Complexity of classical dynamics of molecular systems. I. Methodology

Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. “Computational mechanics” is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process.

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

Multicriteria Evaluation and Optimization of Hierarchical Systems

It is shown that any multicriteria problem can be represented by a hierarchical system. Separate properties of the object are evaluated at the lower level of the system, using a criteria vector, and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriteria problems of evaluation and optimization. It is based on nested scalar convolutions of vector- valued criteria and allows simple structural and parametrical synthesis of multicriteria hierarchical systems.

About Methods of Mathematical Modelling in the Development of Information Systems

This article describes the approach, which allows to develop information systems without taking into consideration details of physical storage of the relational model and type database management system. Described in terms of graph model, this approach allows to construct several algorithms, for example, for verification application domain. This theory was introduced into operation testing as a part of CASE-system METAS.

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

The evolution of learning systems:to Bayes or not to be

Bayesian algorithms pose a limit to the performance learning algorithms can achieve. Natural selection should guide the evolution of information processing systems towards those limits. What can we learn from this evolution and what properties do the intermediate stages have? While this question is too general to permit any answer, progress can be made by restricting the class of information processing systems under study. We present analytical and numerical results for the evolution of on-line algorithms for learning from examples for neural network classifiers, which might include or not a hidden layer. The analytical results are obtained by solving a variational problem to determine the learning algorithm that leads to maximum generalization ability. Simulations using evolutionary programming, for programs that implement learning algorithms, confirm and expand the results. The principal result is not just that the evolution is towards a Bayesian limit. Indeed it is essentially reached. In addition we find that evolution is driven by the discovery of useful structures or combinations of variables and operators. In different runs the temporal order of the discovery of such combinations is unique. The main result is that combinations that signal the surprise brought by an example arise always before combinations that serve to gauge the performance of the learning algorithm. This latter structures can be used to implement annealing schedules. The temporal ordering can be understood analytically as well by doing the functional optimization in restricted functional spaces. We also show that there is data suggesting that the appearance of these traits also follows the same temporal ordering in biological systems. © 2006 American Institute of Physics.

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Evolutionary Clustering of Complex Systems and Processes

In a paper the method of complex systems and processes clustering based use of genetic algorithm is offered. The aspects of its realization and shaping of fitness-function are considered. The solution of clustering task of Ukraine areas on socio-economic indexes is represented and comparative analysis with outcomes of classical methods is realized.

Synthesis Methods of Multiple-valued Structures of Language Systems

The basic construction concepts of many-valued intellectual systems, which are adequate to primal problems of person activity and using hybrid tools with many-valued of coding are considered. The many-valued intellectual systems being two-place, but simulating neuron processes of space toting which are different on a level of actions, inertial and threshold of properties of neurons diaphragms, and also modification of frequency of following of the transmitted messages are created. All enumerated properties and functions in point of fact are essential not only are discrete on time, but also many-valued.

A Knowledge-Oriented Technology of System-Objective Analysis and Modelling of Business-Systems

A new original method and CASE-tool of system analysis and modelling are represented. They are for the first time consistent with the requirements of object-oriented technology of informational systems design. They essentially facilitate the construction of organisational systems models and increase the quality of the organisational designing and basic technological processes of object application developing.

Simultaneous Control of Chaotic Systems Using RBF Networks

Chaos control is a concept that recently acquiring more attention among the research community, concerning the fields of engineering, physics, chemistry, biology and mathematic. This paper presents a method to simultaneous control of deterministic chaos in several nonlinear dynamical systems. A radial basis function networks (RBFNs) has been used to control chaotic trajectories in the equilibrium points. Such neural network improves results, avoiding those problems that appear in other control methods, being also efficient dealing with a relatively small random dynamical noise.

Multiple-Valued Structures of Intellectual Systems

The basic construction concepts of many-valued intellectual systems, which are adequate to primal problems of person activity and using hybrid tools with many-valued intellectual systems being two-place, but simulating neuron processes of space toting which are different on a level of actions, inertial and threshold of properties of neuron diaphragms, and also frequency modification of the following transmitted messages are created. All enumerated properties and functions in point of fact are essential not only are discrete on time, but also many-valued.

Experience of Development and Application of Expert Systems for Economic Macroparameters Forecasting and Operation

In this article there are considered problems of forecasting economical macroparameters, and in the first place, index of inflation. Concept of development of synthetical forecasting methods which use directly specified expert information as well as calculation result on the basis of objective economical and mathematical models for forecasting separate “slowly changeable parameters” are offered. This article discusses problems of macroparameters operation on the basis of analysis of received prognostic magnitude.

Analysis of P-Systems under a Multiagent Systems Perspective

Membrane computing is a recent area that belongs to natural computing. This field works on computational models based on nature's behavior to process the information. Recently, numerous models have been developed and implemented with this purpose. P-systems are the structures which have been defined, developed and implemented to simulate the behavior and the evolution of membrane systems which we find in nature. What we show in this paper is an application capable to simulate the P-systems based on a multiagent systems (MAS) technology. The main goal we want to achieve is to take advantage of the inner qualities of the multiagent systems. This way we can analyse the proper functioning of any given p-system. When we observe a P-system from a different perspective, we can be assured that it is a particular case of the multiagent systems. This opens a new possibility, in the future, to always evaluate the P-systems in terms of the multiagent systems technology.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.