Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle

It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of {\fR}^2. A renormalization approach has been used in a "hard" computer-assisted proof of existence of an area-preserving map with orbits of all binary periods in Eckmann et al (1984). As it is the case with all non-trivial universality problems in non-dissipative systems in dimensions more than one, no analytic proof of this period doubling universality exists to date. In this paper we attempt to reduce computer assistance in the argument, and present a mild computer aided proof of the analyticity and compactness of the renormalization operator in a neighborhood of a renormalization fixed point: that is a proof that does not use generalizations of interval arithmetics to functional spaces - but rather relies on interval arithmetics on real numbers only to estimate otherwise explicit expressions. The proof relies on several instance of the Contraction Mapping Principle, which is, again, verified via mild computer assistance

Lyapunov Mode Dynamics in Hard-Disk Systems

The tangent dynamics of the Lyapunov modes and their dynamics as generated numerically - {\it the numerical dynamics} - is considered. We present a new phenomenological description of the numerical dynamical structure that accurately reproduces the experimental data for the quasi-one-dimensional hard-disk system, and shows that the Lyapunov mode numerical dynamics is linear and separate from the rest of the tangent space. Moreover, we propose a new, detailed structure for the Lyapunov mode tangent dynamics, which implies that the Lyapunov modes have well-defined (in)stability in either direction of time. We test this tangent dynamics and its derivative properties numerically with partial success. The phenomenological description involves a time-modal linear combination of all other Lyapunov modes on the same polarization branch and our proposed Lyapunov mode tangent dynamics is based upon the form of the tangent dynamics for the zero modes

Decay of Correlations in a Topological Glass

In this paper we continue the study of a topological glassy system. The state space of the model is given by all triangulations of a sphere with $N$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with other numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal between two adjacent triangles, with a temperature dependent probability. We consider the system at very low temperatures. We concentrate on several new aspects of this model: Starting from a detailed description of the stationary state, we conclude that pairs of defects (nodes with the "wrong" degree) move with very high mobility along 1-dimensional paths. As they wander around, they encounter single defects, which they then move "sideways" with a geometrically defined probability. This induces a diffusive motion of the single defects. If they meet, they annihilate, lowering the energy of the system. We both estimate the decay of energy to equilibrium, as well as the correlations. In particular, we find a decay like $t^{-0.4}$

Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems

We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model. It was shown in \cite{eckmann-young} that when the cells are weakly coupled, to a good approximation, the jump rates of particles and the energy-exchange rates from cell to cell follow linear profiles. Here, we refine that study by analyzing higher-order effects which are induced by the presence of external gradients for situations in which memory effects, typical of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a set of balance equations for the particle number and energy in terms of the reflection probabilities of the cell and solve it phenomenologically. Using this approximate theory we explain how these asymmetries affect various aspects of heat and particle transport in systems of the general type described above and obtain in the infinite volume limit the deviation from the theory in \cite{eckmann-young} to first-order. We verify our assumptions with extensive numerical simulations.Comment: Several change

POOL File Catalog, Collection and Metadata Components

The POOL project is the common persistency framework for the LHC experiments to store petabytes of experiment data and metadata in a distributed and grid enabled way. POOL is a hybrid event store consisting of a data streaming layer and a relational layer. This paper describes the design of file catalog, collection and metadata components which are not part of the data streaming layer of POOL and outlines how POOL aims to provide transparent and efficient data access for a wide range of environments and use cases - ranging from a large production site down to a single disconnected laptops. The file catalog is the central POOL component translating logical data references to physical data files in a grid environment. POOL collections with their associated metadata provide an abstract way of accessing experiment data via their logical grouping into sets of related data objects.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 4 pages, 1 eps figure, PSN MOKT00

