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- 92-XX Biology and other natural sciences
In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....
We construct a stochastic model of
bacteriophage parasitism of a host bacteria that accounts for
demographic stochasticity of host and parasite and allows for
multiple bacteriophage adsorption to host. We analyze the associated
deterministic model, identifying the basic reproductive number for
phage proliferation, showing that host and phage persist when it
exceeds unity, and establishing that the distribution of adsorbed
phage on a host is binomial with slowly evolving mean. Not
surprisingly,...
Simple epidemiological models with information dependent vaccination functions can
generate sustained oscillations via Hopf bifurcation of the endemic state. The onset of
these oscillations depend on the shape of the vaccination function. A “global” approach
is used to characterize the instability condition and identify classes of functions
that always lead to stability/instability. The analysis allows the identification of an
analytically determined “threshold vaccination function” having...
While alternans in a single cardiac cell appears through a simple
period-doubling bifurcation, in extended tissue the exact nature
of the bifurcation is unclear. In particular, the phase of
alternans can exhibit wave-like spatial dependence, either
stationary or travelling, which is known as discordant
alternans. We study these phenomena in simple cardiac models
through a modulation equation proposed by Echebarria-Karma. As
shown in our previous paper, the zero solution of their equation
may lose...
A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...
The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production...
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