Conditions of Effectiveness of Pattern Recognition Problem Solution Using Logical Level Descriptions of Classes

Earlier the authors have suggested a logical level description of classes which allows to reduce a solution of various pattern recognition problems to solution of a sequence of one-type problems with the less dimension. Here conditions of the effectiveness of the use of such a level descriptions are proposed.

Bottleneck Problem Solution using Biological Models of Attention in High Resolution Tracking Sensors

Every high resolution imaging system suffers from the bottleneck problem. This problem relates to the huge amount of data transmission from the sensor array to a digital signal processing (DSP) and to bottleneck in performance, caused by the requirement to process a large amount of information in parallel. The same problem exists in biological vision systems, where the information, sensed by many millions of receptors should be transmitted and processed in real time. Models, describing the bottleneck problem solutions in biological systems fall in the field of visual attention. This paper presents the bottleneck problem existing in imagers used for real time salient target tracking and proposes a simple solution by employing models of attention, found in biological systems. The bottleneck problem in imaging systems is presented, the existing models of visual attention are discussed and the architecture of the proposed imager is shown.

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.

Reduction Measurements for Calculation in Fuzzy Experiment Scheme

The papers is dedicated to the questions of modeling and basing super-resolution measuring- calculating systems in the context of the conception “device + PC = new possibilities”. By the authors of the article the new mathematical method of solution of the multi-criteria optimization problems was developed. The method is based on physic-mathematical formalism of reduction of fuzzy disfigured measurements. It is shown, that determinative part is played by mathematical properties of physical models of the object, which is measured, surroundings, measuring components of measuring-calculating systems and theirs cooperation as well as the developed mathematical method of processing and interpretation of measurements problem solution.

A Software Platform for Educational Board Games

Educational games such as quizzes, quests, puzzles, mazes and logical problems may be modeled as multimedia board games. In the scope of the ADOPTA project1 being under development at the Faculty of Mathematics and Informatics at Sofia University, a formal model for presentation of such educational board games was invented and elaborated. Educational games can be modeled as special board mini-games, with a board of any form and any types of positions. Over defined positions, figures (objects) with certain properties are placed and, next, there are to be defined formal rules for manipulation of these figures and resulted effects. The model has been found to be general enough in order to allow description and execution control of more complex logical problems to be solved by several actions delivered to/by the player according some formal rules and context conditions and, in general, of any learning activities and their workflow. It is used as a base for creation of a software platform providing facilities for easy construction of multimedia board games and their execution. The platform consists of game designer (i.e., a game authoring tool) and game run-time controller communicating each other through game repository. There are created and modeled many examples of educational board games appropriate for didactic purposes, self evaluations, etc., which are supposed to be designed easily by authors with no IT skills and experience. By means of game metadata descriptions, these games are going be included into narrative storyboards and, next, delivered to learners with appropriate profile according their learning style, preferences, etc. Moreover, usage of artificial intelligence agents is planned as well – once as playing virtual opponents of the player or, otherwise, being virtual advisers of the gamer helping him/her in finding the right problem solution within given domain such as discovering a treasure using a location map, finding best tour in a virtual museum, guessing an unknown word in a hangman game, and many others.

Explicit Solution of Bitsadze-Samarskii Problem

Иван Димовски, Юлиан Цанков - В статията е намерено точно решение на задачата на Бицадзе-Самрски (1) за уравнението на Лаплас, като е използвано операционно смятане основано на некласическа двумернa конволюция. На това точно решение може да се гледа като начин за сумиране на нехармоничния ред по синуси на решението, получен по метода на Фурие.

A solution of the trigonometric moment problem via Tagamlitzki's "Theorem of the Cones"

In 1952 Y. Tagamlitzki gave an elegant proof of the classical Bochner’s theorem on the positively definite functions. Unfortunately, he never published his proof. In this paper we consider a related but simpler problem, the trigonometric moment problem, by using Tagamlitzki’s approach.

Decomposition of Boolean Functions – Recognizing a Good Solution by Traces

The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Active Monitoring and Decision Making Problem

Active monitoring and problem of non-stable of sound signal parameters in the regime of piling up response signal of environment is under consideration. Math model of testing object by set of weak stationary dynamic actions is offered. The response of structures to the set of signals is under processing for getting important information about object condition in high frequency band. Making decision procedure by using researcher’s heuristic and aprioristic knowledge is discussed as well. As an example the result of numerical solution is given.

Training a Linear Neural Network with a Stable LSP Solution for Jamming Cancellation

Two jamming cancellation algorithms are developed based on a stable solution of least squares problem (LSP) provided by regularization. They are based on filtered singular value decomposition (SVD) and modifications of the Greville formula. Both algorithms allow an efficient hardware implementation. Testing results on artificial data modeling difficult real-world situations are also provided.

Stability of an Optimal Schedule for a Job-Shop Problem with Two Jobs

The usual assumption that the processing times of the operations are known in advance is the strictest one in scheduling theory. This assumption essentially restricts practical aspects of deterministic scheduling theory since it is not valid for the most processes arising in practice. The paper is devoted to a stability analysis of an optimal schedule, which may help to extend the significance of scheduling theory for decision-making in the real-world applications. The term stability is generally used for the phase of an algorithm, at which an optimal solution of a problem has already been found, and additional calculations are performed in order to study how solution optimality depends on variation of the numerical input data.

On a Direct Approach to the Solution of Inverse Optical Problems

The evaluation from experimental data, of physical quantities, which enter into the electromagnetic Maxwell equations, is described as inverse optical problem. The functional relations between the dependent and independent variables are of transcendental character and numeric procedures for evaluation of the unknowns are largely used. Herein, we discuss a direct approach to the solution, illustrated by a specific example of determination of thin films optical constants from spectrophotometric data. New algorithm is proposed for the parameters evaluation, which does not need an initial guess of the unknowns and does not use iterative procedures. Thus we overcome the intrinsic deficiency of minimization techniques, such as gradient search methods, Simplex methods, etc. The price of it is a need of more computing power, but our algorithm is easily implemented in structures such as grid clusters. We show the advantages of this approach and its potential for generalization to other inverse optical problems.

Performance Comparison of MATLAB and Neuro Solution Software on Estimation of Fuel Economy by Using Artificial Neural Network

In the world, scientific studies increase day by day and computer programs facilitate the human’s life. Scientists examine the human’s brain’s neural structure and they try to be model in the computer and they give the name of artificial neural network. For this reason, they think to develop more complex problem’s solution. The purpose of this study is to estimate fuel economy of an automobile engine by using artificial neural network (ANN) algorithm. Engine characteristics were simulated by using “Neuro Solution” software. The same data is used in MATLAB to compare the performance of MATLAB is such a problem and show its validity. The cylinder, displacement, power, weight, acceleration and vehicle production year are used as input data and miles per gallon (MPG) are used as target data. An Artificial Neural Network model was developed and 70% of data were used as training data, 15% of data were used as testing data and 15% of data is used as validation data. In creating our model, proper neuron number is carefully selected to increase the speed of the network. Since the problem has a nonlinear structure, multi layer are used in our model.

Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear differential equation of complex order with the Caputo fractional derivative. The equivalence of this problem and a nonlinear Volterra integral equation in the space of continuously differentiable functions is established. On the basis of this result, the existence and uniqueness of the solution of the considered Cauchy problem is proved. The approximate-iterative method by Dzjadyk is used to obtain the approximate solution of this problem. Two numerical examples are given.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12