| 1. |
- Bauer, Pavol, et al.
(författare)
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Fast event-based epidemiological simulations on national scales
- 2016
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Ingår i: The international journal of high performance computing applications. - : SAGE Publications. - 1094-3420 .- 1741-2846. ; 30, s. 438-453
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Tidskriftsartikel (refereegranskat)abstract
- 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 spatiotemporal resolution, we demonstrate that our approach not only is resilient to varying model configurations but also scales on all physical cores at realistic workloads. Finally, we show that these very features enable the solution of inverse problems on national scales.
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| 2. |
- Engblom, Stefan, et al.
(författare)
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Bayesian epidemiological modeling over high-resolution network data
- 2020
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Ingår i: Epidemics. - : Elsevier BV. - 1755-4365 .- 1878-0067. ; 32
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical epidemiological models have a broad use, including both qualitative and quantitative applications. With the increasing availability of data, large-scale quantitative disease spread models can nowadays be formulated. Such models have a great potential, e.g., in risk assessments in public health. Their main challenge is model parameterization given surveillance data, a problem which often limits their practical usage. We offer a solution to this problem by developing a Bayesian methodology suitable to epidemiological models driven by network data. The greatest difficulty in obtaining a concentrated parameter posterior is the quality of surveillance data; disease measurements are often scarce and carry little information about the parameters. The often overlooked problem of the model's identifiability therefore needs to be addressed, and we do so using a hierarchy of increasingly realistic known truth experiments. Our proposed Bayesian approach performs convincingly across all our synthetic tests. From pathogen measurements of shiga toxin-producing Escherichia coli O157 in Swedish cattle, we are able to produce an accurate statistical model of first-principles confronted with data. Within this model we explore the potential of a Bayesian public health framework by assessing the efficiency of disease detection and -intervention scenarios.
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| 3. |
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| 4. |
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| 5. |
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| 6. |
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| 7. |
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| 8. |
- Widgren, Stefan, et al.
(författare)
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Spatio-temporal modelling of verotoxigenic Escherichia coli O157 in cattle in Sweden: exploring options for control
- 2018
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Ingår i: Veterinary Research. - : Springer Science and Business Media LLC. - 0928-4249 .- 1297-9716. ; 49
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Tidskriftsartikel (refereegranskat)abstract
- A spatial data-driven stochastic model was developed to explore the spread of verotoxigenic Escherichia coli O157 (VTEC O157) by livestock movements and local transmission among neighbouring holdings in the complete Swedish cattle population. Livestock data were incorporated to model the time-varying contact network between holdings and population demographics. Furthermore, meteorological data with the average temperature at the geographical location of each holding was used to incorporate season. The model was fitted against observed data and extensive numerical experiments were conducted to investigate the model's response to control strategies aimed at reducing shedding and susceptibility, as well as interventions informed by network measures. The results showed that including local spread and season improved agreement with prevalence studies. Also, control strategies aimed at reducing the average shedding rate were more efficient in reducing the VTEC O157 prevalence than strategies based on network measures. The methodology presented in this study could provide a basis for developing disease surveillance on regional and national scales, where observed data are combined with readily available high-resolution data in simulations to get an overview of potential disease spread in unobserved regions.
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| 9. |
- Andersson, Emma, et al.
(författare)
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Impact of first parity litter size on sow stayability and lifetime production
- 2015
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- To increase production level increase of number of piglets born per litter has been one of the main breeding goals during the last decades. The negative welfare consequences on piglets being born in a large litter are well known while the welfare impacts on sows that produce large litters are more uncertain. The aim of this study was to investigate the effect of first parity litter size on sow stayability and lifetime production. Sows having a small (<12 piglets total born; SL) or medium (12-14 piglets total born; ML) first parity litter size had significantly (p <0.001) more litters before end of production than sows having a large (>14 piglets total born; LL) first parity litter size. Sows with LL was significant (p<0.001) less likely to have a second litter than sows with SL and ML. Sows with SL and ML had the highest lifetime production of weaned piglets. The results of this study indicate that it is important take first parity litter size into account when assessing sow welfare and profitability in commercial piglet producing herds. Having a SL or ML was found to have a positive effect on sow stayability and lifetime production.
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| 10. |
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| 11. |
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| 12. |
- Andersson, Emma, et al.
