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.

Solving the Task Assignment Problem with a Variable Neighborhood Search

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches all optimal solutions in a quite short amount of computational time.

Individual identification using electrocardiogram morphology

The use of electrocardiogram as biometric has raised attention in the last decade and a wide variety of ECG features were explored to verify the feasibility of such a signal. In this work the authors aim to describe a simple template based approach to the electrocardiographic biometric identification using the morphology of individual's heartbeat. The developed algorithm was tested on different recordings made available in the Physionet public database Fantasia: two different sets of heartbeats were extracted from individual recordings one was used for the template building while the second for the tests. The performances of the algorithm are encouraging with a true acceptance rate of 99.4%, however, the procedure needs to be tested on different recordings of the same individual, or during the course of a whole day or physical activity. © 2013 IEEE.

An algorithm for FHR estimation from foetal phonocardiographic signals

The long-term foetal surveillance is often to be recommended. Hence, the fully non-invasive acoustic recording, through maternal abdomen, represents a valuable alternative to the ultrasonic cardiotocography. Unfortunately, the recorded heart sound signal is heavily loaded by noise, thus the determination of the foetal heart rate raises serious signal processing issues. In this paper, we present a new algorithm for foetal heart rate estimation from foetal phonocardiographic recordings. A filtering is employed as a first step of the algorithm to reduce the background noise. A block for first heart sounds enhancing is then used to further reduce other components of foetal heart sound signals. A complex logic block, guided by a number of rules concerning foetal heart beat regularity, is proposed as a successive block, for the detection of most probable first heart sounds from several candidates. A final block is used for exact first heart sound timing and in turn foetal heart rate estimation. Filtering and enhancing blocks are actually implemented by means of different techniques, so that different processing paths are proposed. Furthermore, a reliability index is introduced to quantify the consistency of the estimated foetal heart rate and, based on statistic parameters; [,] a software quality index is designed to indicate the most reliable analysis procedure (that is, combining the best processing path and the most accurate time mark of the first heart sound, provides the lowest estimation errors). The algorithm performances have been tested on phonocardiographic signals recorded in a local gynaecology private practice from a sample group of about 50 pregnant women. Phonocardiographic signals have been recorded simultaneously to ultrasonic cardiotocographic signals in order to compare the two foetal heart rate series (the one estimated by our algorithm and the other provided by cardiotocographic device). Our results show that the proposed algorithm, in particular some analysis procedures, provides reliable foetal heart rate signals, very close to the reference cardiotocographic recordings. © 2010 Elsevier Ltd. All rights reserved.

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

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Many Facet, Common Latent Trait Polytomous IRT Model and EM Algorithm

2000 Mathematics Subject Classification: 91E45.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Em Algorithm for MLE of a Probit Model for Multiple Ordinal Outcomes

The correlated probit model is frequently used for multiple ordered data since it allows to incorporate seamlessly different correlation structures. The estimation of the probit model parameters based on direct maximization of the limited information maximum likelihood is a numerically intensive procedure. We propose an extension of the EM algorithm for obtaining maximum likelihood estimates for a correlated probit model for multiple ordinal outcomes. The algorithm is implemented in the free software environment for statistical computing and graphics R. We present two simulation studies to examine the performance of the developed algorithm. We apply the model to data on 121 women with cervical or endometrial cancer. Patients developed normal tissue reactions as a result of post-operative external beam pelvic radiotherapy. In this work we focused on modeling the effects of a genetic factor on early skin and early urogenital tissue reactions and on assessing the strength of association between the two types of reactions. We established that there was an association between skin reactions and polymorphism XRCC3 codon 241 (C>T) (rs861539) and that skin and urogenital reactions were positively correlated. ACM Computing Classification System (1998): G.3.

Variable Neighborhood Search for Solving the Capacitated Single Allocation Hub Location Problem

In this paper a Variable Neighborhood Search (VNS) algorithm for solving the Capacitated Single Allocation Hub Location Problem (CSAHLP) is presented. CSAHLP consists of two subproblems; the first is choosing a set of hubs from all nodes in a network, while the other comprises finding the optimal allocation of non-hubs to hubs when a set of hubs is already known. The VNS algorithm was used for the first subproblem, while the CPLEX solver was used for the second. Computational results demonstrate that the proposed algorithm has reached optimal solutions on all 20 test instances for which optimal solutions are known, and this in short computational time.

Denoising Manifolds for Dimension

2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.

