Computer algebra for x-ray spectral reconstruction between 6 and 25 MV

A previously presented algorithm for the reconstruction of bremsstrahlung spectra from transmission data has been implemented into MATHEMATICA. Spectra vectorial algebra has been used to solve the matrix system A * F = T. The new implementation has been tested by reconstructing photon spectra from transmission data acquired in narrow beam conditions, for nominal energies of 6, 15, and 25 MV. The results were in excellent agreement with the original calculations. Our implementation has the advantage to be based on a well-tested mathematical kernel. Furthermore it offers a comfortable user interface.

An example of Learning based on competences: Use of Maxima in Linear Algebra for Engineers

This paper analyzes the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is defined as an indicator of the generic ompetence: Use of Technology. Additionally, we show that using CAS could help to enhance the following generic competences: Self Learning, Planning and Organization, Communication and Writing, Mathematical and Technical Writing, Information Management and Critical Thinking.

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Analysis of computer communication systems by use of digital signal processing methods

Queueing theory is an effective tool in the analysis of canputer camrunication systems. Many results in queueing analysis have teen derived in the form of Laplace and z-transform expressions. Accurate inversion of these transforms is very important in the study of computer systems, but the inversion is very often difficult. In this thesis, methods for solving some of these queueing problems, by use of digital signal processing techniques, are presented. The z-transform of the queue length distribution for the Mj GY jl system is derived. Two numerical methods for the inversion of the transfom, together with the standard numerical technique for solving transforms with multiple queue-state dependence, are presented. Bilinear and Poisson transform sequences are presented as useful ways of representing continuous-time functions in numerical computations.

Distributed control of computer communication systems

Flow control in Computer Communication systems is generally a multi-layered structure, consisting of several mechanisms operating independently at different levels. Evaluation of the performance of networks in which different flow control mechanisms act simultaneously is an important area of research, and is examined in depth in this thesis. This thesis presents the modelling of a finite resource computer communication network equipped with three levels of flow control, based on closed queueing network theory. The flow control mechanisms considered are: end-to-end control of virtual circuits, network access control of external messages at the entry nodes and the hop level control between nodes. The model is solved by a heuristic technique, based on an equivalent reduced network and the heuristic extensions to the mean value analysis algorithm. The method has significant computational advantages, and overcomes the limitations of the exact methods. It can be used to solve large network models with finite buffers and many virtual circuits. The model and its heuristic solution are validated by simulation. The interaction between the three levels of flow control are investigated. A queueing model is developed for the admission delay on virtual circuits with end-to-end control, in which messages arrive from independent Poisson sources. The selection of optimum window limit is considered. Several advanced network access schemes are postulated to improve the network performance as well as that of selected traffic streams, and numerical results are presented. A model for the dynamic control of input traffic is developed. Based on Markov decision theory, an optimal control policy is formulated. Numerical results are given and throughput-delay performance is shown to be better with dynamic control than with static control.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

The Conception of Creation of Integrated Development Environment for Computer Training Systems

The various questions of creation of integrated development environment for computer training systems are considered in the given paper. The information technologies that can be used for creation of the integrated development environment are described. The different didactic aspects of realization of such systems are analyzed. The ways to improve the efficiency and quality of learning process with computer training systems for distance education are pointed.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Computer Mathematics with MuPAD in School Years 6. To 9

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

A Model of a Diagnostic Test for Controlling the Results of a Computer Based Education in Applied Mathematics at the University of Ruse

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

Adaptive Brain-Computer Interface Systems For Communication in People with Severe Neuromuscular Disabilities

Brain-computer interfaces (BCI) have the potential to restore communication or control abilities in individuals with severe neuromuscular limitations, such as those with amyotrophic lateral sclerosis (ALS). The role of a BCI is to extract and decode relevant information that conveys a user's intent directly from brain electro-physiological signals and translate this information into executable commands to control external devices. However, the BCI decision-making process is error-prone due to noisy electro-physiological data, representing the classic problem of efficiently transmitting and receiving information via a noisy communication channel.

This research focuses on P300-based BCIs which rely predominantly on event-related potentials (ERP) that are elicited as a function of a user's uncertainty regarding stimulus events, in either an acoustic or a visual oddball recognition task. The P300-based BCI system enables users to communicate messages from a set of choices by selecting a target character or icon that conveys a desired intent or action. P300-based BCIs have been widely researched as a communication alternative, especially in individuals with ALS who represent a target BCI user population. For the P300-based BCI, repeated data measurements are required to enhance the low signal-to-noise ratio of the elicited ERPs embedded in electroencephalography (EEG) data, in order to improve the accuracy of the target character estimation process. As a result, BCIs have relatively slower speeds when compared to other commercial assistive communication devices, and this limits BCI adoption by their target user population. The goal of this research is to develop algorithms that take into account the physical limitations of the target BCI population to improve the efficiency of ERP-based spellers for real-world communication.

In this work, it is hypothesised that building adaptive capabilities into the BCI framework can potentially give the BCI system the flexibility to improve performance by adjusting system parameters in response to changing user inputs. The research in this work addresses three potential areas for improvement within the P300 speller framework: information optimisation, target character estimation and error correction. The visual interface and its operation control the method by which the ERPs are elicited through the presentation of stimulus events. The parameters of the stimulus presentation paradigm can be modified to modulate and enhance the elicited ERPs. A new stimulus presentation paradigm is developed in order to maximise the information content that is presented to the user by tuning stimulus paradigm parameters to positively affect performance. Internally, the BCI system determines the amount of data to collect and the method by which these data are processed to estimate the user's target character. Algorithms that exploit language information are developed to enhance the target character estimation process and to correct erroneous BCI selections. In addition, a new model-based method to predict BCI performance is developed, an approach which is independent of stimulus presentation paradigm and accounts for dynamic data collection. The studies presented in this work provide evidence that the proposed methods for incorporating adaptive strategies in the three areas have the potential to significantly improve BCI communication rates, and the proposed method for predicting BCI performance provides a reliable means to pre-assess BCI performance without extensive online testing.