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

Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

The Theory of Island Biogeography

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

J. Appl. Cryst.の発刊に際して

Photosynthesis provides the primary energy source for almost all life on Earth. One of its remarkable features is the efficiency with which energy is transferred within the light harvesting complexes comprising the photosynthetic apparatus. Suspicions that quantum trickery might be involved in the energy transfer processes at the core of photosynthesis are now confirmed by a new spectroscopic study. The study reveals electronic quantum beats characteristic of wavelike energy motion within the bacteriochlorophyll complex from the green sulphur bacterium Chlorobium tepidum. This wavelike characteristic of the energy transfer process can explain the extreme efficiency of photosynthesis, in that vast areas of phase space can be sampled effectively to find the most efficient path for energy transfer. A spectroscopic study has directly monitored the quantum beating arising from remarkably long-lived electronic quantum coherence in a bacteriochlorophyll complex. This wavelike characteristic of the energy transfer process can explain the extreme efficiency of photosynthesis, in that vast areas of phase space can be sampled effectively to find the most efficient path for energy transfer. Photosynthetic complexes are exquisitely tuned to capture solar light efficiently, and then transmit the excitation energy to reaction centres, where long term energy storage is initiated. The energy transfer mechanism is often described by semiclassical models that invoke ‘hopping’ of excited-state populations along discrete energy levels1,2. Two-dimensional Fourier transform electronic spectroscopy3,4,5 has mapped6 these energy levels and their coupling in the Fenna–Matthews–Olson (FMO) bacteriochlorophyll complex, which is found in green sulphur bacteria and acts as an energy ‘wire’ connecting a large peripheral light-harvesting antenna, the chlorosome, to the reaction centre7,8,9. The spectroscopic data clearly document the dependence of the dominant energy transport pathways on the spatial properties of the excited-state wavefunctions of the whole bacteriochlorophyll complex6,10. But the intricate dynamics of quantum coherence, which has no classical analogue, was largely neglected in the analyses—even though electronic energy transfer involving oscillatory populations of donors and acceptors was first discussed more than 70 years ago11, and electronic quantum beats arising from quantum coherence in photosynthetic complexes have been predicted12,13 and indirectly observed14. Here we extend previous two-dimensional electronic spectroscopy investigations of the FMO bacteriochlorophyll complex, and obtain direct evidence for remarkably long-lived electronic quantum coherence playing an important part in energy transfer processes within this system. The quantum coherence manifests itself in characteristic, directly observable quantum beating signals among the excitons within the Chlorobium tepidum FMO complex at 77 K. This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path.

Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems

This paper is concerned with the solution of a system of linear equations T M, N X=b, where T M, N denotes a positive definite doubly symmetric block-Toeplitz matrix with Toeplitz blocks arising from a generating function f of the Wiener class. We derive optimal and Strang-type trigonometric preconditioners P M, N of T M, N from the Fejer and Fourier sum of f, respectively. Using relations between trigonometric transforms and Toeplitz matrices, we prove that for all e > 0 and sufficiently large M, N, at most O(M) + O(N) eigenvalues of lie outside the interval (1 — e, l + e) such that the preconditioned conjugate gradient method converges in at most O(M) + O(N) steps.

Trigonometric Preconditioners for Block Toeplitz Systems

This contribution features an accelerated computation of the Sinkhorn's algorithm, which approximates the Wasserstein transportation distance, by employing nonequispaced fast Fourier transforms (NFFT). The algorithm proposed allows approximations of the Wasserstein distance by involving not more than $\mathcal O(n\log n)$ operations for probability measures supported by~$n$ points. Furthermore, the proposed method avoids expensive allocations of the characterizing matrices. With this numerical acceleration, the transportation distance is accessible to probability measures out of reach so far. Numerical experiments using synthetic and real data affirm the computational advantage and superiority.

Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm

We combine a periodization strategy for weighted $L_{2}$-integrands with efficient approximation methods in order to approximate multivariate non-periodic functions on the high-dimensional cube $\left[-\frac{1}{2},\frac{1}{2}\right]^{d}$. Our concept allows to determine conditions on the $d$-variate torus-to-cube transformations ${\psi:\left[-\frac{1}{2},\frac{1}{2}\right]^{d}\to\left[-\frac{1}{2},\frac{1}{2}\right]^{d}}$ such that a non-periodic function is transformed into a smooth function in the Sobolev space $\mathcal H^{m}(\mathbb{T}^{d})$ when applying $\psi$. We adapt some $L_{\infty}(\mathbb{T}^{d})$- and $L_{2}(\mathbb{T}^{d})$-approximation error estimates for single rank-$1$ lattice approximation methods and adjust algorithms for the fast evaluation and fast reconstruction of multivariate trigonometric polynomials on the torus in order to apply these methods to the non-periodic setting. We illustrate the theoretical findings by means of numerical tests in up to $d=5$ dimensions.

Efficient multivariate approximation on the cube.

i i 2 1 N N t e e m s ρ ω ρ κ ρ κ κ ρ r k or − = ≈ 1 0 i - i - M t e e s d m κ ω κ κ ρ ρ κ κ ρ r k , where s denotes the estimated signal at position k at time t , m the magnetiza- tion and the angular off-resonance frequency at position r , N1N2 the number of pixels, M the number of samples in the k-space domain, and d an optional sam- pling density compensation. In principle, and t may be considered as extra di- mensions in image and k-space, respectively. Evaluating one of the sums then amounts to calculating a trivariate Fourier transform with non-equispaced sam- pling in both domains. To improve accuracy and efficiency, we suggest to directly apply the above approximation to the field inhomogeneity-induced exponential. For this purpose, we define

/pdf/field-inhomogeneity-correction-based-on-gridding-4pl7c7fqv5.pdf

Field Inhomogeneity Correction based on Gridding Reconstruction

Several useful representations of a function f : Ωp 7→ IR exist which are usually related to specific purposes: (i) series expansion into spherical harmonics to do mathematics, (ii) series expansion into (unimodal) radial basis functions to do probability and statistics, (iii) series expansion into spline functions to do numerics. In many practical applications the common problem is to reconstruct an approximation of f from sampled data (ri, f(ri)), i = 1, . . . , n, with some convenient properties using one of the above representations. Their critical parameter, e.g. (i) the degree of the harmonic series expansion, (ii) the spherical dispersion of unimodal radial functions, (iii) the choice of the knots, may to some extent be adjusted to the total number and/or the geometric arrangement of the measurement locations. However, these representations are in no way involved in the sampling process itself. After briefly reviewing the basics of wavelets and the specifics of spherical wavelets, another representation of f in terms of spherical wavelets is introduced. It will be shown that spherical wavelets are well suited to render functions defined on a sphere. Moreover, it will be demonstrated that wavelets are well apt to allow for locally varying spatial resolution, thus providing a digital device to zoom into those spherical areas where the function f is of special interest. Such a device seems to be required to increase the spatial resolution by a factor of 1000 or greater locally. Thus, spherical wavelets provide the means to control the sampling process to gradually adapt automatically to a local refinement of the spatial resolution. In particular, it is shown that spherical wavelets apply to X–ray pole intensity data as well as to crystallographic orientation density functions, and that the multiscale resolution easily transfers from pole spheres to orientation space.

Daniel Potts

Papers

Trigonometric Preconditioners for Block Toeplitz Systems

Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm

Efficient multivariate approximation on the cube.

Field Inhomogeneity Correction based on Gridding Reconstruction

Spherical Wavelets with an Application in Preferred Crystallographic Orientation