Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Global identifiability of linear compartmental models--a computer algebra algorithm.
Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C
1998-01-01
A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.
International Nuclear Information System (INIS)
Littlefield, R.J.; Maschhoff, K.J.
1991-04-01
Many linear algebra algorithms utilize an array of processors across which matrices are distributed. Given a particular matrix size and a maximum number of processors, what configuration of processors, i.e., what size and shape array, will execute the fastest? The answer to this question depends on tradeoffs between load balancing, communication startup and transfer costs, and computational overhead. In this paper we analyze in detail one algorithm: the blocked factored Jacobi method for solving dense eigensystems. A performance model is developed to predict execution time as a function of the processor array and matrix sizes, plus the basic computation and communication speeds of the underlying computer system. In experiments on a large hypercube (up to 512 processors), this model has been found to be highly accurate (mean error ∼ 2%) over a wide range of matrix sizes (10 x 10 through 200 x 200) and processor counts (1 to 512). The model reveals, and direct experiment confirms, that the tradeoffs mentioned above can be surprisingly complex and counterintuitive. We propose decision procedures based directly on the performance model to choose configurations for fastest execution. The model-based decision procedures are compared to a heuristic strategy and shown to be significantly better. 7 refs., 8 figs., 1 tab
Algebraic Algorithm Design and Local Search
National Research Council Canada - National Science Library
Graham, Robert
1996-01-01
.... Algebraic techniques have been applied successfully to algorithm synthesis by the use of algorithm theories and design tactics, an approach pioneered in the Kestrel Interactive Development System (KIDS...
Institute of Scientific and Technical Information of China (English)
WANG ShunJin; ZHANG Hua
2007-01-01
Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.
Parallel algorithms for numerical linear algebra
van der Vorst, H
1990-01-01
This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for p
Construction Example for Algebra System Using Harmony Search Algorithm
Directory of Open Access Journals (Sweden)
FangAn Deng
2015-01-01
Full Text Available The construction example of algebra system is to verify the existence of a complex algebra system, and it is a NP-hard problem. In this paper, to solve this kind of problems, firstly, a mathematical optimization model for construction example of algebra system is established. Secondly, an improved harmony search algorithm based on NGHS algorithm (INGHS is proposed to find as more solutions as possible for the optimization model; in the proposed INGHS algorithm, to achieve the balance between exploration power and exploitation power in the search process, a global best strategy and parameters dynamic adjustment method are present. Finally, nine construction examples of algebra system are used to evaluate the optimization model and performance of INGHS. The experimental results show that the proposed algorithm has strong performance for solving complex construction example problems of algebra system.
Algorithmic algebraic geometry and flux vacua
International Nuclear Information System (INIS)
Gray, James; He Yanghui; Lukas, Andre
2006-01-01
We develop a new and efficient method to systematically analyse four dimensional effective supergravities which descend from flux compactifications. The issue of finding vacua of such systems, both supersymmetric and non-supersymmetric, is mapped into a problem in computational algebraic geometry. Using recent developments in computer algebra, the problem can then be rapidly dealt with in a completely algorithmic fashion. Two main results are (1) a procedure for calculating constraints which the flux parameters must satisfy in these models if any given type of vacuum is to exist; (2) a stepwise process for finding all of the isolated vacua of such systems and their physical properties. We illustrate our discussion with several concrete examples, some of which have eluded conventional methods so far
Robust Algebraic Multilevel Methods and Algorithms
Kraus, Johannes
2009-01-01
This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. Provides a systematic presentation of the recent advances in robust algebraic multilevel methods. Can be used for advanced courses on the topic.
An algorithm to construct the basic algebra of a skew group algebra
Horobeţ, E.
2016-01-01
We give an algorithm for the computation of the basic algebra Morita equivalent to a skew group algebra of a path algebra by obtaining formulas for the number of vertices and arrows of the new quiver Qb. We apply this algorithm to compute the basic algebra corresponding to all simple quaternion
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
The algebraic collective model
International Nuclear Information System (INIS)
Rowe, D.J.; Turner, P.S.
2005-01-01
A recently proposed computationally tractable version of the Bohr collective model is developed to the extent that we are now justified in describing it as an algebraic collective model. The model has an SU(1,1)xSO(5) algebraic structure and a continuous set of exactly solvable limits. Moreover, it provides bases for mixed symmetry collective model calculations. However, unlike the standard realization of SU(1,1), used for computing beta wave functions and their matrix elements in a spherical basis, the algebraic collective model makes use of an SU(1,1) algebra that generates wave functions appropriate for deformed nuclei with intrinsic quadrupole moments ranging from zero to any large value. A previous paper focused on the SO(5) wave functions, as SO(5) (hyper-)spherical harmonics, and computation of their matrix elements. This paper gives analytical expressions for the beta matrix elements needed in applications of the model and illustrative results to show the remarkable gain in efficiency that is achieved by using such a basis in collective model calculations for deformed nuclei
Homogeneous Buchberger algorithms and Sullivant's computational commutative algebra challenge
DEFF Research Database (Denmark)
Lauritzen, Niels
2005-01-01
We give a variant of the homogeneous Buchberger algorithm for positively graded lattice ideals. Using this algorithm we solve the Sullivant computational commutative algebra challenge.......We give a variant of the homogeneous Buchberger algorithm for positively graded lattice ideals. Using this algorithm we solve the Sullivant computational commutative algebra challenge....
Optical linear algebra processors - Architectures and algorithms
Casasent, David
1986-01-01
Attention is given to the component design and optical configuration features of a generic optical linear algebra processor (OLAP) architecture, as well as the large number of OLAP architectures, number representations, algorithms and applications encountered in current literature. Number-representation issues associated with bipolar and complex-valued data representations, high-accuracy (including floating point) performance, and the base or radix to be employed, are discussed, together with case studies on a space-integrating frequency-multiplexed architecture and a hybrid space-integrating and time-integrating multichannel architecture.
Institute of Scientific and Technical Information of China (English)
WANG; Shunjin; ZHANG; Hua
2006-01-01
The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.
Performance Analysis of a Decoding Algorithm for Algebraic Geometry Codes
DEFF Research Database (Denmark)
Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund; Høholdt, Tom
1998-01-01
We analyse the known decoding algorithms for algebraic geometry codes in the case where the number of errors is greater than or equal to [(dFR-1)/2]+1, where dFR is the Feng-Rao distance......We analyse the known decoding algorithms for algebraic geometry codes in the case where the number of errors is greater than or equal to [(dFR-1)/2]+1, where dFR is the Feng-Rao distance...
An algorithm for analysis of the structure of finitely presented Lie algebras
Directory of Open Access Journals (Sweden)
Vladimir P. Gerdt
1997-12-01
Full Text Available We consider the following problem: what is the most general Lie algebra satisfying a given set of Lie polynomial equations? The presentation of Lie algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. That problem is of great practical importance, covering applications ranging from mathematical physics to combinatorial algebra. Some particular applications are constructionof prolongation algebras in the Wahlquist-Estabrook method for integrability analysis of nonlinear partial differential equations and investigation of Lie algebras arising in different physical models. The finite presentations also indicate a way to q-quantize Lie algebras. To solve this problem, one should perform a large volume of algebraic transformations which is sharply increased with growth of the number of generators and relations. For this reason, in practice one needs to use a computer algebra tool. We describe here an algorithm for constructing the basis of a finitely presented Lie algebra and its commutator table, and its implementation in the C language. Some computer results illustrating our algorithmand its actual implementation are also presented.
Applied algebra codes, ciphers and discrete algorithms
Hardy, Darel W; Walker, Carol L
2009-01-01
This book attempts to show the power of algebra in a relatively simple setting.-Mathematical Reviews, 2010… The book supports learning by doing. In each section we can find many examples which clarify the mathematics introduced in the section and each section is followed by a series of exercises of which approximately half are solved in the end of the book. Additional the book comes with a CD-ROM containing an interactive version of the book powered by the computer algebra system Scientific Notebook. … the mathematics in the book are developed as needed and the focus of the book lies clearly o
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
High performance linear algebra algorithms: An introduction
DEFF Research Database (Denmark)
Gustavson, F.G.; Wasniewski, Jerzy
2006-01-01
his Mini-Symposium consisted of two back to back sessions, each consisting of five presentations, held on the afternoon of Monday, June 21, 2004. A major theme of both sessions was novel data structures for the matrices of dense linear algebra, DLA. Talks one to four of session one all centered...
Algorithmic and experimental methods in algebra, geometry, and number theory
Decker, Wolfram; Malle, Gunter
2017-01-01
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It off...
An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications
Directory of Open Access Journals (Sweden)
Daniel J. Dougherty
2010-03-01
Full Text Available Alloy is a lightweight modeling formalism based on relational algebra. In prior work with Fisler, Giannakopoulos, Krishnamurthi, and Yoo, we have presented a tool, Alchemy, that compiles Alloy specifications into implementations that execute against persistent databases. The foundation of Alchemy is an algorithm for rewriting relational algebra formulas into code for database transactions. In this paper we report on recent progress in improving the robustness and efficiency of this transformation.
Algorithmic Algebraic Combinatorics and Gröbner Bases
Klin, Mikhail; Jurisic, Aleksandar
2009-01-01
This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries with a special emphasis on algorithmic aspects and the use of the theory of Grobner bases. Topics covered include coherent configurations, association schemes, permutation groups, Latin squares, the Jacobian conjecture, mathematical chemistry, extremal combinatorics, coding theory, designs, etc. Special attention is paid to the description of innovative practical algorithms and their implementation in software packages such as GAP and MAGM
Algebraic Modeling of Topological and Computational Structures and Applications
Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis
2017-01-01
This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w...
Matrix algebra for linear models
Gruber, Marvin H J
2013-01-01
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f
Algebraic aspects of exact models
International Nuclear Information System (INIS)
Gaudin, M.
1983-01-01
Spin chains, 2-D spin lattices, chemical crystals, and particles in delta function interaction share the same underlying structures: the applicability of Bethe's superposition ansatz for wave functions, the commutativity of transfer matrices, and the existence of a ternary operator algebra. The appearance of these structures and interrelations from the eight vortex model, for delta function interreacting particles of general spin, and for spin 1/2, are outlined as follows: I. Eight Vortex Model. Equivalences to Ising model and the dimer system. Transfer matrix and symmetry of the Self Conjugate model. Relation between the XYZ Hamiltonian and the transfer matrix. One parameter family of commuting transfer matrices. A representation of the symmetric group spin. Diagonalization of the transfer matrix. The Coupled Spectrum equations. II. Identical particles with Delta Function interaction. The Bethe ansatz. Yang's representation. The Ternary Algebra and intergrability. III. Identical particles with delta function interaction: general solution for two internal states. The problem of spin 1/2 fermions. The Operator method
The Automation of Stochastization Algorithm with Use of SymPy Computer Algebra Library
Demidova, Anastasya; Gevorkyan, Migran; Kulyabov, Dmitry; Korolkova, Anna; Sevastianov, Leonid
2018-02-01
SymPy computer algebra library is used for automatic generation of ordinary and stochastic systems of differential equations from the schemes of kinetic interaction. Schemes of this type are used not only in chemical kinetics but also in biological, ecological and technical models. This paper describes the automatic generation algorithm with an emphasis on application details.
Algorithm for solving polynomial algebraic Riccati equations and its application
Czech Academy of Sciences Publication Activity Database
Augusta, Petr; Augustová, Petra
2012-01-01
Roč. 1, č. 4 (2012), s. 237-242 ISSN 2223-7038 R&D Projects: GA ČR GPP103/12/P494 Institutional support: RVO:67985556 Keywords : Numerical algorithms * algebraic Riccati equation * spatially distributed systems * optimal control Subject RIV: BC - Control Systems Theory http://lib.physcon.ru/doc?id=8b4876d6a57d
ALGEBRA: ALgorithm for the heterogeneous dosimetry based on GEANT4 for BRAchytherapy.
Afsharpour, H; Landry, G; D'Amours, M; Enger, S; Reniers, B; Poon, E; Carrier, J-F; Verhaegen, F; Beaulieu, L
2012-06-07
Task group 43 (TG43)-based dosimetry algorithms are efficient for brachytherapy dose calculation in water. However, human tissues have chemical compositions and densities different than water. Moreover, the mutual shielding effect of seeds on each other (interseed attenuation) is neglected in the TG43-based dosimetry platforms. The scientific community has expressed the need for an accurate dosimetry platform in brachytherapy. The purpose of this paper is to present ALGEBRA, a Monte Carlo platform for dosimetry in brachytherapy which is sufficiently fast and accurate for clinical and research purposes. ALGEBRA is based on the GEANT4 Monte Carlo code and is capable of handling the DICOM RT standard to recreate a virtual model of the treated site. Here, the performance of ALGEBRA is presented for the special case of LDR brachytherapy in permanent prostate and breast seed implants. However, the algorithm is also capable of handling other treatments such as HDR brachytherapy.
MultiAspect Graphs: Algebraic Representation and Algorithms
Directory of Open Access Journals (Sweden)
Klaus Wehmuth
2016-12-01
Full Text Available We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs. A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS, and Depth First Search (DFS. These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graphs. We also make available Python implementations of all the algorithms presented in this paper.
Critical analysis of algebraic collective models
International Nuclear Information System (INIS)
Moshinsky, M.
1986-01-01
The author shall understand by algebraic collective models all those based on specific Lie algebras, whether the latter are suggested through simple shell model considerations like in the case of the Interacting Boson Approximation (IBA), or have a detailed microscopic foundation like the symplectic model. To analyze these models critically, it is convenient to take a simple conceptual example of them in which all steps can be implemented analytically or through elementary numerical analysis. In this note he takes as an example the symplectic model in a two dimensional space i.e. based on a sp(4,R) Lie algebra, and show how through its complete discussion we can get a clearer understanding of the structure of algebraic collective models of nuclei. In particular he discusses the association of Hamiltonians, related to maximal subalgebras of our basic Lie algebra, with specific types of spectra, and the connections between spectra and shapes
Acoustooptic linear algebra processors - Architectures, algorithms, and applications
Casasent, D.
1984-01-01
Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.
ADART: an adaptive algebraic reconstruction algorithm for discrete tomography.
Maestre-Deusto, F Javier; Scavello, Giovanni; Pizarro, Joaquín; Galindo, Pedro L
2011-08-01
In this paper we suggest an algorithm based on the Discrete Algebraic Reconstruction Technique (DART) which is capable of computing high quality reconstructions from substantially fewer projections than required for conventional continuous tomography. Adaptive DART (ADART) goes a step further than DART on the reduction of the number of unknowns of the associated linear system achieving a significant reduction in the pixel error rate of reconstructed objects. The proposed methodology automatically adapts the border definition criterion at each iteration, resulting in a reduction of the number of pixels belonging to the border, and consequently of the number of unknowns in the general algebraic reconstruction linear system to be solved, being this reduction specially important at the final stage of the iterative process. Experimental results show that reconstruction errors are considerably reduced using ADART when compared to original DART, both in clean and noisy environments.
An Algorithm for Isolating the Real Solutions of Piecewise Algebraic Curves
Directory of Open Access Journals (Sweden)
Jinming Wu
2011-01-01
to compute the real solutions of two piecewise algebraic curves. It is primarily based on the Krawczyk-Moore iterative algorithm and good initial iterative interval searching algorithm. The proposed algorithm is relatively easy to implement.
Modeling digital switching circuits with linear algebra
Thornton, Mitchell A
2014-01-01
Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transf
Towards Model Checking Stochastic Process Algebra
Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.
2000-01-01
Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of
Advanced computer algebra algorithms for the expansion of Feynman integrals
International Nuclear Information System (INIS)
Ablinger, Jakob; Round, Mark; Schneider, Carsten
2012-10-01
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+ε-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.
Advanced computer algebra algorithms for the expansion of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2012-10-15
Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+{epsilon}-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.
Computational algebraic geometry of epidemic models
Rodríguez Vega, Martín.
2014-06-01
Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.
Polynomial algebra of discrete models in systems biology.
Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2010-07-01
An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.
W algebra in the SU(3) parafermion model
International Nuclear Information System (INIS)
Ding, X.; Fan, H.; Shi, K.; Wang, P.; Zhu, C.
