Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L=1024.Comment: 32 pages, 8 eps figures. Corrected Eq. (36), which is wrong in the published pape

The self distributing virtual machine (SDVM): making computer clusters adaptive

The Self Distributing Virtual Machine (SDVM) is a middleware concept to form a parallel computing machine consisting of a any set of processing units, such as functional units in a processor or FPGA, processing units in a multiprocessor chip, or computers in a computer cluster. Its structure and functionality is biologically inspired aiming towards forming a combined workforce of independent units (”sites”), each acting on the same set of simple rules. The SDVM supports growing and shrinking the cluster at runtime as well as heterogeneous clusters. It uses the work-stealing principle to dynamically distribute the workload among all sites. The SDVM’s energy management targets the health of all sites by adjusting their power states according to workload and temperature. Dynamic reassignment of the current workload facilitates a new energy policy which focuses on increasing the reliability of each site. This paper presents the structure and the functionality of the SDVM.1st IFIP International Conference on Biologically Inspired Cooperative Computing - Mechatronics and Computer ClustersRed de Universidades con Carreras en Informática (RedUNCI

Compressive Wave Computation

This paper considers large-scale simulations of wave propagation phenomena. We argue that it is possible to accurately compute a wavefield by decomposing it onto a largely incomplete set of eigenfunctions of the Helmholtz operator, chosen at random, and that this provides a natural way of parallelizing wave simulations for memory-intensive applications. This paper shows that L1-Helmholtz recovery makes sense for wave computation, and identifies a regime in which it is provably effective: the one-dimensional wave equation with coefficients of small bounded variation. Under suitable assumptions we show that the number of eigenfunctions needed to evolve a sparse wavefield defined on N points, accurately with very high probability, is bounded by C log(N) log(log(N)), where C is related to the desired accuracy and can be made to grow at a much slower rate than N when the solution is sparse. The PDE estimates that underlie this result are new to the authors' knowledge and may be of independent mathematical interest; they include an L1 estimate for the wave equation, an estimate of extension of eigenfunctions, and a bound for eigenvalue gaps in Sturm-Liouville problems. Numerical examples are presented in one spatial dimension and show that as few as 10 percents of all eigenfunctions can suffice for accurate results. Finally, we argue that the compressive viewpoint suggests a competitive parallel algorithm for an adjoint-state inversion method in reflection seismology.Comment: 45 pages, 4 figure

Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator

In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower semicontinuous function $\Phi$, and $B$ is a monotone cocoercive operator. We first consider the extension to this setting of the regularized Newton dynamic with two potentials. Then, we revisit some related dynamical systems, namely the semigroup of contractions generated by $A$, and the continuous gradient projection dynamic. By a Lyapunov analysis, we show the convergence properties of the orbits of these systems. The time discretization of these dynamics gives various forward-backward splitting methods (some new) for solving structured monotone inclusions involving non-potential terms. The convergence of these algorithms is obtained under classical step size limitation. Perspectives are given in the field of numerical splitting methods for optimization, and multi-criteria decision processes.Comment: 25 page

Polarized Scattering in the Vicinty of Galaxies

Some bright cD galaxies in cluster cooling flows have Thomson optical depths exceeding 0.01. A few percent of their luminosity is scattered and appears as diffuse polarized emission. We calculate the scattering process for different geometric combinations of luminosity sources and scattering media. We apply our results to galaxies, with and without active nuclei, immersed in cooling flows. We model observations of NGC 1275 and M87 (without active nuclei) in the presence of sky and galactic background fluxes which hinder the measurement of the scattered light at optical wavelengths. Current instruments are unable to detect the scattered light from such objects. However, when a galaxy has an active nucleus of roughly the same luminosity as the remainder of the galaxy in V, both the total and polarized scattered intensity should observable on large scales (5--30kpc), meaning intensity levels greater than 1% of the background level. For typical AGN and galaxy spectral distributions, the scattering is most easily detected at short (U) wavelengths. We point out that a number of such cases will occur. We show that the radiation pattern from the central nuclear region can be mapped using the scattering. We also show that the scattered light can be used to measure inhomogeneities in the cooling flow.Comment: 29 pages of TEX, 14 figs, CRSR-1046, in ApJ Nov 20, 199

Big-Data-Driven Materials Science and its FAIR Data Infrastructure

This chapter addresses the forth paradigm of materials research -- big-data driven materials science. Its concepts and state-of-the-art are described, and its challenges and chances are discussed. For furthering the field, Open Data and an all-embracing sharing, an efficient data infrastructure, and the rich ecosystem of computer codes used in the community are of critical importance. For shaping this forth paradigm and contributing to the development or discovery of improved and novel materials, data must be what is now called FAIR -- Findable, Accessible, Interoperable and Re-purposable/Re-usable. This sets the stage for advances of methods from artificial intelligence that operate on large data sets to find trends and patterns that cannot be obtained from individual calculations and not even directly from high-throughput studies. Recent progress is reviewed and demonstrated, and the chapter is concluded by a forward-looking perspective, addressing important not yet solved challenges.Comment: submitted to the Handbook of Materials Modeling (eds. S. Yip and W. Andreoni), Springer 2018/201

The self distributing virtual machine (SDVM): making computer clusters adaptive

The Self Distributing Virtual Machine (SDVM) is a middleware concept to form a parallel computing machine consisting of a any set of processing units, such as functional units in a processor or FPGA, processing units in a multiprocessor chip, or computers in a computer cluster. Its structure and functionality is biologically inspired aiming towards forming a combined workforce of independent units (”sites”), each acting on the same set of simple rules. The SDVM supports growing and shrinking the cluster at runtime as well as heterogeneous clusters. It uses the work-stealing principle to dynamically distribute the workload among all sites. The SDVM’s energy management targets the health of all sites by adjusting their power states according to workload and temperature. Dynamic reassignment of the current workload facilitates a new energy policy which focuses on increasing the reliability of each site. This paper presents the structure and the functionality of the SDVM.1st IFIP International Conference on Biologically Inspired Cooperative Computing - Mechatronics and Computer ClustersRed de Universidades con Carreras en Informática (RedUNCI

Wavelet and Multiscale Methods

[no abstract available