Some properties of the solutions of obstacle problems with measure data

We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not depend on the components of the negative parts of the data which are concentrated on sets of capacity zero. The proof is based on a careful analysis of the behaviour of the potentials of two mutually singular measures near the points where both potentials tend to infinity.Comment: 18 page

Bayesian Posteriors Without Bayes' Theorem

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics.Comment: 6 pages, no figure

Bayesian Posteriors Without Bayes' Theorem

The classical Bayesian posterior arises naturally as the unique solution of several different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes' Theorem. For example, the classical Bayesian posterior is the unique posterior that minimizes the loss of Shannon information in combining the prior and the likelihood distributions. These results, direct corollaries of recent results about conflations of probability distributions, reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics

Characterization of the Bayesian Posterior Distribution in Terms of Self-information

It is well known that the classical Bayesian posterior arises naturally as the unique solution of different optimization problems, without the necessity of interpreting data as conditional probabilities and then using Bayes\u2019 Theorem. Here it is shown that the Bayesian posterior is also the unique minimax optimizer of the loss of self-information in combining the prior and the likelihood distributions, and is the unique proportional consolidation of the same distributions. These results, direct corollaries of recent results about conflations of probability distributions, further reinforce the use of Bayesian posteriors, and may help partially reconcile some of the differences between classical and Bayesian statistics

Leptin system in obese dog skin: A pilot study

Obesity predisposes to several health problems including skin diseases. However, information on the relationship between obesity and skin disorders in pets is very scarce. Leptin (LEP) is mainly produced by adipose tissue and has a prominent role in skin biology. This study evaluated the LEP system in the skin of obese dogs compared to normal-weight animals. The investigation was carried out on 10 obese (Obese group) and 10 normal-weight (Normal-weight group) dogs through Real-time PCR and immunohistochemistry. Cells of skin associated immune system were also evaluated. No differences were evidenced between the two groups as well as skin inflammation. LEP differences were no significant, while LEPR transcript appeared 10-fold higher in obesedogs than in normal-weight ones. Immunostaining for both molecules was observed in several skin structures such as the epidermis, hair follicles, and glands. No differences appeared in the skin associated immune system composition. This study is a preliminary report showing that LEP system changes in obese dog skin. The increased LEPR expression observed in the obese group suggests that the receptor plays a modulating role in the system control. However, the exact role of LEPin the skin under obesity conditions needs further elucidation

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

Effects of obesity on adiponectin system skin expression in dogs: A comparative study

Obesity is an important health issue in dogs since it influences a plethora of associated pathologies, including dermatological disorders. Considering the scarcity of information in pets, this work aimed to evaluate the localization and expression of adiponectin (ADIPOQ) and its two receptors (ADIPOR1 and ADIPOR2) in the skin of 10 obese dogs, compared with serum ADIPOQ level. Through immunohistochemistry, ADIPOQ and ADIPOR2 were observed in the adipose tissue, sweat and sebaceous glands, endothelium, and some connective cells. Both receptors were observed in the epidermis and the hair follicles, other than in the sweat and sebaceous glands. Real-time PCR evidenced that the ADIPOQ and ADIPOR2 transcripts were expressed 5.4-fold (p < 0.01) and 2.3-fold less (p < 0.01), respectively, in obese than in normal weight dogs, while ADIPOR1 expression did not change. Obese dogs showed lower serum ADIPOQ levels than the normal weight group. Accordingly, ADIPOQ and ADIPOR2 expression in the skin appear negatively correlated with obesity in the same way as the serum ADIPOQ level. These findings evidence that ADIPOQ system changes in the skin of obese dogs and suggest that the ADIPOQ effect on the skin is at least in part regulated by the reduced expression of ADIPOR2