(författare)
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Impact of litter size on sow stayability in Swedish commercial piglet producing herds
- 2016
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Ingår i: Acta Veterinaria Scandinavica. - : Springer Science and Business Media LLC. - 0044-605X .- 1751-0147. ; 58
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Tidskriftsartikel (refereegranskat)abstract
- Background: Sows' ability to produce an excessive amount of piglets has shaped modern piglet production and there has been a steady increase in litter size during the last decades. This development has caused some negative side-effects, such as an increase in the proportion of stillborn piglets, a decrease in the proportion of weaned piglets and a larger variation in quality of piglets. Swedish commercial piglet producing herds have, like other countries with high production levels, high piglet mortality and high annual removal rate of gilts and sow. These problems seem to have increased during the same period that litter sizes have increased. Therefore present study aim to investigate whether there is an association between litter sizes and sow stayability. Results: The probability to produce ≥4 litters during a lifetime was significantly lower for sows giving birth to ≤8, 15 and ≥17 piglets in total in their first parity litter compared to sows giving birth to 13 piglets. Except for the group of sows having a small (≤11 piglets born in total) first parity litter size in combination with a medium (12-14 piglets born in total) second parity litter size, all other groups were significantly associated with an impaired ability to stay ≥4 litters compared to sows having a medium both first and second parity litter size. There were differences in removal reason between sows having small, medium or large first parities litter sizes. Conclusions: Associations between litter sizes in low parities and sow stayability were found. Our results indicate that aiming for keeping sows giving birth to a medium-sized litter, with approximately 12-14 piglets born in total may improve sows stayability and decrease the risk of unplanned removal. This should be considered when planning breeding strategy and annual removal in Swedish commercial piglets producing herds.
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| 13. |
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| 14. |
- Arjmand, Doghonay, et al.
(författare)
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Temporal upscaling in micromagnetism via heterogeneous multiscale methods
- 2019
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier BV. - 0377-0427 .- 1879-1778. ; 345, s. 99-113
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Tidskriftsartikel (refereegranskat)abstract
- We consider a multiscale strategy addressing the disparate scales in the Landau–Lifschitz equations in micromagnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic scale we are interested in simulating the dynamics of the magnetisation without fully resolving the microscopic scales.The method follows the framework of heterogeneous multiscale methods and it has two main ingredients: a micro- and a macroscale model. The microscopic model is assumed to be known exactly whereas the macromodel is incomplete as it lacks effective quantities. The two models use different temporal and spatial scales and effective parameter values for the macromodel are computed on the fly, allowing for improved efficiency over traditional one-scale schemes.For the analysis, we consider a single spin under a high frequency field and show that effective quantities can be obtained accurately with step-sizes much larger than the size of the microscopic scales required to resolve the microscopic features. Numerical results both for a single magnetic particle as well as a chain of interacting magnetic particles are given to validate the theory.
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| 15. |
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| 16. |
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| 17. |
- Bauer, Pavol
(författare)
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Parallelism and efficiency in discrete-event simulation
- 2015
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Discrete-event models depict systems where a discrete state is repeatedly altered by instantaneous changes in time, the events of the model. Such models have gained popularity in fields such as Computational Systems Biology or Computational Epidemiology due to the high modeling flexibility and the possibility to easily combine stochastic and deterministic dynamics. However, the system size of modern discrete-event models is growing and/or they need to be simulated at long time periods. Thus, efficient simulation algorithms are required, as well as the possibility to harness the compute potential of modern multicore computers. Due to the sequential design of simulators, parallelization of discrete event simulations is not trivial. This thesis discusses event-based modeling and sensitivity analysis and also examines ways to increase the efficiency of discrete-event simulations and to scale models involving deterministic and stochastic spatial dynamics on a large number of processor cores.
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| 18. |
- Bauer, Pavol
(författare)
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Parallelism in Event-Based Computations with Applications in Biology
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Event-based models find frequent usage in fields such as computational physics and biology as they may contain both continuous and discrete state variables and may incorporate both deterministic and stochastic state transitions. If the state transitions are stochastic, computer-generated random numbers are used to obtain the model solution. This type of event-based computations is also known as Monte-Carlo simulation.In this thesis, I study different approaches to execute event-based computations on parallel computers. This ultimately allows users to retrieve their simulation results in a fraction of the original computation time. As system sizes grow continuously or models have to be simulated at longer time scales, this is a necessary approach for current computational tasks.More specifically, I propose several ways to asynchronously simulate such models on parallel shared-memory computers, for example using parallel discrete-event simulation or task-based computing. The particular event-based models studied herein find applications in systems biology, computational epidemiology and computational neuroscience.In the presented studies, the proposed methods allow for high efficiency of the parallel simulation, typically scaling well with the number of used computer cores. As the scaling typically depends on individual model properties, the studies also investigate which quantities have the greatest impact on the simulation performance.Finally, the presented studies include other insights into event-based computations, such as methods how to estimate parameter sensitivity in stochastic models and how to simulate models that include both deterministic and stochastic state transitions.
