The full Fisher matrix for galaxy surveys

Starting from the Fisher matrix for counts in cells, we derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key step is the classical approximation, which allows us to write the inverse of the covariance of the galaxy counts in terms of the naive matrix inverse of the covariance in a mixed position-space and Fourier-space basis. We then compute the Fisher matrix for the power spectrum in bins of the 3D wavenumber , the Fisher matrix for functions of position (or redshift z) such as the linear bias of the tracers and/or the growth function and the cross-terms of the Fisher matrix that expresses the correlations between estimations of the power spectrum and estimations of the bias. When the bias and growth function are fully specified, and the Fourier-space bins are large enough that the covariance between them can be neglected, the Fisher matrix for the power spectrum reduces to the widely used result that was first derived by Feldman, Kaiser & Peacock. Assuming isotropy, a fully analytical calculation of the Fisher matrix in the classical approximation can be performed in the case of a constant-density, volume-limited survey.

Hubble parameter reconstruction from a principal component analysis: minimizing the bias

Aims. A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Methods. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. Results. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.

The signature of dark energy perturbations in galaxy cluster surveys

Models of dynamical dark energy unavoidably possess fluctuations in the energy density and pressure of that new component. In this paper we estimate the impact of dark energy fluctuations on the number of galaxy clusters in the Universe using a generalization of the spherical collapse model and the Press-Schechter formalism. The observations we consider are several hypothetical Sunyaev-Zel`dovich and weak lensing (shear maps) cluster surveys, with limiting masses similar to ongoing (SPT, DES) as well as future (LSST, Euclid) surveys. Our statistical analysis is performed in a 7-dimensional cosmological parameter space using the Fisher matrix method. We find that, in some scenarios, the impact of these fluctuations is large enough that their effect could already be detected by existing instruments such as the South Pole Telescope, when priors from other standard cosmological probes are included. We also show how dark energy fluctuations can be a nuisance for constraining cosmological parameters with cluster counts, and point to a degeneracy between the parameter that describes dark energy pressure on small scales (the effective sound speed) and the parameters describing its equation of state.

The signature of dark energy perturbations in galaxy cluster surveys

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Forecasts on the dark energy anisotropic stress for the esa euclid survey

The cosmological constant Λ seems to be a not satisfactory explanation of the late-time accelerated expansion of the Universe, for which a number of experimental evidences exist; therefore, it has become necessary in the last years to consider alternative models of dark energy, meant as cause of the accelerated expansion. In the study of dark energy models, it is important to understand which quantities can be determined starting from observational data, without assuming any hypothesis on the cosmological model; such quantities have been determined in Amendola, Kunz et al., 2012. In the same paper it has been further shown that it is possible to estabilish a relation between the model-independent parameters and the anisotropic stress η, which can be also expressed as a combination of the functions appearing in the most general Lagrangian for the scalar-tensor theories, the Horndeski Lagrangian. In the present thesis, the Fisher matrix formalism is used to perform a forecast on the constraints that will be possible to make on the anisotropic stress η in the future, starting from the estimated uncertainties for the galaxy clustering and weak lensing measurements which will be performed by the European Space Agency Euclid mission, to be launched in 2020. Further, constraints coming from supernovae-Ia observations are considered. The forecast is performed for two cases in which (a) η is considered as depending from redshift only and (b) η is constant and equal to one, as in the ΛCDM model.

