Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Statistics for Spatial Data.

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

비만아 부모의 돌봄 경험: q 방법론

Organic and hybrid bulk heterojunction (BHJ) solar cells are investigated. We describe the synthesis and solar cell characteristics of well-defined functional thiophene dendrimers. Three-dimensional morphologies of the polymer–metal oxide BHJs are analyzed with electron tomography and stochastic models, and are simulated with the latter, to establish the effect of processing on morphology. Device models based on stochastically simulated data of morphologies and transport parameters are used to provide accurate descriptions of solar cell performance.

Organic and Hybrid Solar Cells Based on Well-Defined Organic Semiconductors and Morphologies

We discuss a simple methodology to enable a statistical comparison of human population with the vegetation of North America over the past 13000 years. Nonparametric kernel methods are applied for temporal and spatial smoothing of point data obtained from the Neotoma Paleoecology Database and the Canadian Archaeological Radiocarbon Database, which results in sequences of maps showing the development of population and different plant taxa during the Holocene. The estimation of smooth spatial and spatio-temporal cross-correlation functions is proposed in order to detect relationships between population and vegetation in fixed time intervals. Furthermore, the effects of varying environment on demographic changes as well as potential impacts of populations on plant taxa over time are analyzed. Pointwise confidence bands for cross-correlation functions are computed and a robustness analysis is performed to assess the significance of obtained results. Considering the example of oak, an interpretation of our results for eastern North America shows the value of this methodology.

Estimation of Spatio‐Temporal Correlations of Prehistoric Population and Vegetation in North America

Wir definieren, ausgehend von den inhaltlichen Ausfuhrungen in Kapitel 1, einen zufalligen Punktprozes in R zunachst als ein zufalliges Zahlmas auf der σ-Algebra ℛ der Borel-Mengen von R.

Definition, Existenz und Eindeutigkeit zufälliger Punktprozesse

Classification of FIB/SEM-tomography images for highly porous multiphase materials using random forest classifiers

Summary


This paper deals with statistical inference on the parameters of a stochastic model, describing curved fibrous objects in three dimensions, that is based on multivariate autoregressive processes. The model is fitted to experimental data consisting of a large number of short independently sampled trajectories of multivariate autoregressive processes. We discuss relevant statistical properties (e.g. asymptotic behaviour as the number of trajectories tends to infinity) of the maximum likelihood (ML) estimators for such processes. Numerical studies are also performed to analyse some of the more intractable properties of the ML estimators. Finally the whole methodology, i.e., the fibre model and its statistical inference, is applied to appropriately describe the tracking of fibres in real materials.

Volker Schmidt

Papers

Organic and Hybrid Solar Cells Based on Well-Defined Organic Semiconductors and Morphologies

Estimation of Spatio‐Temporal Correlations of Prehistoric Population and Vegetation in North America

Definition, Existenz und Eindeutigkeit zufälliger Punktprozesse

Classification of FIB/SEM-tomography images for highly porous multiphase materials using random forest classifiers

Statistical Inference for Curved Fibrous Objects in 3D – Based on Multiple Short Observations of Multivariate Autoregressive Processes