A Froggatt-Nielsen flavor model for neutrino physics

Superheavy neutrinos can, via the seesaw model, provide a mechanism for lepton number violation. If they are combined with flavor violation as characterized by the Froggatt-Nielsen mechanism, then the phenomenology for the neutrinos in oscillation experiments, neutrinoless double beta decay, and other experiments can be described by a relatively few number of parameters. We describe the low-energy neutrino mass matrix and show that the results are consistent with currently available data.Comment: 7 pages, no figure

Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

On the Equivalence of Three-Particle Scattering Formalisms

In recent years, different on-shell $\mathbf{3}\to\mathbf{3}$ scattering formalisms have been proposed to be applied to both lattice QCD and infinite volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in Phys.~Rev.~D92, 114509 (2015) and subsequently Brice\~no, Hansen, and Sharpe in Phys.~Rev.~D95, 074510 (2017) can be recovered from the $B$-matrix representation, derived on the basis of $S$-matrix unitarity, presented by Mai {\em et al.} in Eur.~Phys.~J.~A53, 177 (2017) and Jackura {\em et al.} in Eur.~Phys.~J.~C79, 56 (2019). Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the non-relativistic limit of both representations.Comment: 13 pages, 5 figure

Information Aggregation in Exponential Family Markets

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability distribution template used in statistics. We give a full development of this relationship and explore a range of benefits. We draw connections between the information aggregation of market prices and the belief aggregation of learning agents that rely on exponential family distributions. We develop a very natural analysis of the market behavior as well as the price equilibrium under the assumption that the traders exhibit risk aversion according to exponential utility. We also consider similar aspects under alternative models, such as when traders are budget constrained

Significance in gamma-ray astronomy - the Li & Ma problem in Bayesian statistics

The significance of having detected an astrophysical gamma ray source is usually calculated by means of a formula derived by Li & Ma in 1983. We solve the same problem in terms of Bayesian statistics, which provides a logically more satisfactory framework. We do not use any subjective elements in the present version of Bayesian statistics. We show that for large count numbers and a weak source the Li & Ma formula agrees with the Bayesian result. For other cases the two results differ, both due to the mathematically different treatment and the fact that only Bayesian inference can take into account prior knowldege.Comment: 12 pages, 3 figures, accepted for publication in A&

Computational algebraic methods in efficient estimation

A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed, such as bias corrected Maximum Likelihood and more general estimators, and for which the estimating equations are purely algebraic. In addition it is shown how Gr\"obner basis technology, which is at the heart of algebraic statistics, can be used to reduce the degrees of the terms in the estimating equations. This points the way to the feasible use, to find the estimators, of special methods for solving polynomial equations, such as homotopy continuation methods. Simple examples are given showing both equations and computations. *** The proof of Theorem 2 was corrected by the latest version. Some minor errors were also corrected.Comment: 21 pages, 5 figure

Effects of Epistasis and Pleiotropy on Fitness Landscapes

The factors that influence genetic architecture shape the structure of the fitness landscape, and therefore play a large role in the evolutionary dynamics. Here the NK model is used to investigate how epistasis and pleiotropy -- key components of genetic architecture -- affect the structure of the fitness landscape, and how they affect the ability of evolving populations to adapt despite the difficulty of crossing valleys present in rugged landscapes. Populations are seen to make use of epistatic interactions and pleiotropy to attain higher fitness, and are not inhibited by the fact that valleys have to be crossed to reach peaks of higher fitness.Comment: 10 pages, 6 figures. To appear in "Origin of Life and Evolutionary Mechanisms" (P. Pontarotti, ed.). Evolutionary Biology: 16th Meeting 2012, Springer-Verla

Métodos de avaliação da segurança de pontes existentes

O presente trabalho pretende descrever, de uma forma acessível, os métodos de análise de fiabilidade e a metodologia de verificação da segurança por etapas, que podem ser úteis na avaliação da segurança de pontes existentes. A metodologia apresentada sugere o recurso a uma análise mais avançada sempre que a ponte não cumpra os requisitos estabelecidos no nível de avaliação anterior, culminando no método de avaliação que combina a análise não-linear com a análise probabilística.The present work aims to describe, in an accessible way, the methods of reliability analysis and the step-level assessment methodology, which might be useful in the safety evaluation of existent bridges. The presented methodology suggest to use a more advanced analysis when the bridge doesn’t fulfill the requirements established in the previous safety evaluation level, culminating in the method of evaluation that combines the non-linear and probabilistic analysis.Comissão Europeia - VI Programa Quadro "Sustainable Bridges” FP6-PLT-0165