GRAPH ISOMORPHISMS AND MATRIX SIMILARITY: SWITCHING BETWEEN REPRESENTATIONS

A proof whether two graphs (possibly oriented graphs or multigraphs, etc.) are isomorphic or not can be derived by various methods. Some of them are reasonable for small numbers of vertices and/or edges, but not for larger numbers. Switching from iconic representation to a matrix representation transforms the problem of Graph Theory into a problem in Linear Algebra. The support provided by a Computer Algebra System is analyzed, in particular with regard to the building of new mathematical knowledge through a transition from graphical to algebraic representation. Moreover two important issues are discussed: a. the need for more than one representation; b. the direction of the switch between representations, which is non standard, from graphical to algebraic

Numerical and perturbation theoretic methods for the solution of the Schrödinger equation

In the present work we present a numerical and perturbation theoretic approach to the solution of the one-particle Schrödinger equation. Thenumerical methods developed can be used to find energy eigenvalues for one-dimensional problems as well as for radial ones. Expectation values are determined by an approach based on eigenvalue calculations, without the explicit use of wave functions.Hypervirial and Hellmann-Feynman theorems are used to obtain perturbation series to high order for polynomial type radial perturbations of the hydrogen atom. One such perturbation leads to an apparently new phenomenon in Rayleigh-Schrödinger perturbation theory.Wynn's algorithm is used to get Padé approximants for the perturbation series. The series for the energy and for the quantities are treated, and both types of series can be found using the hypervirial method.Several applications of the numerical techniques are given; it is emphasized that theoretical manipulations are needed to transform the problem to an appropriate numerical form. It is demonstrated that a slight modification in the numerical techniques developed permits treatment of quasi-bound states as well as bound states. It is also shown how to calculate a local quantity Ψ(O), using energy calculations, and how to reduce the problem of treating angular terms in the quadratic Zeeman effect problem to a radial integration problem

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension

Algorithm and architecture for simultaneous diagonalization of matrices applied to subspace-based speech enhancement

This thesis presents algorithm and architecture for simultaneous diagonalization of matrices. As an example, a subspace-based speech enhancement problem is considered, where in the covariance matrices of the speech and noise are diagonalized simultaneously. In order to compare the system performance of the proposed algorithm, objective measurements of speech enhancement is shown in terms of the signal to noise ratio and mean bark spectral distortion at various noise levels. In addition, an innovative subband analysis technique for subspace-based time-domain constrained speech enhancement technique is proposed. The proposed technique analyses the signal in its subbands to build accurate estimates of the covariance matrices of speech and noise, exploiting the inherent low varying characteristics of speech and noise signals in narrow bands. The subband approach also decreases the computation time by reducing the order of the matrices to be simultaneously diagonalized. Simulation results indicate that the proposed technique performs well under extreme low signal-to-noise-ratio conditions. Further, an architecture is proposed to implement the simultaneous diagonalization scheme. The architecture is implemented on an FPGA primarily to compare the performance measures on hardware and the feasibility of the speech enhancement algorithm in terms of resource utilization, throughput, etc. A Xilinx FPGA is targeted for implementation. FPGA resource utilization re-enforces on the practicability of the design. Also a projection of the design feasibility for an ASIC implementation in terms of transistor count only is include

Using reconfigurable computing technology to accelerate matrix decomposition and applications

Matrix decomposition plays an increasingly significant role in many scientific and engineering applications. Among numerous techniques, Singular Value Decomposition (SVD) and Eigenvalue Decomposition (EVD) are widely used as factorization tools to perform Principal Component Analysis for dimensionality reduction and pattern recognition in image processing, text mining and wireless communications, while QR Decomposition (QRD) and sparse LU Decomposition (LUD) are employed to solve the dense or sparse linear system of equations in bioinformatics, power system and computer vision. Matrix decompositions are computationally expensive and their sequential implementations often fail to meet the requirements of many time-sensitive applications. The emergence of reconfigurable computing has provided a flexible and low-cost opportunity to pursue high-performance parallel designs, and the use of FPGAs has shown promise in accelerating this class of computation. In this research, we have proposed and implemented several highly parallel FPGA-based architectures to accelerate matrix decompositions and their applications in data mining and signal processing. Specifically, in this dissertation we describe the following contributions: • We propose an efficient FPGA-based double-precision floating-point architecture for EVD, which can efficiently analyze large-scale matrices. • We implement a floating-point Hestenes-Jacobi architecture for SVD, which is capable of analyzing arbitrary sized matrices. • We introduce a novel deeply pipelined reconfigurable architecture for QRD, which can be dynamically configured to perform either Householder transformation or Givens rotation in a manner that takes advantage of the strengths of each. • We design a configurable architecture for sparse LUD that supports both symmetric and asymmetric sparse matrices with arbitrary sparsity patterns. • By further extending the proposed hardware solution for SVD, we parallelize a popular text mining tool-Latent Semantic Indexing with an FPGA-based architecture. • We present a configurable architecture to accelerate Homotopy l1-minimization, in which the modification of the proposed FPGA architecture for sparse LUD is used at its core to parallelize both Cholesky decomposition and rank-1 update. Our experimental results using an FPGA-based acceleration system indicate the efficiency of our proposed novel architectures, with application and dimension-dependent speedups over an optimized software implementation that range from 1.5ÃÂ to 43.6ÃÂ in terms of computation time

Topics in Programming Languages, a Philosophical Analysis through the case of Prolog

[EN]Programming languages seldom find proper anchorage in philosophy of logic, language and science. is more, philosophy of language seems to be restricted to natural languages and linguistics, and even philosophy of logic is rarely framed into programming languages topics. The logic programming paradigm and Prolog are, thus, the most adequate paradigm and programming language to work on this subject, combining natural language processing and linguistics, logic programming and constriction methodology on both algorithms and procedures, on an overall philosophizing declarative status. Not only this, but the dimension of the Fifth Generation Computer system related to strong Al wherein Prolog took a major role. and its historical frame in the very crucial dialectic between procedural and declarative paradigms, structuralist and empiricist biases, serves, in exemplar form, to treat straight ahead philosophy of logic, language and science in the contemporaneous age as well. In recounting Prolog's philosophical, mechanical and algorithmic harbingers, the opportunity is open to various routes. We herein shall exemplify some: - the mechanical-computational background explored by Pascal, Leibniz, Boole, Jacquard, Babbage, Konrad Zuse, until reaching to the ACE (Alan Turing) and EDVAC (von Neumann), offering the backbone in computer architecture, and the work of Turing, Church, Gödel, Kleene, von Neumann, Shannon, and others on computability, in parallel lines, throughly studied in detail, permit us to interpret ahead the evolving realm of programming languages. The proper line from lambda-calculus, to the Algol-family, the declarative and procedural split with the C language and Prolog, and the ensuing branching and programming languages explosion and further delimitation, are thereupon inspected as to relate them with the proper syntax, semantics and philosophical élan of logic programming and Prolog

NASA Space Engineering Research Center Symposium on VLSI Design

The NASA Space Engineering Research Center (SERC) is proud to offer, at its second symposium on VLSI design, presentations by an outstanding set of individuals from national laboratories and the electronics industry. These featured speakers share insights into next generation advances that will serve as a basis for future VLSI design. Questions of reliability in the space environment along with new directions in CAD and design are addressed by the featured speakers