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polynomial approximation of experimental curves of two interacting Th1(t) - Th2(t)
systems by methods of Genetic Programming;
parameter identification of the nonlinear interval dynamic time-delay mathematical
model of two interacting Th1(t) - Th2(t) systems by means of using the interval
methods of global unconstrained optimization;
investigation of the dynamical properties (absolute stability, attraction and so on)
of nonlinear interval dynamic time-delay mathematical model with the nonlinearity
of the sector type.
Computer Immunology System with Variable Configuration has the next subsystems:
analysis of the state computer network on the base principle of cytokines interac-
tions Th1(t) - Th2(t) systems (strong state or intrusion state);
pattern recognition procedures of the non-standard alarm information;
attraction, stabilization and putting into operation.
These subsystems allows to decide the next tasks:
parameter identification in the conception of “input-output” mapping with the use dis-
crete analogues of the Volterra series known as Gabor-Kolmogorov polynomials (power
series) on the base Genetic Programming;
parameter identification in the form of nonlinear interval dynamic time-delay equations;
investigation the dynamics properties (absolute stability, attraction) these equations with the
use of Lyapunov-Klassovsky functional.
2
Main Results
Cytokines are small protein messenger molecules that convey information from one
cell to another. The relationship between cytokines and their specific receptors is
very complex. As it is known the cytokines networks have the next properties:
combinatorial complexity since the number of potential interactions between indi-
vidual elements (e.g. proteins) in a system grows extremely rapidly with the num-
ber of elements;
negative and positive feedback loops operate at various levels.
delays, for instance, when a T-cell receives a proliferate signal, it first needs to
synthesize DNA and undergo the biochemical changes required for cell division;
nonlinearity is all-pervasive in these systems, and indeed is essential for their
functioning.
Mathematical models of two interacting Th1(t)-Th2(t) systems have been investigated
with a variety of approaches and areas of emphasis in [1,3]. Such properties as the
regulation by cytokines, T cell activation, proliferation, death and so on were learning
there. However, these models haven't time-delay. Also in these mathematical models
the next considerable factor did not include. Many processes in the interacting Th1(t)-
Th2(t) systems are uncertain. This uncertainty has as a rule, a non-statistic nature, or
there is not enough information in order to refer it to one of the group of random
processes. The parametric uncertainties are characterized by a relationship of the true
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