Parallel Semi-supervised EM-algorithm (MT-SSEM)

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

A Multi-View Learning Algorithm

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Neural Networks: A Diagnostic Tool for Gastric Electrical Uncoupling?

Neural Networks have been successfully employed in different biomedical settings. They have been useful for feature extractions from images and biomedical data in a variety of diagnostic applications. In this paper, they are applied as a diagnostic tool for classifying different levels of gastric electrical uncoupling in controlled acute experiments on dogs. Data was collected from 16 dogs using six bipolar electrodes inserted into the serosa of the antral wall. Each dog underwent three recordings under different conditions: (1) basal state, (2) mild surgically-induced uncoupling, and (3) severe surgically-induced uncoupling. For each condition half-hour recordings were made. The neural network was implemented according to the Learning Vector Quantization model. This is a supervised learning model of the Kohonen Self-Organizing Maps. Majority of the recordings collected from the dogs were used for network training. Remaining recordings served as a testing tool to examine the validity of the training procedure. Approximately 90% of the dogs from the neural network training set were classified properly. However, only 31% of the dogs not included in the training process were accurately diagnosed. The poor neural-network based diagnosis of recordings that did not participate in the training process might have been caused by inappropriate representation of input data. Previous research has suggested characterizing signals according to certain features of the recorded data. This method, if employed, would reduce the noise and possibly improve the diagnostic abilities of the neural network.

Anomalous Singularities for Hyperbolic Equations with Degeneracy of Infinite Order

2002 Mathematics Subject Classification: 35L80

Forming of Learning Set for Neural Networks in Problems of Losless Data Compression

questions of forming of learning sets for artificial neural networks in problems of lossless data compression are considered. Methods of construction and use of learning sets are studied. The way of forming of learning set during training an artificial neural network on the data stream is offered.

On Neuron Mechanisms Used to Resolve Mental Problems of Identification and Learning in Sensorium

The paper considers some possible neuron mechanisms that do not contradict biological data. They are represented in terms of the notion of an elementary sensorium discussed in the previous authors’ works. Such mechanisms resolve problems of two large classes: when identification mechanisms are used and when sensory learning mechanisms are applied along with identification.

Developing a Mobile Distance Learning System

This article considers the basic problems of client-server electronic learning systems based on mobile platforms. Such questions as relational learning course model and student’s transitions prediction through the learning course items are considered. Besides, technical questions of electronic learning system “E-Learning Suite” realization and questions of developing portable applications using .NET Framework are discussed.

The Principles of Creation of Teaching Materials and Organization of Ukrainian Language Learning Process using Distance Support in Senior Classes

The article deals with the topicality and problems of using information and communication technologies in secondary education, conditions and methods for Ukrainian language learning with the distance support in senior classes. The article shows the principal similarity of distance learning to training one. The common and specific principles of creation of teaching materials for a distance learning course are described. It reveals the conditions of effective organization of Ukrainian language learning with distance support on the material of distance course “Business Ukrainian and Culture of Communication”.

Conceptual Model and Security Requirements for DRM Techniques Used for e-Learning Objects Protection

This paper deals with the security problems of DRM protected e-learning content. After a short review of the main DRM systems and methods used in e-learning, an examination is made of participators in DRM schemes (e-learning object author, content creator, content publisher, license creator and end user). Then a conceptual model of security related processes of DRM implementation is proposed which is improved afterwards to reflect some particularities in DRM protection of e-learning objects. A methodical way is used to describe the security related motives, responsibilities and goals of the main participators involved in the DRM system. Taken together with the process model, these security properties are used to establish a list of requirements to fulfill and a possibility for formal verification of real DRM systems compliance with these requirements.

Using Elements of Semantic Parsing in e-Learning Environments

Possibilities for using semantic parsing to estimate the correspondence of text materials to teaching aims, correspondence of test task to theoretical materials and other problems arising during the distance course designing and educational process itself in e-learning environments.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

Filtered Networks of Evolutionary Processors

* Supported by INTAS 00-626 and TIC 2003-09319-c03-03.

Learning Technology in Scheduling Based on the Mixed Graphs

We propose the adaptive algorithm for solving a set of similar scheduling problems using learning technology. It is devised to combine the merits of an exact algorithm based on the mixed graph model and heuristics oriented on the real-world scheduling problems. The former may ensure high quality of the solution by means of an implicit exhausting enumeration of the feasible schedules. The latter may be developed for certain type of problems using their peculiarities. The main idea of the learning technology is to produce effective (in performance measure) and efficient (in computational time) heuristics by adapting local decisions for the scheduling problems under consideration. Adaptation is realized at the stage of learning while solving a set of sample scheduling problems using a branch-and-bound algorithm and structuring knowledge using pattern recognition apparatus.

Digital Creativity: Advantages, Problems, Responsibilities

The paper focuses on the rapid development of the digital culture and the challenges it imposes to human creativity. It analyses e-learning, digital entertainment, digital art and the issues of creativity and improvisation. It also presents a classification of the levels in the creative structure including hardware and software tools; product developers; creators and end users. Special attention is paid to the advantages of the new digital culture and the responsibilities of all people who create it or use it. We conclude that more attention should be paid to the threats and to ways of boosting positive creativity in the various fields of application of information and communication technologies.