Superregular matrices and applications to convolutional codes

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature.

Demonstrador para rede tempo-real HaRTES

A utilização de sistemas embutidos distribuídos em diversas áreas como a robótica, automação industrial e aviónica tem vindo a generalizar-se no decorrer dos últimos anos. Este tipo de sistemas são compostos por vários nós, geralmente designados por sistemas embutidos. Estes nós encontram-se interligados através de uma infra-estrutura de comunicação de forma a possibilitar a troca de informação entre eles de maneira a concretizar um objetivo comum. Por norma os sistemas embutidos distribuídos apresentam requisitos temporais bastante exigentes. A tecnologia Ethernet e os protocolos de comunicação, com propriedades de tempo real, desenvolvidos para esta não conseguem associar de uma forma eficaz os requisitos temporais das aplicações de tempo real aos requisitos Quality of Service (QoS) dos diferentes tipos de tráfego. O switch Hard Real-Time Ethernet Switching (HaRTES) foi desenvolvido e implementado com o objetivo de solucionar estes problemas devido às suas capacidades como a sincronização de fluxos diferentes e gestão de diferentes tipos de tráfego. Esta dissertação apresenta a adaptação de um sistemas físico de modo a possibilitar a demonstração do correto funcionamento do sistema de comunicação, que será desenvolvido e implementado, utilizando um switch HaRTES como o elemento responsável pela troca de informação na rede entre os nós. O desempenho da arquitetura de rede desenvolvida será também testada e avaliada.

Mediator framework for inserting xDRs into hadoop

During the last decades, we assisted to what is called “information explosion”. With the advent of the new technologies and new contexts, the volume, velocity and variety of data has increased exponentially, becoming what is known today as big data. Among them, we emphasize telecommunications operators, which gather, using network monitoring equipment, millions of network event records, the Call Detail Records (CDRs) and the Event Detail Records (EDRs), commonly known as xDRs. These records are stored and later processed to compute network performance and quality of service metrics. With the ever increasing number of collected xDRs, its generated volume needing to be stored has increased exponentially, making the current solutions based on relational databases not suited anymore. To tackle this problem, the relational data store can be replaced by Hadoop File System (HDFS). However, HDFS is simply a distributed file system, this way not supporting any aspect of the relational paradigm. To overcome this difficulty, this paper presents a framework that enables the current systems inserting data into relational databases, to keep doing it transparently when migrating to Hadoop. As proof of concept, the developed platform was integrated with the Altaia - a performance and QoS management of telecommunications networks and services.

A lower bound for the energy of symmetric matrices and graphs

The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph.