Monte Carlo simulations of systems with complex energy landscapes

Non-traditional Monte Carlo simulations are a powerful approach to the study of systems with complex energy landscapes. After reviewing several of these specialized algorithms we shall describe the behavior of typical systems including spin glasses, lattice proteins, and models for “real” proteins. In the Edwards-Anderson spin glass it is now possible to produce probability distributions in the canonical ensemble and thermodynamic results of high numerical quality. In the hydrophobic-polar (HP) lattice protein model Wang-Landau sampling with an improved move set (pull-moves) produces results of very high quality. These can be compared with the results of other methods of statistical physics. A more realistic membrane protein model for Glycophorin A is also examined. Wang-Landau sampling allows the study of the dimerization process including an elucidation of the nature of the process.     

Replica Exchange Light Transport

We solve the light transport problem by introducing a novel unbiased Monte Carlo algorithm called replica exchange light transport, inspired by the replica exchange Monte Carlo method in the fields of computational physics and statistical information processing. The replica exchange Monte Carlo method is a sampling technique whose operation resembles simulated annealing in optimization algorithms using a set of sampling distributions. We apply it to the solution of light transport integration by extending the probability density function of an integrand of the integration to a set of distributions. That set of distributions is composed of combinations of the path densities of different path generation types: uniform distributions in the integral domain, explicit and implicit paths in light (particle/photon) tracing, indirect paths in bidirectional path tracing, explicit and implicit paths in path tracing, and implicit caustics paths seen through specular surfaces including the delta function in path tracing. The replica‐exchange light transport algorithm generates a sequence of path samples from each distribution and samples the simultaneous distribution of those distributions as a stationary distribution by using the Markov chain Monte Carlo method. Then the algorithm combines the obtained path samples from each distribution using multiple importance sampling. We compare the images generated with our algorithm to those generated with bidirectional path tracing and Metropolis light transport based on the primary sample space. Our proposing algorithm has better convergence property than bidirectional path tracing and the Metropolis light transport, and it is easy to implement by extending the Metropolis light transport.     

后验Monte Carlo-Gaussian采样粒子滤波WSN网络定位*

环境因素导致无线传感器网络定位存在噪声影响,实质上是非平滑的非线性问题,针对传统粒子滤波算法在处理该问题时精度不高的缺点,提出一种基于后验泊松分布的Monte Carlo-Gaussian重采样粒子滤波算法的无线传感器网络定位算法。首先,基于粒子滤波算法,借鉴扩展卡尔曼滤波算法采用近似后验高斯分布思想,设计了后验泊松分布Monte Carlo-Gaussian重采样粒子滤波器。其次,采用该滤波器设计实现了无线传感器网络定位算法,解决了非平滑非线性的噪声干扰定位问题。最后,分别对滤波器和定位算法的性能进行了对比仿真实验,结果验证了所提算法的有效性。     

Parameter estimation and uncertainty analysis of the Spatial Agro Hydro Salinity Model (SAHYSMOD) in the semi-arid climate of Rechna Doab,Pakistan

Manual calibration of distributed models with many unknown parameters can result in problems of equifinality and high uncertainty. In this study, the Generalized Likelihood Uncertainty Estimation (GLUE) technique was used to address these issues through uncertainty and sensitivity analysis of a distributed watershed scale model (SAHYSMOD) for predicting changes in the groundwater levels of the Rechna Doab basin, Pakistan. The study proposes and then describes a stepwise methodology for SAHYSMOD uncertainty analysis that has not been explored in any study before. One thousand input data files created through Monte Carlo simulations were classified as behavior and non-behavior sets using threshold likelihood values. The model was calibrated (1983–1988) and validated (1998–2003) through satisfactory agreement between simulated and observed data. Acceptable values were observed in the statistical performance indices. Approximately 70% of the observed groundwater level values fell within uncertainty bounds. Groundwater pumping (Gw) and hydraulic conductivity (Kaq) were found to be highly sensitive parameters affecting groundwater recharge.     

一种德州扑克的牌力评估方法

德州扑克是机器博弈领域中一种很好的研究对象,与国际象棋、西洋棋等不同,其涉及了诸如不完整信息抽象与处理、多智能体竞争、风险评估与管理、对手建模等多方面的问题研究。其中,不完备信息抽象与处理是其他问题研究的基础,抽象与处理信息就是要对当前牌局进行评估以供后续工作使用。针对牌局信息不完整的情况,讨论了一些评估牌力方法,分析了这些方法的利弊,并提出了一种新的牌力评估方法,以提升计算速度,减少资源占用。实验结果表明,新的方法摒弃了查找表,达到了节省空间的目的,同时也具备较快的计算速度。     

基于蒙特卡洛方法的移动传感网节点定位优化算法

无线传感器网络正在被应用到各种各样的监测环境中,在这些应用场景中,传感器节点的位置信息大都是至关重要的.目前对传感器节点定位方面的研究大都只针对静态WSN的情况,对于移动WSN节点定位的研究仍然十分有限.该文提出了移动WSN中节点间互相优化定位的新思路,通过判断式筛选出定位精度高的节点,并协助其他节点进行定位条件的优化.所提出的算法TSBMCL通过更精确的裁剪待定位节点的蒙特卡洛盒,并增加节点的粒子滤波条件来实现节点的精确定位.大规模的仿真结果表明,该算法可精确的锁定节点位置区域,高效的采样得到节点的位置样本,相比于传统的移动WSN蒙特卡洛定位方法,大大提高了节点的定位精度.     

Generating heavy particles with energy and momentum conservation

We propose a novel algorithm, called REGGAE, for the generation of momenta of a given sample of particle masses, evenly distributed in Lorentz-invariant phase space and obeying energy and momentum conservation. In comparison to other existing algorithms, REGGAE is designed for the use in multiparticle production in hadronic and nuclear collisions where many hadrons are produced and a large part of the available energy is stored in the form of their masses. The algorithm uses a loop simulating multiple collisions which lead to production of configurations with reasonably large weights.

Program summary

Program title: REGGAE (REscattering-after-Genbod GenerAtor of Events)Catalogue identifier: AEJR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1523No. of bytes in distributed program, including test data, etc.: 9608Distribution format: tar.gzProgramming language: C++Computer: PC Pentium 4, though no particular tuning for this machine was performed.Operating system: Originally designed on Linux PC with g++, but it has been compiled and ran successfully on OS X with g++ and MS Windows with Microsoft Visual C++ 2008 Express Edition, as well.RAM: This depends on the number of particles which are generated. For 10 particles like in the attached example it requires about 120 kB.Classification: 11.2Nature of problem: The task is to generate momenta of a sample of particles with given masses which obey energy and momentum conservation. Generated samples should be evenly distributed in the available Lorentz-invariant phase space.Solution method: In general, the algorithm works in two steps. First, all momenta are generated with the GENBOD algorithm. There, particle production is modeled as a sequence of two-body decays of heavy resonances. After all momenta are generated this way, they are reshuffled. Each particle undergoes a collision with some other partner such that in the pair center of mass system the new directions of momenta are distributed isotropically. After each particle collides only a few times, the momenta are distributed evenly across the whole available phase space. Starting with GENBOD is not essential for the procedure but it improves the performance.Running time: This depends on the number of particles and number of events one wants to generate. On a LINUX PC with 2 GHz processor, generation of 1000 events with 10 particles each takes about 3 s.     

QSATS: MPI-driven quantum simulations of atomic solids at zero temperature

We describe QSATS, a parallel code for performing variational path integral simulations of the quantum mechanical ground state of monatomic solids. QSATS is designed to treat Boltzmann quantum solids, in which individual atoms are permanently associated with distinguishable crystal lattice sites and undergo large-amplitude zero-point motions around these sites. We demonstrate the capabilities of QSATS by using it to compute the total energy and potential energy of hexagonal close packed solid ⁴He at the density .

Program summary

Program title:QSATSCatalogue identifier: AEJE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 7329No. of bytes in distributed program, including test data, etc.: 61 685Distribution format: tar.gzProgramming language: Fortran 77.Computer: QSATS should execute on any distributed parallel computing system that has the Message Passing Interface (MPI) [1] libraries installed.Operating system: Unix or Linux.Has the code been vectorized or parallelized?: Yes, parallelized using MPI [1].RAM: The memory requirements of QSATS depend on both the number of atoms in the crystal and the number of replicas in the variational path integral chain. For parameter sets A and C (described in the long write-up), approximately 4.5 Mbytes and 12 Mbytes, respectively, are required for data storage by QSATS (exclusive of the executable code).Classification: 7.7, 16.13.External routines: Message Passing Interface (MPI) [1]Nature of problem: QSATS simulates the quantum mechanical ground state for a monatomic crystal characterized by large-amplitude zero-point motions of individual (distinguishable) atoms around their nominal lattice sites.Solution method: QSATS employs variational path integral quantum Monte Carlo techniques to project the system?s ground state wave function out of a suitably-chosen trial wave function.Restrictions: QSATS neglects quantum statistical effects associated with the exchange of identical particles. As distributed, QSATS assumes that the potential energy function for the crystal is a pairwise additive sum of atom–atom interactions.Additional comments: An auxiliary program, ELOC, is provided that uses the output generated by QSATS to compute both the crystal?s ground state energy and the expectation value of the crystal?s potential energy. End users can modify ELOC as needed to compute the expectation value of other coordinate-space observables.Running time: QSATS requires roughly 3 hours to run a simulation using parameter set A on a cluster of 12 Xeon processors with clock speed 2.8 GHz. Roughly 15 hours are needed to run a simulation using parameter set C on the same cluster.References:

• [1] 

  For information about MPI, visit http://www.mcs.anl.gov/mpi/.

     

A Quantum Monte Carlo method at fixed energy

In this paper we explore ways to study the zero temperature limit of quantum statistical mechanics using Quantum Monte Carlo simulations. We develop a Quantum Monte Carlo method in which one fixes the ground state energy as a parameter. The Hamiltonians we consider are of the form H=H₀+λV with ground state energy E. For fixed H₀ and V, one can view E as a function of λ whereas we view λ as a function of E. We fix E and define a path integral Quantum Monte Carlo method in which a path makes no reference to the times (discrete or continuous) at which transitions occur between states. For fixed E we can determine λ(E) and other ground state properties of H.