Testes cosmológicos aplicados a modelos de energia escura

A significant observational effort has been directed to investigate the nature of the so-called dark energy. In this dissertation we derive constraints on dark energy models using three different observable: measurements of the Hubble rate H(z) (compiled by Meng et al. in 2015.); distance modulus of 580 Supernovae Type Ia (Union catalog Compilation 2.1, 2011); and the observations of baryon acoustic oscilations (BAO) and the cosmic microwave background (CMB) by using the so-called CMB/BAO of six peaks of BAO (a peak determined through the Survey 6dFGS data, two through the SDSS and three through WiggleZ). The statistical analysis used was the method of the χ2 minimum (marginalized or minimized over h whenever possible) to link the cosmological parameter: m, ω and δω0. These tests were applied in two parameterization of the parameter ω of the equation of state of dark energy, p = ωρ (here, p is the pressure and ρ is the component of energy density). In one, ω is considered constant and less than -1/3, known as XCDM model; in the other the parameter of state equantion varies with the redshift, where we the call model GS. This last model is based on arguments that arise from the theory of cosmological inflation. For comparison it was also made the analysis of model CDM. Comparison of cosmological models with different observations lead to different optimal settings. Thus, to classify the observational viability of different theoretical models we use two criteria information, the Bayesian information criterion (BIC) and the Akaike information criteria (AIC). The Fisher matrix tool was incorporated into our testing to provide us with the uncertainty of the parameters of each theoretical model. We found that the complementarity of tests is necessary inorder we do not have degenerate parametric spaces. Making the minimization process we found (68%), for the Model XCDM the best fit parameters are m = 0.28 ± 0, 012 and ωX = −1.01 ± 0, 052. While for Model GS the best settings are m = 0.28 ± 0, 011 and δω0 = 0.00 ± 0, 059. Performing a marginalization we found (68%), for the Model XCDM the best fit parameters are m = 0.28 ± 0, 012 and ωX = −1.01 ± 0, 052. While for Model GS the best settings are M = 0.28 ± 0, 011 and δω0 = 0.00 ± 0, 059.

Testes cosmológicos aplicados a modelos de energia escura

A significant observational effort has been directed to investigate the nature of the so-called dark energy. In this dissertation we derive constraints on dark energy models using three different observable: measurements of the Hubble rate H(z) (compiled by Meng et al. in 2015.); distance modulus of 580 Supernovae Type Ia (Union catalog Compilation 2.1, 2011); and the observations of baryon acoustic oscilations (BAO) and the cosmic microwave background (CMB) by using the so-called CMB/BAO of six peaks of BAO (a peak determined through the Survey 6dFGS data, two through the SDSS and three through WiggleZ). The statistical analysis used was the method of the χ2 minimum (marginalized or minimized over h whenever possible) to link the cosmological parameter: m, ω and δω0. These tests were applied in two parameterization of the parameter ω of the equation of state of dark energy, p = ωρ (here, p is the pressure and ρ is the component of energy density). In one, ω is considered constant and less than -1/3, known as XCDM model; in the other the parameter of state equantion varies with the redshift, where we the call model GS. This last model is based on arguments that arise from the theory of cosmological inflation. For comparison it was also made the analysis of model CDM. Comparison of cosmological models with different observations lead to different optimal settings. Thus, to classify the observational viability of different theoretical models we use two criteria information, the Bayesian information criterion (BIC) and the Akaike information criteria (AIC). The Fisher matrix tool was incorporated into our testing to provide us with the uncertainty of the parameters of each theoretical model. We found that the complementarity of tests is necessary inorder we do not have degenerate parametric spaces. Making the minimization process we found (68%), for the Model XCDM the best fit parameters are m = 0.28 ± 0, 012 and ωX = −1.01 ± 0, 052. While for Model GS the best settings are m = 0.28 ± 0, 011 and δω0 = 0.00 ± 0, 059. Performing a marginalization we found (68%), for the Model XCDM the best fit parameters are m = 0.28 ± 0, 012 and ωX = −1.01 ± 0, 052. While for Model GS the best settings are M = 0.28 ± 0, 011 and δω0 = 0.00 ± 0, 059.

Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs.

In population pharmacokinetic studies, the precision of parameter estimates is dependent on the population design. Methods based on the Fisher information matrix have been developed and extended to population studies to evaluate and optimize designs. In this paper we propose simple programming tools to evaluate population pharmacokinetic designs. This involved the development of an expression for the Fisher information matrix for nonlinear mixed-effects models, including estimation of the variance of the residual error. We implemented this expression as a generic function for two software applications: S-PLUS and MATLAB. The evaluation of population designs based on two pharmacokinetic examples from the literature is shown to illustrate the efficiency and the simplicity of this theoretic approach. Although no optimization method of the design is provided, these functions can be used to select and compare population designs among a large set of possible designs, avoiding a lot of simulations.