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| 19. |
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| 20. |
- Bauer, Pavol, et al.
(författare)
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The URDME manual Version 1.3
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We have developed URDME, a general software for simulation of stochastic reaction-diffusion processes on unstructured meshes. This allows for a more flexible handling of complicated geometries and curved boundaries compared to simulations on structured, cartesian meshes. The underlying algorithm is the next subvolume method, extended to unstructured meshes by obtaining jump coefficients from a finite element formulation of the corresponding macroscopic equation. This manual describes version 1.3 of the software. URDME 1.3 includes support for Comsol Multiphysics 5.x and PDE Toolbox version 1.5 and above.
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| 21. |
- Bauer, Pavol, et al.
(författare)
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URDME v. 1.2: User's manual
- 2012
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We have developed URDME, a general software for simulation of stochastic reaction-diffusion processes on unstructured meshes. This allows for a more flexible handling of complicated geometries and curved boundaries compared to simulations on structured, cartesian meshes. The underlying algorithm is the next subvolume method, extended to unstructured meshes by obtaining jump coefficients from a finite element formulation of the corresponding macroscopic equation. This manual describes version 1.2 of the software. URDME 1.2 includes support for Comsol Multiphysics 4.1, 4.2, 4.3 as well as the previous version 3.5a. Additionally, support for basic SBML has been added along with the possibility to compile in stand-alone mode.
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| 22. |
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| 23. |
- Bronstein, Samuel, et al.
(författare)
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Bayesian inference in epidemics : linear noise analysis
- 2023
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; 20:2, s. 4128-4152
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Tidskriftsartikel (refereegranskat)abstract
- This paper offers a qualitative insight into the convergence of bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the Bayesian model’s convergence with increasing amounts of data under measurement limitations. Depending on how weakly informative the disease measurements are, we offer a kind of ‘best case’ as well as a ‘worst case’ analysis where, in the former case, we assume that the prevalence is directly accessible, while in the latter that only a binary signal corresponding toa prevalence detection threshold is available. Both cases are studied under an assumed so-called linear noise approximation as to the true dynamics. Numerical experiments test the sharpness of our results when confronted with more realistic situations for which analytical results are unavailable.
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| 24. |
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| 25. |
- Bull, Jonathan R., et al.
(författare)
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Distributed and Adaptive Fast Multipole Method in Three Dimensions
- 2021
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Ingår i: Communications in Computational Physics. - : Global Science Press. - 1815-2406 .- 1991-7120. ; 30:4, s. 959-984
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Tidskriftsartikel (refereegranskat)abstract
- We develop a general distributed implementation of an adaptive fast multipole method in three space dimensions. We rely on a balanced type of adaptive space discretization which supports a highly transparent and fully distributed implementation. A complexity analysis indicates favorable scaling properties and numerical experiments on up to 512 cores and 1 billion source points verify them. The parameters controlling the algorithm are subject to in-depth experiments and the performance response to the input parameters implies that the overall implementation is well-suited to automated tuning.
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| 26. |
- Börjesson, Stefan, 1979-, et al.