Primary Numbers Database for ATLAS Detector Description Parameters

We present the design and the status of the database for detector description parameters in ATLAS experiment. The ATLAS Primary Numbers are the parameters defining the detector geometry and digitization in simulations, as well as certain reconstruction parameters. Since the detailed ATLAS detector description needs more than 10,000 such parameters, a preferred solution is to have a single verified source for all these data. The database stores the data dictionary for each parameter collection object, providing schema evolution support for object-based retrieval of parameters. The same Primary Numbers are served to many different clients accessing the database: the ATLAS software framework Athena, the Geant3 heritage framework Atlsim, the Geant4 developers framework FADS/Goofy, the generator of XML output for detector description, and several end-user clients for interactive data navigation, including web-based browsers and ROOT. The choice of the MySQL database product for the implementation provides additional benefits: the Primary Numbers database can be used on the developers laptop when disconnected (using the MySQL embedded server technology), with data being updated when the laptop is connected (using the MySQL database replication).Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 6 pages, 5 figures, pdf. PSN MOKT00

Influence of real-world characteristics on outcomes for patients with methicillin-resistant Staphylococcal skin and soft tissue infections:a multi-country medical chart review in Europe

BACKGROUND: Patient-related (demographic/disease) and treatment-related (drug/clinician/hospital) characteristics were evaluated as potential predictors of healthcare resource use and opportunities for early switch (ES) from intravenous (IV)-to-oral methicillin-resistant Staphylococcus aureus (MRSA)-active antibiotic therapy and early hospital discharge (ED). METHODS: This retrospective observational medical chart study analyzed patients (across 12 European countries) with microbiologically confirmed MRSA complicated skin and soft tissue infections (cSSTI), ≥3 days of IV anti-MRSA antibiotics during hospitalization (July 1, 2010-June 30, 2011), and discharged alive by July 31, 2011. Logistic/linear regression models evaluated characteristics potentially associated with actual resource use (length of IV therapy, length of hospital stay [LOS], IV-to-oral antibiotic switch), and ES and ED (using literature-based and expert-verified criteria) outcomes. RESULTS: 1542 patients (mean ± SD age 60.8 ± 16.5 years; 61.5% males) were assessed with 81.0% hospitalized for MRSA cSSTI as the primary reason. Several patient demographic, infection, complication, treatment, and hospital characteristics were predictive of length of IV therapy, LOS, IV-to-oral antibiotic switch, or ES and ED opportunities. Outcomes and ES and ED opportunities varied across countries. Length of IV therapy and LOS (r = 0.66, p < 0.0001) and eligibilities for ES and ED (r = 0.44, p < 0.0001) showed relatively strong correlations. IV-to-oral antibiotic switch patients had significantly shorter length of IV therapy (−5.19 days, p < 0.001) and non-significantly shorter LOS (−1.86 days, p > 0.05). Certain patient and treatment characteristics were associated with increased odds of ES (healthcare-associated/ hospital-acquired infection) and ED (patient living arrangements, healthcare-associated/ hospital-acquired infection, initiating MRSA-active treatment 1–2 days post cSSTI index date, existing ED protocol), while other factors decreased the odds of ES (no documented MRSA culture, ≥4 days from admission to cSSTI index date, IV-to-oral switch, IV line infection) and ED (dementia, no documented MRSA culture, initiating MRSA-active treatment ≥3 days post cSSTI index date, existing ES protocol). CONCLUSIONS: Practice patterns and opportunity for further ES and ED were affected by several infection, treatment, hospital, and geographical characteristics, which should be considered in identifying ES and ED opportunities and designing interventions for MRSA cSSTI to reduce IV days and LOS while maintaining the quality of care. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/1471-2334-14-476) contains supplementary material, which is available to authorized users

A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system

We study the stationary nonequilibrium states of N point particles moving under the influence of an electric field E among fixed obstacles (discs) in a two dimensional torus. The total kinetic energy of the system is kept constant through a Gaussian thermostat which produces a velocity dependent mean field interaction between the particles. The current and the particle distribution functions are obtained numerically and compared for small E with analytic solutions of a Boltzmann type equation obtained by treating the collisions with the obstacles as random independent scatterings. The agreement is surprisingly good for both small and large N. The latter system in turn agrees with a self consistent one particle evolution expected to hold in the limit of N going to infinity.Comment: 14 pages, 9 figure