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

In this paper, we discuss the numerical solution of two nonlinear approximation problems. Many applications in electrical engineering, signal processing, and mathematical physics lead to the following problem. Let $h$ be a linear combination of exponentials with real frequencies. Determine all frequencies, all coefficients, and the number of summands if finitely many perturbed, uniformly sampled data of $h$ are given. We solve this problem by an approximate Prony method (APM) and prove the stability of the solution in the square and uniform norm. Further, an APM for nonuniformly sampled data is proposed too. The second approximation problem is related to the first one and reads as follows: Let $\varphi$ be a given 1-periodic window function as defined in section 4. Further let $f$ be a linear combination of translates of $\varphi$. Determine all shift parameters, all coefficients, and the number of translates if finitely many perturbed, uniformly sampled data of $f$ are given. Using Fourier technique, this problem is transferred into the above parameter estimation problem for an exponential sum which is solved by APM. The stability of the solution is discussed in the square and uniform norm too. Numerical experiments show the performance of our approximation methods.

/pdf/nonlinear-approximation-by-sums-of-exponentials-and-4xnn2pt0xa.pdf

Nonlinear Approximation by Sums of Exponentials and Translates

We develop a new algorithm for the fast evaluation of linear combinations of radial functions * based on the recently developed fast Fourier transform at nonequispaced knots. For smooth kernels, e.g. the Gaussian, our algorithm requires * arithmetic operations. In case of singular kernels an additional regularization procedure must be incorporated and the algorithm has the arithmetic complexity * if either the points yj or the points xk are “reasonably uniformly distributed”. We prove error estimates to obtain clues about the choice of the involved parameters and present numerical examples for various singular and smooth kernels in two dimensions.

Fast convolution with radial kernels at nonequispaced knots

Recently, fast and reliable algorithms for the evaluation of spherical harmonic expansions have been developed. The corresponding sampling problem is the computation of Fourier coefficients of a function from sampled values at scattered nodes. We consider a least squares approximation and an interpolation of the given data. Our main result is that the rate of convergence of the two proposed iterative schemes depends only on the mesh norm and the separation distance of the nodes. In conjunction with the nonequispaced FFT on the sphere, the reconstruction of N2 Fourier coefficients from M reasonably distributed samples is shown to take O(N2 log2 N + M) floating point operations. Numerical results support our theoretical findings.

https://www-user.tu-chemnitz.de/~potts/paper/itersphereproc.pdf

Efficient Reconstruction of Functions on the Sphere from Scattered Data

Climate variability and human activities interact to increase the abundance of woody plants in arid and semi-arid ecosystems worldwide. How woody plants interact with rainfall to influence patterns of soil moisture through time, at different depths in the soil profile and between neighboring landscape patches is poorly known. In a semi-arid mesquite savanna, we deployed a paired array of sensors beneath a mesquite canopy and in an adjacent open area to measure volumetric soil water content (theta) every 30 min at several depths between 2004 and 2007. In addition, to quantify temporally dynamic variation in soil moisture between the two microsites and across soil depths we analysed theta time-series using fast Fourier transforms (FFT). FFT analyses were consistent with the prediction that by reducing evaporative losses through shade and reducing rainfall inputs through canopy interception of small rainfall events, the mesquite canopy was associated with a decline in high-frequency (hour-to-hour and day-to-day) variation in shallow theta. Finally, we found that, in both microsites, high-frequency theta variation declined with increasing soil depth as the influence of evaporative losses and inputs associated with smaller rainfall events declined. In this case, we argue that the buffering of shallow soil moisture against high-frequency variations can enhance nutrient cycling and alter the carbon cycle in dryland ecosystems.

/pdf/woody-plants-modulate-the-temporal-dynamics-of-soil-moisture-12g118jou9.pdf

Woody plants modulate the temporal dynamics of soil moisture in a semi-arid mesquite savanna

In semiarid ecosystems, physiography (landscape setting) may interact with woody-plant and soil microbe communities to constrain seasonal exchanges of material and energy at the ecosystem scale. In an upland and riparian shrubland, we examined the seasonally dynamic linkage between ecosystem CO2 exchange, woody-plant water status and photosynthesis, and soil respiration responses to summer rainfall. At each site, we compared tower-based measurements of net ecosystem CO2 exchange (NEE) with ecophysiological measurements among velvet mesquite (Prosopis velutina Woot.) in three size classes and soil respiration in sub-canopy and inter-canopy micro-sites. Monsoonal rainfall influenced a greater shift in the magnitude of ecosystem CO2 assimilation in the upland shrubland than in the riparian shrubland. Mesquite water status and photosynthetic gas exchange were closely linked to the onset of the North American monsoon in the upland shrubland. In contrast, the presence of shallow alluvial groundwater in the riparian shrubland caused larger size classes of mesquite to be physiologically insensitive to monsoonal rains. In both shrublands, soil respiration was greatest beneath mesquite canopies and was coupled to shallow soil moisture abundance. Physiography, through its constraint on the physiological sensitivity of deeply rooted woody plants, may interact with plant-mediated rates of soil respiration to affect the sensitivity of semiarid-ecosystem carbon exchange in response to episodic rainfall.

/pdf/sensitivity-of-mesquite-shrubland-co2-exchange-to-20gkefxaob.pdf

Daniel Potts

Papers

Nonlinear Approximation by Sums of Exponentials and Translates

Fast convolution with radial kernels at nonequispaced knots

Efficient Reconstruction of Functions on the Sphere from Scattered Data

Woody plants modulate the temporal dynamics of soil moisture in a semi-arid mesquite savanna

Sensitivity of mesquite shrubland co2 exchange to precipitation in contrasting landscape settings