Particle competition and cooperation to prevent error propagation from mislabeled data in semi-supervised learning

Semi-supervised learning is applied to classification problems where only a small portion of the data items is labeled. In these cases, the reliability of the labels is a crucial factor, because mislabeled items may propagate wrong labels to a large portion or even the entire data set. This paper aims to address this problem by presenting a graph-based (network-based) semi-supervised learning method, specifically designed to handle data sets with mislabeled samples. The method uses teams of walking particles, with competitive and cooperative behavior, for label propagation in the network constructed from the input data set. The proposed model is nature-inspired and it incorporates some features to make it robust to a considerable amount of mislabeled data items. Computer simulations show the performance of the method in the presence of different percentage of mislabeled data, in networks of different sizes and average node degree. Importantly, these simulations reveals the existence of the critical points of the mislabeled subset size, below which the network is free of wrong label contamination, but above which the mislabeled samples start to propagate their labels to the rest of the network. Moreover, numerical comparisons have been made among the proposed method and other representative graph-based semi-supervised learning methods using both artificial and real-world data sets. Interestingly, the proposed method has increasing better performance than the others as the percentage of mislabeled samples is getting larger. © 2012 IEEE.

Stochastic competitive learning in complex networks

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning.

Network-based stochastic semisupervised learning

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Formazione, apprendimento e nuove prospettive e-learning. Lo sviluppo delle nuove tecnologie didattiche e la creazione di sistemi di apprendimento lungo l’intero arco della vita

The thesis of this paper is based on the assumption that the socio-economic system in which we are living is characterised by three great trends: growing attention to the promotion of human capital; extremely rapid technological progress, based above all on the information and communication technologies (ICT); the establishment of new production and organizational set-ups. These transformation processes pose a concrete challenge to the training sector, which is called to satisfy the demand for new skills that need to be developed and disseminated. Hence the growing interest that the various training sub-systems devote to the issues of lifelong learning and distance learning. In such a context, the so-called e-learning acquires a central role. The first chapter proposes a reference theoretical framework for the transformations that are shaping post-industrial society. It analyzes some key issues such as: how work is changing, the evolution of organizational set-ups and the introduction of learning organization, the advent of the knowledge society and of knowledge companies, the innovation of training processes, and the key role of ICT in the new training and learning systems. The second chapter focuses on the topic of e-learning as an effective training model in response to the need for constant learning that is emerging in the knowledge society. This chapter starts with a reflection on the importance of lifelong learning and introduces the key arguments of this thesis, i.e. distance learning (DL) and the didactic methodology called e-learning. It goes on with an analysis of the various theoretic and technical aspects of e-learning. In particular, it delves into the theme of e-learning as an integrated and constant training environment, characterized by customized programmes and collaborative learning, didactic assistance and constant monitoring of the results. Thus, all the aspects of e-learning are taken into exam: the actors and the new professionals, the virtual communities as learning subjects, the organization of contents in learning objects, the conformity to international standards, the integrated platforms and so on. The third chapter, which concludes the theoretic-interpretative part, starts with a short presentation of the state-of-the-art e-learning international market that aims to understand its peculiarities and its current trends. Finally, we focus on some important regulation aspects related to the strong impulse given by the European Commission first, and by the Italian governments secondly, to the development and diffusion of e-learning. The second part of the thesis (chapters 4, 5 and 6) focus on field research, which aims to define the Italian scenario for e-learning. In particular, we have examined some key topics such as: the challenges of training and the instruments to face such challenges; the new didactic methods and technologies for lifelong learning; the level of diffusion of e-learning in Italy; the relation between classroom training and online training; the main factors of success as well as the most critical aspects of the introduction of e-learning in the various learning environments. As far as the methodological aspects are concerned, we have favoured a qualitative and quantitative analysis. A background analysis has been done to collect the statistical data available on this topic, as well as the research previously carried out in this area. The main source of data is constituted by the results of the Observatory on e-learning of Aitech-Assinform, which covers the 2000s and four areas of implementation (firms, public administration, universities, school): the thesis has reviewed the results of the last three available surveys, offering a comparative interpretation of them. We have then carried out an in-depth empirical examination of two case studies, which have been selected by virtue of the excellence they have achieved and can therefore be considered advanced and emblematic experiences (a large firm and a Graduate School).

