Ce travail de thèse s’inscrit dans le projet à long terme COSFLOS qui a pour but de comprendre l’évolution des structures de l’univers local. Pour cela nous utilisons la relation de Tully-Fisher qui permet de mesurer des distances indépendamment de la loi de Hubble pour des galaxies spirales dans un rayon de 80 Mpc. Mon travail a consisté à collecter, mesurer et analyser les données nécessaires pour cette relation également appelée Luminosity LineWidth (LLW). Cette relation relie la luminosité intrinsèque d’une galaxie à la vitesse maximale de rotation de son gaz neutre. La meilleure façon d’obtenir cette vitesse est de mesurer la largeur de la raie de l’hydrogène neutre (HI) à 21 cm. J’ai effectué de nouvelles observations ainsi que de nouvelles mesures au sein de ce programme, qui aujourd’hui compte 15411 profils HI dans la base de données EDD. J’ai également amélioré l’interface graphique du logiciel de photométrie ARCHANGEL qui nous permet d’obtenir les magnitudes apparentes afin de calculer les distances. Nous verrons que nous avons porté une grande attention sur le calcul du paramètre d’inclinaison de la galaxie observée. Enfin, parmi tous les échantillons en notre possession, j’ai choisi d’étudier plus en détail l’amas de galaxies d’Antlia qui permettra une calibration de la pente de la LLW. Ce travail a commencé par la sélection des candidates, a continué avec les observations puis les mesures et pour se finir sur la détermination des distances nécessaires à la calibration de la relation de Tully-Fisher / This phD thesis is part of the COSFLOS’project. Its goal is to understand the galaxy structure evolution in the local universe. For this purpose, we make use of the Tully-Fisher relation in order to measure the distances for galaxies within 80 Mpc. My research area in the project is to collect, measure and analyze the data needed for the Luminosity LineWidth (LLW). This relation is a direct link between intrinsic luminosity of a spiral galaxy and its maximal gas rotation velocity. The best way to compute this velocity is to measure HI linewidth. Including my new observations and measurements, the current extragalactic database EDD contains 15 411 HI profiles. To obtain the apparent magnitude needed for the distances, I improve the ARCHANGEL software, implementing new displays. We took a great care to a special parameter : the inclination of observed galaxy. Finally, I present the Antlia cluster, one of the cluster I use to calibrate the slope of the LLW. I start with the candidates selection, then with observations to finally obtain the distances for the calibration

The present thesis is located within the context of the diffusion approximation of Wright–Fisher models and the Kolmogorov equations describing their evolution. On the one hand, a full account of recombinational Wright–Fisher model is developed as well as their enhancement by other evolutionary mechanisms, including some information geometrical analysis. On the other hand, the thesis addresses several issues arising in the context of analytical solution schemes for such Kolmogorov equations, namely the inclusion of the entire boundary of the state space. For this, a hierarchical extension scheme is developed, both for the forward and the backward evolution, and the uniqueness of such extensions is proven. First, a systematic approach to the diffusion approximation of recombinational two- or more loci Wright–Fisher models is presented. As a point of departure a specific Kolmogorov backward equation for the diffusion approximation of a recombinational two-loci Wright–Fisher model is chosen, to which – with the help of some information geometrical methods, i. e. by calculating the sectional curvatures of the corresponding statistical manifold (which is the domain equipped with the corresponding Fisher metric) – one succeeds to identify the underlying Wright–Fisher model. Accompanying this, for all methods and tools involved a suitable introduction is presented. Furthermore, the considerations span a separate analysis for the two most common underlying models (RUZ and RUG) as well as a comparison of the two models. Finally, transferring corresponding results for a simpler model described by Antonelli and Strobeck, solutions of the Kolmogorov equations are contrasted with Brownian motion in the same domain. Furthermore, the perspective of the diffusion approximation of recombinational Wright–Fisher models is widened as the model underlying the Ohta–Kimura formula is subsequently extended by an integration of the concepts of natural fitness and mutation. Simultaneously, the corresponding extensions of the Ohta–Kimura formula are stated. Crucial for this is the development of a suitable fitness scheme, which is accomplished by a multiplicative aggregation of fitness values for pairs of gametes/zygotes. Furthermore, the model is generalised to have an arbitrary number of alleles and – in the following step – an arbitrary number of loci respectively. The latter involves an increased number of recombination modes, for which the concept of recombination masks is also implemented into the model. Another generalisation in terms of coarse-graining is performed via an application of schemata; this also affects the previously introduced concepts, specifically mask recombination, which are adapted accordingly. Eventually, a geometric analysis of linkage equilibrium states of the multi-loci Wright–Fisher models is carried out, relating to the concept of hierarchical probability distributions in information geometry, which concludes the considerations of recombinational Wright–Fisher models and their extensions. Subsequently, the discussion of analytical solution schemes for the Kolmogorov equations corresponding to the