A Review on the Characterization of Signals and Systems by Power Law Distributions

Power laws, also known as Pareto-like laws or Zipf-like laws, are commonly used to explain a variety of real world distinct phenomena, often described merely by the produced signals. In this paper, we study twelve cases, namely worldwide technological accidents, the annual revenue of America׳s largest private companies, the number of inhabitants in America׳s largest cities, the magnitude of earthquakes with minimum moment magnitude equal to 4, the total burned area in forest fires occurred in Portugal, the net worth of the richer people in America, the frequency of occurrence of words in the novel Ulysses, by James Joyce, the total number of deaths in worldwide terrorist attacks, the number of linking root domains of the top internet domains, the number of linking root domains of the top internet pages, the total number of human victims of tornadoes occurred in the U.S., and the number of inhabitants in the 60 most populated countries. The results demonstrate the emergence of statistical characteristics, very close to a power law behavior. Furthermore, the parametric characterization reveals complex relationships present at higher level of description.

Fractional Order Junctions

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional “parasitic” elements. The novel γ-junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Casualties distribution in human and natural hazards

Catastrophic events, such as wars and terrorist attacks, big tornadoes and hurricanes, huge earthquakes, tsunamis, floods, and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties have separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data set is better approximated by two PLs instead of one. We have plotted the two PL parameters corresponding to all terrorist events occurred in every year, from 1980 to 2010. We observe an interesting pattern in the chart, where the lines, that connect each pair of points defining the double PLs, are roughly aligned to each other.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Estudo da corrosão provocada pelo cloro e procura de materiais alternativos

Muitas instalações municipais são alvo de manutenção permanente, devido ao uso de produtos químicos que provocam a corrosão e degradação dos mais diversos materiais. Esta degradação acarreta custos elevados para os municípios e privação de uso de algumas instalações devido a manutenção curativa ou preventiva. Um estudo adequado do efeito dos produtos utilizados, poderia conduzir à utilização de materiais mais nobres, que aumentasse significativamente o tempo de vida dos produtos mais atacados pela degradação por corrosão, através de estudos que permitissem avaliar a relação custo-benefício e, caso esta fosse favorável, proceder à substituição de determinados componentes em materiais relativamente fracos, por outros com uma maior capacidade para resistir aos ataques produzidos pelo meio em que estão inseridos. Este estudo foi efectuado com vista a estudar a degradação de determinados materiais expostos essencialmente à acção do Cloro em instalações municipais, permitindo assim seleccionar novos materiais que permitissem uma vida útil dos componentes mais alargada, estudando convenientemente a relação custo-benefício. Foi possível observar que a introdução de alguns materiais mais nobres, poderá reduzir drasticamente as operações de manutenção, diminuindo os custos e reduzindo também o tempo de indisponibilidade dos equipamentos municipais.

Estudo de vulnerabilidades em aplicações web e o seu reflexo em domínios Portugueses

Muito se tem falado sobre revolução tecnológica e do aparecimento constante de novas aplicações Web, com novas funcionalidades que visam facilitar o trabalho dos utilizadores. Mas será que estas aplicações garantem que os dados transmitidos são tratados e enviados por canais seguros (protocolos)? Que garantias é que o utilizador tem que mesmo que a aplicação utilize um canal, que prevê a privacidade e integridade de dados, esta não apresente alguma vulnerabilidade pondo em causa a informação sensível do utilizador? Software que não foi devidamente testado, aliado à falta de sensibilização por parte dos responsáveis pelo desenvolvimento de software para questões de segurança, levam ao aumento de vulnerabilidades e assim exponenciam o número de potenciais vítimas. Isto aliado ao efeito de desinibição que o sentimento de invisibilidade pode provocar, conduz ao facilitismo e consequentemente ao aumento do número de vítimas alvos de ataques informáticos. O utilizador, por vezes, não sabe muito bem do que se deve proteger, pois a confiança que depõem no software não pressupõem que os seus dados estejam em risco. Neste contexto foram recolhidos dados históricos relativos a vulnerabilidades nos protocolos SSL/TLS, para perceber o impacto que as mesmas apresentam e avaliar o grau de risco. Para além disso, foram avaliados um número significativo de domínios portugueses para perceber se os mesmos têm uma vulnerabilidade específica do protocolo SSL/TLS.