The E-learning Circle – a holistic software design tool for e-learning

The article introduces the E-learning Circle, a tool developed to assure the quality of the software design process of e-learning systems, considering pedagogical principles as well as technology. The E-learning Circle consists of a number of concentric circles which are divided into three sectors. The content of the inner circles is based on pedagogical principles, while the outer circle specifies how the pedagogical principles may be implemented with technology. The circle’s centre is dedicated to the subject taught, ensuring focus on the specific subject’s properties. The three sectors represent the student, the teacher and the learning objectives. The strengths of the E-learning Circle are the compact presentation combined with the overview it provides, as well as the usefulness of a design tool dealing with complexity, providing a common language and embedding best practice. The E-learning Circle is not a prescriptive method, but is useful in several design models and processes. The article presents two projects where the E-learning Circle was used as a design tool.

Cooperation & Competition Between Navigation Systems in the Rat Brain: The Role of the Hippocampus and Striatum During a Dissociative Maze Task

While many tend to think of memory systems in the brain as a single process, in reality several experiments have supported multiple dissociations of different forms of learning, such as spatial learning and response learning. In both humans and rats, the hippocampus has long been shown to be specialized in the storage of spatial and contextual memory whereas the striatum is associated with motor responses and habitual behaviors. Previous studies have examined how damage to hippocampus or striatum has affected the acquisition of either a spatial or response navigation task. However even in a very familiar environment organisms must continuously switch between place and response strategies depending upon circumstances. The current research investigates how these two brain systems interact under normal conditions to produce navigational behavior. Rats were tested using a task developed by Jacobson and colleagues (2006) in which the two types of navigation could be controlled and studied simultaneously. Rats were trained to solve a plus maze using both a spatial and a response strategy. A cue (flashing light) was employed to indicate the correct strategy on a given trial. When no light was present, the animals were rewarded for making a 90º right turn (motor response). When the light was on, the animals were rewarded for going to a specific goal location (place strategy). After learning the task, animals had a sham surgery or dorsal striatum or hippocampus damaged. In order to investigate the individual role of each brain system and evaluate whether these brain regions compete or cooperate for control over strategy, we utilized a within-animal comparisons. The configuration of the maze allowed for the comparison of behavior in individual animals before and after specific brain areas were damaged. Animals with hippocampal lesions showed selective deficits on place trials after surgery and learned the reversal of the motor response more rapidly than striatal lesioned or sham rats. Unlike previous findings regarding maze learning, animals with striatal lesions showed deficits in both place and response trials and had difficulty learning the reversal of motor response. Therefore, the effects of lesions on the ability to switch back and forth between strategies were more complex than previously suggested. This work may reveal important new insight on the integration of hippocampal and striatal learning systems, and facilitate a better understanding of the brain dynamics underlying similar navigational processes in humans.

A policy-driven architecture for supporting joint degrees through e-learning services

En un mercado de educación superior cada vez más competitivo, la colaboración entre universidades es una efectiva estrategia para acceder al mercado global. El desarrollo de titulaciones conjuntas es un importante mecanismo para fortalecer las colaboraciones académicas y diversificar los conocimientos. Las titulaciones conjuntas están siendo cada vez más implementadas en las universidades de todo el mundo. En Europa, el proceso de Bolonia y el programa Erasmus, están fomentado el reconocimiento de titulaciones conjuntas y dobles y promoviendo la colaboración entre las instituciones académicas. En el imparable proceso de la globalización y convergencia educativa, el uso de sistemas de e-learning para soportar cursos tanto semipresencial como online es una tendencia en crecimiento. Dado que los sistemas de e-learning soportan una amplia variedad de cursos, es necesario encontrar una solución adecuada que permita a las universidades soportar y gestionar las titulaciones conjuntas a través de sus sistemas de e-learning en conformidad con los acuerdos de colaboración establecidos por las universidades participantes. Esta tesis doctoral abordará las siguientes preguntas de investigación: 1. ¿Qué factores deben tenerse en cuenta en la implementación y gestión de titulaciones conjuntas? 2. ¿Cómo pueden los sistemas actuales de e-learning soportar el desarrollo de titulaciones conjuntas? 3. ¿Qué otros servicios y sistemas necesitan ser adaptados por las universidades interesadas en participar en una titulación conjunta a través de sus sistemas de e-learning? La implementación de titulaciones conjuntas a través de sistemas de e-learning es compleja e implica retos técnicos, administrativos, culturales, financieros, jurídicos y de seguridad. Esta tesis doctoral propone una serie de contribuciones que pueden ayudar a resolver algunos de los retos identificados. En primer lugar se ha elaborado un modelo conceptual que incluye la información del contexto de las titulaciones conjuntas que es relevante para la implementación de estas titulaciones en los sistemas de e-learning. Después de definir el modelo conceptual, se ha propuesto una arquitectura basada en políticas para la implementación de titulaciones interinstitucionales a través de sistemas de e-learning de acuerdo a los términos estipulados en los acuerdos de colaboración que son firmados por las universidades participantes. El autor se ha centrado en el componente de gestión de flujos de trabajo de esta arquitectura. Por último y con el fin de permitir la interoperabilidad de repositorios de objetos educativos, los componentes básicos a implementar han sido identificados y validados. El uso de servicios multimedia en educación es una tendencia creciente, proporcionando servicios de e-learning que permiten mejorar la comunicación y la interacción entre profesores y alumnos. Dentro de estos servicios, nos hemos centrado en el uso de la videoconferencia y la grabación de clases como servicios adecuados para el desarrollo de cursos impartidos en escenarios de educación colaborativos. Las contribuciones han sido validadas en proyectos de investigación de ámbito nacional y europeo en los que el autor ha participado. Abstract In an increasingly competitive higher education market, collaboration between universities is an effective strategy for gaining access to the global market. The development of joint degrees is an important mechanism for strengthening academic research collaborations and diversifying knowledge. Joint degrees are becoming increasingly implemented in universities around the world. In Europe, the Bologna process and the Erasmus programme have encouraged both the global recognition of joint and double degrees and promoted close collaboration between academic institutions. In the unstoppable process of globalization and educational convergence, the use of e-learning systems for supporting both blended and online courses is becoming a growing trend. Since e-learning systems covers a wide range of courses, it becomes necessary to find a suitable solution that enables universities to support and manage joint degrees through their e-learning systems in accordance with the collaboration agreements established by the universities involved. This dissertation will address the following research questions: 1. What factors need to be considered in the implementation and management of joint degrees? 2. How can the current e-learning systems support the development of joint degrees? 3. What other services and systems need to be adapted by universities interested in participating in a joint degree through their e-learning systems? The implementation of joint degrees using e-learning systems is complex and involves technical, administrative, security, cultural, financial and legal challenges. This dissertation proposes a series of contributions to help solve some of the identified challenges. One of the cornerstones of this proposal is a conceptual model of all the relevant issues related to the support of joint degrees by means of e-learning systems. After defining the conceptual model, this dissertation proposes a policy-driven architecture for implementing inter-institutional degree collaborations through e-learning systems as stipulated by a collaboration agreement signed by two universities. The author has focused on the workflow management component of this architecture. Finally, the building blocks for achieving interoperability of learning object repositories have been identified and validated. The use of multimedia services in education is a growing trend, providing rich e-learning services that improve the communication and interaction between teachers and students. Within these e-learning services, we have focused on the use of videoconferencing and lecture recording as the best-suited services to support collaborative learning scenarios. The contributions have been validated within national and European research projects that the author has been involved in.