diffusion approximation of Wright–Fisher models is ushered in, which represents the second part of the thesis. This is started with the simplest setting of a 1-dimensional Wright–Fisher model, for which the solution strategy for the corresponding Kolmogorov forward equation given by M. Kimura is recalled. From this, one may construct a unique extended solution which also accounts for the dynamics of the model on lower-dimensional entities of the state space, i. e. configurations of the model where one of the alleles no longer exists in the population, utilising the concept of (boundary) flux of a solution; a discussion of the moments of the distribution confirms the findings. A similar treatment is then carried out for the corresponding Kolmogorov backward equation, yielding analogous results of existence and uniqueness for an extended solution. For the latter in particular, a corresponding account of the configuration on the boundary turns out to be crucial, which is also reflected in the probabilistic interpretation of the backward solution. Additionally, the long-term behaviour of solutions is analysed, and a comparison between such solutions of the forward and the backward equation is made. Next, it is basically aimed to transfer the results obtained in the previous chapter to the subsequent increasingly complicated setting of a Wright–Fisher model with 1 locus and an arbitrary number of alleles: With solution schemes for the interior of the state space (i. e. not encompassing the boundary) already existing in the literature, an extension scheme for a successive determination of the solution on lower-dimensional entities of the domain is developed. This scheme, again, makes use of the concept of the (boundary) flux of solutions, and one may therefore show that this extended solution fulfils additional properties regarding the completeness of the diffusion approximation with respect to the boundary. These properties may be formulated in terms of the moments of the distribution, and their connection to the underlying Wright–Fisher model is illustrated. Altogether, stipulating such a moments condition, existence and uniqueness of an extended solution on the entire domain are shown. Furthermore, the corresponding Kolmogorov backward equation is examined, for which similarly a (backward) extension scheme is presented, which allows extending a solution in a domain (perceived as a boundary instance of a larger domain) to all adjacent higher-dimensional entities of the larger domain along a certain path. This generalises the integration of boundary data observed in the previous chapter; in total, the existence of a solution of the Kolmogorov backward equation in the entire domain is shown for arbitrary boundary data. Of particular interest to the discussion are stationary solutions of the Kolmogorov backward equation as they describe eventual hit probabilities for a certain target set of the model (in accordance with the probabilistic interpretation of solutions of the backward equation). The presented backward extension scheme allows the construction of solutions for all relevant cases, reconfirming some results by R. A. Littler for the stationary case, but now providing a previously missing systematic derivation. Eventually, the hitherto missing uniqueness assertion for this type of solutions is established by means of a specific iterated transformation which resolves the critical incompatibilities of solutions by a successive blow-up while the domain is converted from a simplex into a cube. Then – under certain additional assumptions on the regularity of the transformed solution – the uniqueness directly follows from general principles. Lastly, several other aspects of the blow-up scheme are discussed; in particular, it is illustrated in what way the required extra regularity relates to reasonable additional properties of the underlying Wright–Fisher model.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-08-24T17:57:59Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertaçãosuper_final_(1).pdf: 1088878 bytes, checksum: f1d95f7419b99281751c7ea750e47cf8 (MD5) / Made available in DSpace on 2016-08-24T17:57:59Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertaçãosuper_final_(1).pdf: 1088878 bytes, checksum: f1d95f7419b99281751c7ea750e47cf8 (MD5) Previous issue date: 2011-08-31 / CAPES / Nesta dissertação é apresentada uma solução estacionária para um modelo de dinâmica populacional de uma única espécie, considerando a dispersão da população num espaço heterogêneo e um crescimento logístico da população. No primeiro capítulo, para dar ao leitor alguma intimidade com os conceitos apresentados estudamos alguns modelos de dinâmica populacional de uma única espécie. Referimo-nos a uma única população para dizer que não analisamos aqui a interação entre diversas espécies. No segundo capítulo concentra-se a parte substancial do nosso trabalho. Na seção 1 apresentamos o modelo, na seção 2 apresentamos a solução estacionária para o problema e na seção 3 fazemos uma discussão sobre efeitos de isolamento para uma população. / This thesis presents a stationary solution to a model of population dynamics of a single species, considering the dispersion of biological population in a heterogeneous space and a logistic population growth. In the rst chapter, to give the reader some familiarity with the concepts presented study some models of population dynamics of a single species. We refer to a single population to say we do not analyze the interaction between di erent species. The second chapter focuses on the substantial part of our work. In Section 1 presents the problem and the model, section 2 presents the stationary solution to the problem and in Section 3 we make a discussion about isolation e ects on a population

Signal formation in a photon-counting x-ray/gamma-ray imaging detector is a complex process resulting in detector signals governed by multiple random effects. Recovering maximum possible information about event attributes of interest requires a systematic collection of calibration data and analysis provided by estimation theory. In this context, a likelihood model provides a description of the connection between the observed signals and the event attributes. A quantitative measure of how well the measured signals can be used to produce an estimate of the parameters is given by Fisher Information analysis. In this work, we demonstrate several applications of the Fisher Information Matrix (FIM) as a powerful and practical tool for investigating and optimizing potential next-generation x-ray/gamma-ray detector designs, with an emphasis on medical-imaging applications. Using FIM as a design tool means to explore the physical detector design choices that have a relationship with the FIM through the likelihood function, how are they interrelated, and determining whether it is possible to modify any of these choices to yield or retain higher values for Fisher Information. We begin by testing these ideas by investigating a new type of a semiconductor detector, a Cadmium Telluride (CdTe) detector with double-sided-strip geometry developed by our collaborators at the Japan Aerospace Exploration Agency (JAXA). The statistical properties of the detector signals as a function of interaction positions in 3D (x, y, z) are presented with mathematical expressions as well as experimental data from measurements using synchrotron radiation at the Advanced Photon Source at Argonne National Laboratory. We show the computation of FIM for evaluating positioning performance and discuss how various detector parameters, that are identified to affect FIM, can be used in detector optimization. Next, we show the application of FIM analysis in a detector system based on multi-anode photomultiplier tubes coupled to a monolithic scintillator in the design of smart electronic read-out strategies. We conclude by arguing that a detector system is expected to perform the best when the hardware is optimized jointly with the estimation algorithm (simply referred to as the "software" in this context) that will be used with it. The results of this work lead to the idea of a detector development approach where the detector hardware platform is developed concurrently with the software and firmware in order to achieve optimal performance.

Population coding—the transmission of information by the combined activity of many neurons—is a feature of many neural systems. Identifying the role played by individual neurons within a population code is vital for the understanding of neural codes. In this thesis I examine which stimuli are best encoded by a given neuron within a population and how this depends on the informational measure used, on commonly-measured neuronal properties, and on the population size and the spacing between stimuli. I also show how correlative measures of topography can be used to test for significant topography in the anatomical arrangement of arbitrary neuronal properties. The neurons involved in a population code are generally clustered together in one region of the brain, and moreover their response selectivity is often reflected in their anatomical arrangement within that region. Although such topographic maps are an often-encountered feature in the brains of many species, there are no standard, objective procedures for quantifying topography. Topography in neural maps is typically identified and described subjectively, but in cases where the scale of the map is close to the resolution limit of the measurement technique, identifying the presence of a topographic map can be a challenging subjective task. In such cases, an objective statistical test for detecting topography would be advantageous. To address these issues, I assess seven measures by quantifying topography in simulated neural maps, and show that all but one of these are effective at detecting statistically significant topography even in weakly topographic maps. The precision of the neural code is commonly investigated using two different families of statistical measures: (i) Shannon mutual information and derived quantities when investigating very small populations of neurons and (ii) Fisher information when studying large populations. The Fisher information always predicts that neurons convey most information about stimuli coinciding with the steepest regions of the tuning curve, but it is known that information theoretic measures can give very different predictions. Using a Monte Carlo approach to compute a stimulus-specific decomposition of the mutual information (the stimulus-specific information, or SSI) for populations up to hundreds of neurons in size, I address the following questions: (i) Under what conditions can Fisher information accurately predict the information transmitted by a neuron within a population code? (ii) What are the effects of level of trial-to-trial variability (noise), correlations in the noise, and population size on the best-encoded stimulus? (iii) How does the type of task in a behavioural experiment (i.e. fine and coarse discrimination, classification) affect the best-encoded stimulus? I show that, for both unimodal and monotonic tuning curves, the shape of the SSI is dependent upon trial-to-trial variability, population size and stimulus spacing, in addition to the shape of the tuning curve. It is therefore important to take these factors into account when assessing which stimuli a neuron is informative about; just knowing the tuning curve may not be sufficient.

