Representation of Neural Networks by Dynamical Systems

Representation of neural networks by dynamical systems is considered. The method of training of neural networks with the help of the theory of optimal control is offered.

Almost Separable Data Aggregation by Layers of Formal Neurons

Information extraction or knowledge discovery from large data sets should be linked to data aggregation process. Data aggregation process can result in a new data representation with decreased number of objects of a given set. A deterministic approach to separable data aggregation means a lesser number of objects without mixing of objects from different categories. A statistical approach is less restrictive and allows for almost separable data aggregation with a low level of mixing of objects from different categories. Layers of formal neurons can be designed for the purpose of data aggregation both in the case of deterministic and statistical approach. The proposed designing method is based on minimization of the of the convex and piecewise linear (CPL) criterion functions.

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Generalization by Computation Through Memory

Usually, generalization is considered as a function of learning from a set of examples. In present work on the basis of recent neural network assembly memory model (NNAMM), a biologically plausible 'grandmother' model for vision, where each separate memory unit itself can generalize, has been proposed. For such a generalization by computation through memory, analytical formulae and numerical procedure are found to calculate exactly the perfectly learned memory unit's generalization ability. The model's memory has complex hierarchical structure, can be learned from one example by a one-step process, and may be considered as a semi-representational one. A simple binary neural network for bell-shaped tuning is described.

Emotions and a Prior Knowledge Representation in Artificial General Intelligence

In this paper a prior knowledge representation for Artificial General Intelligence is proposed based on fuzzy rules using linguistic variables. These linguistic variables may be produced by neural network. Rules may be used for generation of basic emotions – positive and negative, which influence on planning and execution of behavior. The representation of Three Laws of Robotics as such prior knowledge is suggested as highest level of motivation in AGI.

Automatic ECG Analysis for Preliminary and Detailed Diagnostics Based on Scale-space Representation

A novel approach of automatic ECG analysis based on scale-scale signal representation is proposed. The approach uses curvature scale-space representation to locate main ECG waveform limits and peaks and may be used to correct results of other ECG analysis techniques or independently. Moreover dynamic matching of ECG CSS representations provides robust preliminary recognition of ECG abnormalities which has been proven by experimental results.

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

Method for Analytical Representation of the Maximum Inaccuracies of Indirectly Measurable Variable

Let us have an indirectly measurable variable which is a function of directly measurable variables. In this survey we present the introduced by us method for analytical representation of its maximum absolute and relative inaccuracy as functions, respectively, of the maximum absolute and of the relative inaccuracies of the directly measurable variables. Our new approach consists of assuming for fixed variables the statistical mean values of the absolute values of the coefficients of influence, respectively, of the absolute and relative inaccuracies of the directly measurable variables in order to determine the analytical form of the maximum absolute and relative inaccuracies of an indirectly measurable variable. Moreover, we give a method for determining the numerical values of the maximum absolute and relative inaccuracies. We define a sample plane of the ideal perfectly accurate experiment and using it we give a universal numerical characteristic – a dimensionless scale for determining the quality (accuracy) of the experiment.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

The Knowledge in Automotive Field Representation with Modern Technologies

Modern technologies have changed the way of presenting information in archives. This makes it possible to introduce new services, which was unimaginable a few years ago. Digitalization, security and virtual presentation of objects in the sphere of motoring by application of technologies, based on knowledge about how to create digital resources is the theme of this project. The aim of AutoKnow project is to carry out a research and create a multi- media digital archive AutoKnow and Experimental Virtual Motor Laboratory (EVML) with Motor Library (ML) from digital multi-media patterns from a selected group of objects in the sphere of automobile technology, presented by NMU. This makes it possible to widely apply multi-media collections in automobile engineering, teaching, research work in that sphere and serve the interests of a large number of auto-amateurs as well in Bulgaria. The research and development of АutoKnow is in the following mutually related fields: - Creation and annotation of collections of objects in the sphere of automobiles; - Creation, analysis and security of a digital archive AutoKnow; - Design and creation of Digital Motor Library; - Socially-oriented applications in education, scientific studies and Experimental Virtual Motor Laboratory; - Informational System for teaching and testing of knowledge in the sphere of automobiles MindCheck.

Digital Representation of Knitting Patterns in Traditional Costumes

The paper presents the application of a CAD system for digital representation of traditional knitting. The CAD system is oriented to hand knitting. As a software application the system is developed by using C# programming language and .NET platform. The paper focuses on the applied side of the software and its usage as a means of representing and storing ethnographic exhibits.

Riccati Representation for Elements in H^(-1) and Its Applications

2002 Mathematics Subject Classification: 35L05, 34L15, 35D05, 35Q53

Piecewise Convex Curves and their Integral Representation

2000 Mathematics Subject Classification: 52A10.