A Minimally Intrusive Low-Memory Approach to Resilience for Existing Transient Solvers

We propose a novel, minimally intrusive approach to adding fault tolerance to existing complex scientific simulation codes, used for addressing a broad range of time-dependent problems on the next generation of supercomputers. Exascale systems have the potential to allow much larger, more accurate and scale-resolving simulations of transient processes than can be performed on current petascale systems. However, with a much larger number of components, exascale computers are expected to suffer a node failure every few minutes. Many existing parallel simulation codes are not tolerant of these failures and existing resilience methodologies would necessitate major modifications or redesign of the application. Our approach combines the proposed user-level failure mitigation extensions to the Message-Passing Interface (MPI), with the concepts of message-logging and remote in-memory checkpointing, to demonstrate how to add scalable resilience to transient solvers. Logging MPI communication reduces the storage requirement of static data, such as finite element operators, and allows a spare MPI process to rebuild these data structures independently of other ranks. Remote in-memory checkpointing avoids disk I/O contention on large parallel filesystems. A prototype implementation is applied to Nektar++, a scalable, production-ready transient simulation framework. Forward-path and recovery-path performance of the resilience algorithm is analysed through experiments using the solver for the incompressible Navier-Stokes equations, and strong scaling of the approach is observed

Entanglement Dissipation: Unitary and Non-unitary Processes

Dissipative processes in physics are usually associated with non-unitary actions. However, the important resource of entanglement is not invariant under general unitary transformations, and is thus susceptible to unitary "dissipation". In this note we discuss both unitary and non-unitary dissipative processes, showing that the former is ultimately of value, since reversible, and enables the production of entanglement; while even in the presence of the latter, more conventional non-unitary and non-reversible, process there exist nonetheless invariant entangled states.Comment: 9 pages, 2 figures, Symmetries in Science XV (Bregenz Symposiun 2011

Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial dierential equations

In the strong scaling limit, the performance of conventional spatial domain decomposition techniques for the parallel solution of PDEs saturates. When sub-domains become small, halo-communication and other overheard come to dominate. A potential path beyond this scaling limit is to introduce domain-decomposition in time, with one such popular approach being the Parareal algorithm which has received a lot of attention due to its generality and potential scalability. Low efficiency, particularly on convection dominated problems, has however limited the adoption of the method. In this paper we introduce a new strategy, Communication Aware Adaptive Parareal (CAAP) to overcome some of the challenges. With CAAP, we choose time-subdomains short enough that convergence of the Parareal algorithm is quick, yet long enough that the overheard of communicating time-subdomain interfaces does not induce a new limit to parallel speed-up. Furthermore, we propose an adaptive work scheduling algorithm that overlaps consecutive Parareal cycles and decouples the number of time-subdomains and number of active node-groups in an efficient manner to allow for comparatively high parallel eciency. We demonstrate the viability of CAAP trough the parallel-in-time integration of a hyperbolic system of PDEs in the form of the two-dimensional nonlinear shallow-water wave equation solved using a 3rd order accurate WENO-RK discretization. For the computational cheap approximate operator needed as a preconditioner in the Parareal corrections we use a lower order Roe type discretization. Time-parallel integration of purely hyperbolic type evolution problems is traditionally considered impractical. Trough large-scale numerical experiments we demonstrate that with CAAP, it is possible not only to obtain time-parallel speedup on this class of evolution problems, but also that we may obtain parallel acceleration beyond what is possible using conventional spatial domain-decomposition techniques alone. The approach is widely applicable for parallel-in-time integration over long time domains, regardless of the class of evolution problem

The First Passage Probability of Intracellular Particle Trafficking

The first passage probability (FPP), of trafficked intracellular particles reaching a displacement L, in a given time t or inverse velocity S = t/L, can be calculated robustly from measured particle tracks, and gives a measure of particle movement in which different types of motion, e.g. diffusion, ballistic motion, and transient run-rest motion, can readily be distinguished in a single graph, and compared with mathematical models. The FPP is attractive in that it offers a means of reducing the data in the measured tracks, without making assumptions about the mechanism of motion: for example, it does not employ smoothing, segementation or arbitrary thresholds to discriminate between different types of motion in a particle track. Taking experimental data from tracked endocytic vesicles, and calculating the FPP, we see how three molecular treatments affect the trafficking. We show the FPP can quantify complicated movement which is neither completely random nor completely deterministic, making it highly applicable to trafficked particles in cell biology.Comment: Article: 13 pages, 8 figure

An Adjoint Approach for Stabilizing the Parareal Method

The parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-dissipative problems. We express the method through an iteration matrix and show that the problematic behavior is related to the non-normal structure of the iteration matrix. To enforce monotone convergence we propose an adjoint parareal algorithm, accelerated by the Conjugate Gradient Method. Numerical experiments confirm the stability and suggest directions for further improving the performance

Combining insulin with metformin or an insulin secretagogue in non-obese patients with type 2 diabetes: 12 month, randomised, double blind trial

Objectives To study the effect of insulin treatment in combination with metformin or an insulin secretagogue, repaglinide, on glycaemic regulation in non-obese patients with type 2 diabetes

Thermal entanglement in three-qubit Heisenberg models

We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic $XXZ$ model, and the ferromagnetic $XXZ$ model with anisotropy parameter $\Delta\ge 1$. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the magnetic field can induce entanglement in the antiferromagnetic $XXX$ model, but cannot induce entanglement in the ferromagnetic $XXX$ model.Comment: 9 pages, 6 figures, minor revisions, resubmitted to J. Phys.

Polyautoimmunity in patients with cutaneous lupus erythematosus:A nationwide sex- and age-matched cohort study from Denmark

BACKGROUND: Polyautoimmunity is defined as having 2 or more autoimmune diseases. Little is known about polyautoimmunity in patients with cutaneous lupus erythematosus (CLE).OBJECTIVES: To estimate prevalence and 5-year incidence of non-lupus erythematosus (LE) autoimmune diseases in patients with CLE.METHODS: Patients with CLE were identified In the Danish National Patient Registry and each patient was age- and sex-matched with 10 general population controls. Outcome information on non-LE autoimmune diseases was obtained by register-linkage between Danish National Patient Registry and the National Prescription Register. The risk ratio (RR) for prevalent non-LE autoimmune disease at time of CLE diagnosis was calculated in modified Poisson regression; and hazard ratios (HRs) for incident non-LE autoimmune disease were estimated in Cox regression analyses.RESULTS: Overall, 1674 patients with CLE had a higher prevalence of a non-LE autoimmune disease than the comparators (18.5 vs 7.9%; RR 2.4; 95% CI, 2.1 to 2.6). Correspondingly, the cumulative incidence of a non-LE autoimmune disease during 5 years of follow-up was increased for the patients with CLE: HR 3.5 (95% CI, 3.0 to 4.0).LIMITATIONS: Risk of detection and misclassification bias, mainly pertaining to the CLE group.CONCLUSION: Patients with CLE had higher prevalence and 5-year cumulative incidence of a non-LE autoimmune disease than the general population.</p