Monte Carlo Methods and Applications
Description
This is the proceedings of the "8 th IMACS Seminar on Monte Carlo Methods" held from August 29 to September 2, 2011 in Borovets, Bulgaria, and organized by the Institute of Information and Communication Technologies of the Bulgarian Academy of Sciences in cooperation with the International Association for Mathematics and Computers in Simulation (IMACS). Included are 24 papers which cover all topics presented in the sessions of the seminar: stochastic computation and complexity of high dimensional problems, sensitivity analysis, high-performance computations for Monte Carlo applications, stochastic metaheuristics for optimization problems, sequential Monte Carlo methods for large-scale problems, semiconductor devices and nanostructures.
The history of the IMACS Seminar on Monte Carlo Methods goes back to April 1997 when the first MCM Seminar was organized in Brussels:
1
st
IMACS Seminar, 1997, Brussels, Belgium
2
nd
IMACS Seminar, 1999, Varna, Bulgaria
3
rd
IMACS Seminar, 2001, Salzburg, Austria
4
th
IMACS Seminar, 2003, Berlin, Germany
5
th
IMACS Seminar, 2005, Tallahassee, USA
6
th
IMACS Seminar, 2007, Reading, UK
7
th
IMACS Seminar, 2009, Brussels, Belgium
8
th
IMACS Seminar, 2011, Borovets, Bulgaria
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Content
2 - 1 Improvement of Multi-population Genetic Algorithms Convergence Time [Seite 15]
2.1 - 1.1 Introduction [Seite 15]
2.2 - 1.2 Short Overview of MpGA Modifications [Seite 16]
2.3 - 1.3 Parameter Identification of S. cerevisiae Fed-Batch Cultivation Using Different Kinds of MpGA [Seite 18]
2.4 - 1.4 Analysis and Conclusions [Seite 21]
3 - 2 Parallelization and Optimization of 4D Binary Mixture Monte Carlo Simulations Using Open MPI and CUDA [Seite 25]
3.1 - 2.1 Introduction [Seite 25]
3.2 - 2.2 The Metropolis Monte Carlo Method [Seite 26]
3.3 - 2.3 Decomposition into Subdomains and the Virtual Topology Using OpenMPI [Seite 27]
3.4 - 2.4 Management of Hypersphere Coordinate Migration Between Domains [Seite 28]
3.4.1 - 2.4.1 Communication between the CPU and the GPU [Seite 29]
3.5 - 2.5 Pseudorandom Number Generation [Seite 29]
3.6 - 2.6 Results of Running the Modified Code [Seite 29]
3.7 - 2.7 Conclusions [Seite 32]
4 - 3 Efficient Implementation of the Heston Model Using GPGPU [Seite 35]
4.1 - 3.1 Introduction [Seite 35]
4.2 - 3.2 Our GPGPU-Based Algorithm for Option Pricing [Seite 37]
4.3 - 3.3 Numerical Results [Seite 39]
4.4 - 3.4 Conclusions and Future Work [Seite 41]
5 - 4 On a Game-Method for Modeling with Intuitionistic Fuzzy Estimations. Part 2 [Seite 43]
5.1 - 4.1 Introduction [Seite 43]
5.2 - 4.2 Short Remarks on the Game-Method for Modeling from Crisp Point of View [Seite 43]
5.3 - 4.3 On the Game-Method for Modeling with Intuitionistic Fuzzy Estimations [Seite 45]
5.4 - 4.4 Main Results [Seite 48]
5.5 - 4.5 Conclusion [Seite 50]
6 - 5 Generalized Nets, ACO Algorithms, and Genetic Algorithms [Seite 53]
6.1 - 5.1 Introduction [Seite 53]
6.2 - 5.2 ACO and GA [Seite 54]
6.3 - 5.3 GN for Hybrid ACO-GA Algorithm [Seite 56]
6.4 - 5.4 Conclusion [Seite 58]
7 - 6 Bias Evaluation and Reduction for Sample-Path Optimization [Seite 61]
7.1 - 6.1 Introduction [Seite 61]
7.2 - 6.2 Problem Formulation [Seite 63]
7.3 - 6.3 Taylor-Based Bias Correction [Seite 65]
7.4 - 6.4 Impact on the Optimization Bias [Seite 66]
7.5 - 6.5 Numerical Experiments [Seite 67]
7.6 - 6.6 Conclusions [Seite 69]
8 - 7 Monte Carlo Simulation of Electron Transport in Quantum Cascade Lasers [Seite 73]