Conceptual framework for the design, implementation and validation of psychomotor skills’ assessment systems in minimally invasive surgery

Las técnicas de cirugía de mínima invasión (CMI) se están consolidando hoy en día como alternativa a la cirugía tradicional, debido a sus numerosos beneficios para los pacientes. Este cambio de paradigma implica que los cirujanos deben aprender una serie de habilidades distintas de aquellas requeridas en cirugía abierta. El entrenamiento y evaluación de estas habilidades se ha convertido en una de las mayores preocupaciones en los programas de formación de cirujanos, debido en gran parte a la presión de una sociedad que exige cirujanos bien preparados y una reducción en el número de errores médicos. Por tanto, se está prestando especial atención a la definición de nuevos programas que permitan el entrenamiento y la evaluación de las habilidades psicomotoras en entornos seguros antes de que los nuevos cirujanos puedan operar sobre pacientes reales. Para tal fin, hospitales y centros de formación están gradualmente incorporando instalaciones de entrenamiento donde los residentes puedan practicar y aprender sin riesgos. Es cada vez más común que estos laboratorios dispongan de simuladores virtuales o simuladores físicos capaces de registrar los movimientos del instrumental de cada residente. Estos simuladores ofrecen una gran variedad de tareas de entrenamiento y evaluación, así como la posibilidad de obtener información objetiva de los ejercicios. Los diferentes estudios de validación llevados a cabo dan muestra de su utilidad; pese a todo, los niveles de evidencia presentados son en muchas ocasiones insuficientes. Lo que es más importante, no existe un consenso claro a la hora de definir qué métricas son más útiles para caracterizar la pericia quirúrgica. El objetivo de esta tesis doctoral es diseñar y validar un marco de trabajo conceptual para la definición y validación de entornos para la evaluación de habilidades en CMI, en base a un modelo en tres fases: pedagógica (tareas y métricas a emplear), tecnológica (tecnologías de adquisición de métricas) y analítica (interpretación de la competencia en base a las métricas). Para tal fin, se describe la implementación práctica de un entorno basado en (1) un sistema de seguimiento de instrumental fundamentado en el análisis del vídeo laparoscópico; y (2) la determinación de la pericia en base a métricas de movimiento del instrumental. Para la fase pedagógica se diseñó e implementó un conjunto de tareas para la evaluación de habilidades psicomotoras básicas, así como una serie de métricas de movimiento. La validación de construcción llevada a cabo sobre ellas mostró buenos resultados para tiempo, camino recorrido, profundidad, velocidad media, aceleración media, economía de área y economía de volumen. Adicionalmente, los resultados obtenidos en la validación de apariencia fueron en general positivos en todos los grupos considerados (noveles, residentes, expertos). Para la fase tecnológica, se introdujo el EVA Tracking System, una solución para el seguimiento del instrumental quirúrgico basado en el análisis del vídeo endoscópico. La precisión del sistema se evaluó a 16,33ppRMS para el seguimiento 2D de la herramienta en la imagen; y a 13mmRMS para el seguimiento espacial de la misma. La validación de construcción con una de las tareas de evaluación mostró buenos resultados para tiempo, camino recorrido, profundidad, velocidad media, aceleración media, economía de área y economía de volumen. La validación concurrente con el TrEndo® Tracking System por su parte presentó valores altos de correlación para 8 de las 9 métricas analizadas. Finalmente, para la fase analítica se comparó el comportamiento de tres clasificadores supervisados a la hora de determinar automáticamente la pericia quirúrgica en base a la información de movimiento del instrumental, basados en aproximaciones lineales (análisis lineal discriminante, LDA), no lineales (máquinas de soporte vectorial, SVM) y difusas (sistemas adaptativos de inferencia neurodifusa, ANFIS). Los resultados muestran que en media SVM presenta un comportamiento ligeramente superior: 78,2% frente a los 71% y 71,7% obtenidos por ANFIS y LDA respectivamente. Sin embargo las diferencias estadísticas medidas entre los tres no fueron demostradas significativas. En general, esta tesis doctoral corrobora las hipótesis de investigación postuladas relativas a la definición de sistemas de evaluación de habilidades para cirugía de mínima invasión, a la utilidad del análisis de vídeo como fuente de información y a la importancia de la información de movimiento de instrumental a la hora de caracterizar la pericia quirúrgica. Basándose en estos cimientos, se han de abrir nuevos campos de investigación que contribuyan a la definición de programas de formación estructurados y objetivos, que puedan garantizar la acreditación