WNT-5A, but not matrix metalloproteinase 3 or beta-catenin protein, expression is related to early stages of lip carcinogenesis

Background: Oncogenic Wnt/beta-catenin signaling occurs in numerous types of cancers, but little is known about the role of the Wnt protein family member, WNT-5A, in lip carcinogenesis. The aim of this study was to investigate WNT-5A, beta-catenin, and matrix metalloproteinase (MMP)-3 protein expression in actinic cheilitis (AC), and lip squamous cell carcinoma (LSCC). Methods: Twenty-one cases of AC, and fifty-one cases of LSCC were analyzed, with normal lip mucosa used as a control. Qualitative and semi-quantitative analyses of WNT-5A, beta-catenin, and MMP-3 immunostaining pattern and cellular distribution were performed. Results: WNT-5A was observed in more than 50% of the cells, scattered in all layers of AC, in contrast to the absence of immunostaining in normal lip mucosa. AC presented a higher level of WNT-5A expression than LSCC (P = 0.0289, Fisher test), while MMP-3 immunoexpression was statistically more significant in LSCC than in AC (P = 0.0285, Fisher test). Immunolabeling of beta-catenin protein was differentially distributed between samples; the majority of AC cases (61.90%) demonstrated a membranous-cytoplasmic pattern, while a considerable number of LSCC cases (29.41%) revealed a cytoplasmic pattern, instead of the usual membranous pattern. Conclusions: The present results suggest that WNT-5A may be an important marker during initial events of AC malignant transformation, in which non-canonical and canonical Wnt/beta-catenin signaling pathways could be involved. Additionally, WNT-5A might recruit other events in LSCC, such as MMP-3 protein synthesis, as its presence is increased in established malignant processes without beta-catenin dependency.

Kernel classifier construction using orthogonal forward selection and boosting with Fisher ratio class separability measure

A greedy technique is proposed to construct parsimonious kernel classifiers using the orthogonal forward selection method and boosting based on Fisher ratio for class separability measure. Unlike most kernel classification methods, which restrict kernel means to the training input data and use a fixed common variance for all the kernel terms, the proposed technique can tune both the mean vector and diagonal covariance matrix of individual kernel by incrementally maximizing Fisher ratio for class separability measure. An efficient weighted optimization method is developed based on boosting to append kernels one by one in an orthogonal forward selection procedure. Experimental results obtained using this construction technique demonstrate that it offers a viable alternative to the existing state-of-the-art kernel modeling methods for constructing sparse Gaussian radial basis function network classifiers. that generalize well.

Measurement of the top quark mass in the lepton plus jets final state with the matrix element method

We present a measurement of the top quark mass with the matrix element method in the lepton+jets final state. As the energy scale for calorimeter jets represents the dominant source of systematic uncertainty, the matrix element likelihood is extended by an additional parameter, which is defined as a global multiplicative factor applied to the standard energy scale. The top quark mass is obtained from a fit that yields the combined statistical and systematic jet energy scale uncertainty. Using a data set of 0.4 fb(-1) taken with the D0 experiment at Run II of the Fermilab Tevatron Collider, the mass of the top quark is measured using topological information to be: m(top)(center dot+jets)(topo)=169.2(-7.4)(+5.0)(stat+JES)(-1.4)(+1.5)(syst) GeV, and when information about identified b jets is included: m(top)(center dot+jets)(b-tag)=170.3(-4.5)(+4.1)(stat+ JES)(-1.8)(+1.2)(syst) GeV. The measurements yield a jet energy scale consistent with the reference scale.

Patch-size and isolation effects in the Fisher-Kolmogorov equation

We examine the classical problem of the existence of a threshold size for a patch to allow for survival of a given population in the case where the patch is not completely isolated. The surrounding habitat matrix is characterized by a non-zero carrying capacity. We show that a critical patch size cannot be strictly defined in this case. We also obtain the saturation density in such a patch as a function of the size of the patch and the relative carrying capacity of the outer region. We argue that this relative carrying capacity is a measure of the isolation of the patch. Our results are then compared with conclusions drawn from observations of the population dynamics of understorey birds in fragments of the Amazonian forest and shown to qualitatively agree with them, offering an explanation for the importance of dispersal and isolation in these observations. Finally, we show that a generalized critical patch size can be introduced resorting to threshold densities for the observation of a given species.

Measurement of Spin Correlation in t(t)over-bar Production Using a Matrix Element Approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)