Rational parametrization of conchoids to algebraic curves

We study the rationality of each of the components of the conchoid to an irreducible algebraic affine plane curve, excluding the trivial cases of the lines through the focus and the circle centered at the focus and radius the distance involved in the conchoid. We prove that conchoids having all their components rational can only be generated by rational curves. Moreover, we show that reducible conchoids to rational curves have always their two components rational. In addition, we prove that the rationality of the conchoid component, to a rational curve, does depend on the base curve and on the focus but not on the distance. As a consequence, we provide an algorithm that analyzes the rationality of all the components of the conchoid and, in the affirmative case, parametrizes them. The algorithm only uses a proper parametrization of the base curve and the focus and, hence, does not require the previous computation of the conchoid. As a corollary, we show that the conchoid to the irreducible conics, with conchoid-focus on the conic, are rational and we give parametrizations. In particular we parametrize the Limaçons of Pascal. We also parametrize the conchoids of Nicomedes. Finally, we show how to find the foci from where the conchoid is rational or with two rational components

Total Degree Formula for the Generic Offset to a Parametric Surface

We provide a resultant-based formula for the total degree w.r.t. the spatial variables of the generic offset to a parametric surface. The parametrization of the surface is not assumed to be proper.Comment: Preprint of an article to be published at the International Journal of Algebra and Computation, World Scientific Publishing, DOI:10.1142/S021819671100680

Conchoidal transform of two plane curves

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in \PP^2 \times \PP^2. We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve $C$ we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.Comment: 18 pages Revised version: slight title change, improved exposition, fixed proof of Theorem 5.3 Accepted for publication in Appl. Algebra Eng., Commun. Comput

An Algebraic Analysis of Conchoids to Algebraic Curves

We study the conchoid to an algebraic affine plane curve C from the perspective of algebraic geometry, analyzing their main algebraic properties. Beside C, the notion of conchoid involves a point A in the affine plane (the focus) and a nonzero field element d (the distance).We introduce the formal definition of conchoid by means of incidence diagrams.We prove that the conchoid is a 1-dimensional algebraic set having atmost two irreducible components. Moreover, with the exception of circles centered at the focus A and taking d as its radius, all components of the corresponding conchoid have dimension 1. In addition, we introduce the notions of special and simple components of a conchoid. Furthermore we state that, with the exception of lines passing through A, the conchoid always has at least one simple component and that, for almost every distance, all the components of the conchoid are simple. We state that, in the reducible case, simple conchoid components are birationally equivalent to C, and we show how special components can be used to decide whether a given algebraic curve is the conchoid of another curve

SVMs for Automatic Speech Recognition: a Survey

Hidden Markov Models (HMMs) are, undoubtedly, the most employed core technique for Automatic Speech Recognition (ASR). Nevertheless, we are still far from achieving high-performance ASR systems. Some alternative approaches, most of them based on Artificial Neural Networks (ANNs), were proposed during the late eighties and early nineties. Some of them tackled the ASR problem using predictive ANNs, while others proposed hybrid HMM/ANN systems. However, despite some achievements, nowadays, the preponderance of Markov Models is a fact. During the last decade, however, a new tool appeared in the field of machine learning that has proved to be able to cope with hard classification problems in several fields of application: the Support Vector Machines (SVMs). The SVMs are effective discriminative classifiers with several outstanding characteristics, namely: their solution is that with maximum margin; they are capable to deal with samples of a very higher dimensionality; and their convergence to the minimum of the associated cost function is guaranteed. These characteristics have made SVMs very popular and successful. In this chapter we discuss their strengths and weakness in the ASR context and make a review of the current state-of-the-art techniques. We organize the contributions in two parts: isolated-word recognition and continuous speech recognition. Within the first part we review several techniques to produce the fixed-dimension vectors needed for original SVMs. Afterwards we explore more sophisticated techniques based on the use of kernels capable to deal with sequences of different length. Among them is the DTAK kernel, simple and effective, which rescues an old technique of speech recognition: Dynamic Time Warping (DTW). Within the second part, we describe some recent approaches to tackle more complex tasks like connected digit recognition or continuous speech recognition using SVMs. Finally we draw some conclusions and outline several ongoing lines of research

Reviews of the genera Schaefferia Absolon, 1900, Deuteraphorura Absolon, 1901, Plutomurus Yosii, 1956 and the Anurida Laboulbène, 1865 species group without eyes, with the description of four new species of cave springtails (Collembola) from Krubera-Voronya cave, Arabika Massif, Abkhazia

Krubera-Voronya cave and other deep systems in Arabika Massif are being explored during many speleological expeditions. A recent Ibero-Russian exploration expedition (summer of 2010) took place in this cave with the aim of providing a study of the biocenosis of the deepest known cave in the world. Four new species of Collembola were found at different depths: Schaefferia profundissima n. sp., Anurida stereoodorata n. sp., Deuteraphorura kruberaensis n. sp., and Plutomurus ortobalaganensis n. sp., the last one at -1980 m deep. The identification and description of the new species have required the careful study of all congeneric species, implying a revision of each genus. As a result of this work tables and keys to all significant characters for each species are presented