Trust and cooperation in buyer–seller relationships and networks. The co-evolution of structural balance and trust in iterated PD games

Our study has two aims: to elaborate theoretical frameworks and introduce social mechanisms of spontaneous co-operation in repeated buyer-seller relationships and to formulate hypotheses which can be empirically tested. The basis of our chain of ideas is the simple two-person Prisoner’s Dilemma game. On the one hand, its repeated variation can be applicable for the distinction of the analytical types of trust (iteration trust, strategy trust) in co-operations. On the other hand, it provides a chance to reveal those dyadic sympathy-antipathy relations, which make us understand the evolution of trust. Then we introduce the analysis of the more complicated (more than two-person) buyer-seller relationship. Firstly, we outline the possible role of the structural balancing mechanisms in forming trust in three-person buyer-seller relationships. Secondly, we put forward hypotheses to explain complex buyer-seller networks. In our research project we try to theoretically combine some of the simple concepts of game theory with certain ideas of the social-structural balance theory. Finally, it is followed by a short summary.

On the accuracy of nonsurvey regional input-output multipliers: An empirical study

Correct specification of the simple location quotients in regionalizing the national direct requirements table is essential to the accuracy of regional input-output multipliers. The purpose of this research is to examine the relative accuracy of these multipliers when earnings, employment, number of establishments, and payroll data specify the simple location quotients.^ For each specification type, I derive a column of total output multipliers and a column of total income multipliers. These multipliers are based on the 1987 benchmark input-output accounts of the U.S. economy and 1988-1992 state of Florida data.^ Error sign tests, and Standardized Mean Absolute Deviation (SMAD) statistics indicate that the output multiplier estimates overestimate the output multipliers published by the Department of Commerce-Bureau of Economic Analysis (BEA) for the state of Florida. In contrast, the income multiplier estimates underestimate the BEA's income multipliers. For a given multiplier type, the Spearman-rank correlation analysis shows that the multiplier estimates and the BEA multipliers have statistically different rank ordering of row elements. The above tests also find no significant different differences, both in size and ranking distributions, among the vectors of multiplier estimates. ^

Clash of identities in South Florida: An examination of the complexity of racial and national identity and their impact on ethnic solidarity between black Americans and Jamaicans

Immigrants from the West Indies and other nations challenge the simple United States dichotomy of blacks versus whites. Many apparently black Caribbean immigrants proclaim that they did not know they were “black” until they arrived in the U.S. They seek to maintain their national identity and resist identity and solidarity with Black Americans. In response, many Black Americans respond that the immigrants are simply being naive, that U.S. society demands simple racial identity. Regardless of one's self-identity and personal history, in the U.S., if you look black, you are black, was their thinking. ^ This study examines the contemporary struggle of identity and solidarity among and between Black Americans and Jamaicans living in South Florida (Broward and Miami-Dade counties). Even though the primary focus of this study is to examine the relationship between Black Americans and Jamaicans, other West Indian nationals will be addressed more generally. The primary research problem of this study is to determine why the existence of common ancestry and physical traits are insufficient for an assumption of ethnic solidarity between Black Americans and Jamaicans. ^ In examining this problem, I felt that depth rather than breadth would provide insight into the current state of polarization between Black Americans and Jamaicans. To this end, a qualitative study was designed. A non-random snowball sample consisting of forty-seven informants was selected for this study. Realizing that such a technique presents problems with generalizations beyond the sample, this approach was, nonetheless, the most suitable for the current research problem. One of the initial challenges of this research was the use of the label “black” in discussing Caribbean immigrants. Unlike America, where distinctions based on skin color were at the bedrock of America's formation, this was not the case in the Caribbean. In the Caribbean skin color was an important marker as an indicator of class, rather than of race. Therefore, I refrained from using the label, “black Jamaicans,” but rather used Jamaicans throughout. ^

Optimizing the radiation pattern of smart antennas using genetic algorithms

This work is directed towards optimizing the radiation pattern of smart antennas using genetic algorithms. The structure of the smart antennas based on Space Division Multiple Access (SDMA) is proposed. It is composed of adaptive antennas, each of which has adjustable weight elements for amplitudes and phases of signals. The corresponding radiation pattern formula available for the utilization of numerical optimization techniques is deduced. Genetic algorithms are applied to search the best phase-amplitude weights or phase-only weights with which the optimal radiation pattern can be achieved. ^ One highlight of this work is the proposed optimal radiation pattern concept and its implementation by genetic algorithms. The results show that genetic algorithms are effective for the true Signal-Interference-Ratio (SIR) design of smart antennas. This means that not only nulls can be put in the directions of the interfering signals but also simultaneously main lobes can be formed in the directions of the desired signals. The optimal radiation pattern of a smart antenna possessing SDMA ability has been achieved. ^ The second highlight is on the weight search by genetic algorithms for the optimal radiation pattern design of antennas having more than one interfering signal. The regular criterion for determining which chromosome should be kept for the next step iteration is modified so as to improve the performance of the genetic algorithm iteration. The results show that the modified criterion can speed up and guarantee the iteration to be convergent. ^ In addition, the comparison between phase-amplitude perturbations and phase-only perturbations for the radiation pattern design of smart antennas are carried out. The effects of parameters used by the genetic algorithm on the optimal radiation pattern design are investigated. Valuable results are obtained. ^