The Likelihood Ratio Test and Full Bayesian Significance Test under small sample sizes for contingency tables

Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples. To study these tests in small samples, we consider the likelihood ratio test and define an accurate index, the P-value, for the celebrated hypotheses of homogeneity, independence, and Hardy-Weinberg equilibrium. The aim is to understand the use of the asymptotic results of the frequentist Likelihood Ratio Test and the Bayesian FBST -- Full Bayesian Significance Test -- under small-sample scenarios. The proposed exact P-value is used as a benchmark to understand the other indices. We perform analysis in different scenarios, considering different sample sizes and different table dimensions. The exact Fisher test for $2 \times 2$ tables that drastically reduces the sample space is also discussed. The main message of this paper is that all indices have very similar behavior, so the tests based on asymptotic results are very good to be used in any circumstance, even with small sample sizes

Constraints on Supersymmetric Theories from μ→e,γ\mu\to e,\gamma

In the absence of any additional assumption it is natural to conjecture that sizeable flavour-mixing mass entries, $\Delta m^2$, may appear in the mass matrices of the scalars of the MSSM, i.e. $\Delta m^2\sim O(m^2)$. This flavour violation can still be reconciled with the experiment if the gaugino mass, $M_{1/2}$, is large enough, leading to a {\em gaugino dominance} framework (i.e. $M_{1/2}^2\gg m^2$), which permits a remarkably model--independent analysis. We study this possibility focussing our attention on the $\mu\rightarrow e,\gamma$ decay. In this way we obtain very strong and general constraints, in particular \frac{M_{1/2}^2}{\Delta m}\simgt 34\ {\rm TeV}. On the other hand, we show that our analysis and results remain valid for values of $m^2$ much larger than $\Delta m^2$, namely for \frac{\Delta m^2}{m^2}\simgt \frac{m^2} {10\ {\rm TeV^2}}, thus extending enormously their scope of application. Finally, we discuss the implications for superstring scenarios.Comment: 12 pages, Latex, 5 figures as uuencoded compressed postscript files, uses psfig.st

Flavor Symmetries and The Problem of Squark Degeneracy

If supersymmetry exists at low energies, it is necessary to understand why the squark spectrum exhibits sufficient degeneracy to suppress flavor changing neutral currents. In this note, we point out that gauged horizontal symmetries can yield realistic quark mass matrices, while at the same time giving just barely enough squark degeneracy to account for neutral $K$-meson phenomenology. This approach suggests likely patterns for squark masses, and indicates that there could be significant supersymmetric contributions to $B-\bar{B}$ and $D-\bar{D}$ mixing and CP violation in the $K$ and $B$ systems.Comment: preprint SCIPP 93/04,SLAC-PUB-6147, 14 pages, 4 tables included; uses macro package TABLES.TEX and phyzzx forma

Reductive decarboxylation of bicyclic prolinic systems: a new approach to the enantioselective synthesis of the Geissman-Waiss lactone. X-ray structure determination of a key lactone intermediate

