Several experiments illustrating the performance of the roughneuro-fuzzy classifier working in the case of missing features are described.
On geodesics of phyllotaxis
Seeds of sunflowers are often modelled by leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance for the golden ratio. We associate to such a map a geodesic path of the modular curve and use it for local descriptions of the image of the phyllotactic map .
On geometry of binary symmetric models of phylogenetic trees
We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for...
On global exponential stability of discrete-time Hopfield neural networks with variable delays.
On linearizing systems of diffusion equations.
On neural networks
On permutation symmetries of Hopfield model neural network.
On Popov-type stability criteria for neural networks.
On the controllability of a type of large scale CNN with delays.
On the Dynamics of a Two-Strain Influenza Model with Isolation
Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling...
On the expectation and variance of the reversal distance.
On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion
Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological phenomena. This paper begins with a survey of applications to ecology, cell biology and bacterial colony patterns. The author then reviews mathematical results on the existence of travelling wave front solutions of these equations, and their generation from given initial data. A detailed study is then presented of the form of smooth-front...
On the strong convergence to equilibrium for randomly perturbed dynamical systems
On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time,...
Optimal Poiseuille flow in a finite elastic dyadic tree
In this paper we construct a model to describe some aspects of the deformation of the central region of the human lung considered as a continuous elastically deformable medium. To achieve this purpose, we study the interaction between the pipes composing the tree and the fluid that goes through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key...
Optimal Proliferation Rate in a Cell Division Model
We consider a size structured cell population model where a mother cell gives birth to two daughter cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a...