Semiring induced valuation algebras: Exact and approximate local computation algorithms

Local computation in join trees or acyclic hypertrees has been shown to be linked to a particular algebraic structure, called valuation algebra.There are many models of this algebraic structure ranging from probability theory to numerical analysis, relational databases and various classical and non-classical logics. It turns out that many interesting models of valuation algebras may be derived from semiring valued mappings. In this paper we study how valuation algebras are induced by semirings and how the structure of the valuation algebra is related to the algebraic structure of the semiring. In particular, c-semirings with idempotent multiplication induce idempotent valuation algebras and therefore permit particularly efficient architectures for local computation. Also important are semirings whose multiplicative semigroup is embedded in a union of groups. They induce valuation algebras with a partially defined division. For these valuation algebras, the well-known architectures for Bayesian networks apply. We also extend the general computational framework to allow derivation of bounds and approximations, for when exact computation is not feasible.

Ixaru's Extended Frequency Dependent Quadrature Rules for Slater Integrals: Parallel Computation Issues

We describe recent progress of an ongoing research programme aimed at producing computational science software that can exploit high performance architectures in the atomic physics application domain. We examine the computational bottleneck of matrix construction in a suite of two-dimensional R-matrix propagation programs, 2DRMP, that are aimed at creating virtual electron collision experiments on HPC architectures. We build on Ixaru's extended frequency dependent quadrature rules (EFDQR) for Slater integrals and examine the challenge of constructing Hamiltonian matrices in parallel across an m-processor compute node in a block cyclic distribution for subsequent diagonalization by ScaLAPACK.

Computation of stress intensity factors in functionally graded materials using partition-of-unity meshfee method

This paper describes the computation of stress intensity factors (SIFs) for cracks in functionally graded materials (FGMs) using an extended element-free Galerkin (XEFG) method. The SIFs are extracted through the crack closure integral (CCI) with a local smoothing technique, non-equilibrium and incompatibility formulations of the interaction integral and the displacement method. The results for mode I and mixed mode case studies are presented and compared with those available in the literature. They are found to be in good agreement where the average absolute error for the CCI with local smoothing, despite its simplicity, yielded a high level of accuracy.

Gapped Two-Body Hamiltonian for Continuous-Variable Quantum Computation

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv) possess a constant energy gap proportional to the squared inverse of the squeezing. Their ground states are the celebrated Gaussian graph states, which are universal resources for quantum computation in the limit of infinite squeezing. These Hamiltonians constitute the basic ingredient for the adiabatic preparation of graph states and thus open new venues for the physical realization of continuous-variable quantum computing beyond the standard optical approaches. We characterize the correlations in these systems at thermal equilibrium. In particular, we prove that the correlations across any multipartition are contained exactly in its boundary, automatically yielding a correlation area law. © 2011 American Physical Society.

COMPUTATION OF SYNTHETIC SPECTRA FROM SIMULATIONS OF RELATIVISTIC SHOCKS

Particle-in-cell (PIC) simulations of relativistic shocks are in principle capable of predicting the spectra of photons that are radiated incoherently by the accelerated particles. The most direct method evaluates the spectrum using the fields given by the Lienard-Wiechart potentials. However, for relativistic particles this procedure is computationally expensive. Here we present an alternative method that uses the concept of the photon formation length. The algorithm is suitable for evaluating spectra both from particles moving in a specific realization of a turbulent electromagnetic field or from trajectories given as a finite, discrete time series by a PIC simulation. The main advantage of the method is that it identifies the intrinsic spectral features and filters out those that are artifacts of the limited time resolution and finite duration of input trajectories.

A Wavelet Approach to the Selective Computation of Eigenvalues for Small Signal Stability Analysis

This paper proposes a method to assess the small signal stability of a power system network by selective determination of the modal eigenvalues. This uses an accelerating polynomial transform, designed using approximate eigenvalues
obtained from a wavelet approximation. Application to the IEEE 14 bus network model produced computational savings of 20%,over the QR algorithm.

A Wavelet Approach to the Selective Computation of Domninant Eigenvalues

This paper introduces an algorithm that calculates the dominant eigenvalues (in terms of system stability) of a linear model and neglects the exact computation of the non-dominant eigenvalues. The method estimates all of the eigenvalues using wavelet based compression techniques. These estimates are used to find a suitable invariant subspace such that projection by this subspace will provide one containing the eigenvalues of interest. The proposed algorithm is exemplified by application to a power system model.

Significance Driven Computation: A Voltage-Scalable, Variation-Aware, Quality-Tuning Motion Estimator

In this paper we present a design methodology for algorithm/architecture co-design of a voltage-scalable, process variation aware motion estimator based on significance driven computation. The fundamental premise of our approach lies in the fact that all computations are not equally significant in shaping the output response of video systems. We use a statistical technique to intelligently identify these significant/not-so-significant computations at the algorithmic level and subsequently change the underlying architecture such that the significant computations are computed in an error free manner under voltage over-scaling. Furthermore, our design includes an adaptive quality compensation (AQC) block which "tunes" the algorithm and architecture depending on the magnitude of voltage over-scaling and severity of process variations. Simulation results show average power savings of similar to 33% for the proposed architecture when compared to conventional implementation in the 90 nm CMOS technology. The maximum output quality loss in terms of Peak Signal to Noise Ratio (PSNR) was similar to 1 dB without incurring any throughput penalty.