Two concise and enantioselective syntheses of the necine base precursors (1R,5R)-N-Cbz and N-Boc-2-oxa-6-azabicyclo[3.3.0]octan-3-ones (Geissman-Waiss lactones) were carried out from two enantiomerically pure endocyclic five-membered enecarbamates with overall yields of 23% and 26%, respectively. The synthetic strategy made use of a highly effective and stereoselective [2+2]cycloaddition of enantiomerically pure endocyclic enecarbamates with dichloroketene, as well as an efficient decarboxylation step of a bicyclic alpha-amino acid employing Boger's acyl selenide protocol employing tributyltin hydride. Interesting aspects concerning the regiochemical outcome of Baeyer-Villiger oxidations of bicyclic cyclobutanones are also reported, in which the usual stereoelectronic bias of Baeyer-Villiger oxidation seems to be counterbalanced by steric effects on the putative Criegee intermediate.Duas sínteses do conhecido precursor de bases necínicas, (1R,5R)-N-Cbz e N-Boc 2-oxa-6-azabiciclo[3.3.0]octan-3-onas (lactonas de Geissman-Waiss) foram realizadas com rendimentos globais de 23% e 26%, em seis e cinco etapas respectivamente, a partir de enecarbamatos endocíclicos de cinco membros enantiomericamente puros. A estratégia sintética adotada está fundamentada em uma reação de cicloadição [2+2] eficiente e altamente estereosseletiva de enecarbamatos de cinco membros com diclorocetenos, assim como em uma eficaz descarboxilação de alfa-amino ácidos bicíclicos pelo método de Boger, que utiliza a redução de selenetos de acila por hidretos de estanho. Aspectos relativos a regiosseletividade da reação de oxidação de azabiciclo ciclobutanonas pelo método de Baeyer-Villiger são também descritos, com destaque para um potencial controle regioquímico advindo de aspectos estéreos em contraposição a aspectos estereoeletrônicos.2738Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Strike-slip faults in the south Haouz (Calcareous Dorsal, Internal Rif, N of Tetouan, Maroc). Comparison with the Betics (Spain)

4 páginas, 4 figuras.-- Trabajo presentado en la 41ª Sesión Científica, Barcelona, 2006.Different sets of strike-slip faults of the Haouz Mountains (from Tetouan to the strait of Gibraltar) deform the tectonic slices of the Calcareous Dorsal there present. In this paper we study those faults at the southern part of the Haouz. Three fault formation stages can be distinguished and correspond to the progressive s1 rotation during the Neogene from a near E-W position to approximately N-S, in a progressive anticlockwise rotation. The faults and other related structures are compared with similar ones existing in the Betic Cordillera, in equivalent areas of the arc of Gibraltar.Este artículo es una contribución del grupo de Travaux de Recherches de l’Unité Risques Géologiques et Télédetection, 2006, Rabat y de los proyectos BTE2001-5230-E, CGL200401636/BTE, CGL2004-03333/ BTE, y el grupo RNM 217 de la Junta de Andalucía.Peer reviewe

On non-perturbative corrections to the Kahler potential

We present the results of a detailed investigation into the consequences of adding specific string motivated non-perturbative corrections to the usual tree level Kahler potential in dilaton dominated scenarios. The success of the model is judged through our ability to obtain a realistic VEV for the dilaton < Re S > ~ 2, corresponding to the true minima of the scalar potential and being associated with a reasonable value for the SUSY breaking scale via the gravitino mass. The status of the so-called moduli problem is also reviewed in each of the ansatze studied. Those include previous proposals made in the context of both the chiral and the linear multiplet formalisms to describe gaugino condensation, and a new ansatz which shows explicitly the equivalence between the two.Comment: 11 pages, LaTex, uses psfig.sty with 4 figure

A non-perturbative renormalization group study of the stochastic Navier--Stokes equation

We study the renormalization group flow of the average action of the stochastic Navier--Stokes equation with power-law forcing. Using Galilean invariance we introduce a non-perturbative approximation adapted to the zero frequency sector of the theory in the parametric range of the H\"older exponent $4-2\,\varepsilon$ of the forcing where real-space local interactions are relevant. In any spatial dimension $d$, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for $\varepsilon=2$ as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a \emph{saturation} in the $\varepsilon$-dependence of the scaling dimension of the eddy diffusivity at $\varepsilon=3/2$ when, according to perturbative renormalization, the velocity field becomes infra-red relevant.Comment: RevTeX, 18 pages, 5 figures. Minor changes and new discussion

Isotropic and Anisotropic Bouncing Cosmologies in Palatini Gravity

We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini $f(R)$ and $f(R,R_{\mu\nu}R^{\mu\nu})$ theories of gravity and consider the existence of non-singular bouncing solutions in the early universe. We find that all $f(R)$ models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model $R+a R^2/R_P+R_{\mu\nu}R^{\mu\nu}/R_P$ exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for $a<0$) and radiation (for arbitrary $a$). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic ($w>1$) sources of matter/energy.Comment: 25 pages, 7 figure