1993-01-01
A construction of W 3 algebra for the SU(3) parafermion model is proposed, in which a Z algebra technique is used instead of the popular free-field realization. The central charge of the underlying algebra is different from known W algebras
Chiral algebras in Landau-Ginzburg models
Dedushenko, Mykola
2018-03-01
Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.
Cox, David A; O'Shea, Donal
2015-01-01
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geom...
A process algebra model of QED
International Nuclear Information System (INIS)
Sulis, William
2016-01-01
The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics. (paper)
Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint
Martínez-Guerra, Rafael
2017-01-01
This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.
Current algebra, statistical mechanics and quantum models
Vilela Mendes, R.
2017-11-01
Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.
Searching dependency between algebraic equations: An algorithm applied to automated reasoning
International Nuclear Information System (INIS)
Yang Lu; Zhang Jingzhong
1990-01-01
An efficient computer algorithm is given to decide how many branches of the solution to a system of algebraic also solve another equation. As one of the applications, this can be used in practice to verify a conjecture with hypotheses and conclusion expressed by algebraic equations, despite the variety of reducible or irreducible. (author). 10 refs
Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
Directory of Open Access Journals (Sweden)
Gene Frantz
2007-01-01
Full Text Available Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.
Fusion algebras of logarithmic minimal models
International Nuclear Information System (INIS)
Rasmussen, Joergen; Pearce, Paul A
2007-01-01
We present explicit conjectures for the chiral fusion algebras of the logarithmic minimal models LM(p,p') considering Virasoro representations with no enlarged or extended symmetry algebra. The generators of fusion are countably infinite in number but the ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of representations decomposes into a finite direct sum of representations. The fusion rules are commutative, associative and exhibit an sl(2) structure but require so-called Kac representations which are typically reducible yet indecomposable representations of rank 1. In particular, the identity of the fundamental fusion algebra p ≠ 1 is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the results of Gaberdiel and Kausch for p = 1 and with Eberle and Flohr for (p, p') = (2, 5) corresponding to the logarithmic Yang-Lee model. In the latter case, we confirm the appearance of indecomposable representations of rank 3. We also find that closure of a fundamental fusion algebra is achieved without the introduction of indecomposable representations of rank higher than 3. The conjectured fusion rules are supported, within our lattice approach, by extensive numerical studies of the associated integrable lattice models. Details of our lattice findings and numerical results will be presented elsewhere. The agreement of our fusion rules with the previous fusion rules lends considerable support for the identification of the logarithmic minimal models LM(p,p') with the augmented c p,p' (minimal) models defined algebraically
Map algebra and model algebra for integrated model building
Schmitz, O.; Karssenberg, D.J.; Jong, K. de; Kok, J.-L. de; Jong, S.M. de
2013-01-01
Computer models are important tools for the assessment of environmental systems. A seamless workflow of construction and coupling of model components is essential for environmental scientists. However, currently available software packages are often tailored either to the construction of model
Tabak, John
2004-01-01
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.
Coherent states and classical limit of algebraic quantum models
International Nuclear Information System (INIS)
Scutaru, H.
1983-01-01
The algebraic models for collective motion in nuclear physics belong to a class of theories the basic observables of which generate selfadjoint representations of finite dimensional, real Lie algebras, or of the enveloping algebras of these Lie algebras. The simplest and most used for illustrations model of this kind is the Lipkin model, which is associated with the Lie algebra of the three dimensional rotations group, and which presents all characteristic features of an algebraic model. The Lipkin Hamiltonian is the image, of an element of the enveloping algebra of the algebra SO under a representation. In order to understand the structure of the algebraic models the author remarks that in both classical and quantum mechanics the dynamics is associated to a typical algebraic structure which we shall call a dynamical algebra. In this paper he shows how the constructions can be made in the case of the algebraic quantum systems. The construction of the symplectic manifold M can be made in this case using a quantum analog of the momentum map which he defines
Flanders, Harley
1975-01-01
Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a
Lectures on algebraic model theory
Hart, Bradd
2001-01-01
In recent years, model theory has had remarkable success in solving important problems as well as in shedding new light on our understanding of them. The three lectures collected here present recent developments in three such areas: Anand Pillay on differential fields, Patrick Speissegger on o-minimality and Matthias Clasen and Matthew Valeriote on tame congruence theory.
Performance analysis of a decoding algorithm for algebraic-geometry codes
DEFF Research Database (Denmark)
Høholdt, Tom; Jensen, Helge Elbrønd; Nielsen, Rasmus Refslund
1999-01-01
The fast decoding algorithm for one point algebraic-geometry codes of Sakata, Elbrond Jensen, and Hoholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this correspondence we analyze the performance of the algorithm for heavier error patterns. It turns out...
A polynomial time algorithm for checking regularity of totally normed process algebra
Yang, F.; Huang, H.
2015-01-01
A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra (PA) processes is given. Its time complexity is O(n 3 +mn) O(n3+mn), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for
An algebraic model for three-cluster giant molecules
International Nuclear Information System (INIS)
Hess, P.O.; Bijker, R.; Misicu, S.
2001-01-01
After an introduction to the algebraic U(7) model for three bodies, we present a relation of a geometrical description of three-cluster molecule to the algebraic U(7) model. Stiffness parameters of oscillations between each of two clusters are calculated and translated to the model parameter values of the algebraic model. The model is applied to the trinuclear system l32 Sn+ α + ll6 Pd which occurs in the ternary cold fission of 252 Cf. (Author)
Ghosh, A
1988-08-01
Lanczos and conjugate gradient algorithms are important in computational linear algebra. In this paper, a parallel pipelined realization of these algorithms on a ring of optical linear algebra processors is described. The flow of data is designed to minimize the idle times of the optical multiprocessor and the redundancy of computations. The effects of optical round-off errors on the solutions obtained by the optical Lanczos and conjugate gradient algorithms are analyzed, and it is shown that optical preconditioning can improve the accuracy of these algorithms substantially. Algorithms for optical preconditioning and results of numerical experiments on solving linear systems of equations arising from partial differential equations are discussed. Since the Lanczos algorithm is used mostly with sparse matrices, a folded storage scheme to represent sparse matrices on spatial light modulators is also described.
Exchange algebra and exotic supersymmetry in the Chiral Potts model
International Nuclear Information System (INIS)
Bernard, D.; Pasquier, V.
1989-01-01
We obtain an exchange algebra for the Chiral Potts model, the elements of which are linear in the parameters defining the rapidity curve. This enables us to connect the Chiral Potts model to a U q (GL(2)) algebra. On the other hand, looking at the model from the S-matrix point of view relates it to a Z N generalisation of the supersymmetric algebra
Application of Symplectic Algebraic Dynamics Algorithm to Circular Restricted Three-Body Problem
International Nuclear Information System (INIS)
Wei-Tao, Lu; Hua, Zhang; Shun-Jin, Wang
2008-01-01
Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge–Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP. (general)
Lu, Wei-Tao; Zhang, Hua; Wang, Shun-Jin
2008-07-01
Symplectic algebraic dynamics algorithm (SADA) for ordinary differential equations is applied to solve numerically the circular restricted three-body problem (CR3BP) in dynamical astronomy for both stable motion and chaotic motion. The result is compared with those of Runge-Kutta algorithm and symplectic algorithm under the fourth order, which shows that SADA has higher accuracy than the others in the long-term calculations of the CR3BP.
Sepanski, Mark R
2010-01-01
Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems
Current algebra of WZNW models at and away from criticality
International Nuclear Information System (INIS)
Abdalla, E.; Forger, M.
1992-01-01
In this paper, the authors derive the current algebra of principal chiral models with a Wess-Zumino term. At the critical coupling where the model becomes conformally invariant (Wess-Zumino-Novikov-Witten theory), this algebra reduces to two commuting Kac-Moody algebras, while in the limit where the coupling constant is taken to zero (ordinary chiral model), we recover the current algebra of that model. In this way, the latter is explicitly realized as a deformation of the former, with the coupling constant as the deformation parameter
Dongarra, Jack; Ltaief, Hatem; Luszczek, Piotr R.; Weaver, Vincent M.
2012-01-01
We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.
Dongarra, Jack
2012-11-01
We propose to study the impact on the energy footprint of two advanced algorithmic strategies in the context of high performance dense linear algebra libraries: (1) mixed precision algorithms with iterative refinement allow to run at the peak performance of single precision floating-point arithmetic while achieving double precision accuracy and (2) tree reduction technique exposes more parallelism when factorizing tall and skinny matrices for solving over determined systems of linear equations or calculating the singular value decomposition. Integrated within the PLASMA library using tile algorithms, which will eventually supersede the block algorithms from LAPACK, both strategies further excel in performance in the presence of a dynamic task scheduler while targeting multicore architecture. Energy consumption measurements are reported along with parallel performance numbers on a dual-socket quad-core Intel Xeon as well as a quad-socket quad-core Intel Sandy Bridge chip, both providing component-based energy monitoring at all levels of the system, through the Power Pack framework and the Running Average Power Limit model, respectively. © 2012 IEEE.
Isovectorial pairing in solvable and algebraic models
International Nuclear Information System (INIS)
Lerma, Sergio; Vargas, Carlos E; Hirsch, Jorge G
2011-01-01
Schematic interactions are useful to gain some insight in the behavior of very complicated systems such as the atomic nuclei. Prototypical examples are, in this context, the pairing interaction and the quadrupole interaction of the Elliot model. In this contribution the interplay between isovectorial pairing, spin-orbit, and quadrupole terms in a harmonic oscillator shell (the so-called pairing-plus-quadrupole model) is studied by algebraic methods. The ability of this model to provide a realistic description of N = Z even-even nuclei in the fp-shell is illustrated with 44 Ti. Our calculations which derive from schematic and simple terms confirm earlier conclusions obtained by using realistic interactions: the SU(3) symmetry of the quadrupole term is broken mainly by the spin-orbit term, but the energies depends strongly on pairing.
Phase Transitions in Algebraic Cluster Models
International Nuclear Information System (INIS)
Yepez-Martinez, H.; Cseh, J.; Hess, P.O.
2006-01-01
Complete text of publication follows. Phase transitions in nuclear systems are of utmost interest. An interesting class of phase transitions can be seen in algebraic models of nuclear structure. They are called shapephase transitions due to the following reason. These models have analytically solvable limiting cases, called dynamical symmetries, which are characterized by a chain of nested subgroups. They correspond to well-defined geometrical shape and behaviour, e.g. to rotation of an ellipsoid, or spherical vibration. The general case of the model, which includes interactions described by more than one groupchain, breaks the symmetry, and changing the relative strengths of these interactions, one can go from one shape to the other. In doing so a phase-transition can be seen. A phase transition is defined as a discontinuity of some quantity as a function of the control parameter, which gives the relative strength of the interactions of different symmetries. Real phase transitions can take place only in infinite systems, like in the classical limits of these algebraic models, when the particle number N is very large: N → ∞. For finite N the discontinuities are smoothed out, nevertheless, some indications of the phase-transitions can still be there. A controlled way of breaking the dynamical symmetries may reveal another very interesting phenomenon, i.e. the appearance of a quasidynamical (or effective) symmetry. This rather general symmetry-concept of quantum mechanics corresponds to a situation, in which the symmetry-breaking interactions are so strong that the energy-eigenfunctions are not symmetric, i.e. are not basis states of an irreducible representation of the symmetry group, rather they are linear combinations of these basis states. However, they are very special linear combinations in the sense that their coefficients are (approximately) identical for states with different spin values. When this is the case, then the underlying intrinsic state is the
Toda theories, W-algebras, and minimal models
International Nuclear Information System (INIS)
Mansfield, P.; Spence, B.
1991-01-01
We discuss the classical W-algebra symmetries of Toda field theories in terms of the pseudo-differential Lax operator associated with the Toda Lax pair. We then show how the W-algebra transformations can be understood as the non-abelian gauge transformations which preserve the form of the Lax pair. This provides a new understanding of the W-algebras, and we discuss their closure and co-cycle structure using this approach. The quantum Lax operator is investigated, and we show that this operator, which generates the quantum W-algebra currents, is conserved in the conformally extended Toda theories. The W-algebra minimal model primary fields are shown to arise naturally in these theories, leading to the conjecture that the conformally extended Toda theories provide a lagrangian formulation of the W-algebra minimal models. (orig.)
Algebraic computability and enumeration models recursion theory and descriptive complexity
Nourani, Cyrus F
2016-01-01
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...
N=2 current algebra and coset models
International Nuclear Information System (INIS)
Hull, C.M.; Spence, B.
1990-01-01
The N=2 supersymmetric extension of the Kac-Moody algebra and the corresponding Sugawara construction of the N=2 superconformal algebra are discussed both in components and in N=1 superspace. A formulation of the Kac-Moody algebra and Sugawara construction is given in N=2 superspace in terms of supercurrents satisfying a non-linear chiral constraint. The operator product of two supercurrents includes terms that are non-linear in the supercurrents. The N=2 generalization of the GKO coset construction is then given and the conditions found by Kazama and Suzuki are seen to arise from the non-linearity of the algebra. (orig.)
Ltaief, Hatem; Luszczek, Piotr R.; Dongarra, Jack
2011-01-01
This paper presents the power profile of two high performance dense linear algebra libraries i.e., LAPACK and PLASMA. The former is based on block algorithms that use the fork-join paradigm to achieve parallel performance. The latter uses fine
Experimental Tests of the Algebraic Cluster Model
Gai, Moshe
2018-02-01
The Algebraic Cluster Model (ACM) of Bijker and Iachello that was proposed already in 2000 has been recently applied to 12C and 16O with much success. We review the current status in 12C with the outstanding observation of the ground state rotational band composed of the spin-parity states of: 0+, 2+, 3-, 4± and 5-. The observation of the 4± parity doublet is a characteristic of (tri-atomic) molecular configuration where the three alpha- particles are arranged in an equilateral triangular configuration of a symmetric spinning top. We discuss future measurement with electron scattering, 12C(e,e’) to test the predicted B(Eλ) of the ACM.
Current algebra of classical non-linear sigma models
International Nuclear Information System (INIS)
Forger, M.; Laartz, J.; Schaeper, U.
1992-01-01
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)
Algebraic Factoring algorithm to recognise read-once functions.
Naidu, S.R.
2003-01-01
A fast polynomial-time algorithm was recently proposed to determine whether a logic function expressed as a unate DNF (disjunctive normal form) can be expressed as a read-once formula where each variable appears no more than once. The paper uses a combinatorial characterisation of read-once formulas
Algebraic models of local period maps and Yukawa algebras
Bandiera, Ruggero; Manetti, Marco
2018-02-01
We describe some L_{∞} model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.
The development of an algebraic multigrid algorithm for symmetric positive definite linear systems
Energy Technology Data Exchange (ETDEWEB)
Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)
1996-12-31
An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.
Action Algebras and Model Algebras in Denotational Semantics
Guedes, Luiz Carlos Castro; Haeusler, Edward Hermann
This article describes some results concerning the conceptual separation of model dependent and language inherent aspects in a denotational semantics of a programming language. Before going into the technical explanation, the authors wish to relate a story that illustrates how correctly and precisely posed questions can influence the direction of research. By means of his questions, Professor Mosses aided the PhD research of one of the authors of this article and taught the other, who at the time was a novice supervisor, the real meaning of careful PhD supervision. The student’s research had been partially developed towards the implementation of programming languages through denotational semantics specification, and the student had developed a prototype [12] that compared relatively well to some industrial compilers of the PASCAL language. During a visit to the BRICS lab in Aarhus, the student’s supervisor gave Professor Mosses a draft of an article describing the prototype and its implementation experiments. The next day, Professor Mosses asked the supervisor, “Why is the generated code so efficient when compared to that generated by an industrial compiler?” and “You claim that the efficiency is simply a consequence of the Object- Orientation mechanisms used by the prototype programming language (C++); this should be better investigated. Pay more attention to the class of programs that might have this good comparison profile.” As a result of these aptly chosen questions and comments, the student and supervisor made great strides in the subsequent research; the advice provided by Professor Mosses made them perceive that the code generated for certain semantic domains was efficient because it mapped to the “right aspect” of the language semantics. (Certain functional types, used to represent mappings such as Stores and Environments, were pushed to the level of the object language (as in gcc). This had the side-effect of generating code for arrays in
Additional operations in algebra of structural numbers for control algorithm development
Directory of Open Access Journals (Sweden)
Morhun A.V.
