Rhapsody in fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Increase of the delivered energy probability in DES using a fuzzy probabilistic modeling

The paper proposes a methodology to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The proposed methodology is based on statistical failure and repair data of distribution components and it uses a fuzzy-probabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A mixed integer nonlinear programming optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

Use of negative information in positioning and tracking algorithms

To avoid additional hardware deployment, indoor localization systems have to be designed in such a way that they rely on existing infrastructure only. Besides the processing of measurements between nodes, localization procedure can include the information of all available environment information. In order to enhance the performance of Wi-Fi based localization systems, the innovative solution presented in this paper considers also the negative information. An indoor tracking method inspired by Kalman filtering is also proposed.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Probability and statistics: selected problems

Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Conditional probability applied to the definition of limestone geochemical facies: A new Methodological Approach

A new method, based on linear correlation and phase diagrams was successfully developed for processes like the sedimentary process, where the deposition phase can have different time duration - represented by repeated values in a series - and where the erosion can play an important rule deleting values of a series. The sampling process itself can be the cause of repeated values - large strata twice sampled - or deleted values: tiny strata fitted between two consecutive samples. What we developed was a mathematical procedure which, based upon the depth chemical composition evolution, allows the establishment of frontiers as well as the periodicity of different sedimentary environments. The basic tool isn't more than a linear correlation analysis which allow us to detect the existence of eventual evolution rules, connected with cyclical phenomena within time series (considering the space assimilated to time), with the final objective of prevision. A very interesting discovery was the phenomenon of repeated sliding windows that represent quasi-cycles of a series of quasi-periods. An accurate forecast can be obtained if we are inside a quasi-cycle (it is possible to predict the other elements of the cycle with the probability related with the number of repeated and deleted points). We deal with an innovator methodology, reason why it's efficiency is being tested in some case studies, with remarkable results that shows it's efficacy. Keywords: sedimentary environments, sequence stratigraphy, data analysis, time-series, conditional probability.

Optimização e Validação da Produção de [13n]-Nh3 para Estudos Clínicos de Tomografia por Emissão de Positrões na Avaliação da Perfusão Miocárdica

A par das patologias oncológicas, as doenças do foro cardíaco, em particular a doença arterial coronária, são uma das principais causas de morte nos países industrializados, devido sobretudo, à grande incidência de enfartes do miocárdio. Uma das formas de diagnóstico e avaliação desta condição passa pela obtenção de imagens de perfusão miocárdica com radionuclídeos, realizada por Tomografia por Emissão de Positrões (PET). As soluções injectáveis de [15O]-H2O, [82Rb] e [13N]-NH3 são as mais utilizadas neste tipo de exame clínico. No Instituto de Ciências Nucleares Aplicadas à Saúde (ICNAS), a existência de um ciclotrão tem permitido a produção de uma variedade de radiofármacos, com aplicações em neurologia, oncologia e cardiologia. Recentemente, surgiu a oportunidade de iniciar exames clínicos com [13N]-NH3 para avaliação da perfusão miocárdica. É neste âmbito que surge a oportunidade do presente trabalho, pois antes da sua utilização clínica é necessário realizar a optimização da produção e a validação de todo o processo segundo as normas de Boas Práticas Radiofarmacêuticas. Após uma fase de optimização do processo, procedeu-se à avaliação dos parâmetros físico-químicos e biológicos da preparação de [13N]-NH3, de acordo com as indicações da Farmacopeia Europeia (Ph. Eur.) 8.2. De acordo com as normas farmacêuticas, foram realizados 3 lotes de produção consecutivos para validação da produção de [13N]-NH3. Os resultados mostraram um produto final límpido e ausente de cor, com valores de pH dentro do limite especificado, isto é, entre 4,5 e 8,5. A pureza química das amostras foi verificada, uma vez que relativamente ao teste colorimétrico, a tonalidade da cor da solução de [13N]-NH3 não era mais intensa que a solução de referência. As preparações foram identificadas como sendo [13N]-NH3, através dos resultados obtidos por cromatografia iónica, espectrometria de radiação gama e tempo de semi-vida. Por examinação do cromatograma obtido com a solução a ser testada, observou-se que o pico principal possuia um tempo de retenção aproximadamente igual ao pico do cromatograma obtido para a solução de referência. Além disso, o espectro de radiação gama mostrou um pico de energia 0,511 MeV e um outro adicional de 1,022 MeV para os fotões gama, característico de radionuclídeos emissores de positrões. O tempo de semi-vida manteve-se dentro do intervalo indicado, entre 9 e 11 minutos. Verificou-se, igualmente, a pureza radioquímica das amostras, correspondendo um mínimo de 99% da radioactividade total ao [13N], bem como a pureza radionuclídica, observando-se uma percentagem de impurezas inferiores a 1%, 2h após o fim da síntese. Os testes realizados para verificação da esterilidade e determinação da presença de endotoxinas bacterianas nas preparações de [13N]-NH3 apresentaram-se negativos.Os resultados obtidos contribuem, assim, para a validação do método para a produção de [13N]-NH3, uma vez que cumprem os requisitos especificados nas normas europeias, indicando a obtenção de um produto seguro e com a qualidade necessária para ser administrado em pacientes para avaliação da perfusão cardíaca por PET.

Modified Discrete PSO to Increase the Delivered Energy Probability in Distribution energy Systems

This paper proposes a PSO based approach to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The statistical failure and repair data of distribution components is the main basis of the proposed methodology that uses a fuzzyprobabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A Modified Discrete PSO optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

DC Fuzzy Multicriteria Approach to Increase the Probability of Delivering Power in Distribution Networks

This paper proposes a methodology to increase the probability of delivering power to any load point through the identification of new investments. The methodology uses a fuzzy set approach to model the uncertainty of outage parameters, load and generation. A DC fuzzy multicriteria optimization model considering the Pareto front and based on mixed integer non-linear optimization programming is developed in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power to all customers in the distribution network at the minimum possible cost for the system operator, while minimizing the non supplied energy cost. To illustrate the application of the proposed methodology, the paper includes a case study which considers an 33 bus distribution network.

Increase of the Delivered Power Probability in Distribution Networks using Pareto DC Programming

A methodology to increase the probability of delivering power to any load point through the identification of new investments in distribution network components is proposed in this paper. The method minimizes the investment cost as well as the cost of energy not supplied in the network. A DC optimization model based on mixed integer non-linear programming is developed considering the Pareto front technique in order to identify the adequate investments in distribution networks components which allow increasing the probability of delivering power for any customer in the distribution system at the minimum possible cost for the system operator, while minimizing the energy not supplied cost. Thus, a multi-objective problem is formulated. To illustrate the application of the proposed methodology, the paper includes a case study which considers a 180 bus distribution network