8.1 - 7.1 Introduction [Seite 73]
8.2 - 7.2 QCL Transport Model [Seite 73]
8.2.1 - 7.2.1 Pauli Master Equation [Seite 74]
8.2.2 - 7.2.2 Calculation of Basis States [Seite 75]
8.2.3 - 7.2.3 Monte Carlo Solver [Seite 76]
8.3 - 7.3 Results and Discussion [Seite 78]
8.4 - 7.4 Conclusion [Seite 79]
9 - 8 Markov Chain Monte Carlo Particle Algorithms for Discrete-Time Nonlinear Filtering [Seite 83]
9.1 - 8.1 Introduction [Seite 83]
9.2 - 8.2 General Particle Filtering Framework [Seite 84]
9.3 - 8.3 High Dimensional Particle Schemes [Seite 85]
9.3.1 - 8.3.1 Sequential MCMC Filtering [Seite 85]
9.3.2 - 8.3.2 Efficient Sampling in High Dimensions [Seite 86]
9.3.3 - 8.3.3 Setting Proposal and Steering Distributions [Seite 87]
9.4 - 8.4 Illustrative Examples [Seite 87]
9.5 - 8.5 Conclusions [Seite 90]
10 - 9 Game-Method for Modeling and WRF-Fire Model Working Together [Seite 93]
10.1 - 9.1 Introduction [Seite 93]
10.2 - 9.2 Description of the Game-Method for Modeling [Seite 94]
10.3 - 9.3 General Description of the Coupled Atmosphere Fire Modeling and WRF-Fire [Seite 95]
10.4 - 9.4 Wind Simulation Approach [Seite 97]
10.5 - 9.5 Conclusion [Seite 98]
11 - 10 Wireless Sensor Network Layout [Seite 101]
11.1 - 10.1 Introduction [Seite 101]
11.2 - 10.2 Wireless Sensor Network Layout Problem [Seite 102]
11.3 - 10.3 ACO for WSN Layout Problem [Seite 104]
11.4 - 10.4 Experimental Results [Seite 106]
11.5 - 10.5 Conclusion [Seite 107]
12 - 11 A Two-Dimensional Lorentzian Distribution for an Atomic Force Microscopy Simulator [Seite 111]
12.1 - 11.1 Introduction [Seite 111]
12.2 - 11.2 Modeling Oxidation Kinetics [Seite 112]
12.3 - 11.3 Development of the Lorentzian Model [Seite 114]
12.3.1 - 11.3.1 Algorithm for the Gaussian Model [Seite 114]
12.3.2 - 11.3.2 Development of the Lorentzian Model [Seite 115]
12.4 - 11.4 Conclusion [Seite 117]
13 - 12 Stratified Monte Carlo Integration [Seite 119]
13.1 - 12.1 Introduction [Seite 119]
13.2 - 12.2 Numerical Integration [Seite 120]
13.3 - 12.3 Conclusion [Seite 126]
14 - 13 Monte Carlo Simulation of Asymmetric Flow Field Flow Fractionation [Seite 129]
14.1 - 13.1 Motivation [Seite 129]
14.2 - 13.2 AFFFF [Seite 130]
14.3 - 13.3 Mathematical Model and Numerical Algorithm [Seite 131]
14.3.1 - 13.3.1 Mathematical Model [Seite 131]
14.3.2 - 13.3.2 The MLMC Algorithm [Seite 132]
14.4 - 13.4 Numerical Results [Seite 133]
15 - 14 Convexization in Markov Chain Monte Carlo [Seite 139]
15.1 - 14.1 Introduction [Seite 139]
15.2 - 14.2 Auxiliary Functions [Seite 140]
15.2.1 - 14.2.1 Definition of Auxiliary Functions [Seite 140]
15.2.2 - 14.2.2 Optimization Process for Auxiliary Functions [Seite 140]
15.2.3 - 14.2.3 Auxiliary Functions for Convex Functions [Seite 142]
15.2.4 - 14.2.4 Objective Function Which Is the Sum of Convex and Concave Functions [Seite 142]
15.3 - 14.3 Stochastic Auxiliary Functions [Seite 143]
15.3.1 - 14.3.1 Stochastic Convex Learning (Summary) [Seite 143]
15.3.2 - 14.3.2 Auxiliary Stochastic Functions [Seite 144]
15.4 - 14.4 Metropolis-Hastings Auxiliary Algorithm [Seite 144]
15.5 - 14.5 Numerical Experiments [Seite 145]
15.6 - 14.6 Conclusion [Seite 146]
16 - 15 Value Simulation of the Interacting Pair Number for Solution of the Monodisperse Coagulation Equation [Seite 149]
16.1 - 15.1 Introduction [Seite 149]
16.2 - 15.2 Value Simulation for Integral Equations [Seite 151]
16.2.1 - 15.2.1 Value Simulation of the Time Interval Between Interactions [Seite 152]
16.2.2 - 15.2.2 VSIPN to Estimate the Monomer Concentration Jh1 [Seite 153]
