Quasi linear parabolic equations with degenerate coercivity having a quadratic gradient term

We study existence and regularity of distributional solutions for possibly degenerate quasi-linear parabolic problems having non linear lower order terms which depends on the solution and on its gradient

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

Semilinear parabolic equations with superlinear reaction terms, and application to some convection-diffusion problems

We are interested in the existence of distributional solutions for two types of nonlinear evolution problems, whose models are (1.1) and (1.2) below. In the first one the nonlinear reaction term depends on the solution with a slightly superlinear growth. In the second one we consider a first order term depending also on the gradient of the solution in a quadratic way. The two problems are strictly related from the point of view of the a priori estimates we can obtain on their solutions. We point out that no boundedness is assumed on the data of the problems. This implies that the methods involving sub/super-solutions do not apply, and we have to use some convenient test-function to prove the a priori estimates

Pasta consumption and connected dietary habits: Associations with glucose control, adiposity measures, and cardiovascular risk factors in people with type 2 diabetes—TOSCA.IT study

Background: Pasta is a refined carbohydrate with a low glycemic index. Whether pasta shares the metabolic advantages of other low glycemic index foods has not really been investigated. The aim of this study is to document, in people with type-2 diabetes, the consumption of pasta, the connected dietary habits, and the association with glucose control, measures of adiposity, and major cardiovascular risk factors. Methods: We studied 2562 participants. The dietary habits were assessed with the European Prospective Investigation into Cancer and Nutrition (EPIC) questionnaire. Sex-specific quartiles of pasta consumption were created in order to explore the study aims. Results: A higher pasta consumption was associated with a lower intake of proteins, total and saturated fat, cholesterol, added sugar, and fiber. Glucose control, body mass index, prevalence of obesity, and visceral obesity were not significantly different across the quartiles of pasta intake. No relation was found with LDL cholesterol and triglycerides, but there was an inverse relation with HDL-cholesterol. Systolic blood pressure increased with pasta consumption; but this relation was not confirmed after correction for confounders. Conclusions: In people with type-2 diabetes, the consumption of pasta, within the limits recommended for total carbohydrates intake, is not associated with worsening of glucose control, measures of adiposity, and major cardiovascular risk factors

A low escape fraction of ionizing photons of L>L* Lyman break galaxies at z=3.3

We present an upper limit for the relative escape fraction (f_{esc}^{rel}) of ionizing radiation at z~3.3 using a sample of 11 Lyman Break Galaxies (LBGs) with deep imaging in the U band obtained with the Large Binocular Camera, mounted on the prime focus of the Large Binocular Telescope. We selected 11 LBGs with secure redshift in the range 3.27<z<3.35, from 3 independent fields. We stacked the images of our sources in the R and U band, which correspond to an effective rest-frame wavelength of 1500\AA and 900\AA respectively, obtaining a limit in the U band image of >=30.7(AB)mag at 1 sigma. We derive a 1 sigma upper limit of f_{esc}^{rel}~5%, which is one of the lowest values found in the literature so far at z~3.3. Assuming that the upper limit for the escape fraction that we derived from our sample holds for all galaxies at this redshift, the hydrogen ionization rate that we obtain (Gamma_{-12}<0.3 s^{-1}) is not enough to keep the IGM ionized and a substantial contribution to the UV background by faint AGNs is required. Since our sample is clearly still limited in size, larger z~3 LBG samples, at similar or even greater depths are necessary to confirm these results on a more firm statistical basis.Comment: 15 pages, 2 figures, 1 table, accepted for publication in Ap

Monge Distance between Quantum States

We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q--functions). This quantity fulfills the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states.Comment: 9 pages in LaTex - RevTex + 2 figures in ps. submitted to Phys. Rev.