de cirujanos sobradamente preparados y promocionen la seguridad del paciente en el quirófano. Abstract Minimally invasive surgery (MIS) techniques have become a standard in many surgical sub-specialties, due to their many benefits for patients. However, this shift in paradigm implies that surgeons must acquire a complete different set of skills than those normally attributed to open surgery. Training and assessment of these skills has become a major concern in surgical learning programmes, especially considering the social demand for better-prepared professionals and for the decrease of medical errors. Therefore, much effort is being put in the definition of structured MIS learning programmes, where practice with real patients in the operating room (OR) can be delayed until the resident can attest for a minimum level of psychomotor competence. To this end, skills’ laboratory settings are being introduced in hospitals and training centres where residents may practice and be assessed on their psychomotor skills. Technological advances in the field of tracking technologies and virtual reality (VR) have enabled the creation of new learning systems such as VR simulators or enhanced box trainers. These systems offer a wide range of tasks, as well as the capability of registering objective data on the trainees’ performance. Validation studies give proof of their usefulness; however, levels of evidence reported are in many cases low. More importantly, there is still no clear consensus on topics such as the optimal metrics that must be used to assess competence, the validity of VR simulation, the portability of tracking technologies into real surgeries (for advanced assessment) or the degree to which the skills measured and obtained in laboratory environments transfer to the OR. The purpose of this PhD is to design and validate a conceptual framework for the definition and validation of MIS assessment environments based on a three-pillared model defining three main stages: pedagogical (tasks and metrics to employ), technological (metric acquisition technologies) and analytical (interpretation of competence based on metrics). To this end, a practical implementation of the framework is presented, focused on (1) a video-based tracking system and (2) the determination of surgical competence based on the laparoscopic instruments’ motionrelated data. The pedagogical stage’s results led to the design and implementation of a set of basic tasks for MIS psychomotor skills’ assessment, as well as the definition of motion analysis parameters (MAPs) to measure performance on said tasks. Validation yielded good construct results for parameters such as time, path length, depth, average speed, average acceleration, economy of area and economy of volume. Additionally, face validation results showed positive acceptance on behalf of the experts, residents and novices. For the technological stage the EVA Tracking System is introduced. EVA provides a solution for tracking laparoscopic instruments from the analysis of the monoscopic video image. Accuracy tests for the system are presented, which yielded an average RMSE of 16.33pp for 2D tracking of the instrument on the image and of 13mm for 3D spatial tracking. A validation experiment was conducted using one of the tasks and the most relevant MAPs. Construct validation showed significant differences for time, path length, depth, average speed, average acceleration, economy of area and economy of volume; especially between novices and residents/experts. More importantly, concurrent validation with the TrEndo® Tracking System presented high correlation values (>0.7) for 8 of the 9 MAPs proposed. Finally, the analytical stage allowed comparing the performance of three different supervised classification strategies in the determination of surgical competence based on motion-related information. The three classifiers were based on linear (linear discriminant analysis, LDA), non-linear (support vector machines, SVM) and fuzzy (adaptive neuro fuzzy inference systems, ANFIS) approaches. Results for SVM show slightly better performance than the other two classifiers: on average, accuracy for LDA, SVM and ANFIS was of 71.7%, 78.2% and 71% respectively. However, when confronted, no statistical significance was found between any of the three. Overall, this PhD corroborates the investigated research hypotheses regarding the definition of MIS assessment systems, the use of endoscopic video analysis as the main source of information and the relevance of motion analysis in the determination of surgical competence. New research fields in the training and assessment of MIS surgeons can be proposed based on these foundations, in order to contribute to the definition of structured and objective learning programmes that guarantee the accreditation of well-prepared professionals and the promotion of patient safety in the OR.