16.2.3 - 15.2.3 VSIPN to Estimate the Monomer and Dimer Concentration Jh12 [Seite 154]
16.3 - 15.3 Results of the Numerical Experiments [Seite 155]
16.4 - 15.4 Conclusion [Seite 157]
17 - 16 Parallelization of Algorithms for Solving a Three-Dimensional Sudoku Puzzle [Seite 159]
17.1 - 16.1 Introduction [Seite 159]
17.2 - 16.2 The Simulated Annealing Method [Seite 160]
17.3 - 16.3 Successful Algorithms for Solving the Three-Dimensional Puzzle Using MPI [Seite 161]
17.3.1 - 16.3.1 An Embarrassingly Parallel Algorithm [Seite 162]
17.3.2 - 16.3.2 Distributed Simulated Annealing Using a Master/Worker Organization [Seite 163]
17.4 - 16.4 Results [Seite 163]
17.5 - 16.5 Conclusions [Seite 166]
18 - 17 The Efficiency Study of Splitting and Branching in the Monte Carlo Method [Seite 169]
18.1 - 17.1 Introduction [Seite 169]
18.2 - 17.2 Randomized Branching [Seite 170]
18.3 - 17.3 Splitting [Seite 173]
19 - 18 On the Asymptotics of a Lower Bound for the Diaphony of Generalized van der Corput Sequences [Seite 177]
19.1 - 18.1 Introduction and Main Result [Seite 177]
19.2 - 18.2 Definitions and Previous Results [Seite 179]
19.3 - 18.3 Proof of Theorem 18.1 [Seite 180]
20 - 19 Group Object Tracking with a Sequential Monte Carlo Method Based on a Parameterized Likelihood Function [Seite 185]
20.1 - 19.1 Motivation [Seite 185]
20.2 - 19.2 Group Object Tracking within the Sequential Monte Carlo Framework [Seite 186]
20.3 - 19.3 Measurement Likelihood for Group Object Tracking [Seite 187]
20.3.1 - 19.3.1 Introduction of the Notion of the Visible Surface [Seite 188]
20.3.2 - 19.3.2 Parametrization of the Visible Surface [Seite 189]
20.4 - 19.4 Performance Evaluation [Seite 189]
20.5 - 19.5 Conclusions [Seite 191]
21 - 20 The Template Design Problem: A Perspective with Metaheuristics [Seite 195]
21.1 - 20.1 Introduction [Seite 195]
21.2 - 20.2 The Template Design Problem [Seite 196]
21.3 - 20.3 Solving the TDP under Deterministic Demand [Seite 197]
21.3.1 - 20.3.1 Representation and Evaluation [Seite 197]
21.3.2 - 20.3.2 Metaheuristic Approaches [Seite 199]
21.4 - 20.4 Experimental Results [Seite 200]
21.5 - 20.5 Conclusions and Future Work [Seite 204]
22 - 21 A Comparison of Simulated Annealing and Genetic Algorithm Approaches for Cultivation Model Identification [Seite 207]
22.1 - 21.1 Introduction [Seite 207]
22.2 - 21.2 Genetic Algorithm [Seite 208]
22.3 - 21.3 Simulated Annealing [Seite 209]
22.4 - 21.4 E. coli MC4110 Fed-Batch Cultivation Process Model [Seite 210]
22.5 - 21.5 Numerical Results and Discussion [Seite 211]
22.6 - 21.6 Conclusion [Seite 212]
23 - 22 Monte Carlo Investigations of Electron Decoherence due to Phonons [Seite 217]
23.1 - 22.1 Introduction [Seite 217]
23.2 - 22.2 The Algorithms [Seite 219]
23.2.1 - 22.2.1 Algorithm A [Seite 220]
23.2.2 - 22.2.2 Algorithm B [Seite 221]
23.2.3 - 22.2.3 Algorithm C [Seite 221]
24 - 23 Geometric Allocation Approach for the Transition Kernel of a Markov Chain [Seite 227]
24.1 - 23.1 Introduction [Seite 227]
24.2 - 23.2 Geometric Approach [Seite 228]
24.2.1 - 23.2.1 Reversible Kernel [Seite 230]
24.2.2 - 23.2.2 Irreversible Kernel [Seite 231]
24.3 - 23.3 Benchmark Test [Seite 231]
24.4 - 23.4 Conclusion [Seite 233]
25 - 24 Exact Sampling for the Ising Model at All Temperatures [Seite 237]
25.1 - 24.1 Introduction [Seite 237]
25.2 - 24.2 The Ising Model [Seite 238]
25.3 - 24.3 Exact Sampling [Seite 241]
25.4 - 24.4 The Random Cluster Model [Seite 242]
25.5 - 24.5 Exact Sampling for the Ising Model [Seite 244]