This paper discusses characteristics of standard conjugate priors and their induced posteriors in Bayesian inference for von Mises-Fisher distributions, using either the canonical natural exponential family or the more commonly employed polar coordinate parameterizations. We analyze when standard conjugate priors as well as posteriors are proper, and investigate the Jeffreys prior for the von Mises-Fisher family. Finally, we characterize the proper distributions in the standard conjugate family of the (matrixvalued) von Mises-Fisher distributions on Stiefel manifolds.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / In this work we study from both classical and quantum point of view the position dependent mass harmonic oscillator (PDMHO). Classically, we use the Legendre transformation to find the Hamiltonian of the system. Next, we define two functions, and , to simplify the hamiltonian of the PDMHO. By using the Poisson algebra we find the expressions for the position and moment. At last, by using a canonical transformation we relate the equations of the PDMHO to those of the simple harmonic oscillator (SHO). Quantically, we write the Hamiltonian of the PDMHO in terms of the operators and . Next, we consider that these operators satisfy the same algebra that those of the SHO. By assuming that both the classical and quantum PDMHO have the same form, we are able to find a simple form for the PDMHO Hamiltonian. Finally, by transforming the SchrÃdinger equation (SE) of the PDMHO into that of the SHO, we can write the wave function of the PDMHO in terms of that of the SHO. We will study two time-dependent systems, namely and , we observe that as , they tend to a simple harmonic oscillator. For each system we find the position and momentum (classical study), as well as the wave-function (quantum study). For both systems we analyze the the position e momentum uncertainty, the product uncertainty, the fisher information and Shannon entropy, for the ground state, as a function of the parameter . / Neste trabalho estudamos clÃssica e quanticamente o oscilador harmÃnico com massa dependente da posiÃÃo (OHMDP). Na parte clÃssica, utilizamos a transformaÃÃo de Legendre para encontrar a hamiltoniana do sistema. A seguir definimos duas funÃÃes e para escrevermos a hamiltoniana do OHMDP de uma forma mais simples. Utilizando a Ãlgebra de Poisson encontramos as expressÃes para a posiÃÃo e o momento. Por fim, atravÃs de uma transformaÃÃo canÃnica veremos como relacionar as equaÃÃes do OHMDP com aquelas do oscilador harmÃnico simples (OHS). Na parte quÃntica, escrevemos a hamiltoniana do OHMDP em termos de operadores e . Em seguida, vamos supor que estes operadores satisfaÃam a mesma relaÃÃo de comutaÃÃo que os operadores abaixamento e levantamento do OHS. Analisando que condiÃÃo deve ser satisfeita para que os osciladores OHMDP clÃssico e quÃntico tenham o mesmo potencial, encontramos uma forma simplificada da hamiltoniana do OHMDP. Em seguida, transformamos a equaÃÃo de SchrÃdinger (ES) para o OHMDP na ES para o OHS. Assim, obtemos a funÃÃo de onda do OHMDP em termos da funÃÃo de onda do OHS. Estudaremos dois sistemas com massa dependente da posiÃÃo, a saber: e , vemos que quando , recaÃmos no OHS. Para cada sistema encontraremos a posiÃÃo e o momento (estudo clÃssico), bem como a funÃÃo de onda (estudo quÃntico). Para os dois sistemas analisaremos tambÃm o comportamento da incerteza na posiÃÃo, incerteza no momento, produto de incerteza, informaÃÃo de Fisher e entropia de Shannon, para o estado fundamental, em funÃÃo do parÃmetro de deformaÃÃo .