Métodos estatísticos para análise de Y-STRs em genética forense

Tese de mestrado em Bioestatística, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2011A implementação dos marcadores de DNA nas ciências forenses consistiu no maior avanço nesta área nos últimos vinte anos. Os fenómenos de mutação e recombinação genética contribuem para uma grande diversidade genética, o que se traduz no facto de todos os indivíduos, com excepção de gémeos verdadeiros, apresentarem sequências de DNA diferentes entre si, mas invariváveis em todas as suas células. Estas características permitem a sua aplicação na área forense em investigações criminais, relações de parentesco, imigração, pessoas desaparecidas em acidentes de massa e estudos históricos\antropológicos. Nos últimos dez anos os marcadores de DNA específicos dos indivíduos do sexo masculino, Y-STRs, foram estudados e aplicados em diferentes laboratórios na área forense. Estes marcadores permitem a identificação das linhagens paternas do indivíduos e esta informação pode ser de grande importância nos casos de abuso sexual e de investigação de parentesco. No entanto a sua correcta aplicação nos casos do Serviço de Genética e Biologia Forense implica a implementação de um método científico adequado para avaliar a probabilidade de coincidência de dois perfis genéticos. Para este objectivo foi implementado um kit de estudo de Y-STRs, designado por AmpFlSTR® Yfiler™ (Applied Biosystems), previamente desenvolvido e validado para a área forense e aplicado em 197 pares pai\filho, provenientes de uma base de dados da população de referência do Sul de Portugal. Este estudo permitiu realizar inferências populacionais, estimar taxas de mutação da linha germinal paterna e efectuar cálculos de probabilidade de coincidência de perfis genéticos (matching probabilities) em diferentes tipos de casos estudados. As inferências populacionais foram realizadas com diferentes conjuntos deY-STRs, designadas por Haplotipo minimo, Haplotipo Estendido e Haplotipo completo, de forma a verificar qual o conjunto de Y STRs que permite obter a maior diversidade genética A análise com os diferentes conjuntos de haplótipos revelou a presença de 171, 183 e 191 haplotipos diferentes, correspondendo a diversidades genéticas de 0.6411, 0.6403 e 0.6508. No que diz respeito à metodologia aplicada recorrendo à formulação bayesiana, verificou-se que a metodologia recorrendo à distribuição a priori Beta permite estimar valores de taxas de mutação mais próximos dos valores referenciados por outros autores, disponíveis no site www.yhrd.org. O valor mais baixo da taxa de mutação obtido foi de 6.010-4 (5.747-4 – 3.242-4 ) para o marcador DYS438. Estes resultados contribuiram para a estimativa das probabilidades de coincidência de dois perfis genéticos. Estes cálculos foram efetuados recorrendo a diferentes metodologias, nomeadamente, método frequencista, método de “haplotype survyeing” e método de Charles Brenner. Os resultados obtidos com as diferentes metodologias, permitiram concluir que a metodologia “Haplotype Surveying” é presentemente a mais adequada para aplicação na área forense como actualmente está implementada.DNA analysis has been the greatest technological advance in forensic science in the past twenty years. Due to mutation and recombination no two persons, except true twins, have the same DNA sequence, wich enables to determine DNA sequence in every biological sample, and this knowlodge can be used in the investigation of crime, kinship relationships, immigration, missing persons, mass disasters and historical cases. In the last ten years, among DNA markers with forensic interest, a few with potencial to identify male –specific DNA, Y-STRs, were described and implemented in most forensic genetic laboratorys. These markers are very important since they contribute to identify male lineages and this information can be invaluable in cases of sexual assault and in kinship testing, as well as in anthropological and population genetics studies. However to apply Y-STRs in Forensic Genetics Service from National Institute of Legal Medicine, it is convenient to have a scientific method to analyse and evaluate the evidential strength of a Y-haplotype match. For this purpose, a 17 locus microsatellite kit, AmpFlSTR® Yfiler™ (Applied Biosystems), previously developed and validated for forensic cases, was adopted in a 197 father son\pairs south Portugal reference database, in order to make population inferences, Y-STR germline mutation rates estimation, and matching probabilities evaluations. Population inferences were done with different sets of Y STRs markers, classified as Complete Haplotype, Extended Haplotype and Minimal Haplotype, in order to study which set can give the strongest genetic diversity. A total of 171,183, 191 haplotypes were observed when analysed the Minimal Haplotype, Extended Haplotype and Complete Haplotype, respectively, corresponding to genetic diversity 0.6411, 0.6403 and 0.6508. The locus specific mutation rates were estimated with Bayesian formulation, and the best approximation was obtained with a priori Beta distribution. These results contributed to estimate matching probabilities in different kind of cases, kinship and criminal ones, with three distinct methodologies, frequencist, haplotype surveying and Brenner’s, in order to distinguish the best one to apply in the laboratory

Strong Gravitational Lensing by Sgr A*

In recent years, there has been increasing recognition of the potential of the galactic center as a probe of general relativity in the strong field. There is almost certainly a black hole at Sgr A* in the galactic center, and this would allow us the opportunity to probe dynamics near the exterior of the black hole. In the last decade, there has been research into extreme gravitational lensing in the galactic center. Unlike in most applications of gravitational lensing, where the bending angle is of the order of several arc seconds, very large bending angles are possible for light that closely approaches a black hole. Photons may even loop multiple times around a black hole before reaching the observer. There have been many proposals to use light's close approach to the black hole as a probe of the black hole metric. Of particular interest is the property of light lensed by the S stars orbiting in the galactic center. This paper will review some of the attempts made to study extreme lensing as well as extend the analysis of lensing by S stars. In particular, we are interested in the effect of a Reissner-Nordstrom like 1/r^2 term in the metric and how this would affect the properties of relativistic images.Comment: 13 pages, 9 figures. Submitted as invited review article for the GR19 issue of CQ