The combinatorics of interval-vector polytopes

An \emph{interval vector} is a $(0,1)$-vector in $\mathbb{R}^n$ for which all the 1's appear consecutively, and an \emph{interval-vector polytope} is the convex hull of a set of interval vectors in $\mathbb{R}^n$. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers given by the Pascal 3-triangle.Comment: 10 pages, 3 figure

Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM

© EDP Sciences, SMAI 2011This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in Rn (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := Rn\￣Ω. The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD) given in terms of boundary integral operators. The resulting variational formulation becomes a variational inequality with a linear operator. Then we treat the corresponding numerical scheme and discuss an approximation of the NtD mapping with an appropriate discretization of the inverse Poincar´e-Steklov operator. In particular, assuming some abstract approximation properties and a discrete inf-sup condition, we show unique solvability of the discrete scheme and obtain the corresponding a-priori error estimate. Next, we prove that these assumptions are satisfied with Raviart- Thomas elements and piecewise constants in Ω, and continuous piecewise linear functions on Γ. We suggest a solver based on a modified Uzawa algorithm and show convergence. Finally we present some numerical results illustrating our theory

Hypocoercivity properties of adaptive Langevin dynamics

International audienceAdaptive Langevin dynamics is a method for sampling the Boltzmann-Gibbs distribution at prescribed temperature in cases where the potential gradient is subject to stochastic perturbation of unknown magnitude. The method replaces the friction in underdamped Langevin dynamics with a dynamical variable, updated according to a negative feedback loop control law as in the Nose-Hoover thermostat. Using a hypocoercivity analysis we show that the law of Adaptive Langevin dynamics converges exponentially rapidly to the stationary distribution, with a rate that can be quantified in terms of the key parameters of the dynamics. This allows us in particular to obtain a central limit theorem with respect to the time averages computed along a stochastic path. Our theoretical findings are illustrated by numerical simulations involving classification of the MNIST data set of handwritten digits using Bayesian logistic regression

Local suppression of the hidden order phase by impurities in URu2Si2

We consider the effects of impurities on the enigmatic hidden order (HO) state of the heavy-fermion material URu2Si2. In particular, we focus on local effects of Rh impurities as a tool to probe the suppression of the HO state. To study local properties we introduce a lattice free energy, where the time invariant HO order parameter "psi" and local antiferromagnetic (AFM) order parameter M are competing orders. Near each Rh atom the HO order parameter is suppressed, creating a hole in which local AFM order emerges as a result of competition. These local holes are created in the fabric of the HO state like in a Swiss cheese and "filled" with droplets of AFM order. We compare our analysis with recent NMR results on URu2Si2 doped with Rh and find good agreement with the data.Comment: 8 pages, 6 figure

Exploring the Motives of Citizen Reporting Engagement: Self-Concern and Other-Orientation

In smart city contexts, voluntary citizen reporting can be a particularly valuable source of information for local authorities. A key question in this regard is what motivates citizens to contribute their data. Drawing on motivation research in social psychology, the paper examines the question of whether self-concern or other-orientation is a stronger driver of citizen reporting engagement. To test their hypotheses, the authors rely on a sample of users from the mobile application “Zurich as good as new” in Switzerland, which enables citizens to report damages in and other issues with the city’s infrastructure. Data was collected from two different sources: motivation was assessed in an online user survey (n = 650), whereas citizen reporting engagement was measured by the number of reports per user from real platform-use data. The analysis was carried out using negative binomial regression. The findings suggest that both self-concern and other-orientation are significant drivers of citizen reporting engagement, although the effect of self-concern appears to be stronger in comparison. As such, this study contributes to a better understanding of what motivates citizens to participate in citizen reporting platforms, which are a cornerstone application in many smart cities

Reparallelization and Migration of OpenMP Programs

Typical computational grid users target only a single cluster and have to estimate the runtime of their jobs. Job schedulers prefer short-running jobs to maintain a high system utilization. If the user underestimates the runtime, premature termination causes computation loss; overesti-mation is penalized by long queue times. As a solution, we present an automatic reparallelization and migration of OpenMP applications. A reparallelization is dynamically computed for an OpenMP work distribution when the num-ber of CPUs changes. The application can be migrated between clusters when an allocated time slice is exceeded. Migration is based on a coordinated, heterogeneous check-pointing algorithm. Both reparallelization and migration enable the user to freely use computing time at more than a single point of the grid. Our demo applications successfully adapt to the changed CPU setting and smoothly migrate between, for example, clusters in Erlangen, Germany, and Amsterdam, the Netherlands, that use different processors. Benchmarks show that reparallelization and migration im-pose average overheads of about 4 % and 2%. 1