(författare)
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Detection of an IMI-2 carbapenemase-producing Enterobacter asburiae at a Swedish feed mill
- 2022
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Ingår i: Frontiers in Microbiology. - : Frontiers Media S.A.. - 1664-302X. ; 13
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Tidskriftsartikel (refereegranskat)abstract
- Occurrence of multidrug resistant Enterobacteriaceae in livestock is of concern as they can spread to humans. A potential introduction route for these bacteria to livestock could be animal feed. We therefore wanted to identify if Escherichia spp., Enterobacter spp., Klebsiella spp., or Raoutella spp. with transferable resistance to extended spectrum cephalosporins, carbapenems or colistin could be detected in the environment at feed mills in Sweden. A second aim was to compare detected isolates to previous described isolates from humans and animals in Sweden to establish relatedness which could indicate a potential transmission between sectors and feed mills as a source for antibiotic resistant bacteria. However, no isolates with transferable resistance to extended-cephalosporins or colistin could be identified, but one isolate belonging to the Enterobacter cloacae complex was shown to be carbapenem-resistant and showing carbapenemase-activity. Based on sequencing by both short-read Illumina and long-read Oxford Nanopore MinIon technologies it was shown that this isolate was an E. asburiae carrying a bla IMI-2 gene on a 216 Kbp plasmid, designated pSB89A/IMI-2, and contained the plasmid replicons IncFII, IncFIB, and a third replicon showing highest similarity to the IncFII(Yp). In addition, the plasmid contained genes for various functions such as plasmid segregation and stability, plasmid transfer and arsenical transport, but no additional antibiotic resistance genes. This isolate and the pSB89A/IMI-2 was compared to three human clinical isolates positive for bla IMI-2 available from the Swedish antibiotic monitoring program Swedres. It was shown that one of the human isolates carried a plasmid similar with regards to gene content to the pSB89A/IMI-2 except for the plasmid transfer system, but that the order of genes was different. The pSB89A/IMI-2 did however share the same transfer system as the bla IMI-2 carrying plasmids from the other two human isolates. The pSB89A/IMI-2 was also compared to previously published plasmids carrying bla IMI-2, but no identical plasmids could be identified. However, most shared part of the plasmid transfer system and DNA replication genes, and the bla IMI-2 gene was located next the transcription regulator imiR. The IS3-family insertion element downstream of imiR in the pSB89A was also related to the IS elements in other bla IMI-carrying plasmids.
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| 27. |
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| 28. |
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| 29. |
- Cullhed, Josef, et al.
(författare)
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The URDME Manual version 1.0
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We have developed URDME, a general software for simulation of stochastic reaction-diffusion processes on unstructured meshes. This allows for a more flexible handling of complicated geometries and curved boundaries compared to simulations on structured, cartesian meshes. The underlying algorithm is the next subvolume method (NSM), extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. In this manual, we describe how to use the software together with COMSOL Multiphysics 3.4 and Matlab to set up simulations. We provide a detailed account of the code structure and of the available interfaces. This makes modifications and extensions of the code possible. We also give two detailed examples, in which we describe the process of simulating and visualizing two models from the systems biology literature in a step-by-step manner.
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| 30. |
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| 31. |
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| 32. |
- Drawert, Brian, et al.
(författare)
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URDME v. 1.1: User's manual
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We have developed URDME, a general software for simulation of stochastic reaction-diffusion processes on unstructured meshes. This allows for a more flexible handling of complicated geometries and curved boundaries compared to simulations on structured, cartesian meshes. The underlying algorithm is the next subvolume method (NSM), extended to unstructured meshes by obtaining jump coefficients from the finite element formulation of the corresponding macroscopic equation. This manual describes the changes in the software compared to the previous version, URDME 1.0. Notable changes include support for Comsol Multiphysics 3.5a and a stronger decoupling between core simulation routines and the Matlab interface by making core solvers stand-alone executables. This opens up for more flexible simulation workflows when many realizations of the stochastic process need to be generated.
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| 33. |
- Ekeberg, Tomas, et al.
(författare)
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Machine learning for ultrafast X-ray diffraction patterns on large-scale GPU clusters
- 2015
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Ingår i: The international journal of high performance computing applications. - : SAGE Publications. - 1094-3420 .- 1741-2846. ; 29, s. 233-243
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Tidskriftsartikel (refereegranskat)abstract
- 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 the 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.
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| 34. |
- Engblom, Henrik, et al.
(författare)
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The evaluation of an electrocardiographic myocardial ischemia acuteness score to predict the amount of myocardial salvage achieved by early percutaneous coronary intervention Clinical validation with myocardial perfusion single photon emission computed tomography and cardiac magnetic resonance.