2016-12-01
Full Text Available The structural numbers and the algebra of the structural numbers due to the simplicity of representation, flexibility and current algebraic operations are the powerful tool for a wide range of applications. In autonomous power supply systems and systems with distributed generation (Micro Grid mathematical apparatus of structural numbers can be effectively used for the calculation of the parameters of the operating modes of consumption of electric energy. The purpose of the article is the representation of the additional algebra of structural numbers. The standard algebra was proposed to be extended by the additional operations and modification current in order to expand the scope of their use, namely to construct a flexible, adaptive algorithms of control systems. It is achieved due to the possibility to consider each individual component of the system with its parameters and provide easy management of entire system and each individual component. Thus, structural numbers and extended algebra are the perspective line of research and further studying is required.
ADAM: analysis of discrete models of biological systems using computer algebra.
Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2011-07-20
Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web
A note on probabilistic models over strings: the linear algebra approach.
Bouchard-Côté, Alexandre
2013-12-01
Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems.
Hyper-lattice algebraic model for data warehousing
Sen, Soumya; Chaki, Nabendu
2016-01-01
This book presents Hyper-lattice, a new algebraic model for partially ordered sets, and an alternative to lattice. The authors analyze some of the shortcomings of conventional lattice structure and propose a novel algebraic structure in the form of Hyper-lattice to overcome problems with lattice. They establish how Hyper-lattice supports dynamic insertion of elements in a partial order set with a partial hierarchy between the set members. The authors present the characteristics and the different properties, showing how propositions and lemmas formalize Hyper-lattice as a new algebraic structure.
International Nuclear Information System (INIS)
Chang, P.; Lee, S.Y.; Yan, Y.T.
2006-01-01
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders
International Nuclear Information System (INIS)
Chang, P
2004-01-01
A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders
Observable algebras for the rational and trigonometric Euler-Calogero-Moser Models
International Nuclear Information System (INIS)
Avan, J.; Billey, E.
1995-01-01
We construct polynomial Poisson algebras of observables for the classical Euler-Calogero-Moser (ECM) models. Their structure connects them to flavour-indexed non-linear W ∞ algebras, albeit with qualitative differences. The conserved Hamiltonians and symmetry algebras derived in a previous work are subsets of these algebra. We define their linear, N →∞ limits, realizing W ∞ type algebras coupled to current algebras. ((orig.))
Thirty-three miniatures mathematical and algorithmic applications of linear algebra
Matousek, Jiří
2010-01-01
This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lov�sz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for s...
Category-theoretic models of algebraic computer systems
Kovalyov, S. P.
2016-01-01
A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; van den Broek, Pim
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
Model Checking Processes Specified In Join-Calculus Algebra
Directory of Open Access Journals (Sweden)
Sławomir Piotr Maludziński
2014-01-01
Full Text Available This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.
Tensor models, Kronecker coefficients and permutation centralizer algebras
Geloun, Joseph Ben; Ramgoolam, Sanjaye
2017-11-01
We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.
Solving the nuclear shell model with an algebraic method
International Nuclear Information System (INIS)
Feng, D.H.; Pan, X.W.; Guidry, M.
1997-01-01
We illustrate algebraic methods in the nuclear shell model through a concrete example, the fermion dynamical symmetry model (FDSM). We use this model to introduce important concepts such as dynamical symmetry, symmetry breaking, effective symmetry, and diagonalization within a higher-symmetry basis. (orig.)
Zimmermann, Ralf
2016-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm converges locally and exhibits a linear rate of convergence.
DEFF Research Database (Denmark)
Zimmermann, Ralf
2017-01-01
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the optimization-based approach known from the literature, we work from a purely matrix-algebraic perspective. Moreover, we prove that the algorithm...... converges locally and exhibits a linear rate of convergence....
Logarithmic sℓ-hat (2) CFT models from Nichols algebras: I
International Nuclear Information System (INIS)
Semikhatov, A M; Tipunin, I Yu
2013-01-01
We construct chiral algebras that centralize rank-2 Nichols algebras with at least one fermionic generator. This gives ‘logarithmic’ W-algebra extensions of a fractional-level sℓ-hat (2) algebra. We discuss crucial aspects of the emerging general relation between Nichols algebras and logarithmic conformal field theory (CFT) models: (i) the extra input, beyond the Nichols algebra proper, needed to uniquely specify a conformal model; (ii) a relation between the CFT counterparts of Nichols algebras connected by Weyl groupoid maps; and (iii) the common double bosonization U(X) of such Nichols algebras. For an extended chiral algebra, candidates for its simple modules that are counterparts of the U(X) simple modules are proposed, as a first step toward a functorial relation between U(X) and W-algebra representation categories. (paper)
Representations of the Virasoro algebra from lattice models
International Nuclear Information System (INIS)
Koo, W.M.; Saleur, H.
1994-01-01
We investigate in detail how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic relations are obeyed in the scaling limit. The latter is under reasonable control thanks to the Bethe-ansatz solution. The results, which are mostly numerical for technical reasons, are remarkably precise. They are also corroborated by exact pieces of information from various sources, in particular Temperley-Lieb algebra representation theory. Most features of the Virasoro algebra (like central term, null vectors, metric properties, etc.) can thus be observed using the lattice models. This seems of general interest for lattice field theory, and also more specifically for finding relations between conformal invariance and lattice integrability, since a basis for the irreducible representations of the Virasoro algebra should now follow (at least in principle) from Bethe-ansatz computations. ((orig.))
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
Optical linear algebra processors - Noise and error-source modeling
Casasent, D.; Ghosh, A.
1985-01-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Optical linear algebra processors: noise and error-source modeling.
Casasent, D; Ghosh, A
1985-06-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Algebraic Bethe ansatz for 19-vertex models with reflection conditions
International Nuclear Information System (INIS)
Utiel, Wagner
2003-01-01
In this work we solve the 19-vertex models with the use of algebraic Bethe ansatz for diagonal reflection matrices (Sklyanin K-matrices). The eigenvectors, eigenvalues and Bethe equations are given in a general form. Quantum spin chains of spin one derived from the 19-vertex models were also discussed
Generalized algebra-valued models of set theory
Löwe, B.; Tarafder, S.
2015-01-01
We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.
Ltaief, Hatem
2011-08-31
This paper presents the power profile of two high performance dense linear algebra libraries i.e., LAPACK and PLASMA. The former is based on block algorithms that use the fork-join paradigm to achieve parallel performance. The latter uses fine-grained task parallelism that recasts the computation to operate on submatrices called tiles. In this way tile algorithms are formed. We show results from the power profiling of the most common routines, which permits us to clearly identify the different phases of the computations. This allows us to isolate the bottlenecks in terms of energy efficiency. Our results show that PLASMA surpasses LAPACK not only in terms of performance but also in terms of energy efficiency. © 2011 Springer-Verlag.
New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation
Liu, Jianzhou; Wang, Li; Zhang, Juan
2017-11-01
The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.
An algebraic approach to modeling in software engineering
International Nuclear Information System (INIS)
Loegel, C.J.; Ravishankar, C.V.
1993-09-01
Our work couples the formalism of universal algebras with the engineering techniques of mathematical modeling to develop a new approach to the software engineering process. Our purpose in using this combination is twofold. First, abstract data types and their specification using universal algebras can be considered a common point between the practical requirements of software engineering and the formal specification of software systems. Second, mathematical modeling principles provide us with a means for effectively analyzing real-world systems. We first use modeling techniques to analyze a system and then represent the analysis using universal algebras. The rest of the software engineering process exploits properties of universal algebras that preserve the structure of our original model. This paper describes our software engineering process and our experience using it on both research and commercial systems. We need a new approach because current software engineering practices often deliver software that is difficult to develop and maintain. Formal software engineering approaches use universal algebras to describe ''computer science'' objects like abstract data types, but in practice software errors are often caused because ''real-world'' objects are improperly modeled. There is a large semantic gap between the customer's objects and abstract data types. In contrast, mathematical modeling uses engineering techniques to construct valid models for real-world systems, but these models are often implemented in an ad hoc manner. A combination of the best features of both approaches would enable software engineering to formally specify and develop software systems that better model real systems. Software engineering, like mathematical modeling, should concern itself first and foremost with understanding a real system and its behavior under given circumstances, and then with expressing this knowledge in an executable form
Directed Abelian algebras and their application to stochastic models.
Alcaraz, F C; Rittenberg, V
2008-10-01
With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .
Algebraic approach to small-world network models
Rudolph-Lilith, Michelle; Muller, Lyle E.
2014-01-01
We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.
Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard
2014-06-26
A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for
Continual Lie algebras and noncommutative counterparts of exactly solvable models
Zuevsky, A.
2004-01-01
Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.
Model selection for contingency tables with algebraic statistics
Krampe, A.; Kuhnt, S.; Gibilisco, P.; Riccimagno, E.; Rogantin, M.P.; Wynn, H.P.
2009-01-01
Goodness-of-fit tests based on chi-square approximations are commonly used in the analysis of contingency tables. Results from algebraic statistics combined with MCMC methods provide alternatives to the chi-square approximation. However, within a model selection procedure usually a large number of
Extensions of Scott's Graph Model and Kleene's Second Algebra
van Oosten, J.; Voorneveld, Niels
We use a way to extend partial combinatory algebras (pcas) by forcing them to represent certain functions. In the case of Scott’s Graph Model, equality is computable relative to the complement function. However, the converse is not true. This creates a hierarchy of pcas which relates to similar
Algorithms for a parallel implementation of Hidden Markov Models with a small state space
DEFF Research Database (Denmark)
Nielsen, Jesper; Sand, Andreas
2011-01-01
Two of the most important algorithms for Hidden Markov Models are the forward and the Viterbi algorithms. We show how formulating these using linear algebra naturally lends itself to parallelization. Although the obtained algorithms are slow for Hidden Markov Models with large state spaces...
2D sigma models and differential Poisson algebras
International Nuclear Information System (INIS)
Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander
2015-01-01
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
The Hamiltonian of the quantum trigonometric Calogero-Sutherland model in the exceptional algebra E8
International Nuclear Information System (INIS)
Fernandez Nunez, J; Garcia Fuertes, W; Perelomov, A M
2009-01-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model for the Lie algebra E 8 and coupling constant κ by using the fundamental irreducible characters of the algebra as dynamical independent variables
Energy Technology Data Exchange (ETDEWEB)
Bennett, Janine Camille [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Visualization and Scientific Computing Dept.; Day, David Minot [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Applied Mathematics and Applications Dept.; Mitchell, Scott A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Computer Science and Informatics Dept.
2009-11-20
This report summarizes the Combinatorial Algebraic Topology: software, applications & algorithms workshop (CAT Workshop). The workshop was sponsored by the Computer Science Research Institute of Sandia National Laboratories. It was organized by CSRI staff members Scott Mitchell and Shawn Martin. It was held in Santa Fe, New Mexico, August 29-30. The CAT Workshop website has links to some of the talk slides and other information, http://www.cs.sandia.gov/CSRI/Workshops/2009/CAT/index.html. The purpose of the report is to summarize the discussions and recap the sessions. There is a special emphasis on technical areas that are ripe for further exploration, and the plans for follow-up amongst the workshop participants. The intended audiences are the workshop participants, other researchers in the area, and the workshop sponsors.
Developing ontological model of computational linear algebra - preliminary considerations
Wasielewska, K.; Ganzha, M.; Paprzycki, M.; Lirkov, I.
2013-10-01
The aim of this paper is to propose a method for application of ontologically represented domain knowledge to support Grid users. The work is presented in the context provided by the Agents in Grid system, which aims at development of an agent-semantic infrastructure for efficient resource management in the Grid. Decision support within the system should provide functionality beyond the existing Grid middleware, specifically, help the user to choose optimal algorithm and/or resource to solve a problem from a given domain. The system assists the user in at least two situations. First, for users without in-depth knowledge about the domain, it should help them to select the method and the resource that (together) would best fit the problem to be solved (and match the available resources). Second, if the user explicitly indicates the method and the resource configuration, it should "verify" if her choice is consistent with the expert recommendations (encapsulated in the knowledge base). Furthermore, one of the goals is to simplify the use of the selected resource to execute the job; i.e., provide a user-friendly method of submitting jobs, without required technical knowledge about the Grid middleware. To achieve the mentioned goals, an adaptable method of expert knowledge representation for the decision support system has to be implemented. The selected approach is to utilize ontologies and semantic data processing, supported by multicriterial decision making. As a starting point, an area of computational linear algebra was selected to be modeled, however, the paper presents a general approach that shall be easily extendable to other domains.
Soliton surfaces associated with sigma models: differential and algebraic aspects
International Nuclear Information System (INIS)
Goldstein, P P; Grundland, A M; Post, S
2012-01-01
In this paper, we consider both differential and algebraic properties of surfaces associated with sigma models. It is shown that surfaces defined by the generalized Weierstrass formula for immersion for solutions of the CP N-1 sigma model with finite action, defined in the Riemann sphere, are themselves solutions of the Euler–Lagrange equations for sigma models. On the other hand, we show that the Euler–Lagrange equations for surfaces immersed in the Lie algebra su(N), with conformal coordinates, that are extremals of the area functional, subject to a fixed polynomial identity, are exactly the Euler–Lagrange equations for sigma models. In addition to these differential constraints, the algebraic constraints, in the form of eigenvalues of the immersion functions, are systematically treated. The spectrum of the immersion functions, for different dimensions of the model, as well as its symmetry properties and its transformation under the action of the ladder operators are discussed. Another approach to the dynamics is given, i.e. description in terms of the unitary matrix which diagonalizes both the immersion functions and the projectors constituting the model. (paper)
Energy Technology Data Exchange (ETDEWEB)
Lee, E.T.
1983-01-01
Algorithms for the construction of the Chomsky and Greibach normal forms for a fuzzy context-free grammar using the algebraic approach are presented and illustrated by examples. The results obtained in this paper may have useful applications in fuzzy languages, pattern recognition, information storage and retrieval, artificial intelligence, database and pictorial information systems. 16 references.
Model Theory in Algebra, Analysis and Arithmetic
Dries, Lou; Macpherson, H Dugald; Pillay, Anand; Toffalori, Carlo; Wilkie, Alex J
2014-01-01
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Geometric model of topological insulators from the Maxwell algebra
Palumbo, Giandomenico
2017-11-01
We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.
Geometric Model of Topological Insulators from the Maxwell Algebra
Palumbo, Giandomenico
I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).
Algebraic model checking for Boolean gene regulatory networks.
Tran, Quoc-Nam
2011-01-01
We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.
Kac-Moody algebra is not hidden symmetry of chiral models
International Nuclear Information System (INIS)
Devchand, C.; Schiff, J.
1997-01-01
A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional Abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. (author). 15 refs
The algebra of non-local charges in non-linear sigma models
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.
1994-01-01
It is derived the complete Dirac algebra satisfied by non-local charges conserved in non-linear sigma models. Some examples of calculation are given for the O(N) symmetry group. The resulting algebra corresponds to a saturated cubic deformation (with only maximum order terms) of the Kac-Moody algebra. The results are generalized for when a Wess-Zumino term be present. In that case the algebra contains a minor order correction (sub-saturation). (author). 1 ref
Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
Directory of Open Access Journals (Sweden)
Sh. Khachatryan
2015-10-01
Full Text Available We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang–Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.
Algebraic fermion models and nuclear structure physics
International Nuclear Information System (INIS)
Troltenier, Dirk; Blokhin, Andrey; Draayer, Jerry P.; Rompf, Dirk; Hirsch, Jorge G.
