On well-separated sets and fast multipole methods

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more liberal than in conventional codes. Such variants offer a particularly elegant implementation with a balanced multipole tree, a feature which might be very favorable on modern computer architectures

On the stability of stochastic jump kinetics

Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs). Working from simple examples we find reasonable and explicit assumptions on the driving coefficients for the SDE representation to make sense. By `reasonable' we mean that stronger assumptions generally do not hold for systems of practical interest. In particular, we argue against the traditional use of global Lipschitz conditions and certain common growth restrictions. By `explicit', finally, we like to highlight the fact that the various constants occurring among our assumptions all can be determined once the model is fixed. We show how basic long time estimates and some limit results for perturbations can be derived in this setting such that these can be contrasted with the corresponding estimates from deterministic dynamics. The main complication is that the natural path-wise representation is generated by a counting measure with an intensity that depends nonlinearly on the state

Mesoscopic Modeling of Random Walk and Reactions in Crowded Media

We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic description into a previously developed internal state diffusive framework. The observables in the mesoscopic model correspond to solutions of macroscopic partial differential equations driven by stochastically varying diffusion fields in space and time. Analytical solutions and numerical experiments illustrate the framework

Stochastic simulation of pattern formation in growing tissue: a multilevel approach

We take up the challenge of designing realistic computational models of large interacting cell populations. The goal is essentially to bring Gillespie's celebrated stochastic methodology to the level of an interacting population of cells. Specifically, we are interested in how the gold standard of single cell computational modeling, here taken to be spatial stochastic reaction-diffusion models, may be efficiently coupled with a similar approach at the cell population level. Concretely, we target a recently proposed set of pathways for pattern formation involving Notch-Delta signaling mechanisms. These involve cell-to-cell communication as mediated both via direct membrane contact sites as well as via cellular protrusions. We explain how to simulate the process in growing tissue using a multilevel approach and we discuss implications for future development of the associated computational methods

Not Even Cold in Her Grave: How Postbereavement Remarried Couples Perceive Family Acceptance

Following the interviews of 24 participants concerning the death of their spouse and subsequent remarriage, a pattern of unsolicited responses concerning perceived acceptance of family emerged. Through grounded theory qualitative analysis, a continuum of acceptance was developed ranging from welcoming acceptance to active disapproval. Themes that influenced the perceived level of acceptance were (a) the length of time between death and courtship; (b) the length of the courtship itself; and (c) the level of family involvement in the courtship. Findings support and enhance current literature on remarital adjustment, suggesting it is critical to not only include children, but also the extended family in which the family resides. Provisional hypotheses and clinical implications are provided to help clinicians navigate these complex family dynamics and potentially increase family support

Fast event-based epidemiological simulations on national scales

We present a computational modeling framework for data-driven simulations and analysis of infectious disease spread in large populations. For the purpose of efficient simulations, we devise a parallel solution algorithm targeting multi-socket shared memory architectures. The model integrates infectious dynamics as continuous-time Markov chains and available data such as animal movements or aging are incorporated as externally defined events. To bring out parallelism and accelerate the computations, we decompose the spatial domain and optimize cross-boundary communication using dependency-aware task scheduling. Using registered livestock data at a high spatio-temporal resolution, we demonstrate that our approach not only is resilient to varying model configurations, but also scales on all physical cores at realistic work loads. Finally, we show that these very features enable the solution of inverse problems on national scales.Comment: 27 pages, 5 figure

Machine learning for ultrafast X-ray diffraction patterns on large-scale GPU clusters

The classical method of determining the atomic structure of complex molecules by analyzing diffraction patterns is currently undergoing drastic developments. Modern techniques for producing extremely bright and coherent X-ray lasers allow a beam of streaming particles to be intercepted and hit by an ultrashort high energy X-ray beam. Through machine learning methods the data thus collected can be transformed into a three-dimensional volumetric intensity map of the particle itself. The computational complexity associated with this problem is very high such that clusters of data parallel accelerators are required. We have implemented a distributed and highly efficient algorithm for inversion of large collections of diffraction patterns targeting clusters of hundreds of GPUs. With the expected enormous amount of diffraction data to be produced in the foreseeable future, this is the required scale to approach real time processing of data at the beam site. Using both real and synthetic data we look at the scaling properties of the application and discuss the overall computational viability of this exciting and novel imaging technique

SimInf: An R package for Data-driven Stochastic Disease Spread Simulations

We present the R package SimInf which provides an efficient and very flexible framework to conduct data-driven epidemiological modeling in realistic large scale disease spread simulations. The framework integrates infection dynamics in subpopulations as continuous-time Markov chains using the Gillespie stochastic simulation algorithm and incorporates available data such as births, deaths and movements as scheduled events at predefined time-points. Using C code for the numerical solvers and OpenMP to divide work over multiple processors ensures high performance when simulating a sample outcome. One of our design goal was to make SimInf extendable and enable usage of the numerical solvers from other R extension packages in order to facilitate complex epidemiological research. In this paper, we provide a technical description of the framework and demonstrate its use on some basic examples. We also discuss how to specify and extend the framework with user-defined models.Comment: The manual has been updated to the latest version of SimInf (v6.0.0). 41 pages, 16 figure