- 2011
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Ingår i: Journal of Electrocardiology. - : Elsevier BV. - 1532-8430 .- 0022-0736. ; 44, s. 525-532
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: The time from symptom onset to reperfusion in acute myocardial infarction (MI) has been shown to be a poor predictor of patient outcome. Acute electrocardiographic (ECG) changes, however, have been shown useful for estimated acuteness of myocardial ischemia using the Anderson-Wilkins ECG ischemia acuteness score (AW-acuteness score). The aim was to study whether acute ischemic ECG changes can predict the amount of salvageable myocardium in patients with acute ST-elevation MI. METHODS: Thirty-eight patients treated with primary percutaneous coronary intervention for first-time ST-elevation MI were retrospectively enrolled. Myocardium at risk (MaR) was determined by myocardial perfusion single photon emission computed tomography acutely or by T2-weighted cardiac magnetic resonance after 1 week, at the same time when final MI size was determined by late gadolinium enhancement. Myocardial salvage was calculated as (MaR - MI size)/MaR and compared with AW-acuteness score and time from symptom onset to primary percutaneous coronary intervention. RESULTS: The AW-acuteness score correlated significantly with salvageable myocardium for right coronary artery (RCA) occlusions (r = -0.57; P = .02) but not for left anterior descending artery (LAD) occlusions (r = -0.04; P = .88). Time from symptom onset did not correlate with the amount of salvageable myocardium (LAD, r = 0.04 and P = .87; RCA, r = -0.40 and P = .13). CONCLUSIONS: There is a moderate correlation between AW-acuteness score and salvageable myocardium in patients with acute RCA occlusion but not in patients with LAD occlusion.
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| 35. |
- Engblom, Stefan
(författare)
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A discrete spectral method for the chemical master equation
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- As an equivalent formulation of the Markov-assumption of stochastic processes, the master equation of chemical reactions is an accurate description of general systems in chemistry. For D reacting species this is a differential-difference equation in D dimensions, exactly soluble for very simple systems only.We present and analyze a novel solution strategy based upon a Galerkin spectral method with an inherent natural adaptivity and a very favorable choice of basis functions.The method is demonstrated by the numerical solution of two model problems followed by two more realistic systems taken from molecular biology. It is shown that the method remains effective and accurate, providing a viable alternative to other solution methods when the dimensionality is not too high.
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| 36. |
- Engblom, Stefan, et al.
(författare)
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Approximations for the moments of nonstationary and state dependent birth–death queues
- 2014
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Ingår i: Computing Research Repository. ; :1406.6164
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier polynomials, we are able to estimate any moment of the Markov process even though the system of moment equations may not be closed. Using new weighted discrete Sobolev spaces, we derive explicit error bounds of the transition probabilities and new weak a priori estimates for approximating the moments of the Markov processs using a truncated form of the expansion. Using our error bounds and estimates, we are able to show that our approximations converge to the true stochastic process as we add more terms to the expansion and give explicit bounds on the truncation error. As a result, we are the first paper in the queueing literature to provide error bounds and estimates on the performance of a moment closure approximation. Lastly, we perform several numerical experiments for some important models in the queueing theory literature and show that our expansion techniques are accurate at estimating the moment dynamics of these Markov process with only a few terms of the expansion.
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| 37. |
- Engblom, Stefan
(författare)
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Computing the moments of high dimensional solutions of the master equation
- 2005
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Derived from the Markov character only, the master equation of chemical reactions is an accurate stochastic description of quite general systems in chemistry. Exact solutions of this equation are rare and the most frequently used approximative solution method is to write down the corresponding set of reaction rate equations. In many cases this approximation is not valid, or only partially so, as stochastic effects caused by the natural noise present in the full description of the problem are poorly captured. In this paper it is shown how a certain set of higher order equations can be derived. It is shown by theory and example that stochastic effects are better captured using this technique while still maintaining the computational advantages of the reaction rate approach.
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| 38. |
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| 39. |
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| 40. |
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| 41. |
- Engblom, Stefan
(författare)
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Gaussian quadratures with respect to discrete measures
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In analogy to the subject of Gaussian integration formulas we present an overview of some Gaussian summation formulas. The derivation involve polynomials that are orthogonal under discrete inner products and the resulting formulas are useful as a numerical device for summing fairly general series. Several illuminating examples are provided in order to present various aspects of this not very well-known technique.
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| 42. |
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| 43. |
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| 44. |
- Engblom, Stefan
(författare)
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Numerical methods for the chemical master equation
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The numerical solution of chemical reactions described at the meso-scale is the topic of this thesis. This description, the master equation of chemical reactions, is an accurate model of reactions where stochastic effects are crucial for explaining certain effects observed in real life. In particular, this general equation is needed when studying processes inside living cells where other macro-scale models fail to reproduce the actual behavior of the system considered.The main contribution of the thesis is the numerical investigation of two different methods for obtaining numerical solutions of the master equation.The first method produces statistical quantities of the solution and is a generalization of a frequently used macro-scale description. It is shown that the method is efficient while still being able to preserve stochastic effects.By contrast, the other method obtains the full solution of the master equation and gains efficiency by an accurate representation of the state space.The thesis contains necessary background material as well as directions for intended future research. An important conclusion of the thesis is that, depending on the setup of the problem, methods of highly different character are needed.
