Information-theoretic limits of control

Fundamental limits on the controllability of physical systems are discussed in the light of information theory. It is shown that the second law of thermodynamics, when generalized to include information, sets absolute limits to the minimum amount of dissipation required by open-loop control. In addition, an information-theoretic analysis of control systems shows feedback control to be a zero sum game: each bit of information gathered from a dynamical system by a control device can serve to decrease the entropy of that system by at most one bit additional to the reduction of entropy attainable without such information. Consequences for the control of discrete state systems and chaotic maps are discussed.     

Information-theoretic approach to the problem of detection of genuine multipartite classical correlations

We examine the problem of detection of genuine multipartite classical correlations. We first show that genuine multipartite classical correlations cannot be reliably detected by analyzing the multipartite covariances, and then we introduce an information-theoretic approach to the problem of detection of such correlations.     

Information-theoretic approach to single-particle and two-particle interference in multipath interferometers

We propose entropic measures for the strength of single-particle and two-particle interference in interferometric experiments where each particle of a pair traverses a multipath interferometer. Optimal single-particle interference excludes any two-particle interference, and vice versa. We report an inequality that states the compromises allowed by quantum mechanics in intermediate situations, and identify a class of two-particle states for which the upper bound is reached. Our approach is applicable to symmetric two-partite systems of any finite dimension.     

Information-theoretic stochastic resonance in noise-floor limited systems: the case for adding noise

We show that in systems whose output must compete with a noise source, stochastic resonance (maximization of output signal-noise separation as a nonmonotonic function of input noise strength) exists even when measured in terms of fundamental statistical measures and optimal detector performance. This is in contrast to the commonly considered scenario where, without the competing noise, the system (e.g., a driven, overdamped particle moving in a double well potential) is essentially invertible and optimal detector performance monotonically deteriorates with increasing input noise strength.     

An improved impulsive control approach to nonlinear systems with time-varying delays

A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

An orbit analysis approach to the study of superintegrable systems in the Euclidean plane

We classify the superintegrable potentials in the Euclidean plane by means of an orbit analysis of the space of valence two Killing tensors under the action of the group of rigid motions. Our approach generalizes the classical approach of Winternitz and collaborators by considering pairs of Killing tensors that are not both in canonical form. The text was submitted by the authors in English.     

The modular systems biology approach to investigate the control of apoptosis in Alzheimer's disease neurodegeneration

Apoptosis is a programmed cell death that plays a critical role during the development of the nervous system and in many chronic neurodegenerative diseases, including Alzheimer's disease (AD). This pathology, characterized by a progressive degeneration of cholinergic function resulting in a remarkable cognitive decline, is the most common form of dementia with high social and economic impact. Current therapies of AD are only symptomatic, therefore the need to elucidate the mechanisms underlying the onset and progression of the disease is surely needed in order to develop effective pharmacological therapies. Because of its pivotal role in neuronal cell death, apoptosis has been considered one of the most appealing therapeutic targets, however, due to the complexity of the molecular mechanisms involving the various triggering events and the many signaling cascades leading to cell death, a comprehensive understanding of this process is still lacking. Modular systems biology is a very effective strategy in organizing information about complex biological processes and deriving modular and mathematical models that greatly simplify the identification of key steps of a given process. This review aims at describing the main steps underlying the strategy of modular systems biology and briefly summarizes how this approach has been successfully applied for cell cycle studies. Moreover, after giving an overview of the many molecular mechanisms underlying apoptosis in AD, we present both a modular and a molecular model of neuronal apoptosis that suggest new insights on neuroprotection for this disease.     

A pseudobinary approach to study interdiffusion and the Kirkendall effect in multicomponent systems

Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.     

Janes approach to the dynamics of Darwin systems

Within the Janes statistical formalism, a variational principle describing the dynamics of Darwin systems is suggested. Explicit relations describing the dynamics of selection in Darwin systems with random variables and parameters are derived. Biological aspects of basic units of the variational principle are analyzed. Tomsk State University. Translated from Izvestiya Vysshikh, Uchebnykh Zavedenii, Fizika, No. 6, pp. 52–57, June, 2000.     

Hamiltonian approach to the dynamics of Darwinian systems

It is shown that equations describing the dynamics of Darwinian systems (DS) far from the bifurcation points may be expressed in Hamiltonian form. The cases of DS with constant organization and DS with a constant flux through the system are considered. The configurational part of phase space is formed by variables containing information on the structure of the system. Momentum variables may be regarded as specific rates of multiplication. The evolution of DS with constant organization in this phase space is expressed as uniform rectilinear motion. In the case of DS with a constant flux, the motion occurs in some effective constant and uniform field. The meaning of the elements of the Hamiltonian structure is described in terms of theoretical biology. Tomsk State University. Scientific-Research Institute of Biological Systems, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 23–28, July, 1997.     

Logicoalgebraic approach to Lagrangian systems

A logicoalgebraic approach to the geometry of Lagrangian systems is pursued by starting axiomatically with a classical mechanical system whose logic is a separable and atomic Boolean σ algebra.     

Supersymmetric approach to heavy-fermion systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes n _c + 1 states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.     

基于Min-Max方法的混沌系统采样同步控制研究

针对含有扰动的混沌系统, 设计采样同步控制器, 利用输入时滞法将含有采样同步控制器的混杂系统转换为具有输入时滞的连续系统. 并考虑对系统影响最坏的干扰程度, 在该种情况下, 基于线性矩阵不等式(LMI)技术和min-max鲁棒控制方法, 给出了使误差系统稳定的充分条件, 确保混沌系统在所容许的扰动下均能实现完全同步. 仿真结果说明所设计的采样同步控制方案具有很强的鲁棒性, 适合应用于保密通信系统中. 关键词： 混沌同步 采样控制 min-max方法 输入时滞