The intergalactic medium thermal history at redshift z=1.7--3.2 from the Lyman alpha forest: a comparison of measurements using wavelets and the flux distribution

We investigate the thermal history of the intergalactic medium (IGM) in the redshift interval z=1.7--3.2 by studying the small-scale fluctuations in the Lyman alpha forest transmitted flux. We apply a wavelet filtering technique to eighteen high resolution quasar spectra obtained with the Ultraviolet and Visual Echelle Spectrograph (UVES), and compare these data to synthetic spectra drawn from a suite of hydrodynamical simulations in which the IGM thermal state and cosmological parameters are varied. From the wavelet analysis we obtain estimates of the IGM thermal state that are in good agreement with other recent, independent wavelet-based measurements. We also perform a reanalysis of the same data set using the Lyman alpha forest flux probability distribution function (PDF), which has previously been used to measure the IGM temperature-density relation. This provides an important consistency test for measurements of the IGM thermal state, as it enables a direct comparison of the constraints obtained using these two different methodologies. We find the constraints obtained from wavelets and the flux PDF are formally consistent with each other, although in agreement with previous studies, the flux PDF constraints favour an isothermal or inverted IGM temperature-density relation. We also perform a joint analysis by combining our wavelet and flux PDF measurements, constraining the IGM thermal state at z=2.1 to have a temperature at mean density of T0/[10^3 K]=17.3 +/- 1.9 and a power-law temperature-density relation exponent gamma=1.1 +/- 0.1 (1 sigma). Our results are consistent with previous observations that indicate there may be additional sources of heating in the IGM at z<4.Comment: 15 pages, 14 figures, matches version accepted for publication on MNRA

The “Personal Health Budget” intervention model in early psychosis: Preliminary findings from the Parma experience

Objectives Personal Health Budget (PHB) has recently been provided to people with severe mental illness, reflecting a policy shift towards a personalized mental health care based on individual unmet needs. However, evidence on effectiveness of PHB initiatives is still limited. Aim of this research was to provide preliminary data about the beneficial effects of adding PHB to a multicomponent EIP intervention in patients with First-Episode Psychosis (FEP) along a 2-year follow-up period. Methods Participants (n = 49) were FEP patients, aged 18-50 years, entered the “Parma Early Psychosis” program and completing the Health of Nation Outcome Scale (HoNOS), the Brief Psychiatric Rating Scale (BPRS) and the Global Assessment of Functioning (GAF). Friedman test for repeated measure (with Wilcoxon test as post-hoc procedure) was performed to evaluate the longitudinal stability of functioning and clinical parameters. A linear regression analysis was also carried out. Results A significant effect of time on all HoNOS, BPRS and GAF scores along the 2 years of follow-up was found. Regression analysis results specifically showed a relevant association between a PHB multiaxial intervention and the longitudinal decrease in BPRS “Negative Symptoms” subscores, as well as in HoNOS “Behavioral Problems” and “Social Problems” scores. Conclusions Our results support the general applicability of a PHB approach within an “Early Intervention in Psychosis” program for help-seeking adults with FEP

Prevalence of and risk factors for fatty liver in the general population of Northern Italy: The Bagnacavallo Study

Background: The estimation of the burden of disease attributable to fatty liver requires studies performed in the general population. Methods: The Bagnacavallo Study was performed between October 2005 and March 2009. All the citizens of Bagnacavallo (Ravenna, Italy) aged 30 to 60 years as of January 2005 were eligible. Altered liver enzymes were defined as alanine transaminase &gt; 40 U/l and/or aspartate transaminase &gt; 37 U/l. Results: Four thousand and thirty-three (58%) out of 6920 eligible citizens agreed to participate and 3933 (98%) had complete data. 393 (10%) of the latter had altered liver enzymes and 3540 had not. After exclusion of subjects with HBV or HCV infection, liver ultrasonography was available for 93% of subjects with altered liber enzymes and 52% of those with normal liver enzymes. The prevalence of fatty liver, non-alcoholic fatty liver disease (NAFLD) and alcoholic fatty liver disease (AFLD) was 0.74 (95%CI 0.70 to 0.79) vs. 0.35 (0.33 to 0.37), 0.46 (0.41 to 0.51) vs. 0.22 (0.21 to 0.24) and 0.28 (0.24 to 0.33) vs. 0.13 (0.11 to 0.14) in citizens with than in those without altered liver enzymes. Ethanol intake was not associated and all the components of the metabolic syndrome (MS) were associated with fatty liver. All potential risk factors were associated with a lower odds of normal liver vs. NAFLD while they were unable to discriminate AFLD from NAFLD. Conclusions: Fatty liver as a whole was highly prevalent in Bagnacavallo in 2005/9 and was more common among citizens with altered liver enzymes