A fractional perspective to financial indices

The application of mathematical methods and computer algorithms in the analysis of economic and financial data series aims to give empirical descriptions of the hidden relations between many complex or unknown variables and systems. This strategy overcomes the requirement for building models based on a set of ‘fundamental laws’, which is the paradigm for studying phenomena usual in physics and engineering. In spite of this shortcut, the fact is that financial series demonstrate to be hard to tackle, involving complex memory effects and a apparently chaotic behaviour. Several measures for describing these objects were adopted by market agents, but, due to their simplicity, they are not capable to cope with the diversity and complexity embedded in the data. Therefore, it is important to propose new measures that, on one hand, are highly interpretable by standard personal but, on the other hand, are capable of capturing a significant part of the dynamical effects.

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

A governação local no Algarve no contexto de financiamento e responsabilidades

Dissertação de mestrado em Gestão Pública, apresentada à secção autónoma de Ciências Sociais, Jurídicas e Políticas da Universidade de Aveiro,sob orientação da Prof. Doutora Maria Luís Rocha Pinto.

Robot visual localization through local feature fusion: an evaluation of multiple classifiers combination approaches

In the last decade, local image features have been widely used in robot visual localization. In order to assess image similarity, a strategy exploiting these features compares raw descriptors extracted from the current image with those in the models of places. This paper addresses the ensuing step in this process, where a combining function must be used to aggregate results and assign each place a score. Casting the problem in the multiple classifier systems framework, in this paper we compare several candidate combiners with respect to their performance in the visual localization task. For this evaluation, we selected the most popular methods in the class of non-trained combiners, namely the sum rule and product rule. A deeper insight into the potential of these combiners is provided through a discriminativity analysis involving the algebraic rules and two extensions of these methods: the threshold, as well as the weighted modifications. In addition, a voting method, previously used in robot visual localization, is assessed. Furthermore, we address the process of constructing a model of the environment by describing how the model granularity impacts upon performance. All combiners are tested on a visual localization task, carried out on a public dataset. It is experimentally demonstrated that the sum rule extensions globally achieve the best performance, confirming the general agreement on the robustness of this rule in other classification problems. The voting method, whilst competitive with the product rule in its standard form, is shown to be outperformed by its modified versions.

Reply to: Comments on “Particle Swarm Optimization with Fractional-Order Velocity”

We agree with Ling-Yun et al. [5] and Zhang and Duan comments [2] about the typing error in equation (9) of the manuscript [8]. The correct formula was initially proposed in [6, 7]. The formula adopted in our algorithms discussed in our papers [1, 3, 4, 8] is, in fact, the following: ...

Gestão pública : um novo paradigma para a governação da administração local em Portugal

Ao longo da História o Poder Local sempre desempenhou um papel inquestionável na organização do Estado, tendo-se revelado fundamental a sua existência, a qual se traduz na diversidade de competências e materializada em inúmeros domínios de ação que estas entidades têm desempenhado.

Some pioneers of the applications of fractional calculus

In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Lévy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Fractional order modelling of dynamic backlash

This paper studies the dynamical properties of systems with backlash and impact phenomena. This type of non-linearity can be tackled in the perspective of the fractional calculus theory. Fractional and integer order models are compared and their influence upon the emerging dynamics is analysed. It is demonstrated that fractional models can memorize dynamical effects due to multiple micro-collisions.

EcoTerra Model - application of environmental fiscal reform in local government financing in Portugal

Critical Issues in Environmental Taxation: International and Comparative Perspectives: Volume VI, 699-715

Avaliação da eficácia do antiveneno botrópico administrado no local da inoculação intramuscular do veneno de Bothrops jararaca: estudo experimental em camundongos

Foi determinada, em camundongos de 18 a 20 g, a dose efetiva 50% do antiveneno botrópico, por via intraperitoneal (ip), imediatamente (DE50 Oh) e 30 minutos (DE50 30') após a inoculação de 2 DL50 do veneno de B. jararaca, por via intramuscular (im). A DE50 30' foi três vezes maior do que a DE50 Oh. A eficácia do antiveneno administrado no local da inoculação do veneno foi avaliada inoculando-se duas DL50 do veneno, por via im, e administrando-se a DE50 do antiveneno imediatamente (DE50 Oh) e 30 minutos após (DE50 30'), de duas formas a saber: totalmente por via ip (1ª) e metade por via ip e metade por via im (2ª), no mesmo local da inoculação do veneno. O antiveneno ofereceu, por via ip, maior proteção aos camundongos (menor taxa de óbito em 48 horas) do que quando metade do mesmo foi administrado, por via im, no local da inoculação do veneno. Conclui-se que, neste modelo experimental, quando se inicia o tratamento tardiamente há necessidade de maior dose de antiveneno botrópico e que não há benefício em administrá-lo no local da picada.

Philodryas patagoniensis bite and local envenoming

A 5-year-old boy bitten by a specimen of Philodryas patagoniensis, a colubrid snake currently classified as nonvenomous, developed signs of local envenoming characterized by swelling and warmth on the bitten limb. This is the first time that local envenoming following Philodryas patagoniensis bite is recognized. Based on the clinical findings and misidentification of the snake, the patient was treated as a victim of Bothrops bite, having received unnecessarily the specific antivenom. Educational efforts to make doctors and health workers capable to identify correctly venomous snakes are necessary, to avoid inappropriate indication of antivenom and decrease the risk of its potentially harmful untoward effects. Examination of the bite site can be useful to the differential diagnosis between pit viper and colubrid bites.