1996-01-01
Recent experimental and theoretical developments are generating renewed interest in the nuclear SU(3) shell model, and this extends to the symplectic model, with its Sp(6,R) symmetry, which is a natural multi-(ℎ/2π)ω extension of the SU(3) theory. First and foremost, an understanding of how the dynamics of a quantum rotor is embedded in the shell model has established it as the model of choice for describing strongly deformed systems. Second, the symplectic model extension of the 0-(ℎ/2π)ω theory can be used to probe additional degrees of freedom, like core polarization and vorticity modes that play a key role in providing a full description of quadrupole collectivity. Third, the discovery and understanding of pseudo-spin has allowed for an extension of the theory from light (A≤40) to heavy (A≥100) nuclei. Fourth, a user-friendly computer code for calculating reduced matrix elements of operators that couple SU(3) representations is now available. And finally, since the theory is designed to cope with deformation in a natural way, microscopic features of deformed systems can be probed; for example, the theory is now being employed to study double beta decay and thereby serves to probe the validity of the standard model of particles and their interactions. A subset of these topics will be considered in this course--examples cited include: a consideration of the origin of pseudo-spin symmetry; a SU(3)-based interpretation of the coupled-rotor model, early results of double beta decay studies; and some recent developments on the pseudo-SU(3) theory. Nothing will be said about other fermion-based theories; students are referred to reviews in the literature for reports on developments in these related areas
Methods of mathematical modeling using polynomials of algebra of sets
Kazanskiy, Alexandr; Kochetkov, Ivan
2018-03-01
The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.
An algebraic model for quark mass matrices with heavy top
International Nuclear Information System (INIS)
Krolikowski, W.; Warsaw Univ.
1991-01-01
In terms of an intergeneration U(3) algebra, a numerical model is constructed for quark mass matrices, predicting the top-quark mass around 170 GeV and the CP-violating phase around 75 deg. The CKM matrix is nonsymmetric in moduli with |V ub | being very small. All moduli are consistent with their experimental limits. The model is motivated by the author's previous work on three replicas of the Dirac particle, presumably resulting into three generations of leptons and quarks. The paper may be also viewed as an introduction to a new method of intrinsic dynamical description of lepton and quark mass matrices. (author)
Directory of Open Access Journals (Sweden)
A. A. Zolotin
2015-07-01
Full Text Available Posteriori inference is one of the three kinds of probabilistic-logic inferences in the probabilistic graphical models theory and the base for processing of knowledge patterns with probabilistic uncertainty using Bayesian networks. The paper deals with a task of local posteriori inference description in algebraic Bayesian networks that represent a class of probabilistic graphical models by means of matrix-vector equations. The latter are essentially based on the use of tensor product of matrices, Kronecker degree and Hadamard product. Matrix equations for calculating posteriori probabilities vectors within posteriori inference in knowledge patterns with quanta propositions are obtained. Similar equations of the same type have already been discussed within the confines of the theory of algebraic Bayesian networks, but they were built only for the case of posteriori inference in the knowledge patterns on the ideals of conjuncts. During synthesis and development of matrix-vector equations on quanta propositions probability vectors, a number of earlier results concerning normalizing factors in posteriori inference and assignment of linear projective operator with a selector vector was adapted. We consider all three types of incoming evidences - deterministic, stochastic and inaccurate - combined with scalar and interval estimation of probability truth of propositional formulas in the knowledge patterns. Linear programming problems are formed. Their solution gives the desired interval values of posterior probabilities in the case of inaccurate evidence or interval estimates in a knowledge pattern. That sort of description of a posteriori inference gives the possibility to extend the set of knowledge pattern types that we can use in the local and global posteriori inference, as well as simplify complex software implementation by use of existing third-party libraries, effectively supporting submission and processing of matrices and vectors when
Four-parametric two-layer algebraic model of transition boundary layer at a planar plate
International Nuclear Information System (INIS)
Labusov, A.N.; Lapin, Yu.V.
1996-01-01
Consideration is given to four-parametric two-layer algebraic model of transition boundary layer on a plane plate, based on generalization of one-parametric algebraic Prandtl-Loitsjansky-Klauzer-3 model. The algebraic model uses Prandtl formulas for mixing path with Loitsjansky damping multiplier in the internal region and the relation for turbulent viscosity, based on universal scales of external region and named the Klauzer-3 formula. 12 refs., 10 figs
Validation of Simulation Models without Knowledge of Parameters Using Differential Algebra
Directory of Open Access Journals (Sweden)
Björn Haffke
2015-01-01
Full Text Available This study deals with the external validation of simulation models using methods from differential algebra. Without any system identification or iterative numerical methods, this approach provides evidence that the equations of a model can represent measured and simulated sets of data. This is very useful to check if a model is, in general, suitable. In addition, the application of this approach to verification of the similarity between the identifiable parameters of two models with different sets of input and output measurements is demonstrated. We present a discussion on how the method can be used to find parameter deviations between any two models. The advantage of this method is its applicability to nonlinear systems as well as its algorithmic nature, which makes it easy to automate.
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
International Nuclear Information System (INIS)
Gurau, Razvan
2012-01-01
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.
A new (in)finite-dimensional algebra for quantum integrable models
International Nuclear Information System (INIS)
Baseilhac, Pascal; Koizumi, Kozo
2005-01-01
A new (in)finite-dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite-dimensional representations are constructed and mutually commuting quantities-which ensure the integrability of the system-are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite-dimensional algebra is a 'q-deformed' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models
Algebraic formulation of collective models. I. The mass quadrupole collective model
International Nuclear Information System (INIS)
Rosensteel, G.; Rowe, D.J.
1979-01-01
This paper is the first in a series of three which together present a microscopic formulation of the Bohr--Mottelson (BM) collective model of the nucleus. In this article the mass quadrupole collective (MQC) model is defined and shown to be a generalization of the BM model. The MQC model eliminates the small oscillation assumption of BM and also yields the rotational and CM (3) submodels by holonomic constraints on the MQC configuration space. In addition, the MQC model is demonstrated to be an algebraic model, so that the state space of the MQC model carries an irrep of a Lie algebra of microscopic observables, the MQC algebra. An infinite class of new collective models is then given by the various inequivalent irreps of this algebra. A microscopic embedding of the BM model is achieved by decomposing the representation of the MQC algebra on many-particle state space into its irreducible components. In the second paper this decomposition is studied in detail. The third paper presents the symplectic model, which provides the realization of the collective model in the harmonic oscillator shell model
Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.
2009-01-01
The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…
Algebraic Traveling Wave Solutions of a Non-local Hydrodynamic-type Model
International Nuclear Information System (INIS)
Chen, Aiyong; Zhu, Wenjing; Qiao, Zhijun; Huang, Wentao
2014-01-01
In this paper we consider the algebraic traveling wave solutions of a non-local hydrodynamic-type model. It is shown that algebraic traveling wave solutions exist if and only if an associated first order ordinary differential system has invariant algebraic curve. The dynamical behavior of the associated ordinary differential system is analyzed. Phase portraits of the associated ordinary differential system is provided under various parameter conditions. Moreover, we classify algebraic traveling wave solutions of the model. Some explicit formulas of smooth solitary wave and cuspon solutions are obtained
Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models
Suga, Tetsuya; Iijima, Junichi
2018-03-01
Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.
su(1,2) Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame
International Nuclear Information System (INIS)
Jin Shuo; Xie Binghao; Yu Zhaoxian; Hou Jingmin
2008-01-01
The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure: the Hamiltonian can be written as a linear function of the su(1,2) algebra generators. Based on it, the energy eigenvalues are obtained by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics
Anisotropic correlated electron model associated with the Temperley-Lieb algebra
International Nuclear Information System (INIS)
Foerster, Angela; Links, Jon; Roditi, Itzhak
1997-12-01
We present and anisotropic correlated electron model on a periodic lattice, constructed from an R-matrix associated with the Temperley-Lieb algebra. By modification of the coupling of the first and last sites we obtain a model with quantum algebra invariance. (author)
Automatic generation of Fortran programs for algebraic simulation models
International Nuclear Information System (INIS)
Schopf, W.; Rexer, G.; Ruehle, R.
1978-04-01
This report documents a generator program by which econometric simulation models formulated in an application-orientated language can be transformed automatically in a Fortran program. Thus the model designer is able to build up, test and modify models without the need of a Fortran programmer. The development of a computer model is therefore simplified and shortened appreciably; in chapter 1-3 of this report all rules are presented for the application of the generator to the model design. Algebraic models including exogeneous and endogeneous time series variables, lead and lag function can be generated. In addition, to these language elements, Fortran sequences can be applied to the formulation of models in the case of complex model interrelations. Automatically the generated model is a module of the program system RSYST III and is therefore able to exchange input and output data with the central data bank of the system and in connection with the method library modules can be used to handle planning problems. (orig.) [de
Phases and phase transitions in the algebraic microscopic shell model
Directory of Open Access Journals (Sweden)
Georgieva A. I.
2016-01-01
Full Text Available We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott’s SU(3 basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3 basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.
Multiagent scheduling models and algorithms
Agnetis, Alessandro; Gawiejnowicz, Stanisław; Pacciarelli, Dario; Soukhal, Ameur
2014-01-01
This book presents multi-agent scheduling models in which subsets of jobs sharing the same resources are evaluated by different criteria. It discusses complexity results, approximation schemes, heuristics and exact algorithms.
MODELING IN MAPLE AS THE RESEARCHING MEANS OF FUNDAMENTAL CONCEPTS AND PROCEDURES IN LINEAR ALGEBRA
Directory of Open Access Journals (Sweden)
Vasil Kushnir
2016-05-01
Full Text Available The article is devoted to binary technology and "fundamental training technology." Binary training refers to the simultaneous teaching of mathematics and computer science, for example differential equations and Maple, linear algebra and Maple. Moreover the system of traditional course of Maple is not performed. The use of the opportunities of Maple-technology in teaching mathematics is based on the following fundamental concepts of computer science as an algorithm, program, a linear program, cycle, branching, relative operators, etc. That’s why only a certain system of command operators in Maple is considered. They are necessary for fundamental concepts of linear algebra and differential equations studying in Maple-environment. Relative name - "the technology of fundamental training" reflects the study of fundamental mathematical concepts and procedures that express the properties of these concepts in Maple-environment. This article deals with the study of complex fundamental concepts of linear algebra (determinant of the matrix and algorithm of its calculation, the characteristic polynomial of the matrix and the eigenvalues of matrix, canonical form of characteristic matrix, eigenvectors of matrix, elementary divisors of the characteristic matrix, etc., which are discussed in the appropriate courses briefly enough, and sometimes are not considered at all, but they are important in linear systems of differential equations, asymptotic methods for solving differential equations, systems of linear equations. Herewith complex and voluminous procedures of finding of these linear algebra concepts embedded in Maple can be performed as a result of a simple command-operator. Especially important issue is building matrix to canonical form. In fact matrix functions are effectively reduced to the functions of the diagonal matrix or matrix in Jordan canonical form. These matrices are used to rise a square matrix to a power, to extract the roots of the n
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Genetic algorithms in teaching artificial intelligence (automated generation of specific algebras)
Habiballa, Hashim; Jendryscik, Radek
2017-11-01
The problem of teaching essential Artificial Intelligence (AI) methods is an important task for an educator in the branch of soft-computing. The key focus is often given to proper understanding of the principle of AI methods in two essential points - why we use soft-computing methods at all and how we apply these methods to generate reasonable results in sensible time. We present one interesting problem solved in the non-educational research concerning automated generation of specific algebras in the huge search space. We emphasize above mentioned points as an educational case study of an interesting problem in automated generation of specific algebras.
Parallel Algorithms for Model Checking
van de Pol, Jaco; Mousavi, Mohammad Reza; Sgall, Jiri
2017-01-01
Model checking is an automated verification procedure, which checks that a model of a system satisfies certain properties. These properties are typically expressed in some temporal logic, like LTL and CTL. Algorithms for LTL model checking (linear time logic) are based on automata theory and graph
Finite automata over algebraic structures: models and some methods of analysis
Directory of Open Access Journals (Sweden)
Volodymyr V. Skobelev
2015-10-01
Full Text Available In this paper some results of research in two new trends of finite automata theory are presented. For understanding the value and the aim of these researches some short retrospective analysis of development of finite automata theory is given. The first trend deals with families of finite automata defined via recurrence relations on algebraic structures over finite rings. The problem of design of some algorithm that simulates with some accuracy any element of given family of automata is investigated. Some general scheme for design of families of hash functions defined by outputless automata is elaborated. Computational security of these families of hash functions is analyzed. Automata defined on varieties with some algebra are presented and their homomorphisms are characterized. Special case of these automata, namely automata on elliptic curves, are investigated in detail. The second trend deals with quantum automata. Languages accepted by some basic models of quantum automata under supposition that unitary operators associated with input alphabet commute each with the others are characterized.
Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu
2017-03-01
To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.
The algebra of non-local charges in non-linear sigma models
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.
1993-07-01
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower. (author). 22 refs, 5 figs
An algebraic formulation of level one Wess-Zumino-Witten models
International Nuclear Information System (INIS)
Boeckenhauer, J.
1995-07-01
The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven. (orig.)
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Energy Technology Data Exchange (ETDEWEB)
Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)
2012-03-15
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
International Nuclear Information System (INIS)
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-01-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-03-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Analysis of DIRAC's behavior using model checking with process algebra
International Nuclear Information System (INIS)
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof; Diaz, Ricardo Graciani
2012-01-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Analysis of DIRAC's behavior using model checking with process algebra
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-12-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Algorithmic Issues in Modeling Motion
DEFF Research Database (Denmark)
Agarwal, P. K; Guibas, L. J; Edelsbrunner, H.
2003-01-01
This article is a survey of research areas in which motion plays a pivotal role. The aim of the article is to review current approaches to modeling motion together with related data structures and algorithms, and to summarize the challenges that lie ahead in producing a more unified theory of mot...
Off-critical W∞ and Virasoro algebras as dynamical symmetries of the integrable models
International Nuclear Information System (INIS)
Sotkov, G.; Stanishkov, M.
1993-01-01
An infinite set of new non commuting conserved charges in a specific class of perturbed CFT's is founded and a criterion for their existence is presented. They appear to be higher momenta of the already known commuting conserved currents. The algebra they close consists of two non commuting W ∞ algebras. Various Virasoro subalgebras of the full symmetry algebra are founded. It is shown on the examples of the perturbed Ising and Potts models that one of them plays an essential role in the computation of the correlation functions of the fields of the theory. (author)
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving
Engerman, Jason; Rusek, Matthew; Clariana, Roy
2014-01-01
This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…
Directory of Open Access Journals (Sweden)
Naseem Cassim
2017-02-01
Full Text Available Introduction: CD4 testing in South Africa is based on an integrated tiered service delivery model that matches testing demand with capacity. The National Health Laboratory Service has predominantly implemented laboratory-based CD4 testing. Coverage gaps, over-/under-capacitation and optimal placement of point-of-care (POC testing sites need investigation. Objectives: We assessed the impact of relational algebraic capacitated location (RACL algorithm outcomes on the allocation of laboratory and POC testing sites. Methods: The RACL algorithm was developed to allocate laboratories and POC sites to ensure coverage using a set coverage approach for a defined travel time (T. The algorithm was repeated for three scenarios (A: T = 4; B: T = 3; C: T = 2 hours. Drive times for a representative sample of health facility clusters were used to approximate T. Outcomes included allocation of testing sites, Euclidian distances and test volumes. Additional analysis included platform distribution and space requirement assessment. Scenarios were reported as fusion table maps. Results: Scenario A would offer a fully-centralised approach with 15 CD4 laboratories without any POC testing. A significant increase in volumes would result in a four-fold increase at busier laboratories. CD4 laboratories would increase to 41 in scenario B and 61 in scenario C. POC testing would be offered at two sites in scenario B and 20 sites in scenario C. Conclusion: The RACL algorithm provides an objective methodology to address coverage gaps through the allocation of CD4 laboratories and POC sites for a given T. The algorithm outcomes need to be assessed in the context of local conditions.
Complex fluids modeling and algorithms
Saramito, Pierre
2016-01-01
This book presents a comprehensive overview of the modeling of complex fluids, including many common substances, such as toothpaste, hair gel, mayonnaise, liquid foam, cement and blood, which cannot be described by Navier-Stokes equations. It also offers an up-to-date mathematical and numerical analysis of the corresponding equations, as well as several practical numerical algorithms and software solutions for the approximation of the solutions. It discusses industrial (molten plastics, forming process), geophysical (mud flows, volcanic lava, glaciers and snow avalanches), and biological (blood flows, tissues) modeling applications. This book is a valuable resource for undergraduate students and researchers in applied mathematics, mechanical engineering and physics.
