Parallel Tempering Simulation of the three-dimensional Edwards-Anderson Model with Compact Asynchronous Multispin Coding on GPU

Monte Carlo simulations of the Ising model play an important role in the field of computational statistical physics, and they have revealed many properties of the model over the past few decades. However, the effect of frustration due to random disorder, in particular the possible spin glass phase, remains a crucial but poorly understood problem. One of the obstacles in the Monte Carlo simulation of random frustrated systems is their long relaxation time making an efficient parallel implementation on state-of-the-art computation platforms highly desirable. The Graphics Processing Unit (GPU) is such a platform that provides an opportunity to significantly enhance the computational performance and thus gain new insight into this problem. In this paper, we present optimization and tuning approaches for the CUDA implementation of the spin glass simulation on GPUs. We discuss the integration of various design alternatives, such as GPU kernel construction with minimal communication, memory tiling, and look-up tables. We present a binary data format, Compact Asynchronous Multispin Coding (CAMSC), which provides an additional $28.4\%$ speedup compared with the traditionally used Asynchronous Multispin Coding (AMSC). Our overall design sustains a performance of 33.5 picoseconds per spin flip attempt for simulating the three-dimensional Edwards-Anderson model with parallel tempering, which significantly improves the performance over existing GPU implementations.Comment: 15 pages, 18 figure

Optimal Permutation Routing for Low-dimensional Hypercubes

We consider the offline problem of routing a permutation of tokens on the nodes of a d-dimensional hypercube, under a queueless MIMD communication model (under the constraints that each hypercube edge may only communicate one token per communication step, and each node may only be occupied by a single token between communication steps). For a d-dimensional hypercube, it is easy to see that d communication steps are necessary. We develop a theory of “separability ” which enables an analytical proof that d steps suffice for the case d = 3, and facilitates an experimental verification that d steps suffice for d = 4. This result improves the upper bound for the number of communication steps required to route an arbitrary permutation on arbitrarily large hypercubes to 2d − 4. We also find an interesting side-result, that the number of possible communication steps in a d-dimensional hypercube is the same as the number of perfect matchings in a (d + 1)-dimensional hypercube, a combinatorial quantity for which there is no closed-form expression. Finally we present some experimental observations which may lead to a proof of a more general result for arbitrarily large dimension d. 2

Timed circuit synthesis using implicit methods

Journal ArticleThe design and synthesis of asynchronous circuits is gaining importance in both the industrial and academic worlds. Timed circuits are a class of asynchronous circuits that incorporate explicit timing information in the specification. This information is used throughout the synthesis procedure to optimize the design. In order to synthesize a timed circuit, it is necessary to exp lore the timed state space of the specification. The memory required to store the timed state space of a complex specification can be prohibitive for large designs when explicit representation methods are used. This paper describes the application of BDDs and MTBDDs to the representation of timed state spaces and the synthesis of timed circuits. These implicit techniques significantly improve the memory efficiency of timed state space exploration and allow more complex designs to be synthesized. Implicit methods also allow the derivation of solution spaces containing all valid solutions to the synthesis problem facilitating subsequent optimization and technology mapping steps

A Formal Model of Ambiguity and its Applications in Machine Translation

Systems that process natural language must cope with and resolve ambiguity. In this dissertation, a model of language processing is advocated in which multiple inputs and multiple analyses of inputs are considered concurrently and a single analysis is only a last resort. Compared to conventional models, this approach can be understood as replacing single-element inputs and outputs with weighted sets of inputs and outputs. Although processing components must deal with sets (rather than individual elements), constraints are imposed on the elements of these sets, and the representations from existing models may be reused. However, to deal efficiently with large (or infinite) sets, compact representations of sets that share structure between elements, such as weighted finite-state transducers and synchronous context-free grammars, are necessary. These representations and algorithms for manipulating them are discussed in depth in depth. To establish the effectiveness and tractability of the proposed processing model, it is applied to several problems in machine translation. Starting with spoken language translation, it is shown that translating a set of transcription hypotheses yields better translations compared to a baseline in which a single (1-best) transcription hypothesis is selected and then translated, independent of the translation model formalism used. More subtle forms of ambiguity that arise even in text-only translation (such as decisions conventionally made during system development about how to preprocess text) are then discussed, and it is shown that the ambiguity-preserving paradigm can be employed in these cases as well, again leading to improved translation quality. A model for supervised learning that learns from training data where sets (rather than single elements) of correct labels are provided for each training instance and use it to learn a model of compound word segmentation is also introduced, which is used as a preprocessing step in machine translation