An approach to automatic learning assessment based on the computational theory of perceptions

E-learning systems output a huge quantity of data on a learning process. However, it takes a lot of specialist human resources to manually process these data and generate an assessment report. Additionally, for formative assessment, the report should state the attainment level of the learning goals defined by the instructor. This paper describes the use of the granular linguistic model of a phenomenon (GLMP) to model the assessment of the learning process and implement the automated generation of an assessment report. GLMP is based on fuzzy logic and the computational theory of perceptions. This technique is useful for implementing complex assessment criteria using inference systems based on linguistic rules. Apart from the grade, the model also generates a detailed natural language progress report on the achieved proficiency level, based exclusively on the objective data gathered from correct and incorrect responses. This is illustrated by applying the model to the assessment of Dijkstra’s algorithm learning using a visual simulation-based graph algorithm learning environment, called GRAPHs

A flexible open source web platform to facilitate Learning Object evaluation

Systematic evaluation of Learning Objects is essential to make high quality Web-based education possible. For this reason, several educational repositories and e-Learning systems have developed their own evaluation models and tools. However, the differences of the context in which Learning Objects are produced and consumed suggest that no single evaluation model is sufficient for all scenarios. Besides, no much effort has been put in developing open tools to facilitate Learning Object evaluation and use the quality information for the benefit of end users. This paper presents LOEP, an open source web platform that aims to facilitate Learning Object evaluation in different scenarios and educational settings by supporting and integrating several evaluation models and quality metrics. The work exposed in this paper shows that LOEP is capable of providing Learning Object evaluation to e-Learning systems in an open, low cost, reliable and effective way. Possible scenarios where LOEP could be used to implement quality control policies and to enhance search engines are also described. Finally, we report the results of a survey conducted among reviewers that used LOEP, showing that they perceived LOEP as a powerful and easy to use tool for evaluating Learning Objects.

Curvature-driven smoothing: a learning algorithm for feed-forward networks

The performance of feed-forward neural networks in real applications can be often be improved significantly if use is made of a-priori information. For interpolation problems this prior knowledge frequently includes smoothness requirements on the network mapping, and can be imposed by the addition to the error function of suitable regularization terms. The new error function, however, now depends on the derivatives of the network mapping, and so the standard back-propagation algorithm cannot be applied. In this paper, we derive a computationally efficient learning algorithm, for a feed-forward network of arbitrary topology, which can be used to minimize the new error function. Networks having a single hidden layer, for which the learning algorithm simplifies, are treated as a special case.

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.

Towards e+Learning or How to Increase the Learning into e-Learning

It is discussed some changes in the traditional e-learning notion on the point of view of R. Koper’s question 'where is the learning in e-learning?’. We put a focus on the conception of learning as a management process and present the project Bulgarian Educational Site (BEST) – a possible answer to Koper’s question. The BEST is a virtual learning environment, based on the following principles: learning is a goal-directed and didactics-managed process; learners may define their own learning objectives, monitor and regulate the learning process; collaborative e-learning is more effective; etc. The BEST is based on two famous e-learning systems (Moodle, LAMS) and Plovdiv e-University (versions 1.0 and 2.0). The paper brings up a mater about the new ‘electronic’ pedagogy and proposes an approach for pedagogical modeling and interpretation of e-learning applied in the BEST.

E-learning

E-learning means learning via electronic means and is therefore an all-embracing term covering learning via an electronic device. The "expectations" and "realities" for each of the delivery mechanisms within the electronic arena vary greatly for not just the learners themselves, but also the site providers. Because of this, each of these learning systems has vastly different design principles, which is not always understood by those unfamiliar with technology. What is appropriate for a CD-ROM off-line system is generally inappropriate for an on- line internet system. So when designing an e-learning system it is important to understand how the information is to be accessed by the learner. This paper will identify and suggest some ways to avoid e-learning's pitfalls and reap its rewards.

Generalized Nets Model of an E-Learning System Software Architecture

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko ff and Lubomir Tschakaloff , Sofi a, July, 2006.