Quantum state reconstruction using binary data from on/off photodetection

The knowledge of the density matrix of a quantum state plays a fundamental role in several fields ranging from quantum information processing to experiments on foundations of quantum mechanics and quantum optics. Recently, a method has been suggested and implemented in order to obtain the reconstruction of the diagonal elements of the density matrix exploiting the information achievable with realistic on/off detectors, e.g. silicon avalanche photo-diodes, only able to discriminate the presence or the absence of light. The purpose of this paper is to provide an overview of the theoretical and experimental developments of the on/off method, including its extension to the reconstruction of the whole density matrix.Comment: revised version, 11 pages, 6 figures, to appear as a review paper on Adv. Science Let

Symmetries of Riemann surfaces and magnetic monopoles

This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions

Reduction of Limited Angle Artifacts in Medical Tomography via Image Reconstruction

Artifacts are unwanted effects in tomographic images that do not reflect the nature of the object. Their widespread occurrence makes their reduction and if possible removal an important subject in the development of tomographic image reconstruction algorithms. Limited angle artifacts are caused by the limited angular measurements, constraining the available tomographic information. This thesis focuses on reducing these artifacts via image reconstruction in two cases of incomplete measurements from: (1) the gaps left after the removal of high density objects such as dental fillings, screws and implants in computed tomography (CT) and (2) partial ring scanner configurations in positron emission tomography (PET). In order to include knowledge about the measurement and noise, prior terms were used within the reconstruction methods. Careful consideration was given to the trade-off between image blurring and noise reduction upon reconstruction of low-dose measurements.Development of reconstruction methods is an incremental process starting with testing on simple phantoms towards more clinically relevant ones by modeling the respective physical processes involved. In this work, phantoms were constructed to ensure that the proposed reconstruction methods addressed to the limited angle problem. The reconstructed images were assessed qualitatively and quantitatively in terms of noise reduction, edge sharpness and contrast recovery.Maximum a posteriori (MAP) estimation with median root prior (MRP) was selected for the reconstruction of limited angle measurements. MAP with MRP successfully reduced the artifacts caused by limited angle data in various datasets, tested with the reconstruction of both list-mode and projection data. In all cases, its performance was found to be superior to conventional reconstruction methods such as total-variation (TV) prior, maximum likelihood expectation maximization (MLEM) and filtered backprojection (FBP). MAP with MRP was also more robust with respect to parameter selection than MAP with TV prior.This thesis demonstrates the wide-range applicability of MAP with MRP in medical tomography, especially in low-dose imaging. Furthermore, we emphasize the importance of developing and testing reconstruction methods with application-specific phantoms, together with the properties and limitations of the measurements in mind

Flight Mechanics/Estimation Theory Symposium, 1994

This conference publication includes 41 papers and abstracts presented at the Flight Mechanics/Estimation Theory Symposium on May 17-19, 1994. Sponsored by the Flight Dynamics Division of Goddard Space Flight Center, this symposium featured technical papers on a wide range of issues related to orbit-attitude prediction, determination and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Análise de desempenho de métricas de grafos para reconhecimento de tarefas de imaginação motora das mãos a partir de dados de eletroencefalografia

Orientadores: Gabriela Castellano, Romis Ribeiro de Faissol AttuxDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb WataghinResumo: Interfaces cérebro-computador (BCIs, brain-computer interfaces) são sistemas cuja finalidade é fornecer um canal de comunicação direto entre o cérebro e um dispositivo externo, como um computador, uma prótese ou uma cadeira de rodas. Por não utilizarem as vias fisiológicas convencionais, BCIs podem constituir importantes tecnologias assistivas para pessoas que sofreram algum tipo de lesão e, por isso, tiveram sua interação com o ambiente externo comprometida. Os sinais cerebrais a serem extraídos para utilização nestes sistemas devem ser gerados mediante estratégias específicas. Nesta dissertação, trabalhamos com a estratégia de imaginação motora (MI, motor imagery), e extraímos a resposta cerebral correspondente a partir de dados de eletroencefalografia (EEG). Os objetivos do trabalho foram caracterizar as redes cerebrais funcionais oriundas das tarefas de MI das mãos e explorar a viabilidade de utilizar métricas da teoria de grafos para a classificação dos padrões mentais, gerados por esta estratégia, de usuários de um sistema BCI. Para isto, fez-se a hipótese de que as alterações no espectro de frequências dos sinais de eletroencefalografia devidas à MI das mãos deveria, de alguma forma, se refletir nos grafos construídos para representar as interações cerebrais corticais durante estas tarefas. Em termos de classificação, diferentes conjuntos de pares de eletrodos foram testados, assim como diferentes classificadores (análise de discriminantes lineares ¿ LDA, máquina de vetores de suporte ¿ SVM ¿ linear e polinomial). Os três classificadores testados tiveram desempenho similar na maioria dos casos. A taxa média de classificação para todos os voluntários considerando a melhor combinação de eletrodos e classificador foi de 78%, sendo que alguns voluntários tiveram taxas de acerto individuais de até 92%. Ainda assim, a metodologia empregada até o momento possui várias limitações, sendo a principal como encontrar os pares ótimos de eletrodos, que variam entre voluntários e aquisições; além do problema da realização online da análiseAbstract: Brain-computer interfaces (BCIs) are systems that aim to provide a direct communication channel between the brain and an external device, such as a computer, a prosthesis or a wheelchair. Since BCIs do not use the conventional physiological pathways, they can constitute important assistive technologies for people with lesions that compromised their interaction with the external environment. Brain signals to be extracted for these systems must be generated according to specific strategies. In this dissertation, we worked with the motor imagery (MI) strategy, and we extracted the corresponding cerebral response from electroencephalography (EEG) data. Our goals were to characterize the functional brain networks originating from hands¿ MI and investigate the feasibility of using metrics from graph theory for the classification of mental patterns, generated by this strategy, of BCI users. We hypothesized that frequency alterations in the EEG spectra due to MI should reflect themselves, in some manner, in the graphs representing cortical interactions during these tasks. For data classification, different sets of electrode pairs were tested, as well as different classifiers (linear discriminant analysis ¿ LDA, and both linear and polynomial support vector machines ¿ SVMs). All three classifiers tested performed similarly in most cases. The mean classification rate over subjects, considering the best electrode set and classifier, was 78%, while some subjects achieved individual hit rates of up to 92%. Still, the employed methodology has yet some limitations, being the main one how to find the optimum electrode pairs¿ sets, which vary among subjects and among acquisitions; in addition to the problem of performing an online analysisMestradoFísicaMestre em Física165742/2014-31423625/2014CNPQCAPE

