Determining the quality of mathematical software using reference data sets

This paper describes a methodology for evaluating the numerical accuracy of software that performs mathematical calculations. The authors explain how this methodology extends the concept of metrological traceability, which is fundamental to measurement, to include software quality. Overviews of two European Union-funded projects are also presented. The first project developed an infrastructure to allow software to be verified by testing, via the internet, using reference data sets. The primary focus of the project was software used within systems that make physical measurements. The second project, currently underway, explores using this infrastructure to verify mathematical software used within general scientific and engineering disciplines. Publications on using reference data sets for the verification of mathematical software are usually intended for a readership specialising in measurement science or mathematics. This paper is aimed at a more general readership, in particular software quality specialists and computer scientists. Further engagement with experts in these disciplines will be helpful to the continued development of this application of software quality

Fast and numerically stable circle fit

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less than 10 iterations to converge, on average.Comment: 16 page

Evaluation des incertitudes de mesure sur une machine à mesurer tridimensionnelle : Nouvelle méthode d’estimation des paramètres de surface et incertitudes associées

Cette étude présente un algorithme d’estimation des paramètres des courbes et des surfaces et leurs incertitudes, en tenant compte des incertitudes sur les coordonnées des points palpés sur M.M.T. Le problème d’optimisation traité est non linéaire à variables stochastiques. Une maquette informatique basée sur notre méthode est développée en visual C++, permet à partir d’un nuage de points d ‘estimer les paramètres et leurs incertitudes. La démarche est validée par comparaison

Depth-Sensing Indentation as a Micro- and Nanomechanical Approach to Characterisation of Mechanical Properties of Soft, Biological, and Biomimetic Materials

Classical methods of material testing become extremely complicated or impossible at micro-/nanoscale. At the same time, depth-sensing indentation (DSI) can be applied without much change at various length scales. However, interpretation of the DSI data needs to be done carefully, as length-scale dependent effects, such as adhesion, should be taken into account. This review paper is focused on different DSI approaches and factors that can lead to erroneous results, if conventional DSI methods are used for micro-/nanomechanical testing, or testing soft materials. We also review our recent advances in the development of a method that intrinsically takes adhesion effects in DSI into account: the Borodich-Galanov (BG) method, and its extended variant (eBG). The BG/eBG methods can be considered a framework made of the experimental part (DSI by means of spherical indenters), and the data processing part (data fitting based on the mathematical model of the experiment), with such distinctive features as intrinsic model-based account of adhesion, the ability to simultaneously estimate elastic and adhesive properties of materials, and non-destructive nature

Total Least Squares Spline Approximation

Spline approximation, using both values yi and xi as observations, is of vital importance for engineering geodesy, e.g., for approximation of profiles measured with terrestrial laser scanners, because it enables the consideration of arbitrary dispersion matrices for the observations. In the special case of equally weighted and uncorrelated observations, the resulting error vectors are orthogonal to the graph of the spline function and hence can be utilized for deformation monitoring purposes. Based on a functional model that uses cubic polynomials and constraints for continuity, smoothness and continuous curvature, the case of spline approximation with both the values yi and xi as observations is considered. In this case, some of the columns of the functional matrix contain observations and are thus subject to random errors. In the literature on mathematics and statistics this case is known as an errors-in-variables (EIV) model for which a so-called “total least squares” (TLS) solution can be computed. If weights for the observations and additional constraints for the unknowns are introduced, a “constrained weighted total least squares” (CWTLS) problem is obtained. In this contribution, it is shown that the solution for this problem can be obtained from a rigorous solution of an iteratively linearized Gauss-Helmert (GH) model. The advantage of this model is that it does not impose any restrictions on the form of the functional relationship between the involved quantities. Furthermore, dispersion matrices can be introduced without limitations, even the consideration of singular ones is possible. Therefore, the iteratively linearized GH model can be regarded as a generalized approach for solving CWTLS problems. Using a numerical example it is demonstrated how the GH model can be applied to obtain a spline approximation with orthogonal error vectors. The error vectors are compared with those derived from two least squares (LS) approaches.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

Contributions to the three-dimensional virtual treatment planning of orthognathic surgery