Computer algebra and operators
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Saldarriaga Vargas, Clarita
When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.
Algebraic Specifications, Higher-order Types and Set-theoretic Models
DEFF Research Database (Denmark)
Kirchner, Hélène; Mosses, Peter David
2001-01-01
, and power-sets. This paper presents a simple framework for algebraic specifications with higher-order types and set-theoretic models. It may be regarded as the basis for a Horn-clause approximation to the Z framework, and has the advantage of being amenable to prototyping and automated reasoning. Standard......In most algebraic specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higer-order types, interpreted set-theoretically as Cartesian products, function spaces...... set-theoretic models are considered, and conditions are given for the existence of initial reduct's of such models. Algebraic specifications for various set-theoretic concepts are considered....
Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra
Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç
2017-01-01
In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…
Codd, A. L.; Gross, L.
2018-03-01
We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.
AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S
Klumpp, A. R.
1994-01-01
This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.
Mathematical modelling in engineering: A proposal to introduce linear algebra concepts
Directory of Open Access Journals (Sweden)
Andrea Dorila Cárcamo
2016-03-01
Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
Abstract algebra for physicists
International Nuclear Information System (INIS)
Zeman, J.
1975-06-01
Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)
Directory of Open Access Journals (Sweden)
Salvador Lucas
2015-12-01
Full Text Available Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In this setting, Order-Sorted First-Order Logic provides a powerful framework to represent declarative programs. It also provides a target logic to obtain models for other logics via transformations. We investigate the automatic generation of numerical models for order-sorted first-order logics and its use in program analysis, in particular in termination analysis of declarative programs. We use convex domains to give domains to the different sorts of an order-sorted signature; we interpret the ranked symbols of sorted signatures by means of appropriately adapted convex matrix interpretations. Such numerical interpretations permit the use of existing algorithms and tools from linear algebra and arithmetic constraint solving to synthesize the models.
Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
International Nuclear Information System (INIS)
Corichi, Alejandro; Karami, Asieh; Rastgoo, Saeed; Vukašinac, Tatjana
2016-01-01
We consider a class of two-dimensional dilatonic models, and revisit them from the perspective of a new set of ‘polar type’ variables. These are motivated by recently defined variables within the spherically symmetric sector of 4D general relativity. We show that for a large class of dilatonic models, including the case with matter, one can perform a series of canonical transformations in such a way that the Poisson algebra of the constraints becomes a Lie algebra. Furthermore, we construct Dirac observables and a reduced Hamiltonian that accounts for the time evolution of the system. (paper)
Non-freely generated W-algebras and construction of N=2 super W-algebras
International Nuclear Information System (INIS)
Blumenhagen, R.
1994-07-01
Firstly, we investigate the origin of the bosonic W-algebras W(2, 3, 4, 5), W(2, 4, 6) and W(2, 4, 6) found earlier by direct construction. We present a coset construction for all three examples leading to a new type of finitely, non-freely generated quantum W-algebras, which we call unifying W-algebras. Secondly, we develop a manifest covariant formalism to construct N = 2 super W-algebras explicitly on a computer. Applying this algorithm enables us to construct the first four examples of N = 2 super W-algebras with two generators and the N = 2 super W 4 algebra involving three generators. The representation theory of the former ones shows that all examples could be divided into four classes, the largest one containing the N = 2 special type of spectral flow algebras. Besides the W-algebra of the CP(3) Kazama-Suzuki coset model, the latter example with three generators discloses a second solution which could also be explained as a unifying W-algebra for the CP(n) models. (orig.)
Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
2016-01-01
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems
Ng, Swee Fong; Lee, Kerry
2009-01-01
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…
Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings
International Nuclear Information System (INIS)
Arnaudon, D.
1997-01-01
Two quantum spin chains Hamiltonians with quantum sl(2/1) invariance are constructed. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the periodic chain. The two Hamiltonians, respectively built using the distinguished and the fermionic bases of U q (sl(2/1)) differ only in the boundary terms. They are actually equivalent, but the equivalence is non local. Reflection equations are solved to get exact solvability on open chains with non trivial boundary conditions. Two families of diagonal solutions are found. The centre and the s-Casimir of the quantum enveloping algebra of sl(2/1) appear as tools for the construction of exactly solvable Hamiltonians. (author)
Automatic differentiation algorithms in model analysis
Huiskes, M.J.
2002-01-01
Title: Automatic differentiation algorithms in model analysis
Author: M.J. Huiskes
Date: 19 March, 2002
In this thesis automatic differentiation algorithms and derivative-based methods
Algebraic partial Boolean algebras
International Nuclear Information System (INIS)
Smith, Derek
2003-01-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A 5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E 8
Singh, S; Modi, S; Bagga, D; Kaur, P; Shankar, L R; Khushu, S
2013-03-01
The present study aimed to investigate whether brain morphological differences exist between adult hypothyroid subjects and age-matched controls using voxel-based morphometry (VBM) with diffeomorphic anatomic registration via an exponentiated lie algebra algorithm (DARTEL) approach. High-resolution structural magnetic resonance images were taken in ten healthy controls and ten hypothyroid subjects. The analysis was conducted using statistical parametric mapping. The VBM study revealed a reduction in grey matter volume in the left postcentral gyrus and cerebellum of hypothyroid subjects compared to controls. A significant reduction in white matter volume was also found in the cerebellum, right inferior and middle frontal gyrus, right precentral gyrus, right inferior occipital gyrus and right temporal gyrus of hypothyroid patients compared to healthy controls. Moreover, no meaningful cluster for greater grey or white matter volume was obtained in hypothyroid subjects compared to controls. Our study is the first VBM study of hypothyroidism in an adult population and suggests that, compared to controls, this disorder is associated with differences in brain morphology in areas corresponding to known functional deficits in attention, language, motor speed, visuospatial processing and memory in hypothyroidism. © 2012 British Society for Neuroendocrinology.
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
Ashwinkumar, Meer; Cao, Jingnan; Luo, Yuan; Tan, Meng-Chwan; Zhao, Qin
2018-03-01
We study the ground states and left-excited states of the Ak-1 N = (2 , 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU (k). The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
Algebra of orthofermions and equivalence of their thermodynamics to the infinite U Hubbard model
International Nuclear Information System (INIS)
Kishore, R.; Mishra, A.K.
2006-01-01
The equivalence of thermodynamics of independent orthofermions to the infinite U Hubbard model, shown earlier for the one-dimensional infinite lattice, has been extended to a finite system of two lattice sites. Regarding the algebra of orthofermions, the algebraic expressions for the number operator for a given spin and the spin raising (lowering) operators in the form of infinite series are rearranged in such a way that the ith term, having the form of an infinite series, of the number (spin raising (lowering)) operator represents the number (spin raising (lowering)) operator at the ith lattice site
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
Directory of Open Access Journals (Sweden)
Meer Ashwinkumar
2018-03-01
Full Text Available We study the ground states and left-excited states of the Ak−1 N=(2,0 little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU(k. The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
Forward error correction based on algebraic-geometric theory
A Alzubi, Jafar; M Chen, Thomas
2014-01-01
This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over additive white Gaussian noise channel model. Simulation results of Algebraic-geometric codes bit error rate performance using quadrature amplitude modulation (16QAM and 64QAM) are presented for the first time and shown to outperform Reed-Solomon codes at various code rates and channel models. The book proposes algebraic-geometric block turbo codes. It also presents simulation results that show an improved bit error rate performance at the cost of high system complexity due to using algebraic-geometric codes and Chase-Pyndiah’s algorithm simultaneously. The book proposes algebraic-geometric irregular block turbo codes (AG-IBTC) to reduce system complexity. Simulation results for AG-IBTCs are presented for the first time.
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
International Nuclear Information System (INIS)
Calmet, J.
1982-01-01
A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)
Evaluation of global synchronization for iterative algebra algorithms on many-core
ul Hasan Khan, Ayaz; Al-Mouhamed, Mayez; Firdaus, Lutfi A.
2015-01-01
© 2015 IEEE. Massively parallel computing is applied extensively in various scientific and engineering domains. With the growing interest in many-core architectures and due to the lack of explicit support for inter-block synchronization specifically in GPUs, synchronization becomes necessary to minimize inter-block communication time. In this paper, we have proposed two new inter-block synchronization techniques: 1) Relaxed Synchronization, and 2) Block-Query Synchronization. These schemes are used in implementing numerical iterative solvers where computation/communication overlapping is one used optimization to enhance application performance. We have evaluated and analyzed the performance of the proposed synchronization techniques using Jacobi Iterative Solver in comparison to the state of the art inter-block lock-free synchronization techniques. We have achieved about 1-8% performance improvement in terms of execution time over lock-free synchronization depending on the problem size and the number of thread blocks. We have also evaluated the proposed algorithm on GPU and MIC architectures and obtained about 8-26% performance improvement over the barrier synchronization available in OpenMP programming environment depending on the problem size and number of cores used.
Evaluation of global synchronization for iterative algebra algorithms on many-core
ul Hasan Khan, Ayaz
2015-06-01
© 2015 IEEE. Massively parallel computing is applied extensively in various scientific and engineering domains. With the growing interest in many-core architectures and due to the lack of explicit support for inter-block synchronization specifically in GPUs, synchronization becomes necessary to minimize inter-block communication time. In this paper, we have proposed two new inter-block synchronization techniques: 1) Relaxed Synchronization, and 2) Block-Query Synchronization. These schemes are used in implementing numerical iterative solvers where computation/communication overlapping is one used optimization to enhance application performance. We have evaluated and analyzed the performance of the proposed synchronization techniques using Jacobi Iterative Solver in comparison to the state of the art inter-block lock-free synchronization techniques. We have achieved about 1-8% performance improvement in terms of execution time over lock-free synchronization depending on the problem size and the number of thread blocks. We have also evaluated the proposed algorithm on GPU and MIC architectures and obtained about 8-26% performance improvement over the barrier synchronization available in OpenMP programming environment depending on the problem size and number of cores used.
Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation
Trujillo Arredondo, Mariana
2014-06-01
We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.
Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-01-01
Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…
Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis
Czech Academy of Sciences Publication Activity Database
Bulíček, M.; Haslinger, J.; Málek, J.; Stebel, Jan
2009-01-01
Roč. 60, č. 2 (2009), s. 185-212 ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model * outflow boundary condition Subject RIV: BA - General Mathematics Impact factor: 0.757, year: 2009
The Virasoro algebra in integrable hierarchies and the method of matrix models
International Nuclear Information System (INIS)
Semikhatov, A.M.
1992-01-01
The action of the Virasoro algebra on hierarchies of nonlinear integrable equations, and also the structure and consequences of Virasoro constraints on these hierarchies, are studied. It is proposed that a broad class of hierarchies, restricted by Virasoro constraints, can be defined in terms of dressing operators hidden in the structure of integrable systems. The Virasoro-algebra representation constructed on the dressing operators displays a number of analogies with structures in conformal field theory. The formulation of the Virasoro constraints that stems from this representation makes it possible to translate into the language of integrable systems a number of concepts from the method of the 'matrix models' that describe nonperturbative quantum gravity, and, in particular, to realize a 'hierarchical' version of the double scaling limit. From the Virasoro constraints written in terms of the dressing operators generalized loop equations are derived, and this makes it possible to do calculations on a reconstruction of the field-theoretical description. The reduction of the Kadomtsev-Petviashvili (KP) hierarchy, subject to Virasoro constraints, to generalized Korteweg-deVries (KdV) hierarchies is implemented, and the corresponding representation of the Virasoro algebra on these hierarchies is found both in the language of scalar differential operators and in the matrix formalism of Drinfel'd and Sokolov. The string equation in the matrix formalism does not replicate the structure of the scalar string equation. The symmetry algebras of the KP and N-KdV hierarchies restricted by Virasoro constraints are calculated: A relationship is established with algebras from the family W ∞ (J) of infinite W-algebras
Algorithms and Methods for High-Performance Model Predictive Control
DEFF Research Database (Denmark)
Frison, Gianluca
routines employed in the numerical tests. The main focus of this thesis is on linear MPC problems. In this thesis, both the algorithms and their implementation are equally important. About the implementation, a novel implementation strategy for the dense linear algebra routines in embedded optimization...... is proposed, aiming at improving the computational performance in case of small matrices. About the algorithms, they are built on top of the proposed linear algebra, and they are tailored to exploit the high-level structure of the MPC problems, with special care on reducing the computational complexity....
The bounded model property via step algebras and step frames
Bezhanishvili, N.; Ghilardi, S.
2014-01-01
The paper introduces semantic and algorithmic methods for establishing a variant of the analytic subformula property (called ‘the bounded proof property’, bpp) for modal propositional logics. The bpp is much weaker property than full cut-elimination, but it is nevertheless sufficient for
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to
The algebras of higher order currents of the fermionic Gross-Neveu model
International Nuclear Information System (INIS)
Saltini, Luis Eduardo
1996-01-01
Results are reported from our studies on the following 2-dimensional field theories: the supersymmetric non-linear sigma model and the fermionic Gross-Neveu model. About the supersymmetric non-linear sigma model, an attempt is made to solve the the algebraic problem of finding the non-local conserved charges and the corresponding algebra, extending the methods described in a previous article for the case of the purely bosonic non linear sigma model. For the fermionic Gross-Neveu model, we intend to construct the conserved currents and the respective charges, related to the abelian U(1) symmetry and non-abelian SU(n) symmetry, at the conformal point and calculate the correlation functions between them. From these results at the conformal point, we want to study the effects of perturbation to get a massive but integral theory
Applied linear algebra and matrix analysis
Shores, Thomas S
2018-01-01
In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...
Jongen, T.; Machiels, L.; Gatski, T. B.
1997-01-01
Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.
Lectures on algebraic statistics
Drton, Mathias; Sullivant, Seth
2009-01-01
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
Comparison of Co-Temporal Modeling Algorithms on Sparse Experimental Time Series Data Sets.
Allen, Edward E; Norris, James L; John, David J; Thomas, Stan J; Turkett, William H; Fetrow, Jacquelyn S
2010-01-01
Multiple approaches for reverse-engineering biological networks from time-series data have been proposed in the computational biology literature. These approaches can be classified by their underlying mathematical algorithms, such as Bayesian or algebraic techniques, as well as by their time paradigm, which includes next-state and co-temporal modeling. The types of biological relationships, such as parent-child or siblings, discovered by these algorithms are quite varied. It is important to understand the strengths and weaknesses of the various algorithms and time paradigms on actual experimental data. We assess how well the co-temporal implementations of three algorithms, continuous Bayesian, discrete Bayesian, and computational algebraic, can 1) identify two types of entity relationships, parent and sibling, between biological entities, 2) deal with experimental sparse time course data, and 3) handle experimental noise seen in replicate data sets. These algorithms are evaluated, using the shuffle index metric, for how well the resulting models match literature models in terms of siblings and parent relationships. Results indicate that all three co-temporal algorithms perform well, at a statistically significant level, at finding sibling relationships, but perform relatively poorly in finding parent relationships.
Modeling and Engineering Algorithms for Mobile Data
DEFF Research Database (Denmark)
Blunck, Henrik; Hinrichs, Klaus; Sondern, Joëlle
2006-01-01
In this paper, we present an object-oriented approach to modeling mobile data and algorithms operating on such data. Our model is general enough to capture any kind of continuous motion while at the same time allowing for encompassing algorithms optimized for specific types of motion. Such motion...
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
International Nuclear Information System (INIS)
Garcia, R.L.
1983-11-01
The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt
Virasoro algebra action on integrable hierarchies and Virasoro contraints in matrix models
International Nuclear Information System (INIS)
Semikhatov, A.M.
