https://www.sandia.gov/~sjplimp/papers/jcompphys95.pdf

Fast parallel algorithms for short-range molecular dynamics

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.

The use of randomness is now an accepted tool in Theoretical Computer Science but not everyone is aware of the underpinnings of this methodology in Combinatorics - particularly, in what is now called the probabilistic Method as developed primarily by Paul Erdoős over the past half century. Here I will explore a particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets. A central point will be the evolution of these problems from the purely existential proofs of Erdős to the algorithmic aspects of much interest to this audience.

/pdf/the-probabilistic-method-5g63k0itke.pdf

The Probabilistic Method

The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field. Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and their applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, KolmogorovLoveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.

An Introduction to Kolmogorov Complexity and Its Applications

Water, the most abundant constituent of natural foods, is a ubiquitous plasticizer of most natural and fabricated food ingredients and products. Many of the new concepts and developments in modern food science and technology revolve around the role of water, and its manipulation, in food manufacturing, processing, and preservation. This article reviews the effects of water, as a near-universal solvent and plasticizer, on the behavior of polymeric (as well as oligomeric and monomeric) food materials and systems, with emphasis on the impact of water content (in terms of increasing system mobility and eventual water "availability") on food quality, safety, stability, and technological performance. This review describes a new perspective on moisture management, an old and established discipline now evolving to a theoretical basis of fundamental structure-property principles from the field of synthetic polymer science, including the innovative concepts of "water dynamics" and "glass dynamics". These integrated concepts focus on the non-equilibrium nature of all "real world" food products and processes, and stress the importance to successful moisture management of the maintenance of food systems in kinetically metastable, dynamically constrained glassy states rather than equilibrium thermodynamic phases. The understanding derived from this "food polymer science" approach to water relationships in foods has led to new insights and advances beyond the limited applicability of traditional concepts involving water activity. This article is neither a conventional nor comprehensive review of water activity, but rather a critical overview that presents and discusses current, usable information on moisture management theory, research, and practice applicable to food systems covering the broadest ranges of moisture content and processing/storage temperature conditions.

Beyond water activity: recent advances based on an alternative approach to the assessment of food quality and safety

It is shown that every deterministic multitape Turing machine of time complexity t(n) can be simulated by a deterministic Turing machine of tape complexity t(n)/logt(n). Consequently, for tape constructable t(n), the class of languages recognizable by multitape Turing machines of time complexity t(n) is strictly contained in the class of languages recognized by Turing machines of tape complexity t(n). In particular the context-sensitive languages cannot be recognized in linear time by deterministic multitape Turing machines.

On Time Versus Space

We study a one-person game played by placing pebbles, according to certain rules, on the vertices of a directed graph. In [3] it was shown that for each graph withn vertices and maximum in-degreed, there is a pebbling strategy which requires at mostc(d) n/logn pebbles. Here we show that this bound is tight to within a constant factor. We also analyze a variety of pebbling algorithms, including one which achieves the 0(n/logn) bound.

Space bounds for a game on graphs

Realtime ray tracing has recently established itself as a possible alternative to the current rasterization approach for interactive 3D graphics. However, the performance of existing software implementations is still severely limited by today's CPUs, requiring many CPUs for achieving realtime performance.In this paper we present a prototype implementation of the full ray tracing pipeline on a single FPGA chip. Running at only 90 MHz it achieves realtime frame rates of 20 to 60 frames per second over a wide range of 3D scenes and includes support for texturing, multiple light sources, and multiple levels of reflection or transparency. A particular interesting feature of the design in the re-use of the transformation unit necessary for supporting dynamic scenes also for other tasks, including efficient ray-triangle intersection as well as shading computations. Despite the additional support for dynamic scenes this approach reduces the overall hardware cost by 68%.We evaluate the design and its implementation across a wide set of example scenes and demonstrate the benefits of dedicated realtime ray tracing hardware.

/pdf/realtime-ray-tracing-of-dynamic-scenes-on-an-fpga-chip-4jjqll2r3d.pdf

Realtime ray tracing of dynamic scenes on an FPGA chip

Hardware correctness is becoming ever more important in the design of computer systems. The authors introduce a powerful new approach to the design and analysis of modern computer architectures, based on mathematically well-founded formal methods which allows for rigorous correctness proofs, accurate hardware costs determination, and performance evaluation. This book develops, at the gate level, the complete design of a pipelined RISC processor with a fully IEEE-compliant floating-point unit. In contrast to other design approaches, the design presented here is modular, clean and complete.

Computer Architecture: Complexity and Correctness

We show that, for multi-tape Turing machines, non-deterministic linear time is more powerful than deterministic linear time. We also discuss the prospects for extending this result to more general Turing machines.

/pdf/on-determinism-versus-non-determinism-and-related-problems-4pier97j83.pdf

Wolfgang J. Paul

Papers

On Time Versus Space

Space bounds for a game on graphs

Realtime ray tracing of dynamic scenes on an FPGA chip

Computer Architecture: Complexity and Correctness

On determinism versus non-determinism and related problems