Evolution of adaptation mechanisms: adaptation energy, stress, and oscillating death

In 1938, H. Selye proposed the notion of adaptation energy and published "Experimental evidence supporting the conception of adaptation energy". Adaptation of an animal to different factors appears as the spending of one resource. Adaptation energy is a hypothetical extensive quantity spent for adaptation. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. The controversial points of view impede the systematic use of the notion of adaptation energy despite experimental evidence. Nevertheless, the response to many harmful factors often has general non-specific form and we suggest that the mechanisms of physiological adaptation admit a very general and nonspecific description. We aim to demonstrate that Selye's adaptation energy is the cornerstone of the top-down approach to modelling of non-specific adaptation processes. We analyse Selye's axioms of adaptation energy together with Goldstone's modifications and propose a series of models for interpretation of these axioms. {\em Adaptation energy is considered as an internal coordinate on the `dominant path' in the model of adaptation}. The phenomena of `oscillating death' and `oscillating remission' are predicted on the base of the dynamical models of adaptation. Natural selection plays a key role in the evolution of mechanisms of physiological adaptation. We use the fitness optimization approach to study of the distribution of resources for neutralization of harmful factors, during adaptation to a multifactor environment, and analyse the optimal strategies for different systems of factors

Approximation with Random Bases: Pro et Contra

In this work we discuss the problem of selecting suitable approximators from families of parameterized elementary functions that are known to be dense in a Hilbert space of functions. We consider and analyze published procedures, both randomized and deterministic, for selecting elements from these families that have been shown to ensure the rate of convergence in $L_2$ norm of order $O(1/N)$, where $N$ is the number of elements. We show that both randomized and deterministic procedures are successful if additional information about the families of functions to be approximated is provided. In the absence of such additional information one may observe exponential growth of the number of terms needed to approximate the function and/or extreme sensitivity of the outcome of the approximation to parameters. Implications of our analysis for applications of neural networks in modeling and control are illustrated with examples.Comment: arXiv admin note: text overlap with arXiv:0905.067

Further Results on Lyapunov-Like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial solutions of nonlinear systems to unstable equilibria. The conditions are based on the earlier work (A.N. Gorban, I.Yu. Tyukin, E. Steur, and H. Nijmeijer, SIAM Journal on Control and Optimization, Vol. 51, No. 3, 2013) and can be viewed as an extension of the Lyapunov's first method in that they apply to systems in which the corresponding Jacobian has one zero eigenvalue. Second, we show that for a relevant subclass of systems, persistency of excitation of a function of time in the right-hand side of the equations governing dynamics of the system ensure existence of an attractor basin such that solutions passing through this basin in forward time converge to the origin exponentially. Finally we demonstrate that conditions developed in (A.N. Gorban, I.Yu. Tyukin, E. Steur, and H. Nijmeijer, SIAM Journal on Control and Optimization, Vol. 51, No. 3, 2013) may be remarkably tight.Comment: 53d IEEE Conference on Decision and Control, Los-Angeles, USA, 201

Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling

The Influence of Recreational Load on the Biodiversity of the Shatsk National Natural Park

Рекреаційне природокористування на території Шацького НПП сконцентроване поблизу частково оточених лісом озер Світязь та Пісочне. Унаслідок зростаючого рекреаційного навантаження на ці ділянки екосистем утворився острівний ефект рекреації, що формує чотири рекреаційні зони. Антропогенне навантаження на цих ділянках уже перейшло межу стійкості екосистеми до рекреаційного пресу. В останнє десятиліття в наявних рекреаційних зонах стрімко зросла кількість ділянок із V та ІV стадією рекреаційної дигресії. Recreational land use within the Shatsk NNP is concentrated near two, partially surrounded by forest, lakes – Svityaz’ and Pisochne. In consequence of the increased recreational load on the above mentioned ecosystems parts, an insular effect of recreation is appeared, which, in turn, forms four recreation zones. Anthropogenic load on these areas exceeds an ecosystem stability threshold to recreational press. During last decade, within the existent recreational zones, the number of areas with V and IV stages of recreation digression impetuously increased.Роботу виконано у Шацькій екологічній лабораторії ФМІ ім. Г. В. Карпенка НАН Україн