1991-01-01
The action of the Virasoro algebra on integrable hierarchies of non-linear equations and on related objects ('Schroedinger' differential operators) is investigated. The method consists in pushing forward the Virasoro action to the wave function of a hierarchy, and then reconstructing its action on the dressing and Lax operators. This formulation allows one to observe a number of suggestive similarities between the structures involved in the description of the Virasoro algebra on the hierarchies and the structure of conformal field theory on the world-sheet. This includes, in particular, an 'off-shell' hierarchy version of operator products and of the Cauchy kernel. In relation to matrix models, which have been observed to be effectively described by integrable hierarchies subjected to Virasoro constraints, I propose to define general Virasoro-constrained hierarchies also in terms of dressing operators, by certain equations which carry the information of the hierarchy and the Virasoro algebra simultaneously and which suggest an interpretation as operator versions of recursion/loop equations in topological theories. These same equations provide a relation with integrable hierarchies with quantized spectral parameter introduced recently. The formulation in terms of dressing operators allows a scaling (continuum limit) of discrete (i.e. lattice) hierarchies with the Virasoro constraints into 'continuous' Virasoro-constrained hierarchies. In particular, the KP hierarchy subjected to the Virasoro constraints is recovered as a scaling limit of the Virasoro-constrained Toda hierarchy. The dressing operator method also makes is straightforward to identify the full symmetry algebra of Virasoro-constrained hierarchies, which is related to the family of W ∞ (J) algebras introduced recently. (orig./HS)
Entanglement in a model for Hawking radiation: An application of quadratic algebras
International Nuclear Information System (INIS)
Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.
2013-01-01
Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: ► We examine a toy model for Hawking radiation with quantized black hole modes. ► We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. ► We study the “Dicke Superradiance” in black hole radiation using quadratically deformed su(2) algebras. ► We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.
An algebraic stress/flux model for two-phase turbulent flow
International Nuclear Information System (INIS)
Kumar, R.
1995-12-01
An algebraic stress model (ASM) for turbulent Reynolds stress and a flux model for turbulent heat flux are proposed for two-phase bubbly and slug flows. These mathematical models are derived from the two-phase transport equations for Reynolds stress and turbulent heat flux, and provide C μ , a turbulent constant which defines the level of eddy viscosity, as a function of the interfacial terms. These models also include the effect of heat transfer. When the interfacial drag terms and the interfacial momentum transfer terms are absent, the model reduces to a single-phase model used in the literature
Iachello, Francesco
2015-01-01
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...
A Csup(*)-algebra approach to the Schwinger model
International Nuclear Information System (INIS)
Carey, A.L.; Hurst, C.A.
1981-01-01
If cutoffs are introduced then existing results in the literature show that the Schwinger model is dynamically equivalent to a boson model with quadratic Hamiltonian. However, the process of quantising the Schwinger model destroys local gauge invariance. Gauge invariance is restored by the addition of a counterterm, which may be seen as a finite renormalisation, whereupon the Schwinger model becomes dynamically equivalent to a linear boson gauge theory. This linear model is exactly soluble. We find that different treatments of the supplementary (i.e. Lorentz) condition lead to boson models with rather different properties. We choose one model and construct, from the gauge invariant subalgebra, a class of inequivalent charge sectors. We construct sectors which coincide with those found by Lowenstein and Swieca for the Schwinger model. A reconstruction of the Hilbert space on which the Schwinger model exists is described and fermion operators on this space are defined. (orig.)
Exact boson mappings for nuclear neutron (proton) shell-model algebras having SU(3) subalgebras
International Nuclear Information System (INIS)
Bonatsos, D.; Klein, A.
1986-01-01
In this paper the commutation relations of the fermion pair operators of identical nucleons coupled to spin zero are given for the general nuclear major shell in LST coupling. The associated Lie algebras are the unitary symplectic algebras Sp(2M). The corresponding multipole subalgebras are the unitary algebras U(M), which possess SU(3) subalgebras. Number conserving exact boson mappings of both the Dyson and hermitian form are given for the nuclear neutron (proton) s--d, p--f, s--d--g, and p--f--h shells, and their group theoretical structure is emphasized. The results are directly applicable in the case of the s--d shell, while in higher shells the experimentally plausible pseudo-SU(3) symmetry makes them applicable. The final purpose of this work is to provide a link between the shell model and the Interacting Boson Model (IBM) in the deformed limit. As already implied in the work of Draayer and Hecht, it is difficult to associate the boson model developed here with the conventional IBM model. The differences between the two approaches (due mainly to the effects of the Pauli principle) as well as their physical implications are extensively discussed
A Linear Algebra Measure of Cluster Quality.
Mather, Laura A.
2000-01-01
Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)
Algebraic models for the hierarchy structure of evolution equations at small x
International Nuclear Information System (INIS)
Rembiesa, P.; Stasto, A.M.
2005-01-01
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit
On the algebraic structure of self-dual gauge fields and sigma models
International Nuclear Information System (INIS)
Bais, F.A.; Sasaki, R.
1983-01-01
An extensive and detailed analysis of self-dual gauge fields, in particular with axial symmetry, is presented, culminating in a purely algebraic procedure to generate solutions. The method which is particularly suited for the construction of multimonopole solutions for a theory with arbitrary G, is also applicable to a wide class of non-linear sigma models. The relevant symmetries as well as the associated linear problems which underly the exact solubility of the problem, are constructed and discussed in detail. (orig.)
Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena
Bayak, Igor V.
2015-01-01
In this paper we discuss the local algebras of linear vector fields that can be used in the mathematical modelling of physical space by building the dynamical flows of vector fields on eight-dimensional cylindrical or toroidal manifolds. It is shown that the topological features of the vector fields obey the Dirac equation when moving freely within the surface of a pseudo-sphere in the eight-dimensional pseudo-Euclidean space.
Czech Academy of Sciences Publication Activity Database
Haslinger, J.; Stebel, Jan
2011-01-01
Roč. 63, č. 2 (2011), s. 277-308 ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2011 http://link.springer.com/article/10.1007%2Fs00245-010-9121-x
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.
Improved Collaborative Filtering Algorithm using Topic Model
Directory of Open Access Journals (Sweden)
Liu Na
2016-01-01
Full Text Available Collaborative filtering algorithms make use of interactions rates between users and items for generating recommendations. Similarity among users or items is calculated based on rating mostly, without considering explicit properties of users or items involved. In this paper, we proposed collaborative filtering algorithm using topic model. We describe user-item matrix as document-word matrix and user are represented as random mixtures over item, each item is characterized by a distribution over users. The experiments showed that the proposed algorithm achieved better performance compared the other state-of-the-art algorithms on Movie Lens data sets.
International Nuclear Information System (INIS)
Baek, Seong Gu; Park, Seung O.
2003-01-01
This paper provides the assessment of prediction performance of explicit algebraic stress and heat-flux models under conditions of mixed convective gas flows in a strongly-heated vertical tube. Two explicit algebraic stress models and four algebraic heat-flux models are selected for assessment. Eight combinations of explicit algebraic stress and heat-flux models are used in predicting the flows experimentally studied by Shehata and McEligot (IJHMT 41(1998) p.4333) in which property variation was significant. Among the various model combinations, the Wallin and Johansson (JFM 403(2000) p. 89) explicit algebraic stress model-Abe, Kondo, and Nagano (IJHFF 17(1996) p. 228) algebraic heat-flux model combination is found to perform best. We also found that the dimensionless wall distance y + should be calculated based on the local property rather than the property at the wall for property-variation flows. When the buoyancy or the property variation effects are so strong that the flow may relaminarize, the choice of the basic platform two-equation model is a most important factor in improving the predictions
Vertex algebras and algebraic curves
Frenkel, Edward
2004-01-01
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book co...
African Journals Online (AJOL)
Tadesse
In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra of Xu (1993) and further we prove that it is a regular Autometrized. Algebra. Further we remark that the binary operation → on lattice implicative algebra can never be associative. Key words: Implicative ...
A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models
Energy Technology Data Exchange (ETDEWEB)
Kawaguchi, Io; Yoshida, Kentaroh [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
2014-06-01
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
International Nuclear Information System (INIS)
Read, N.; Saleur, H.
2007-01-01
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m>=2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform alternately along the chain in the fundamental m and its conjugate representation m-bar. We find that these spin chains, even with arbitrary coefficients of these interactions, have a symmetry algebra A m much larger than U(m), which implies that the energy eigenstates fall into sectors that for open chains (i.e., free boundary conditions) can be labeled by j=0,1,...,L, for the 2L-site chain such that the degeneracies of all eigenvalues in the jth sector are generically the same and increase rapidly with j. For large j, these degeneracies are much larger than those that would be expected from the U(m) symmetry alone. The enlarged symmetry algebra A m (2L) consists of operators that commute in this space of states with the Temperley-Lieb algebra that is generated by the set of nearest-neighbor interaction terms; A m (2L) is not a Yangian. There are similar results for supersymmetric chains with gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer representation structure for closed chains (i.e., periodic boundary conditions). The symmetries also apply to the loop models that can be obtained from the spin chains in a spacetime or transfer matrix picture. In the loop language, the symmetries arise because the loops cannot cross. We further define tensor products of representations (for the open chains) by joining chains end to end. The fusion rules for decomposing the tensor product of representations labeled j 1 and j 2 take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra A m into a ribbon Hopf algebra, and we show that this is 'Morita equivalent' to the quantum group U q (sl 2 ) for m=q+q -1 . The open-chain results are extended to the cases vertical bar m vertical
Heidergott, Bernd; van der Woude, Jacob
2014-01-01
Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, compu
International Nuclear Information System (INIS)
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2005-01-01
We reexpress the quantum Calogero-Sutherland model for the Lie algebra E 7 and the particular value of the coupling constant κ=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra
Algebraic Structure of tt * Equations for Calabi-Yau Sigma Models
Alim, Murad
2017-08-01
The tt * equations define a flat connection on the moduli spaces of {2d, \\mathcal{N}=2} quantum field theories. For conformal theories with c = 3 d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. We show that the non-holomorphic content of the tt * equations, restricted to the conformal directions, in the cases d = 1, 2, 3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space. This space parameterizes a freedom in choosing representatives of the chiral ring while preserving a constant topological metric. Geometrically, the freedom corresponds to a choice of forms on the target space respecting the Hodge filtration and having a constant pairing. Linear combinations of vector fields on that space are identified with the generators of a Lie algebra. This Lie algebra replaces the non-holomorphic derivatives of tt * and provides these with a finer and algebraic meaning. For sigma models into lattice polarized K3 manifolds, the differential ring of special functions on the moduli space is constructed, extending known structures for d = 1 and 3. The generators of the differential rings of special functions are given by quasi-modular forms for d = 1 and their generalizations in d = 2, 3. Some explicit examples are worked out including the case of the mirror of the quartic in {\\mathbbm{P}^3}, where due to further algebraic constraints, the differential ring coincides with quasi modular forms.
Analysis of DIRAC's behavior using model checking with process algebra
Remenska, Daniela; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Diaz, Ricardo Graciani; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-01-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple, the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike con...
Villarreal, Rafael
2015-01-01
The book stresses the interplay between several areas of pure and applied mathematics, emphasizing the central role of monomial algebras. It unifies the classical results of commutative algebra with central results and notions from graph theory, combinatorics, linear algebra, integer programming, and combinatorial optimization. The book introduces various methods to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings and blowup algebra-emphasizing square free quadratics, hypergraph clutters, and effective computational methods.
Optlang: An algebraic modeling language for mathematical optimization
DEFF Research Database (Denmark)
Jensen, Kristian; Cardoso, Joao; Sonnenschein, Nikolaus
2016-01-01
Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e., maximizing or minimizing an objective function over a set of variables subject to a number of constraints. It provides a common native Python interface to a series of optimization...
Thin-layer approximation and algebraic model for separated turbulent flows
Baldwin, B.; Lomax, H.
1978-01-01
An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.
International Nuclear Information System (INIS)
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2003-01-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D 4 in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra. This parametrization allows us to solve for the energy eigenfunctions of the theory and to study properties of the system of orthogonal polynomials associated with them such as recurrence relations and generating functions
Jaynes-Cummings model and the deformed-oscillator algebra
International Nuclear Information System (INIS)
Crnugelj, J.; Martinis, M.; Mikuta-Martinis, V.
1994-01-01
We study the time evolution of the deformed Jaynes-Cummings model (DJCM). It is shown that the standard JCM and its recent non-linear generalizations involving the intensity-dependent coupling and/or the multiphoton coupling are only particular cases of the DJCM. The time evolution of the mean phonon number and the population inversion are evaluated. A special case of the q-deformed JCM is analyzed explicitly. The long time quasi-periodic revival effects of the q-deformed JCM are observed for q∼1 and an initially large mean photon number. For other values of the deformation parameter q we observe chaotic-like behaviour of the population inversion. Photons are assumed to be initially in the deformed coherent state. ((orig.))
Polishchuk, Alexander
2005-01-01
Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.
The relation between quantum W algebras and Lie algebras
International Nuclear Information System (INIS)
Boer, J. de; Tjin, T.
1994-01-01
By quantizing the generalized Drinfeld-Sokolov reduction scheme for arbitrary sl 2 embeddings we show that a large set W of quantum W algebras can be viewed as (BRST) cohomologies of affine Lie algebras. The set W contains many known W algebras such as W N and W 3 (2) . Our formalism yields a completely algorithmic method for calculating the W algebra generators and their operator product expansions, replacing the cumbersome construction of W algebras as commutants of screening operators. By generalizing and quantizing the Miura transformation we show that any W algebra in W can be embedded into the universal enveloping algebra of a semisimple affine Lie algebra which is, up to shifts in level, isomorphic to a subalgebra of the original affine algebra. Therefore any realization of this semisimple affine Lie algebra leads to a realization of the W algebra. In particular, one obtains in this way a general and explicit method for constructing the free field realizations and Fock resolutions for all algebras in W. Some examples are explicitly worked out. (orig.)
Algebraic equations for the exceptional eigenspectrum of the generalized Rabi model
International Nuclear Information System (INIS)
Li, Zi-Min; Batchelor, Murray T
2015-01-01
We obtain the exceptional part of the eigenspectrum of the generalized Rabi model, also known as the driven Rabi model, in terms of the roots of a set of algebraic equations. This approach provides a product form for the wavefunction components and allows an explicit connection with recent results obtained for the wavefunction in terms of truncated confluent Heun functions. Other approaches are also compared. For particular parameter values the exceptional part of the eigenspectrum consists of doubly degenerate crossing points. We give a proof for the number of roots of the constraint polynomials and discuss the number of crossing points. (paper)
Application of the algebraic RNG model for transition simulation. [renormalization group theory
Lund, Thomas S.
1990-01-01
The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.
International Nuclear Information System (INIS)
Orantin, N.
2007-09-01
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and arrangement of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that the fine tuning of the parameters ensures that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct. (author)
Special set linear algebra and special set fuzzy linear algebra
Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.
2009-01-01
The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...
International Nuclear Information System (INIS)
Forger, M.; Mannheim Univ.; Laartz, J.; Schaeper, U.
1994-01-01
The recently derived current algrbra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor θ μv , the Noether current j μ associated with the global symmetry of the theory and the composite field j appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of j μ and j, generte a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge c=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody/Sugawara type contruction. (orig.)
Model Checking Algorithms for CTMDPs
DEFF Research Database (Denmark)
Buchholz, Peter; Hahn, Ernst Moritz; Hermanns, Holger
2011-01-01
Continuous Stochastic Logic (CSL) can be interpreted over continuoustime Markov decision processes (CTMDPs) to specify quantitative properties of stochastic systems that allow some external control. Model checking CSL formulae over CTMDPs requires then the computation of optimal control strategie...
Shafarevich, Igor Rostislavovich
2005-01-01
This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches
Using process algebra to develop predator-prey models of within-host parasite dynamics.
McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel
2013-07-21
As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system. Copyright © 2013 Elsevier Ltd. All rights reserved.
Contractions of quantum algebraic structures
International Nuclear Information System (INIS)
Doikou, A.; Sfetsos, K.
2010-01-01
A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Identification of control targets in Boolean molecular network models via computational algebra.
Murrugarra, David; Veliz-Cuba, Alan; Aguilar, Boris; Laubenbacher, Reinhard
2016-09-23
Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.
