A Note on Commuting Diffeomorphisms on Surfaces

Let S be a closed surface with nonzero Euler characteristic. We prove the existence of an open neighborhood V of the identity map of S in the C^1-topology with the following property: if G is an abelian subgroup of Diff^1(S) generated by any family of elements in V then the elements of G have common fixed points. This result generalizes a similar result due to Bonatti and announced in his paper "Diffeomorphismes commutants des surfaces et stabilite des fibrations en tores".Comment: 16 page

The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

HiTrust: building cross-organizational trust relationship based on a hybrid negotiation tree

Small-world phenomena have been observed in existing peer-to-peer (P2P) networks which has proved useful in the design of P2P file-sharing systems. Most studies of constructing small world behaviours on P2P are based on the concept of clustering peer nodes into groups, communities, or clusters. However, managing additional multilayer topology increases maintenance overhead, especially in highly dynamic environments. In this paper, we present Social-like P2P systems (Social-P2Ps) for object discovery by self-managing P2P topology with human tactics in social networks. In Social-P2Ps, queries are routed intelligently even with limited cached knowledge and node connections. Unlike community-based P2P file-sharing systems, we do not intend to create and maintain peer groups or communities consciously. In contrast, each node connects to other peer nodes with the same interests spontaneously by the result of daily searches

Persistence of Hepatitis C RNA in Liver Allografts Is Associated with Histologic Progression Independent of Serologic Viral Clearance

Background. Hepatitis C virus (HCV) nondetectability in the liver may predict a sustained viral response (SVR) in patients with an end of treatment response. HCV RNA can be detected in liver tissue by in situ hybridization (ISH). Aim. To determine if HCV nondetectability in liver allografts by ISH can predict SVR in patients who cleared virus serologically on treatment. Methods. Twenty five patients with undetectable serum HCV on Interferon/Ribavirin therapy for HCV recurrence post liver transplant (LT) were studied. All had biopsies at 4 months post LT (baseline) and follow up with HCV ISH analysis performed. Results. 10 were ISH positive (group 1); 15 were ISH negative (group 2). Groups 1 and 2 had similar patient, donor, and viral characteristics at LT, as well as treatment duration at the time of the ISH assayed liver biopsy (13 ± 16 versus 10 ± 4 months P = .24). However, group 1 had longer total treatment duration (24 ± 10 versus 14 ± 5 months, P = .001). Eight (80%) group 1 and 9 (60%) group 2 patients achieved SVR. Mean grade and stage (modified Ishak score) were similar at 4 months, however, group 1 had higher grade (3 ± 1.7 versus 1.6 ± 1.3, P = .039) and stage (1.4 ± 1.4 versus 0.5 ± 0.6, P = .084) on the ISH assayed biopsy, after similar post LT intervals (23 ± 10 versus 24 ± 12 months, P = .91). Conclusion. Allograft HCV ISH nondetectability does not predict SVR in treatment responsive HCV recurrence, but is associated with less severe histologic disease

Ralstonia pickettii—innocent bystander or a potential threat?

ABSTRACTRalstonia pickettii can be isolated from water, soil and plants, and can also form part of the commensal flora of the oral cavity and the upper respiratory tract of healthy individuals. R. pickettii is an infrequent pathogen, but can cause infections, mainly of the respiratory tract, in immunocompromised and cystic fibrosis patients. It can be isolated from a variety of clinical specimens, including sputum, blood, wound infections, urine, ear and nose swabs, and cerebrospinal fluid. Resistance can occur to ciprofloxacin, trimethoprim–sulphamethoxazole, piperacillin–tazobactam, imipenem–cilastatin and ceftazidime. Early detection of R. pickettii allows prompt appropriate antimicrobial therapy with a favourable outcome, but removal of infected indwelling devices is mandatory

Fast-slow partially hyperbolic systems versus Freidlin-Wentzell random systems

We consider a simple class of fast-slow partially hyperbolic dynamical systems and show that the (properly rescaled) behaviour of the slow variable is very close to a Friedlin--Wentzell type random system for times that are rather long, but much shorter than the metastability scale. Also, we show the possibility of a "sink" with all the Lyapunov exponents positive, a phenomenon that turns out to be related to the lack of absolutely continuity of the central foliation.Comment: To appear in Journal of Statistical Physic

A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations

The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations $\dot y(t)=g(y(t))$ on $\mathbb{R}^d$ and those of the parabolic equations $\dot u=\Delta u +f(x,u,\nabla u)$ on a bounded domain $\Omega$. We give details on the similarities of these dynamics in the cases $d=1$, $d=2$ and $d\geq 3$ and in the corresponding cases $\Omega=(0,1)$, $\Omega=\mathbb{T}^1$ and dim($\Omega$)$\geq 2$ respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations

Words, rules, and mechanisms of language acquisition

We review recent artificial language learning studies, especially those following Endress and Bonatti (2007), suggesting that humans can deploy a variety of learning mechanisms to acquire artificial languages. Several experiments provide evidence for multiple learning mechanisms that can be deployed in fluent speech: one mechanism encodes the positions of syllables within words and can be used to extract generalization, while the other registers co-occurrence statistics of syllables and can be used to break a continuum into its components. We review dissociations between these mechanisms and their potential role in language acquisition. We then turn to recent criticisms of the multiple mechanisms hypothesis and show that they are inconsistent with the available data. Our results suggest that artificial and natural language learning is best understood by dissecting the underlying specialized learning abilities, and that these data provide a rare opportunity to link important language phenomena to basic psychological mechanisms

On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$