A new approach of top-down induction of decision trees for knowledge discovery

Top-down induction of decision trees is the most popular technique for classification in the field of data mining and knowledge discovery. Quinlan developed the basic induction algorithm of decision trees, ID3 (1984), and extended to C4.5 (1993). There is a lot of research work for dealing with a single attribute decision-making node (so-called the first-order decision) of decision trees. Murphy and Pazzani (1991) addressed about multiple-attribute conditions at decision-making nodes. They show that higher order decision-making generates smaller decision trees and better accuracy. However, there always exist NP-complete combinations of multiple-attribute decision-makings.;We develop a new algorithm of second-order decision-tree inductions (SODI) for nominal attributes. The induction rules of first-order decision trees are combined by \u27AND\u27 logic only, but those of SODI consist of \u27AND\u27, \u27OR\u27, and \u27OTHERWISE\u27 logics. It generates more accurate results and smaller decision trees than any first-order decision tree inductions.;Quinlan used information gains via VC-dimension (Vapnik-Chevonenkis; Vapnik, 1995) for clustering the experimental values for each numerical attribute. However, many researchers have discovered the weakness of the use of VC-dim analysis. Bennett (1997) sophistically applies support vector machines (SVM) to decision tree induction. We suggest a heuristic algorithm (SVMM; SVM for Multi-category) that combines a TDIDT scheme with SVM. In this thesis it will be also addressed how to solve multiclass classification problems.;Our final goal for this thesis is IDSS (Induction of Decision Trees using SODI and SVMM). We will address how to combine SODI and SVMM for the construction of top-down induction of decision trees in order to minimize the generalized penalty cost

Bifurcations of maps: numerical algorithms and applications

Dynamical systems theory provides mathematical models for systems which evolve in time according to a rule, originally expressed in analytical form as a system of equations. Discrete-time dynamical systems defined by an iterated map depending on control parameters, \begin{equation} \label{Map:g} g(x,\alpha) := f^{(J)}(x,\alpha)= \underbrace{f(f(f(\cdots f}_{J \mbox{~times}}(x,\alpha),\alpha),\alpha),\alpha), \end{equation} appear naturally in, e.g., ecology and economics, where $x\in \R^n$ and $\alpha \in \R^k$ are vectors of state variables and parameters, respectively. %The system dynamics describe a sequence of points \left\{x_k{\right\} \subset \R^n (orbit), provided an initial $x_0 \in \R^n$ is given. The main goal in the study of a dynamical system is to find a complete characterization of the geometry of the orbit structure and the change in orbit structure under parameter variation. An aspect of this study is to identify the invariant objects and the local behaviour around them. This local information then needs to be assembled in a consistent way by means of geometric and topological arguments, to obtain a global picture of the system. At local bifurcations, the number of steady states can change, or the stability properties of a steady state may change. The computational analysis of local bifurcations usually begins with an attempt to compute the coefficients that appear in the normal form after coordinate transformation. These coefficients, called critical normal form coefficients, determine the direction of branching of new objects and their stability near the bifurcation point. After locating a codim 1 bifurcation point, the logical next step is to consider the variation of a second parameter to enhance our knowledge about the system and its dynamical behaviour. % % In codim 2 bifurcation points branches of various codim 1 bifurcation curves are rooted. % These curve can be computed by a combination of parameter-dependent center manifold reduction and asymptotic expressions for the new emanating curves. We implemented new and improved algorithms for the bifurcation analysis of fixed points and periodic orbits of maps in the {\sc Matlab} software package {\sc Cl\_MatcontM}. This includes the numerical continuation of fixed points of iterates of the map with one control parameter, detecting and locating their bifurcation points, and their continuation in two control parameters, as well as detection and location of all codim 2 bifurcation points on the corresponding curves. For all bifurcations of codim 1 and 2, the critical normal form coefficients are computed with finite directional differences, automatic differentiation and symbolic derivatives of the original map. Asymptotics are derived for bifurcation curves of double and quadruple period cycles rooted at codim 2 points of cycles with arbitrary period to continue the double and quadruple period bifurcations. In the case $n=2$ we compute one-dimensional invariant manifolds and their transversal intersections to obtain initial connections of homoclinic and heteroclinic orbits orbits to fixed points of (\ref{Map:g}). We continue connecting orbits, using an algorithm based on the continuation of invariant subspaces, and compute their fold bifurcation curves, corresponding to the tangencies of the invariant manifolds. {\sc Cl\_MatcontM} is freely available at {\bf www.matcont.ugent.be} and {\bf www. sourceforge.net}