The Reality of Virtual Environments: WPE II Paper

Recent advances in computer technology have made it now possible to create and display three-dimensional virtual environments for real-time exploration and interaction by a user. This paper surveys some of the research done in this field at such places as: NASA\u27s Ames Research Center, MIT\u27s Media Laboratory, The University of North Carolina at Chapel Hill, and the University of New Brunswick. Limitations to the reality of these simulations will be examined, focusing on input and output devices, computational complexity, as well as tactile and visual feedback

Information visualisation

Bibliography: leaves 100-102.Information visualisation uses interactive three-dimensional (3D) graphics to create an immersive environment for the exploration of large amounts of data. Unlike scientific visualisation, where the underlying physical process usually takes place in 3D space, information visualisation deals with purely abstract data. Because abstract data often lacks an intuitive visual representation, selecting an appropriate representation of the data becomes a challenge. As a result, the creation of information visualisation involves as much exploration and investigation as the eventual exploration of that data itself. Unless the user of the data is also the creator of the visualisations, the turnaround time can therefore become prohibitive. In our experience, existing visualisation applications often lack the flexibility required to easily create information visualisations. These solutions do not provide sufficiently flexible and powerful means of both visually representing the data, and specifying user-interface interactions with the underlying database. This thesis describes a library of classes that allows the user to easily implement visualisation primitives, with their accompanying interactions. These classes are not individual visualisations but can be combined to form more complex visualisations. Classes for creating various primitive visual representations have been created. In addition to this, a number of auxillary classes have been created that provide the user with the ability to swap between visualisations, scale whole scenes, and use automatic level of detail control. The classes all have built-in interaction methods which allow the user to easily incorporate the forms of interaction that we found the most useful, for example the ability to select a data. item and thereby obtain more information about it, or the ability to allow the user to change the position of certain data items. To demonstrate the effectiveness of the classes we implemented and evaluated a. number of example systems. We found that the result of using the classes was a decrease in development time as well as enabling people with little, or no visualisation experience to create information visualisations

Analysis of Hardware Descriptions

The design process for integrated circuits requires a lot of analysis of circuit descriptions. An important class of analyses determines how easy it will be to determine if a physical component suffers from any manufacturing errors. As circuit complexities grow rapidly, the problem of testing circuits also becomes increasingly difficult. This thesis explores the potential for analysing a recent high level hardware description language called Ruby. In particular, we are interested in performing testability analyses of Ruby circuit descriptions. Ruby is ammenable to algebraic manipulation, so we have sought transformations that improve testability while preserving behaviour. The analysis of Ruby descriptions is performed by adapting a technique called abstract interpretation. This has been used successfully to analyse functional programs. This technique is most applicable where the analysis to be captured operates over structures isomorphic to the structure of the circuit. Many digital systems analysis tools require the circuit description to be given in some special form. This can lead to inconsistency between representations, and involves additional work converting between representations. We propose using the original description medium, in this case Ruby, for performing analyses. A related technique, called non-standard interpretation, is shown to be very useful for capturing many circuit analyses. An implementation of a system that performs non-standard interpretation forms the central part of the work. This allows Ruby descriptions to be analysed using alternative interpretations such test pattern generation and circuit layout interpretations. This system follows a similar approach to Boute's system semantics work and O'Donnell's work on Hydra. However, we have allowed a larger class of interpretations to be captured and offer a richer description language. The implementation presented here is constructed to allow a large degree of code sharing between different analyses. Several analyses have been implemented including simulation, test pattern generation and circuit layout. Non-standard interpretation provides a good framework for implementing these analyses. A general model for making non-standard interpretations is presented. Combining forms that combine two interpretations to produce a new interpretation are also introduced. This allows complex circuit analyses to be decomposed in a modular manner into smaller circuit analyses which can be built independently