Using a structural topic model text analysis approach in a mixed methods framework, these studies seek to better understand the language, rhetoric, and rationales amici curiae employ to defend or deride affirmative action in cases before the Supreme Court. Through a better understanding of the content and framing of these briefs, the next time an affirmative action case is before the court a larger, more articulate, and more united network of advocates from the higher education sector and beyond will be better position to have their voices heard.

Diffusion weighted imaging (DWI) is a branch within the field of magnetic resonance imaging (MRI) that relies on the diffusion of water molecules for its contrast. Its clinical applications include the early diagnosis of ischemic stroke and mapping of the nerve tracts of the brain. The recent development of filter exchange imaging (FEXI) and the introduction of the apparent exchange rate (AXR) present a new DWI based technique that uses the exchange of water between compartments as contrast. FEXI could offer new clinical possibilities in diagnosis, differentiation and treatment follow-up of conditions involving edema or altered membrane permeability, such as tumors, cerebral edema, multiple sclerosis and stroke. Necessary steps in determining the potential of AXR as a new biomarker include running comparative studies between controls and different patient groups, looking for conditions showing large AXR-changes. However, before designing such studies, the experimental protocol of FEXI should be optimized to minimize the experimental variance. Such optimization would improve the data quality, shorten the scan time and keep the required study group sizes smaller.  Here, optimization was done using an active imaging approach and the Cramer-Rao lower bound (CRLB) of Fisher information theory. Three optimal protocols were obtained, each specialized at different tissue types, and the CRLB method was verified by bootstrapping. A test-retest study of 18 volunteers was conducted in order to investigate the reproducibility of the AXR as measured by one of the protocols, adapted for the scanner. Group sizes required were calculated based on both CRLB and the variability of the test-retest data, as well as choices in data analysis such as region of interest (ROI) size. The result of this study is new protocols offering a reduction in coefficient of variation (CV) of around 30%, as compared to previously presented protocols. Calculations of group sizes required showed that they can be used to decide whether any patient group, in a given brain region, has large alterations of AXR using as few as four individuals per group, on average, while still keeping the scan time below 15 minutes. The test-retest study showed a larger than expected variability however, and uncovered artifact like changes in AXR between measurements. Reproducibility of AXR values ranged from modest to acceptable, depending on the brain region. Group size estimations based on the collected data showed that it is still possible to detect AXR difference larger than 50% in most brain regions using fewer than ten individuals. Limitations of this study include an imprecise knowledge of model priors and a possibly suboptimal modeling of the bias caused by weak signals. Future studies on FEXI methodology could improve the method further by addressing these matters and possibly also the unknown source of variability. For minimal variability, comparative studies of AXR in patient groups could use a protocol among those presented here, while choosing large ROI sizes and calculating the AXR based on averaged signals.

PopED is a software developed by the Pharmacometrics Research Group at the Department of Pharmaceutical Biosiences, Uppsala University written mainly in MATLAB. It uses pharmacometric population models to describe the pharmacokinetics and pharmacodynamics of a drug and then estimates an optimal design of a trial for that drug. With optimization calculations in average taking a very long time, it was desirable to increase the calculation speed of the software by parallelizing the serial calculation script. The goal of this project was to investigate different methods of parallelization and implement the method which seemed the best for the circumstances.The parallelization was implemented in C/C++ by using Open MPI and tested on the UPPMAX Kalkyl High-Performance Computation Cluster. Some alterations were made in the original MATLAB script to adapt PopED to the new parallel code. The methods which where parallelized included the Random Search and the Line Search algorithms. The testing showed a significant performance increase, with effectiveness per active core rangingfrom 55% to 89% depending on model and number of evaluated designs.