Significance Driven Computation on Next-Generation Unreliable Platforms

In this paper, we propose a design paradigm for energy efficient and variation-aware operation of next-generation multicore heterogeneous platforms. The main idea behind the proposed approach lies on the observation that not all operations are equally important in shaping the output quality of various applications and of the overall system. Based on such an observation, we suggest that all levels of the software design stack, including the programming model, compiler, operating system (OS) and run-time system should identify the critical tasks and ensure correct operation of such tasks by assigning them to dynamically adjusted reliable cores/units. Specifically, based on error rates and operating conditions identified by a sense-and-adapt (SeA) unit, the OS selects and sets the right mode of operation of the overall system. The run-time system identifies the critical/less-critical tasks based on special directives and schedules them to the appropriate units that are dynamically adjusted for highly-accurate/approximate operation by tuning their voltage/frequency. Units that execute less significant operations can operate at voltages less than what is required for correct operation and consume less power, if required, since such tasks do not need to be always exact as opposed to the critical ones. Such scheme can lead to energy efficient and reliable operation, while reducing the design cost and overheads of conventional circuit/micro-architecture level techniques.

Efficient Marginal Likelihood Computation for Gaussian Process Regression

In a Bayesian learning setting, the posterior distribution of a predictive model arises from a trade-off between its prior distribution and the conditional likelihood of observed data. Such distribution functions usually rely on additional hyperparameters which need to be tuned in order to achieve optimum predictive performance; this operation can be efficiently performed in an Empirical Bayes fashion by maximizing the posterior marginal likelihood of the observed data. Since the score function of this optimization problem is in general characterized by the presence of local optima, it is necessary to resort to global optimization strategies, which require a large number of function evaluations. Given that the evaluation is usually computationally intensive and badly scaled with respect to the dataset size, the maximum number of observations that can be treated simultaneously is quite limited. In this paper, we consider the case of hyperparameter tuning in Gaussian process regression. A straightforward implementation of the posterior log-likelihood for this model requires O(N^3) operations for every iteration of the optimization procedure, where N is the number of examples in the input dataset. We derive a novel set of identities that allow, after an initial overhead of O(N^3), the evaluation of the score function, as well as the Jacobian and Hessian matrices, in O(N) operations. We prove how the proposed identities, that follow from the eigendecomposition of the kernel matrix, yield a reduction of several orders of magnitude in the computation time for the hyperparameter optimization problem. Notably, the proposed solution provides computational advantages even with respect to state of the art approximations that rely on sparse kernel matrices.

Taking Baby Steps in Molecular Logic-based Computation

Molecular logic-based computation is a broad umbrella covering molecular sensors at its simplest level and logic gate arrays involving steadily increasing levels of parallel and serial integration. The fluorescent PET(photoinduced electron transfer) switching principle remains a loyal servant of this entire field. Applications arise from the convenient operation of molecular information processors in very small spaces.

Trio Performance with 'Faint' at "Sounds New Contemporary Music Festival":Graphic Scores and Free improvisation: Canterbury, Kent

The programme contained a performance by the trio FAINT (Pedro Rebelo - Piano and instru- mental parasites, Franziska Schroeder - Saxophone and Steve Davis - Drums). The performance includes short electroacoustic works based on the trio's free improvisation and a performance of Rebelo's Cipher Series graphic scores.

Metallosupramolecular Materials for Electronic Applications: Molecular Boolean Computation

It is an exciting era for molecular computation because molecular logic gates are being pushed in new directions. The use of sulfur rather than the commonplace nitrogen as the key receptor atom in metal ion sensors is one of these directions; plant cells coming within the jurisdiction of fluorescent molecular thermometers is another, combining photochromism with voltammetry for molecular electronics is yet another. Two-input logic gates benefit from old ideas such as rectifying bilayer electrodes, cyclodextrin-enhanced room-temperature phosphorescence, steric hindrance, the polymerase chain reaction, charge transfer absorption of donor–acceptor complexes and lectin–glycocluster interactions. Furthermore, the concept of photo-uncaging enables rational ways of concatenating logic gates. Computational concepts are also applied to potential cancer theranostics and to the selective monitoring of neurotransmitters in situ. Higher numbers of inputs are also accommodated with the concept of functional integration of gates, where complex input–output patterns are sought out and analysed. Molecular emulation of computational components such as demultiplexers and parity generators/checkers are achieved in related ways. Complexity of another order is tackled with molecular edge detection routines.

Enabling Robust and Efficient Distributed Computation in Dynamic Peer-to-Peer Networks

Motivated by the need for designing efficient and robust fully-distributed computation in highly dynamic networks such as Peer-to-Peer (P2P) networks, we study distributed protocols for constructing and maintaining dynamic network topologies with good expansion properties. Our goal is to maintain a sparse (bounded degree) expander topology despite heavy {\em churn} (i.e., nodes joining and leaving the network continuously over time). We assume that the churn is controlled by an adversary that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm. Our main contribution is a randomized distributed protocol that guarantees with high probability the maintenance of a {\em constant} degree graph with {\em high expansion} even under {\em continuous high adversarial} churn. Our protocol can tolerate a churn rate of up to $O(n/\poly\log(n))$ per round (where $n$ is the stable network size). Our protocol is efficient, lightweight, and scalable, and it incurs only $O(\poly\log(n))$ overhead for topology maintenance: only polylogarithmic (in $n$) bits needs to be processed and sent by each node per round and any node's computation cost per round is also polylogarithmic. The given protocol is a fundamental ingredient that is needed for the design of efficient fully-distributed algorithms for solving fundamental distributed computing problems such as agreement, leader election, search, and storage in highly dynamic P2P networks and enables fast and scalable algorithms for these problems that can tolerate a large amount of churn.