Entropy-expansiveness for partially hyperbolic diffeomorphisms

We show that diffeomorphisms with a dominated splitting of the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states.Comment: 15 pages, 1 figur

Statistical properties of Lorenz like flows, recent developments and perspectives

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statisitcal behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated to the existence of physical measures: \emph{in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure}. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial conditions, physical measure, singular-hyperbolicity, expansiveness, robust attractor, robust chaotic flow, positive Lyapunov exponent, large deviations, hitting and recurrence times. Minor typos corrected and precise acknowledgments of financial support added. To appear in Int J of Bif and Chaos in App Sciences and Engineerin

Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

Thermodynamic formalism for contracting Lorenz flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ for the contracting Lorenz flow and for $t$ in an interval containing $[0,1]$. We also analyse the Lyapunov spectrum of the flow in terms of the pressure

Genetic loci linked to Type 1 Diabetes and Multiple Sclerosis families in Sardinia

<p>Abstract</p> <p>Background</p> <p>The Mediterranean island of Sardinia has a strikingly high incidence of the autoimmune disorders Type 1 Diabetes (T1D) and Multiple Sclerosis (MS). Furthermore, the two diseases tend to be co-inherited in the same individuals and in the same families. These observations suggest that some unknown autoimmunity variant with relevant effect size could be fairly common in this founder population and could be detected using linkage analysis.</p> <p>Methods</p> <p>To search for T1D and MS loci as well as any that predispose to both diseases, we performed a whole genome linkage scan, sequentially genotyping 593 microsatellite marker loci in 954 individuals distributed in 175 Sardinian families. In total, 413 patients were studied; 285 with T1D, 116 with MS and 12 with both disorders. Model-free linkage analysis was performed on the genotyped samples using the Kong and Cox logarithm of odds (LOD) score statistic.</p> <p>Results</p> <p>In T1D, aside from the HLA locus, we found four regions showing a lod-score ≥1; 1p31.1, 6q26, 10q21.2 and 22q11.22. In MS we found three regions showing a lod-score ≥1; 1q42.2, 18p11.21 and 20p12.3. In the combined T1D-MS scan for shared autoimmunity loci, four regions showed a LOD >1, including 6q26, 10q21.2, 20p12.3 and 22q11.22. When we typed more markers in these intervals we obtained suggestive evidence of linkage in the T1D scan at 10q21.2 (LOD = 2.1), in the MS scan at 1q42.2 (LOD = 2.5) and at 18p11.22 (LOD = 2.6). When all T1D and MS families were analysed jointly we obtained suggestive evidence in two regions: at 10q21.1 (LOD score = 2.3) and at 20p12.3 (LOD score = 2.5).</p> <p>Conclusion</p> <p>This suggestive evidence of linkage with T1D, MS and both diseases indicates critical chromosome intervals to be followed up in downstream association studies.</p

Linking Chronic Infection and Autoimmune Diseases: Mycobacterium avium Subspecies paratuberculosis, SLC11A1 Polymorphisms and Type-1 Diabetes Mellitus

(MAP) has been reported to be a possible trigger in the development of T1DM. gene (274C/T) associated to type 1 diabetic patients and not to controls. The presence of MAP DNA was also significantly associated with T1DM patients and not with controls. alter the processing or presentation of MAP antigens triggering thereby an autoimmune response in T1DM patients

Chronic Helminth Infections Protect Against Allergic Diseases by Active Regulatory Processes

Developed countries are suffering from an epidemic rise in immunologic disorders, such as allergy-related diseases and certain autoimmunities. Several studies have demonstrated a negative association between helminth infections and inflammatory diseases (eg, allergy), providing a strong case for the involvement of helminth infections in this respect. However, some studies point in the opposite direction. The discrepancy may be explained by differences in frequency, dose, time, and type of helminth. In this review, new studies are discussed that may support the concept that chronic helminth infections in particular—but not acute infections—are associated with the expression of regulatory networks necessary for downmodulating allergic immune responses to harmless antigens. Furthermore, different components of regulatory networks are highlighted, such as the role of regulatory T and B cells, modulation of dendritic cells, early innate signals from structural cells (eg, epithelial cells), and their individual contributions to protection against allergic diseases. It is of great interest to define and characterize specific helminth molecules that have profound immunomodulatory capacities as targets for therapeutic application in the treatment or prophylaxis of allergic manifestations

Measurement of the t-channel single top quark production cross section in pp collisions at √s =7 TeV

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