nlchains: A fast and accurate time integration of 1-D nonlinear chains on GPUs

We present nlchains, a software for simulating ensembles of one-dimensional Hamiltonian systems with nearest neighbor interactions. The implemented models are the α-β Fermi–Pasta–Ulam–Tsingou model, the discrete nonlinear Klein–Gordon model with equal or site-specific masses, the Toda lattice and the discrete nonlinear Schrödinger equation. The integration algorithm in all cases is a symplectic sixth order integrator, hence very accurate and suited for long time simulations. The implementation is focused on performance, and the software runs on graphical processing unit hardware (CUDA). We show some illustrative simulations, we estimate the runtime performance and the effective scaling of the cumulative error during integration. Finally, we give some basic pointers to extend the software to specific needs. Keywords: FPU, Nonlinear chain, GPU, CUD

On Measure Quantifiers in First-Order Arithmetic

We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all possible interpretations of the quantified variable. We show that first-order arithmetic with measure quantifiers is capable of formalizing simple results from probability theory and, most importantly, of representing every recursive random function. Moreover, we introduce a realizability interpretation of this logic in which programs have access to an oracle from the Cantor space

On Counting Propositional Logic and Wagner's Hierarchy

We introduce and study counting propositional logic, an extension of propositional logic with counting quantifiers. This new kind of quantification makes it possible to express that the argument formula is true in a certain portion of all possible interpretations. We show that this logic, beyond admitting a satisfactory proof-theoretical treatment, can be related to computational complexity: the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy

The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

Strain-induced magma degassing: insights from simple-shear experiments on bubble bearing melts

International audienceExperiments have been performed to determine the effect of deformation on degassing of bubble-bearing melts. Cylindrical specimens of phonolitic composition, initial water content of 1.5 wt.% and 2 vol.% bubbles, have been deformed in simple-shear (torsional configuration) in an internally heated Paterson-type pressure vessel at temperatures of 798-848 K, 100-180 MPa confining pressure and different final strains. Micro-structural analyses of the samples before and after deformation have been performed in two and three dimensions using optical microscopy, a nanotomography machine and synchrotron tomography. The water content of the glasses before and after deformation has been measured using Fourier Transform Infrared Spectroscopy (FTIR). In samples strained up to a total of γ ∼ 2 the bubbles record accurately the total strain, whereas at higher strains (γ ∼ 10) the bubbles become very flattened and elongate in the direction of shear. The residual water content of the glasses remains constant up to a strain of γ ∼ 2 and then decreases to about 0.2 wt.% at γ ∼ 10. Results show that strain enhances bubble coalescence and degassing even at low bubble volume-fractions. Noticeably, deformation produced a strongly water under-saturated melt. This suggests that degassing may occur at great depths in the volcanic conduit and may force the magma to become super-cooled early during ascent to the Earth's surface potentially contributing to the genesis of obsidian

Patient satisfaction and food waste in obstetrics and gynaecology wards

Introduction: Patient satisfaction is an indicator of healthcare quality, and expectation is an important determinant. A component of patient satisfaction is the quality of foodservice. An indicator of this quality is the food wasted by hospitalised patients. In the present study, we investigated patient satisfaction regarding food and foodservice, the expectation on food quality and the amount of food wasted in two obstetrics and gynaecology wards in Northern and Southern Italy. Patients and Methods: A questionnaire, including sociodemographic data, rate of food waste, expectations of food quality and characteristics of food and foodservice, was admini-strated to 550 inpatients in obstetrics and gynaecology wards (275 for each hospital). Univariate analysis was performed to describe the results, and multivariate analysis was carried out to control for sociodemographic data. Results: Northern patients were more satisfied with the quality of food (54.2% vs 36.0%) and foodservice (54.5% vs 38.2%) than southern patients. Northern patients had more positive expectations about the quality of food (69.5% vs 31.6%), whereas southern patients stated that they had no expectations. Southern patients gave more importance to mealtime (72.7% vs 26.2%), and many of them brought food from home to the hospital (30.2% vs 2.2%) through relatives who came to visit them. Southern patients discarded about 41.7% of food served, whereas northern patients discarded only about 15.3%. Discussion: Food waste is a worldwide problem due to its economic, social and environmental effects. Especially in hospitals, food waste could have a negative impact on the overall patient satisfaction

Nonparametric Information Geometry

The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the research is focused on parametric statistical models. In series of papers by author and coworkers a particular version of the nonparametric case has been discussed. It consists of a minimalistic structure modeled according the theory of exponential families: given a reference density other densities are represented by the centered log likelihood which is an element of an Orlicz space. This mappings give a system of charts of a Banach manifold. It has been observed that, while the construction is natural, the practical applicability is limited by the technical difficulty to deal with such a class of Banach spaces. It has been suggested recently to replace the exponential function with other functions with similar behavior but polynomial growth at infinity in order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give first a review of our theory with special emphasis on the specific issues of the infinite dimensional setting. In a second part we discuss two specific topics, differential equations and the metric connection. The position of this line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30 2013 Pari