Stochastic passivity of uncertain neural networks with time-varying delays.
Stochastic stability of Cohen-Grossberg neural networks with unbounded distributed delays.
Stochastic stability of neural networks with both Markovian jump parameters and continuously distributed delays.
Study of stationary solutions in gene network models by the homotopy method.
Sum-fuzzy implementation of a choice function using artificial learning procedure with fixed fraction
In one if his paper Luo transformed the problem of sum-fuzzy rationality into artificial learning procedure and gave an algorithm which used the learning rule of perception. This paper extends the Luo method for finding a sum-fuzzy implementation of a choice function and offers an algorithm based on the artificial learning procedure with fixed fraction. We also present a concrete example which uses this algorithm.
Support vector machine skin lesion classification in Clifford algebra subspaces
The present study develops the Clifford algebra within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis - ABCD. To generate the we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D vector onto...
Synchronization for an array of coupled Cohen-Grossberg neural networks with time-varying delay.
Synchronization of discrete-time stochastic neural networks with random delay.
Synchronization of strongly coupled neural networks.
Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space
With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the spatial coexistence,...
The combinatorics of evolutionary trees---a survey.
The conjugacy between Cascades generated by a weakly nonlinear system and the Euler method of a flow
Sufficient conditions for the existence of a topological conjugacy between a cascade obtained from a weakly nonlinear flow by fixing the time step and a cascade obtained by the Euler method are analysed. The aim of this paper is to provide relations between constants in the Fečkan theorem. Given such relations an implementation of a weakly nonlinear neuron is possible.
The dynamics of living and thinking systems, biological networks, and the laws of physics.
The Effect of Bacteria on Epidermal Wound Healing
Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an...
The formation of a tree leaf
In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...
The generalized Turner-Bradley-Kirk-Pruitt equation.
The Immune System – Complexity Exemplified
The Importance of Spatial Distribution of Stemness and Proliferation State in Determining Tumor Radioresponse
Tumor growth and progression is a complex phenomenon dependent on the interaction of multiple intrinsic and extrinsic factors. Necessary for tumor development is a small subpopulation of potent cells, so-called cancer stem cells, that can undergo an unlimited number of cell divisions and which are proposed to divide symmetrically with a small probability to produce more cancer stem cells. We show that the majority of cells in a tumor must indeed be non-stem cancer cells with limited life span and...
The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology
We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding...
The Rothe method for the McKendrick-von Foerster equation
We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in and...