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Hablemos de Soberanía Alimentaria
Gorban,Myriam;
Diaeta , 2010,
Abstract: in april 2009, the argentina association of dietitians and nutritionists-dietitians formed the study group on food sovereignty, made up of graduates in nutrition who have an interest in the subject. this article presents an introduction to said group's findings.
Hablemos de Soberanía Alimentaria Let's Talk about Food Sovereignty
Myriam Gorban
Diaeta , 2010,
Abstract: En abril de 2009 se conformó en la Asociación Argentina de Dietistas y Nutricionistas Dietistas el Grupo de Estudio sobre Soberanía Alimentaria, constituido por un grupo de licenciados en nutrición con interés en el tema. El presente artículo presenta una introducción a las conclusiones de dicho grupo. In April 2009, the Argentina Association of Dietitians and Nutritionists-Dietitians formed the Study Group on Food Sovereignty, made up of graduates in Nutrition who have an interest in the subject. This article presents an introduction to said group's findings.
Monotonically equivalent entropies and solution of additivity equation
Pavel Gorban
Physics , 2003, DOI: 10.1016/S0378-4371(03)00578-8
Abstract: Generalized entropies are studied as Lyapunov functions for the Master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients), trace-form (the form of sum over the states), and additivity (for composition of independent subsystems). All the entropies, which have all three properties simultaneously and are defined for positive probabilities, are found. They form a one-parametric family. We consider also pairs of entropies $S_{1}$, $S_{2}$, which are connected by the monotonous transformation $S_{2}=F(S_{1})$ (equivalent entropies). All classes of pairs of universal equivalent entropies, one of which has a trace-form, and another is additive (these entropies can be different one from another), were found. These classes consist of two one-parametric families: the family of entropies, which are equivalent to the additive trace-form entropies, and the family of Renyi-Tsallis entropies.
Singularities of transition processes in dynamical systems: Qualitative theory of critical delays
Alexander N. Gorban
Electronic Journal of Differential Equations , 2004,
Abstract: This monograph presents a systematic analysis of the singularities in the transition processes for dynamical systems. We study general dynamical systems, with dependence on a parameter, and construct relaxation times that depend on three variables: Initial conditions, parameters $k$ of the system, and accuracy $varepsilon$ of the relaxation. We study the singularities of relaxation times as functions of $(x_0,k)$ under fixed $varepsilon$, and then classify the bifurcations (explosions) of limit sets. We study the relationship between singularities of relaxation times and bifurcations of limit sets. An analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Selection theorem for systems with inheritance
A. N. Gorban
Physics , 2004, DOI: 10.1051/mmnp:2008024
Abstract: The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of "natural" selection. Estimations of the asymptotic dimension are presented. After some initial time, solution of a kinetic equation with conservation of support becomes a finite set of narrow peaks that become increasingly narrow over time and move increasingly slowly. It is possible that these peaks do not tend to fixed positions, and the path covered tends to infinity as t goes to infinity. The drift equations for peak motion are obtained. Various types of distribution stability are studied: internal stability (stability with respect to perturbations that do not extend the support), external stability or uninvadability (stability with respect to strongly small perturbations that extend the support), and stable realizability (stability with respect to small shifts and extensions of the density peaks). Models of self-synchronization of cell division are studied, as an example of selection in systems with additional symmetry. Appropriate construction of the notion of typicalness in infinite-dimensional space is discussed, and the notion of "completely thin" sets is introduced. Key words: Dynamics; Attractor; Evolution; Entropy; Natural selection
Order--disorder separation: Geometric revision
A. N. Gorban
Physics , 2005, DOI: 10.1016/j.physa.2005.07.016
Abstract: After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure concentration effects in analysis and geometry allow us to return from the ensemble--based point of view to a state--based one, at least, partially. In this paper, the order--disorder problem is represented as a problem of relation between distance and measure. The effect of strong order--disorder separation for multiparticle systems is described: the phase space could be divided into two subsets, one of them (set of disordered states) has almost zero diameter, the second one has almost zero measure. The symmetry with respect to permutations of particles is responsible for this type of concentration. Dynamics of systems with strong order--disorder separation has high average acceleration squared, which can be interpreted as evolution through a series of collisions (acceleration--dominated dynamics). The time arrow direction from order to disorder follows from the strong order--disorder separation. But, inverse, for systems in space of symmetric configurations with ``sticky boundaries" the way back from disorder to order is typical (Natural selection). Recommendations for mining of molecular dynamics results are presented also.
Singularities of Transition Processes in Dynamical Systems: Qualitative Theory of Critical Delays
A. N. Gorban
Physics , 1997,
Abstract: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters $k$ of the system and accuracy $\epsilon$ of the relaxation. The singularities of relaxation times as functions of $(x_0,k)$ under fixed $\epsilon$ are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Local Equivalence of Reversible and General Markov Kinetics
A. N. Gorban
Physics , 2012, DOI: 10.1016/j.physa.2012.11.028
Abstract: We consider continuous--time Markov kinetics with a finite number of states and a given positive equilibrium distribution P*. For an arbitrary probability distribution $P$ we study the possible right hand sides, dP/dt, of the Kolmogorov (master) equations. We describe the cone of possible values of the velocity, dP/dt, as a function of P and P*. We prove that, surprisingly, these cones coincide for the class of all Markov processes with equilibrium P* and for the reversible Markov processes with detailed balance at this equilibrium. Therefore, for an arbitrary probability distribution $P$ and a general system there exists a system with detailed balance and the same equilibrium that has the same velocity dP/dt at point P. The set of Lyapunov functions for the reversible Markov processes coincides with the set of Lyapunov functions for general Markov kinetics. The results are extended to nonlinear systems with the generalized mass action law.
Basic Types of Coarse-Graining
A. N. Gorban
Physics , 2006,
Abstract: We consider two basic types of coarse-graining: the Ehrenfests' coarse-graining and its extension to a general principle of non-equilibrium thermodynamics, and the coarse-graining based on uncertainty of dynamical models and Epsilon-motions (orbits). Non-technical discussion of basic notions and main coarse-graining theorems are presented: the theorem about entropy overproduction for the Ehrenfests' coarse-graining and its generalizations, both for conservative and for dissipative systems, and the theorems about stable properties and the Smale order for Epsilon-motions of general dynamical systems including structurally unstable systems. Computational kinetic models of macroscopic dynamics are considered. We construct a theoretical basis for these kinetic models using generalizations of the Ehrenfests' coarse-graining. General theory of reversible regularization and filtering semigroups in kinetics is presented, both for linear and non-linear filters. We obtain explicit expressions and entropic stability conditions for filtered equations. A brief discussion of coarse-graining by rounding and by small noise is also presented.
Neuroinformatics: What are us, where are we going, how to measure our way?
A. N. Gorban
Physics , 2003,
Abstract: What is neuroinformatics? We can define it as a direction of science and information technology, dealing with development and study of the methods for solution of problems by means of neural networks. A field of science cannot be determined only by fixing what it is "dealing with". The main component, actually constituting a scientific direction, is "THE GREAT PROBLEM", around which the efforts are concentrated. One may state even categorically: if there is no a great problem, there is no a field of science, but only more or less skilful imitation. What is "THE GREAT PROBLEM" for neuroinformatics? The problem of effective parallelism, the study of brain (solution of mysteries of thinking), etc are discussed. The neuroinformatics was considered not only as a science, but as a services sector too. The main ideas of generalized technology of extraction of explicit knowledge from data are presented. The mathematical achievements generated by neuroinformatics, the problem of provability of neurocomputations, and benefits of neural network realization of solution of a problem are discussed.
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