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

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

Convergence of Probability Measures

We investigate whether income inequality affects subsequent growth in a cross-country sample for 1965-90, using the models of Barro (1997), Bleaney and Nishiyama (2002) and Sachs and Warner (1997), with negative results. We then investigate the evolution of income inequality over the same period and its correlation with growth. The dominating feature is inequality convergence across countries. This convergence has been significantly faster amongst developed countries. Growth does not appear to influence the evolution of inequality over time. Outline

https://www.econstor.eu/bitstream/10419/81822/1/02-28.pdf

Economic growth and income inequality

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

■ Abstract Apoptosis is a genetically programmed, morphologically distinct form of cell death that can be triggered by a variety of physiological and pathological stimuli. Studies performed over the past 10 years have demonstrated that proteases play critical roles in initiation and execution of this process. The caspases, a family of cysteine-dependent aspartate-directed proteases, are prominent among the death proteases. Caspases are synthesized as relatively inactive zymogens that become activated by scaffold-mediated transactivation or by cleavage via upstream proteases in an intracellular cascade. Regulation of caspase activation and activity occurs at several different levels: ( a) Zymogen gene transcription is regulated; ( b) antiapoptotic members of the Bcl-2 family and other cellular polypeptides block proximity-induced activation of certain procaspases; and ( c) certain cellular inhibitor of apoptosis proteins (cIAPs) can bind to and inhibit active caspases. Once activated, caspases cleave a variety of intracellular polypeptides, including major structural elements of the cytoplasm and nucleus, components of the DNA repair machinery, and a number of protein kinases. Collectively, these scissions disrupt survival pathways and disassemble important architectural components of the cell, contributing to the stereotypic morphological and biochemical changes that characterize apoptotic cell death.

Mammalian caspases: structure ,a ctivation ,s ubstrates, and functions during apoptosis

This article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is when the population distribution has either exponential-type tails or polynomial-type tails. We present convergence rates under the elementwise l∞ norm and Frobenius norm. In addition, we consider graphical model selection. The procedure is easily implemented by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods.

/pdf/a-constrained-l1-minimization-approach-to-sparse-precision-327jekjnmm.pdf

A Constrained ℓ1 Minimization Approach to Sparse Precision Matrix Estimation

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In particular, it is shown that the rate of convergence between the estimator and the true $s$-sparse precision matrix under the spectral norm is $s\sqrt{\log p/n}$ when the population distribution has either exponential-type tails or polynomial-type tails. Convergence rates under the elementwise $L_{\infty}$ norm and Frobenius norm are also presented. In addition, graphical model selection is considered. The procedure is easily implementable by linear programming. Numerical performance of the estimator is investigated using both simulated and real data. In particular, the procedure is applied to analyze a breast cancer dataset. The procedure performs favorably in comparison to existing methods.

A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be suboptimal over the same parameter spaces. Support recovery is discussed as well. The adaptive thresholding estimators are easy to implement. The numerical performance of the estimators is studied using both simulated and real data. Simulation results demonstrate that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumor microarray experiment. A supplement to this ar...

/pdf/adaptive-thresholding-for-sparse-covariance-matrix-29b1r4yzf9.pdf

Adaptive Thresholding for Sparse Covariance Matrix Estimation

Recent studies have shown that the high standard of living enjoyed by people in the richest countries often comes at the expense of CO2 emissions produced with technologies of low efficiency in less affluent, developing countries. Less apparent is that this relationship between developed and developing can exist within a single country's borders, with rich regions consuming and exporting high-value goods and services that depend upon production of low-cost and emission-intensive goods and services from poorer regions in the same country. As the world's largest emitter of CO2, China is a prominent and important example, struggling to balance rapid economic growth and environmental sustainability across provinces that are in very different stages of development. In this study, we track CO2 emissions embodied in products traded among Chinese provinces and internationally. We find that 57% of China's emissions are related to goods that are consumed outside of the province where they are produced. For instance, up to 80% of the emissions related to goods consumed in the highly developed coastal provinces are imported from less developed provinces in central and western China where many low-value-added but high-carbon-intensive goods are produced. Without policy attention to this sort of interprovincial carbon leakage, the less developed provinces will struggle to meet their emissions intensity targets, whereas the more developed provinces might achieve their own targets by further outsourcing. Consumption-based accounting of emissions can thus inform effective and equitable climate policy within China.

https://www.pnas.org/content/pnas/110/28/11654.full.pdf

Outsourcing CO2 within China

The relationship between urbanization and economic growth has been perplexing. In this paper, we identify the pattern of global change and the correlation of urbanization and economic growth, using cross-sectional, panel estimation and geographic information systems (GIS) methods. The analysis has been carried out on a global geographical scale, while the timescale of the study spans the last 30 years. The data shows that urbanization levels have changed substantially during these three decades. Empirical findings from cross-sectional data and panel data support the general notion of close links between urbanization levels and GDP per capita. However, we also present significant evidence that there is no correlation between urbanization speed and economic growth rate at the global level. Hence, we conclude that a given country cannot obtain the expected economic benefits from accelerated urbanization, especially if it takes the form of government-led urbanization. In addition, only when all facets are taken into consideration can we fully assess the urbanization process.

/pdf/the-global-pattern-of-urbanization-and-economic-growth-3hjjw6gwcg.pdf

Weidong Liu

Papers

A Constrained ℓ1 Minimization Approach to Sparse Precision Matrix Estimation

A Constrained L1 Minimization Approach to Sparse Precision Matrix Estimation

Adaptive Thresholding for Sparse Covariance Matrix Estimation

Outsourcing CO2 within China

The Global Pattern of Urbanization and Economic Growth: Evidence from the Last Three Decades