Still no free lunches: the price to pay for tighter PAC-Bayes bounds

“No free lunch” results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling, which is more or less realistic for a given problem. Some models are “expensive” (strong assumptions, such as sub-Gaussian tails), others are “cheap” (simply finite variance). As it is well known, the more you pay, the more you get: in other words, the most expensive models yield the more interesting bounds. Recent advances in robust statistics have investigated procedures to obtain tight bounds while keeping the cost of assumptions minimal. The present paper explores and exhibits what the limits are for obtaining tight probably approximately correct (PAC)-Bayes bounds in a robust setting for cheap models

Critical Behavior of Coupled q-state Potts Models under Weak Disorder

We investigate the effect of weak disorder on different coupled $q$-state Potts models with $q\le 4$ using two loops renormalisation group. This study presents new examples of first order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relations emerge, at a perturbation level, between the disordered $q_1\times q_2$-state Potts model and the two disordered $q_1$, $q_2$-state Potts models ($q_1\ne q_2$), despite their central charges are similar according to recent numerical investigations. Nevertheless, when two $q$-state Potts models are considered ($q>2$), the system remains always driven in a strong coupling regime, violating apparently the Imry-Wortis argument.Comment: 7 pages + 1 PS figure (Latex

A Theory for steady and self-sustained premixed combustion waves

Based on the compressible Navier – Stokes equations for reactive flow problems, an eigenvalue problem for the steady and self-sustained premixed combustion wave propagation is developed. The eigenvalue problem is analytically solved and a set of analytic formulae for description of the wave propagation is found out. The analytic formulae are actually the exact solution of the eigenvalue problem in the form of integration, based on which author develops an iterative and numerical algorithm for calculation of the steady and self-sustained premixed combustion wave propagation and its speed. In order to explore the mathematical model and test the computational method developed in this paper, three groups of combustion wave propagation modes are calculated. The computational results show that the non-trivial modes of the combustion wave propagation exist and their distribution is not continuous but discrete

Nouvelles données sur le Miocène moyen marin ("Sallomacien") de Gironde (Bassin d'Aquitaine-France) Approche des paléoenvironnements New data about the maine Middle Miocene ("Sallomacian") of Gironde (Aquitaine Basin); paleoecological outline

The Mid Miocene marine formations of Salles area (former "Sallomacian" stage) have been studied again from numerous outcrops and cores. The deep structural framework influences notably of the characteristics and distribution of the deposits, which are neritic. The stratigraphy is stated precisely thanks to the planktonic fauna and floradetailed examination (probably Serravallian zones NN6 - N12). Several paleobiofacies are reconstituted from the rich invertebrate faunas, which give also paleoclimatic data

Coupled Ising models with disorder

In this paper we study the phase diagram of two Ising planes coupled by a standard spin-spin interaction with bond randomness in each plane. The whole phase diagram is analyzed by help of Monte Carlo simulations and field theory arguments.Comment: 9 pages and 3 figure

Is the biology of breast cancer changing? A study of hormone receptor status 1984-1986 and 1996-1997

Using archived tumours, those from 1984-1986 and 1996-1997 underwent immunohistochemistry for hormone receptors and grade analysis. A significant shift towards more ER-positive and low-grade disease was found; this appears to reflect screening practices, but could still influence survival

A Non-Perturbative Approach to the Random-Bond Ising Model

We study the N -> 0 limit of the O(N) Gross-Neveu model in the framework of the massless form-factor approach. This model is related to the continuum limit of the Ising model with random bonds via the replica method. We discuss how this method may be useful in calculating correlation functions of physical operators. The identification of non-perturbative fixed points of the O(N) Gross-Neveu model is pursued by its mapping to a WZW model.Comment: 17 pages LaTeX, 1 PostScript figure included using psfig.st

RAD-sequencing for estimating GRM-based heritability in the wild:a case study in roe deer

International audienceEstimating the evolutionary potential of quantitative traits and reliably predicting responses to selection in wild populations are important challenges in evolutionary biology. The genomic revolution has opened up opportunities for measuring relatedness among individuals with precision, enabling pedigree‐free estimation of trait heritabilities in wild populations. However, until now, most quantitative genetic studies based on a genomic relatedness matrix (GRM) have focused on long‐term monitored populations for which traditional pedigrees were also available, and have often had access to knowledge of genome sequence and variability. Here, we investigated the potential of RAD‐sequencing for estimating heritability in a free‐ranging roe deer (Capreolous capreolus) population for which no prior genomic resources were available. We propose a step‐by‐step analytical framework to optimize the quality and quantity of the genomic data and explore the impact of the single nucleotide polymorphism (SNP) calling and filtering processes on the GRM structure and GRMbased heritability estimates. As expected, our results show that sequence coverage strongly affects the number of recovered loci, the genotyping error rate and the amount of missing data. Ultimately, this had little effect on heritability estimates and their standard errors, provided that the GRM was built from a minimum number of loci (above 7,000). Genomic relatedness matrix‐based heritability estimates thus appear robust to a moderate level of genotyping errors in the SNP data set. We also showed that quality filters, such as the removal of low‐frequency variants, affect the relatedness structure of the GRM, generating lower h2 estimates. Our work illustrates the huge potential of RAD‐sequencing for estimating GRM‐based heritability in virtually any natural population

Pleistocene eolianites and low sea levels

Abstract not availabl

Weak Randomness for large q-State Potts models in Two Dimensions

We have studied the effect of weak randomness on q-state Potts models for q > 4 by measuring the central charges of these models using transfer matrix methods. We obtain a set of new values for the central charges and then show that some of these values are related to one another by a factorization law.Comment: 8 pages, Latex, no figure