Orientadores: José Mario De Martino, Luis Augusto PasseriTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: A tecnologia mais recente à disposição da Cirurgia Ortognática possibilita que o diagnóstico e o planejamento do tratamento das deformidades dentofaciais sejam realizados sob uma representação virtual tridimensional (3D) da cabeça do paciente. Com o propósito de contribuir para o aperfeiçoamento desta tecnologia, o trabalho apresentado nesta tese identificou e tratou quatro problemas. A primeira contribuição consistiu na verificação da validade da hipótese de que a mudança de definição do plano horizontal de Frankfort não produz diferenças de medição clinicamente relevantes quando sob indivíduos cujos crânios são consideravelmente simétricos. Os resultados da análise realizada no contexto deste tese indicam que, ao contrário do que se presumia, a hipótese é falsa. A segunda contribuição consistiu na extensão do método de análise cefalométrica de McNamara para que ele pudesse produzir valores 3D. Ao contrário de outros métodos de análise cefalométrica 3D, a extensão criada produz valores verdadeiramente 3D, não perde as informações do método original e preserva as definições geométricas originais das linhas e planos cefalométricos. A terceira contribuição consistiu a) no estabelecimento de normas cefalométricas para brasileiros adultos de ascendência europeia, a partir de imagens de tomografia computadorizada de feixe cônico, que produz uma imagem craniofacial mais precisa e confiável do que a telerradiografia; e b) na avaliação de dimorfismo sexual, para a identificação de características anatômicas diferenciadas entre homens e mulheres desta população. A quarta e última contribuição consistiu na automatização da principal etapa da tecnologia em questão, na qual o cirurgião executa o reposicionamento dos segmentos ósseos maxilares no crânio. O método criado é capaz de corrigir automaticamente os problemas dentofaciais mais comuns tratados pela Cirurgia Ortognática, que envolvem maloclusão esquelética, assimetria facial e discrepância de maxilares. Todas as contribuições deste trabalho foram publicadas em periódicos internacionais do campo da Odontologia e afinsAbstract: The latest technology available for orthognathic surgery allows the diagnosis and treatment planning of dentofacial deformities based on a three-dimensional (3D) virtual representation of the patient's head. In order to contribute to the improvement of this technology, the work presented in this thesis identified and treated four problems. The first contribution consisted in testing the validity of the hypothesis that changing the definition of the Frankfort horizontal plane does not produce clinically relevant measurement differences for subjects whose skulls are considerably symmetrical. The results of the analysis performed in this thesis indicate that, contrary to what was presumed, the hypothesis is false. The second contribution is an extension of the McNamara's method of cephalometric analysis to produce 3D values. Unlike other methods of 3D cephalometric analysis, the extension produces true 3D values, does not lose information captured by the original method, and preserves the original geometric definitions of the cephalometric lines and planes. The third contribution consisted in a) establishing cephalometric norms for Brazilian adults of European descent, based on images from cone-beam computed tomography, which produce a more accurate and reliable craniofacial image than cephalometric radiography; and b) evaluating sexual dimorphism, for the identification of distinct anatomic features between males and females of this population. The fourth contribution consisted in automating the main stage of the technology in question, in which the surgeon performs the positioning of jaw bone segments in the skull. The created method is able to automatically correct the most common dentofacial problems treated by orthognathic surgery, which involves skeletal malocclusion, facial asymmetry, and jaw discrepancy. The contributions of this work were published in international journals of the field of Dentistry and relatedDoutoradoEngenharia de ComputaçãoDoutor em Engenharia ElétricaCAPE

Trajectory-Aware Communication Solution for Underwater Gliders Using WHOI Micro-Modems

Abstract—The predictable trajectory of underwater gliders can be used in geographic routing protocols. Factors such as drifting and localization errors cause uncertainty when estimating a glider’s trajectory. Existing geographic routing protocols in underwater networks generally assume the positions of the nodes are accurately determined by neglecting position uncertainty. In this paper, a paradigm-changing geographic routing protocol that relies on a statistical approach to model position uncertainty is proposed. Our routing protocol is combined with practical cross-layer optimization to minimize energy consumption. Our solution’s performance is tested and compared with existing solutions using a real-time testbed emulation that uses underwater acoustic modems. I

GLOTTAL EXCITATION EXTRACTION OF VOICED SPEECH - JOINTLY PARAMETRIC AND NONPARAMETRIC APPROACHES

The goal of this dissertation is to develop methods to recover glottal flow pulses, which contain biometrical information about the speaker. The excitation information estimated from an observed speech utterance is modeled as the source of an inverse problem. Windowed linear prediction analysis and inverse filtering are first used to deconvolve the speech signal to obtain a rough estimate of glottal flow pulses. Linear prediction and its inverse filtering can largely eliminate the vocal-tract response which is usually modeled as infinite impulse response filter. Some remaining vocal-tract components that reside in the estimate after inverse filtering are next removed by maximum-phase and minimum-phase decomposition which is implemented by applying the complex cepstrum to the initial estimate of the glottal pulses. The additive and residual errors from inverse filtering can be suppressed by higher-order statistics which is the method used to calculate cepstrum representations. Some features directly provided by the glottal source\u27s cepstrum representation as well as fitting parameters for estimated pulses are used to form feature patterns that were applied to a minimum-distance classifier to realize a speaker identification system with very limited subjects