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| 45. |
- Engblom, Stefan, 1976-
(författare)
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Numerical Solution Methods in Stochastic Chemical Kinetics
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This study is concerned with the numerical solution of certain stochastic models of chemical reactions. Such descriptions have been shown to be useful tools when studying biochemical processes inside living cells where classical deterministic rate equations fail to reproduce actual behavior. The main contribution of this thesis lies in its theoretical and practical investigation of different methods for obtaining numerical solutions to such descriptions. In a preliminary study, a simple but often quite effective approach to the moment closure problem is examined. A more advanced program is then developed for obtaining a consistent representation of the high dimensional probability density of the solution. The proposed method gains efficiency by utilizing a rapidly converging representation of certain functions defined over the semi-infinite integer lattice. Another contribution of this study, where the focus instead is on the spatially distributed case, is a suggestion for how to obtain a consistent stochastic reaction-diffusion model over an unstructured grid. Here it is also shown how to efficiently collect samples from the resulting model by making use of a hybrid method. In a final study, a time-parallel stochastic simulation algorithm is suggested and analyzed. Efficiency is here achieved by moving parts of the solution phase into the deterministic regime given that a parallel architecture is available. Necessary background material is developed in three chapters in this summary. An introductory chapter on an accessible level motivates the purpose of considering stochastic models in applied physics. In a second chapter the actual stochastic models considered are developed in a multi-faceted way. Finally, the current state-of-the-art in numerical solution methods is summarized and commented upon.
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| 46. |
- Engblom, Stefan, et al.
(författare)
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On diffuse interface modeling and simulation of surfactants in two-phase fluid flow
- 2013
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Ingår i: Communications in Computational Physics. - : Global Science Press. - 1815-2406 .- 1991-7120. ; 14:4, s. 879-915
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Tidskriftsartikel (refereegranskat)abstract
- An existing phase-fieldmodel of two immiscible fluids with a single soluble surfactant present is discussed in detail. We analyze the well-posedness of the model and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and the qualities of the physical model. A fully coupled hydrodynamic test-case demonstrates the potential to capture also non-trivial effects on the overall flow.
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| 47. |
- Engblom, Stefan
(författare)
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On the stability of stochastic jump kinetics
- 2014
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Ingår i: Applied Mathematics. - : Scientific Research Publishing, Inc.. - 2152-7385 .- 2152-7393. ; 5, s. 3217-3239
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Tidskriftsartikel (refereegranskat)
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| 48. |
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| 49. |
- Engblom, Stefan
(författare)
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On well-separated sets and fast multipole methods
- 2011
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Ingår i: Applied Numerical Mathematics. - : Elsevier BV. - 0168-9274 .- 1873-5460. ; 61:10, s. 1096-1102
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 50. |
- Engblom, Stefan
(författare)
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PARALLEL IN TIME SIMULATION OF MULTISCALE STOCHASTIC CHEMICAL KINETICS
- 2009
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Ingår i: Multiscale Modeling & simulation. - : Society for Industrial & Applied Mathematics (SIAM). - 1540-3459 .- 1540-3467. ; 8:1, s. 46-68
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Tidskriftsartikel (refereegranskat)abstract
- A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate equation. A stochastic simulation algorithm is used to obtain an exact realization of the process at the mesoscopic scale (in parallel). The underlying stochastic description is a jump process driven by the Poisson measure. A convergence result in this arguably difficult setting is established, suggesting that a homogenization of the solution is advantageous. We devise a simple but highly general such technique. Three numerical experiments on models representative to the field of computational systems biology illustrate the method. For nonstiff problems, it is shown that the method is able to quickly converge even when stochastic effects are present. For stiff problems, we are instead able to obtain fast convergence to a homogenized solution. Overall, the method builds an attractive bridge between, on the one hand, macroscopic deterministic scales and, on the other hand, mesoscopic stochastic ones. This construction is clearly possible to apply also to stochastic models within other fields.
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