Fuzzy audit risk modeling algorithm
Directory of Open Access Journals (Sweden)
Zohreh Hajihaa
2011-07-01
Full Text Available Fuzzy logic has created suitable mathematics for making decisions in uncertain environments including professional judgments. One of the situations is to assess auditee risks. During recent years, risk based audit (RBA has been regarded as one of the main tools to fight against fraud. The main issue in RBA is to determine the overall audit risk an auditor accepts, which impact the efficiency of an audit. The primary objective of this research is to redesign the audit risk model (ARM proposed by auditing standards. The proposed model of this paper uses fuzzy inference systems (FIS based on the judgments of audit experts. The implementation of proposed fuzzy technique uses triangular fuzzy numbers to express the inputs and Mamdani method along with center of gravity are incorporated for defuzzification. The proposed model uses three FISs for audit, inherent and control risks, and there are five levels of linguistic variables for outputs. FISs include 25, 25 and 81 rules of if-then respectively and officials of Iranian audit experts confirm all the rules.
Rethinking exchange market models as optimization algorithms
Luquini, Evandro; Omar, Nizam
2018-02-01
The exchange market model has mainly been used to study the inequality problem. Although the human society inequality problem is very important, the exchange market models dynamics until stationary state and its capability of ranking individuals is interesting in itself. This study considers the hypothesis that the exchange market model could be understood as an optimization procedure. We present herein the implications for algorithmic optimization and also the possibility of a new family of exchange market models
Goodstein, R L
2007-01-01
This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
Energy Technology Data Exchange (ETDEWEB)
Cirilo António, N., E-mail: nantonio@math.ist.utl.pt [Centro de Análise Funcional e Aplicações, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Manojlović, N., E-mail: nmanoj@ualg.pt [Grupo de Física Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto 2, PT-1649-003 Lisboa (Portugal); Departamento de Matemática, F.C.T., Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro (Portugal); Salom, I., E-mail: isalom@ipb.ac.rs [Institute of Physics, University of Belgrade, P.O. Box 57, 11080 Belgrade (Serbia)
2014-12-15
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
Cirilo António, N.; Manojlović, N.; Salom, I.
2014-12-01
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.
Thermodiffusion in Multicomponent Mixtures Thermodynamic, Algebraic, and Neuro-Computing Models
Srinivasan, Seshasai
2013-01-01
Thermodiffusion in Multicomponent Mixtures presents the computational approaches that are employed in the study of thermodiffusion in various types of mixtures, namely, hydrocarbons, polymers, water-alcohol, molten metals, and so forth. We present a detailed formalism of these methods that are based on non-equilibrium thermodynamics or algebraic correlations or principles of the artificial neural network. The book will serve as single complete reference to understand the theoretical derivations of thermodiffusion models and its application to different types of multi-component mixtures. An exhaustive discussion of these is used to give a complete perspective of the principles and the key factors that govern the thermodiffusion process.
Model Checking Process Algebra of Communicating Resources for Real-time Systems
DEFF Research Database (Denmark)
Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand
2014-01-01
This paper presents a new process algebra, called PACOR, for real-time systems which deals with resource constrained timed behavior as an improved version of the ACSR algebra. We define PACOR as a Process Algebra of Communicating Resources which allows to express preemptiveness, urgent ness...
Model checking process algebra of communicating resources for real-time systems
DEFF Research Database (Denmark)
Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand
2014-01-01
This paper presents a new process algebra, called PACoR, for real-time systems which deals with resource- constrained timed behavior as an improved version of the ACSR algebra. We define PACoR as a Process Algebra of Communicating Resources which allows to explicitly express preemptiveness...
Müller, Dirk K; Pampel, André; Möller, Harald E
2013-05-01
Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data. Copyright © 2013 Elsevier Inc. All rights reserved.
Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications
International Nuclear Information System (INIS)
Martins, M.J.; Melo, C.S.
2009-01-01
We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U q [SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.
Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications
Martins, M. J.; Melo, C. S.
2009-10-01
We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.
Hirata, So; Doran, Alexander E; Knowles, Peter J; Ortiz, J V
2017-07-28
A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.
Genetic Algorithms for a Parameter Estimation of a Fermentation Process Model: A Comparison
Directory of Open Access Journals (Sweden)
Olympia Roeva
2005-12-01
Full Text Available In this paper the problem of a parameter estimation using genetic algorithms is examined. A case study considering the estimation of 6 parameters of a nonlinear dynamic model of E. coli fermentation is presented as a test problem. The parameter estimation problem is stated as a nonlinear programming problem subject to nonlinear differential-algebraic constraints. This problem is known to be frequently ill-conditioned and multimodal. Thus, traditional (gradient-based local optimization methods fail to arrive satisfied solutions. To overcome their limitations, the use of different genetic algorithms as stochastic global optimization methods is explored. These algorithms are proved to be very suitable for the optimization of highly non-linear problems with many variables. Genetic algorithms can guarantee global optimality and robustness. These facts make them advantageous in use for parameter identification of fermentation models. A comparison between simple, modified and multi-population genetic algorithms is presented. The best result is obtained using the modified genetic algorithm. The considered algorithms converged very closely to the cost value but the modified algorithm is in times faster than other two.
Genetic coding and united-hypercomplex systems in the models of algebraic biology.
Petoukhov, Sergey V
2017-08-01
Structured alphabets of DNA and RNA in their matrix form of representations are connected with Walsh functions and a new type of systems of multidimensional numbers. This type generalizes systems of complex numbers and hypercomplex numbers, which serve as the basis of mathematical natural sciences and many technologies. The new systems of multi-dimensional numbers have interesting mathematical properties and are called in a general case as "systems of united-hypercomplex numbers" (or briefly "U-hypercomplex numbers"). They can be widely used in models of multi-parametrical systems in the field of algebraic biology, artificial life, devices of biological inspired artificial intelligence, etc. In particular, an application of U-hypercomplex numbers reveals hidden properties of genetic alphabets under cyclic permutations in their doublets and triplets. A special attention is devoted to the author's hypothesis about a multi-linguistic in DNA-sequences in a relation with an ensemble of U-numerical sub-alphabets. Genetic multi-linguistic is considered as an important factor to provide noise-immunity properties of the multi-channel genetic coding. Our results attest to the conformity of the algebraic properties of the U-numerical systems with phenomenological properties of the DNA-alphabets and with the complementary device of the double DNA-helix. It seems that in the modeling field of algebraic biology the genetic-informational organization of living bodies can be considered as a set of united-hypercomplex numbers in some association with the famous slogan of Pythagoras "the numbers rule the world". Copyright © 2017 Elsevier B.V. All rights reserved.
Numerical algebraic geometry for model selection and its application to the life sciences
Gross, Elizabeth
2016-10-12
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology.
The quantum Rabi model and Lie algebra representations of sl2
International Nuclear Information System (INIS)
Wakayama, Masato; Yamasaki, Taishi
2014-01-01
The aim of the present paper is to understand the spectral problem of the quantum Rabi model in terms of Lie algebra representations of sl 2 (R). We define a second order element of the universal enveloping algebra U(sl 2 ) of sl 2 (R), which, through the image of a principal series representation of sl 2 (R), provides a picture equivalent to the quantum Rabi model drawn by confluent Heun differential equations. By this description, in particular, we give a representation theoretic interpretation of the degenerate part of the spectrum (i.e., Judd's eigenstates) of the Rabi Hamiltonian due to Kuś in 1985, which is a part of the exceptional spectrum parameterized by integers. We also discuss the non-degenerate part of the exceptional spectrum of the model, in addition to the Judd eigenstates, from a viewpoint of infinite dimensional irreducible submodules (or subquotients) of the non-unitary principal series such as holomorphic discrete series representations of sl 2 (R). (paper)
Algebraic curves and cryptography
Murty, V Kumar
2010-01-01
It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \\ell-adic point counting algorithm, the p-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on
New Parallel Algorithms for Landscape Evolution Model
Jin, Y.; Zhang, H.; Shi, Y.
2017-12-01
Most landscape evolution models (LEM) developed in the last two decades solve the diffusion equation to simulate the transportation of surface sediments. This numerical approach is difficult to parallelize due to the computation of drainage area for each node, which needs huge amount of communication if run in parallel. In order to overcome this difficulty, we developed two parallel algorithms for LEM with a stream net. One algorithm handles the partition of grid with traditional methods and applies an efficient global reduction algorithm to do the computation of drainage areas and transport rates for the stream net; the other algorithm is based on a new partition algorithm, which partitions the nodes in catchments between processes first, and then partitions the cells according to the partition of nodes. Both methods focus on decreasing communication between processes and take the advantage of massive computing techniques, and numerical experiments show that they are both adequate to handle large scale problems with millions of cells. We implemented the two algorithms in our program based on the widely used finite element library deal.II, so that it can be easily coupled with ASPECT.
Jordan algebras versus C*- algebras
International Nuclear Information System (INIS)
Stormer, E.
1976-01-01
The axiomatic formulation of quantum mechanics and the problem of whether the observables form self-adjoint operators on a Hilbert space, are discussed. The relation between C*- algebras and Jordan algebras is studied using spectral theory. (P.D.)
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Process algebra and Markov chains
Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.
2001-01-01
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
Energy Technology Data Exchange (ETDEWEB)
Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil); Universidade Federal de Juiz de Fora, MG (Brazil)
2013-07-01
Full text: In current theoretical physics there is a relevant number of theoretical investigations that lead to believe that at the first moments of our Universe, the geometry was not commutative and the dominating physics at that time was ruled by the laws of noncommutative (NC) geometry. Therefore, the idea is that the physics of the early moments can be constructed based on these concepts. The first published work using the idea of a NC spacetime were carried out by Snyder who believed that NC principles could make the quantum field theory infinities disappear. However, it did not occur and Snyder's ideas were put to sleep for a long time. The main modern motivations that rekindle the investigation about NC field theories came from string theory and quantum gravity. In the context of quantum mechanics for example, R. Banerjee discussed how NC structures appear in planar quantum mechanics providing a useful way for obtaining them. The analysis was based on the NC algebra used in planar quantum mechanics that was originated from 't Hooft's analysis on dissipation and quantization. In this work we carry out a NC algebra analysis of the Friedmann-Robert-Walker model, coupled to a perfect fluid and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. (author)
Equations of motion for a spectrum-generating algebra: Lipkin-Meshkov-Glick model
International Nuclear Information System (INIS)
Rosensteel, G; Rowe, D J; Ho, S Y
2008-01-01
For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 10 6 , computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
International Nuclear Information System (INIS)
Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson
2013-01-01
Full text: In current theoretical physics there is a relevant number of theoretical investigations that lead to believe that at the first moments of our Universe, the geometry was not commutative and the dominating physics at that time was ruled by the laws of noncommutative (NC) geometry. Therefore, the idea is that the physics of the early moments can be constructed based on these concepts. The first published work using the idea of a NC spacetime were carried out by Snyder who believed that NC principles could make the quantum field theory infinities disappear. However, it did not occur and Snyder's ideas were put to sleep for a long time. The main modern motivations that rekindle the investigation about NC field theories came from string theory and quantum gravity. In the context of quantum mechanics for example, R. Banerjee discussed how NC structures appear in planar quantum mechanics providing a useful way for obtaining them. The analysis was based on the NC algebra used in planar quantum mechanics that was originated from 't Hooft's analysis on dissipation and quantization. In this work we carry out a NC algebra analysis of the Friedmann-Robert-Walker model, coupled to a perfect fluid and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. (author)
Templates for Linear Algebra Problems
Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der
1995-01-01
The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and
McCaig, Chris; Begon, Mike; Norman, Rachel; Shankland, Carron
2011-03-01
Changing scale, for example, the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper, we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interactions.
Model based development of engine control algorithms
Dekker, H.J.; Sturm, W.L.
1996-01-01
Model based development of engine control systems has several advantages. The development time and costs are strongly reduced because much of the development and optimization work is carried out by simulating both engine and control system. After optimizing the control algorithm it can be executed
Algorithms and Models for the Web Graph
Gleich, David F.; Komjathy, Julia; Litvak, Nelli
2015-01-01
This volume contains the papers presented at WAW2015, the 12th Workshop on Algorithms and Models for the Web-Graph held during December 10–11, 2015, in Eindhoven. There were 24 submissions. Each submission was reviewed by at least one, and on average two, Program Committee members. The committee
Pérez López, César
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and ...
Dynamic Airspace Managment - Models and Algorithms
Cheng, Peng; Geng, Rui
2010-01-01
This chapter investigates the models and algorithms for implementing the concept of Dynamic Airspace Management. Three models are discussed. First two models are about how to use or adjust air route dynamically in order to speed up air trafï¬c ï¬‚ow and reduce delay. The third model gives a way to dynamically generate the optimal sector conï¬guration for an air trafï¬c control center to both balance the controllerâ€™s workload and save control resources. The ï¬rst model, called the Dynami...
Optimization in engineering models and algorithms
Sioshansi, Ramteen
2017-01-01
This textbook covers the fundamentals of optimization, including linear, mixed-integer linear, nonlinear, and dynamic optimization techniques, with a clear engineering focus. It carefully describes classical optimization models and algorithms using an engineering problem-solving perspective, and emphasizes modeling issues using many real-world examples related to a variety of application areas. Providing an appropriate blend of practical applications and optimization theory makes the text useful to both practitioners and students, and gives the reader a good sense of the power of optimization and the potential difficulties in applying optimization to modeling real-world systems. The book is intended for undergraduate and graduate-level teaching in industrial engineering and other engineering specialties. It is also of use to industry practitioners, due to the inclusion of real-world applications, opening the door to advanced courses on both modeling and algorithm development within the industrial engineering ...
The Einstein action for algebras of matrix valued functions - Toy models
International Nuclear Information System (INIS)
Hajac, P.M.
1995-10-01
Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for M 4 (R). It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made. (author). 14 refs
The Einstein action for algebras of matrix valued functions - Toy models
Energy Technology Data Exchange (ETDEWEB)
Hajac, P M
1995-10-01
Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for M{sub 4}(R). It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made. (author). 14 refs.
Warner, Zachary B.
2013-01-01
This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…
An evolutionary algorithm for model selection
Energy Technology Data Exchange (ETDEWEB)
Bicker, Karl [CERN, Geneva (Switzerland); Chung, Suh-Urk; Friedrich, Jan; Grube, Boris; Haas, Florian; Ketzer, Bernhard; Neubert, Sebastian; Paul, Stephan; Ryabchikov, Dimitry [Technische Univ. Muenchen (Germany)
2013-07-01
When performing partial-wave analyses of multi-body final states, the choice of the fit model, i.e. the set of waves to be used in the fit, can significantly alter the results of the partial wave fit. Traditionally, the models were chosen based on physical arguments and by observing the changes in log-likelihood of the fits. To reduce possible bias in the model selection process, an evolutionary algorithm was developed based on a Bayesian goodness-of-fit criterion which takes into account the model complexity. Starting from systematically constructed pools of waves which contain significantly more waves than the typical fit model, the algorithm yields a model with an optimal log-likelihood and with a number of partial waves which is appropriate for the number of events in the data. Partial waves with small contributions to the total intensity are penalized and likely to be dropped during the selection process, as are models were excessive correlations between single waves occur. Due to the automated nature of the model selection, a much larger part of the model space can be explored than would be possible in a manual selection. In addition the method allows to assess the dependence of the fit result on the fit model which is an important contribution to the systematic uncertainty.
Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
International Nuclear Information System (INIS)
Chamseddine, Ali H.; Connes, Alain
2007-01-01
The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
Study of the 'non-Abelian' current algebra of a non-linear σ-model
International Nuclear Information System (INIS)
Ghosh, Subir
2006-01-01
A particular form of non-linear σ-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-Abelian nature of the invariance, with field dependent structure functions. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in [J.F. Carinena et al., Nonlinearity 17 (2004) 1941, math-ph/0406002; J.F. Carinena et al., in: Proceedings of 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004, p. 39, math-ph/0505028; J.F. Carinena et al., Rep. Math. Phys. 54 (2004) 285, hep-th/0501106]. The connection with non-commutative geometry is also established
International Nuclear Information System (INIS)
Lashkevich, Michael; Pugai, Yaroslav
2013-01-01
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [1]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show that the singular vectors are expressed in terms of the degenerate Macdonald polynomials with rectangular partitions. We study the matrix elements that contain a singular vector in one chirality and a cosingular vector in the other chirality and find them to lead to the resonance identities already known in the conformal perturbation theory. Besides, we give a new derivation of the equation of motion in the sinh-Gordon theory, and a new representation for conserved currents
Ford, Timothy J
2017-01-01
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Jorgensen, Palle E T
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
Elements of algebraic coding systems
Cardoso da Rocha, Jr, Valdemar
2014-01-01
Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...
Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach
Doeswijk, T.G.; Keesman, K.J.
2005-01-01
Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such
Reachability for Finite-State Process Algebras Using Static Analysis
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya; Nielson, Flemming
2011-01-01
of the Data Flow Analysis are used in order to “cut off” some of the branches in the reachability analysis that are not important for determining, whether or not a state is reachable. In this way, it is possible for our reachability algorithm to avoid building large parts of the system altogether and still......In this work we present an algorithm for solving the reachability problem in finite systems that are modelled with process algebras. Our method uses Static Analysis, in particular, Data Flow Analysis, of the syntax of a process algebraic system with multi-way synchronisation. The results...... solve the reachability problem in a precise way....
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Genetic Algorithm Based Microscale Vehicle Emissions Modelling
Directory of Open Access Journals (Sweden)
Sicong Zhu
2015-01-01
Full Text Available There is a need to match emission estimations accuracy with the outputs of transport models. The overall error rate in long-term traffic forecasts resulting from strategic transport models is likely to be significant. Microsimulation models, whilst high-resolution in nature, may have similar measurement errors if they use the outputs of strategic models to obtain traffic demand predictions. At the microlevel, this paper discusses the limitations of existing emissions estimation approaches. Emission models for predicting emission pollutants other than CO2 are proposed. A genetic algorithm approach is adopted to select the predicting variables for the black box model. The approach is capable of solving combinatorial optimization problems. Overall, the emission prediction results reveal that the proposed new models outperform conventional equations in terms of accuracy and robustness.
Modelling Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
New insights in the standard model of quantum physics in Clifford algebra
Daviau, Claude
2013-01-01
Why Clifford algebra is the true mathematical frame of the standard model of quantum physics. Why the time is everywhere oriented and why the left side shall never become the right side. Why positrons have also a positive proper energy. Why there is a Planck constant. Why a mass is not a charge. Why a system of particles implies the existence of the inverse of the individual wave function. Why a fourth neutrino should be a good candidate for black matter. Why concepts as “parity” and “reverse” are essential. Why the electron of a H atom is in only one bound state. Plus 2 very remarkable identities, and the invariant wave equations that they imply. Plus 3 generations and 4 neutrinos. Plus 5 dimensions in the space and 6 dimensions in space-time…
Approach method of the solutions of algebraic models of the N body problem
International Nuclear Information System (INIS)
Dufour, M.
1986-09-01
We have studied a class of algebraic eigenvalue problems that generate tridiagonal matrices. The Lipkin Hamiltonian was chosen as representative. Three methods have been implemented, whose extension to more general many body problems seems possible i) Degenerate Linked Cluster Theory (LCT), which disregards special symmetries of the interaction and defines a hierarchy of approximation based on model spaces at fixed number of particle-hole excitation of the unperturbed Hamiltonian. The method works for small perturbations but does not yield a complete description. ii) A new linearization method that replaces the matrix to be diagonalized by local (tangent) approximations by harmonic matrices. This method generalizes LCT and is a posteriori reminiscent of semi-classical ones. However of is simpler, more precise and yields a complete description of spectra. iii) A global way to characterize spectra based on Gershgorine-Hadamard disks [fr
International Nuclear Information System (INIS)
Schlingemann, D.
1996-10-01
Several two dimensional quantum field theory models have more than one vacuum state. An investigation of super selection sectors in two dimensions from an axiomatic point of view suggests that there should be also states, called soliton or kink states, which interpolate different vacua. Familiar quantum field theory models, for which the existence of kink states have been proven, are the Sine-Gordon and the φ 4 2 -model. In order to establish the existence of kink states for a larger class of models, we investigate the following question: Which are sufficient conditions a pair of vacuum states has to fulfill, such that an interpolating kink state can be constructed? We discuss the problem in the framework of algebraic quantum field theory which includes, for example, the P(φ) 2 -models. We identify a large class of vacuum states, including the vacua of the P(φ) 2 -models, the Yukawa 2 -like models and special types of Wess-Zumino models, for which there is a natural way to construct an interpolating kink state. In two space-time dimensions, massive particle states are kink states. We apply the Haag-Ruelle collision theory to kink sectors in order to analyze the asymptotic scattering states. We show that for special configurations of n kinks the scattering states describe n freely moving non interacting particles. (orig.)
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
International Nuclear Information System (INIS)
Aoyama, Shogo
2014-01-01
The Poisson brackets for non-linear σ-models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is shown to satisfy the classical exchange algebra
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María
2014-06-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the
The Moyal momentum algebra applied to θ-deformed 2d conformal models and KdV-hierarchies
International Nuclear Information System (INIS)
Boulahoual, A.; Sedra, M.B.
2002-08-01
The properties of the Das-Popowicz Moyal momentum algebra that we introduce in hep-th/0207242 are reexamined in detail and used to discuss some aspects of integrable models and 2d conformal field theories. Among the results presented we setup some useful convention notations which lead to extract some non trivial properties of the Moyal momentum algebra. We use the particular sub-algebra sl n -Σ-tilde n (0,n) to construct the sl 2 -Liouville conformal model δδ-barΦ=2/θe -1/θΦ and its sl 3 -Toda extension δδ-bar 1 =Ae -1/2θ(Φ 1 +1/2Φ 2 ) and δδ-barΦ 2 =Be -1/2 / θ (Φ 1 +2Φ 2 ) . We also show that the central charge, a la Feigin-Fuchs, associated to the spin-2 conformal current of the θ-Liouville model is given by c θ =(1+24θ 2 ). Moreover, the results obtained for the Das-Popowicz Mm algebra are applied to study systematically some properties of the Moyal KdV and Boussinesq hierarchies generalizing some known results. We also discuss the primarily condition of conformal w θ -currents and interpret this condition as being a dressing gauge symmetry in the Moyal momentum space. Some computations related to the dressing gauge group are explicitly presented. (author)
The algebra of the general Markov model on phylogenetic trees and networks.
Sumner, J G; Holland, B R; Jarvis, P D
2012-04-01
It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.
Linear Algebra and Smarandache Linear Algebra
Vasantha, Kandasamy
2003-01-01
The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...
Computational algebraic geometry for statistical modeling FY09Q2 progress.
Energy Technology Data Exchange (ETDEWEB)
Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre
2009-03-01
This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones in more detail; the next section provides an overview of the project and how the current progress fits into it.
Davidson, Natalie R; Godfrey, Keith R; Alquaddoomi, Faisal; Nola, David; DiStefano, Joseph J
2017-05-01
We describe and illustrate use of DISTING, a novel web application for computing alternative structurally identifiable linear compartmental models that are input-output indistinguishable from a postulated linear compartmental model. Several computer packages are available for analysing the structural identifiability of such models, but DISTING is the first to be made available for assessing indistinguishability. The computational algorithms embedded in DISTING are based on advanced versions of established geometric and algebraic properties of linear compartmental models, embedded in a user-friendly graphic model user interface. Novel computational tools greatly speed up the overall procedure. These include algorithms for Jacobian matrix reduction, submatrix rank reduction, and parallelization of candidate rank computations in symbolic matrix analysis. The application of DISTING to three postulated models with respectively two, three and four compartments is given. The 2-compartment example is used to illustrate the indistinguishability problem; the original (unidentifiable) model is found to have two structurally identifiable models that are indistinguishable from it. The 3-compartment example has three structurally identifiable indistinguishable models. It is found from DISTING that the four-compartment example has five structurally identifiable models indistinguishable from the original postulated model. This example shows that care is needed when dealing with models that have two or more compartments which are neither perturbed nor observed, because the numbering of these compartments may be arbitrary. DISTING is universally and freely available via the Internet. It is easy to use and circumvents tedious and complicated algebraic analysis previously done by hand. Copyright © 2017 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
Ivonne Burguet Lago
2018-05-01
Full Text Available ABSTRACT The paper describes a proposal of professional pedagogical performance tests to assess teachers’ role in the process of developing the skill of working with algorithms in Linear Algebra. It aims at devising a testing tool to assess teachers’ performance in the skill-developing process. This tool is a finding of Cuba theory of Advanced Education, systematically used in recent years. The findings include the test design and the illustration of its use in a sample of 22 Linear Algebra teachers during the first term of the 2017-2018 academic year at Informatics Sciences Engineering major. Keywords: ABSTRACT The paper describes a proposal of professional pedagogical performance tests to assess teachers’ role in the process of developing the skill of working with algorithms in Linear Algebra. It aims at devising a testing tool to assess teachers’ performance in the skill-developing process. This tool is a finding of Cuba theory of Advanced Education, systematically used in recent years. The findings include the test design and the illustration of its use in a sample of 22 Linear Algebra teachers during the first term of the 2017-2018 academic year at Informatics Sciences Engineering major.
Constructing canonical bases of quantized enveloping algebras
Graaf, W.A. de
2001-01-01
An algorithm for computing the elements of a given weight of the canonical basis of a quantized enveloping algebra is described. Subsequently, a similar algorithm is presented for computing the canonical basis of a finite-dimensional module.
Pyramid algorithms as models of human cognition
Pizlo, Zygmunt; Li, Zheng
2003-06-01
There is growing body of experimental evidence showing that human perception and cognition involves mechanisms that can be adequately modeled by pyramid algorithms. The main aspect of those mechanisms is hierarchical clustering of information: visual images, spatial relations, and states as well as transformations of a problem. In this paper we review prior psychophysical and simulation results on visual size transformation, size discrimination, speed-accuracy tradeoff, figure-ground segregation, and the traveling salesman problem. We also present our new results on graph search and on the 15-puzzle.
Modeling Trees with a Space Colonization Algorithm
Morell Higueras, Marc
2014-01-01
[CATALÀ] Aquest TFG tracta la implementació d'un algorisme de generació procedural que construeixi una estructura reminiscent a la d'un arbre de clima temperat, i també la implementació del pas de l'estructura a un model tridimensional, acompanyat de l'eina per a visualitzar el resultat i fer-ne l'exportació [ANGLÈS] This TFG consists of the implementation of a procedural generation algorithm that builds a structure reminiscent of that of a temperate climate tree, and also consists of the ...
Genetic Algorithms Principles Towards Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-10-01
Full Text Available In this paper we propose a general approach based on Genetic Algorithms (GAs to evolve Hidden Markov Models (HMM. The problem appears when experts assign probability values for HMM, they use only some limited inputs. The assigned probability values might not be accurate to serve in other cases related to the same domain. We introduce an approach based on GAs to find
out the suitable probability values for the HMM to be mostly correct in more cases than what have been used to assign the probability values.
Cierniak, Robert; Lorent, Anna
2016-09-01
The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. Copyright © 2016 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
V. E. Marley
2015-01-01
Full Text Available Summary. The concept of algorithmic models appeared from the algorithmic approach in which the simulated object, the phenomenon appears in the form of process, subject to strict rules of the algorithm, which placed the process of operation of the facility. Under the algorithmic model is the formalized description of the scenario subject specialist for the simulated process, the structure of which is comparable with the structure of the causal and temporal relationships between events of the process being modeled, together with all information necessary for its software implementation. To represent the structure of algorithmic models used algorithmic network. Normally, they were defined as loaded finite directed graph, the vertices which are mapped to operators and arcs are variables, bound by operators. The language of algorithmic networks has great features, the algorithms that it can display indifference the class of all random algorithms. In existing systems, automation modeling based on algorithmic nets, mainly used by operators working with real numbers. Although this reduces their ability, but enough for modeling a wide class of problems related to economy, environment, transport, technical processes. The task of modeling the execution of schedules and network diagrams is relevant and useful. There are many counting systems, network graphs, however, the monitoring process based analysis of gaps and terms of graphs, no analysis of prediction execution schedule or schedules. The library is designed to build similar predictive models. Specifying source data to obtain a set of projections from which to choose one and take it for a new plan.
Garrett, Paul B
2007-01-01
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal
Kolman, Bernard
1985-01-01
College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c
Living on the edge: a toy model for holographic reconstruction of algebras with centers
Energy Technology Data Exchange (ETDEWEB)
Donnelly, William; Marolf, Donald; Michel, Ben; Wien, Jason [Department of Physics, University of California,Santa Barbara, CA 93106 (United States)
2017-04-18
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the ((δArea)/(4G{sub N})) term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this ((δArea)/(4G{sub N})) term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
Algebraic stress model for axial flow in a bare rod-bundle
International Nuclear Information System (INIS)
de Lemos, M.J.S.
1987-01-01
The problem of predicting transport properties for momentum and heat across the boundaries of interconnected channels has been the subject of many investigations. In the particular case of axial flow through rod-bundles, transport coefficients for channel faces aligned with rod centers are known to be considerably higher than those calculated by simple isotropic theories. And yet, it was been found that secondary flows play only a minor role in this overall transport, being turbulence highly enhanced across that hypothetical surface. In order to numerically predict the correct amount of the quantity being transported, the approach taken by many investigators was then to artificially increase the diffusion coefficient obtained via a simple isopropic theory (usually the standard k-ε model) and numerically match the correct experimentally observed mixing rates. The present paper reports an attempt to describe the turbulent stresses by means of an Algebraic Stress Model for turbulence. Relative turbulent kinetic energy distribution in all three directions are presented and compared with experiments in a square lattice. The strong directional dependence of transport terms are then obtained via a model for the Reynolds stresses. The results identify a need for a better representation of the mean-flow field part of the pressure-strain correlation term
Living on the edge: a toy model for holographic reconstruction of algebras with centers
International Nuclear Information System (INIS)
Donnelly, William; Marolf, Donald; Michel, Ben; Wien, Jason
2017-01-01
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the ((δArea)/(4G N )) term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this ((δArea)/(4G N )) term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
Calculus domains modelled using an original bool algebra based on polygons
Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.
2016-08-01
Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.
Motion Model Employment using interacting Motion Model Algorithm
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar
2006-01-01
The paper presents a simulation study to track a maneuvering target using a selective approach in choosing Interacting Multiple Models (IMM) algorithm to provide a wider coverage to track such targets. Initially, there are two motion models in the system to track a target. Probability of each m...
Models and Algorithms for Tracking Target with Coordinated Turn Motion
Directory of Open Access Journals (Sweden)
Xianghui Yuan
2014-01-01
Full Text Available Tracking target with coordinated turn (CT motion is highly dependent on the models and algorithms. First, the widely used models are compared in this paper—coordinated turn (CT model with known turn rate, augmented coordinated turn (ACT model with Cartesian velocity, ACT model with polar velocity, CT model using a kinematic constraint, and maneuver centered circular motion model. Then, in the single model tracking framework, the tracking algorithms for the last four models are compared and the suggestions on the choice of models for different practical target tracking problems are given. Finally, in the multiple models (MM framework, the algorithm based on expectation maximization (EM algorithm is derived, including both the batch form and the recursive form. Compared with the widely used interacting multiple model (IMM algorithm, the EM algorithm shows its effectiveness.
Invariants of triangular Lie algebras
International Nuclear Information System (INIS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-01-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated
Waterloo Workshop on Computer Algebra
Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday
2018-01-01
This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
A review of ocean chlorophyll algorithms and primary production models
Li, Jingwen; Zhou, Song; Lv, Nan
2015-12-01
This paper mainly introduces the five ocean chlorophyll concentration inversion algorithm and 3 main models for computing ocean primary production based on ocean chlorophyll concentration. Through the comparison of five ocean chlorophyll inversion algorithm, sums up the advantages and disadvantages of these algorithm,and briefly analyzes the trend of ocean primary production model.
Adaptive Numerical Algorithms in Space Weather Modeling
Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.;
2010-01-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical
A new algebraic turbulence model for accurate description of airfoil flows
Xiao, Meng-Juan; She, Zhen-Su
2017-11-01
We report a new algebraic turbulence model (SED-SL) based on the SED theory, a symmetry-based approach to quantifying wall turbulence. The model specifies a multi-layer profile of a stress length (SL) function in both the streamwise and wall-normal directions, which thus define the eddy viscosity in the RANS equation (e.g. a zero-equation model). After a successful simulation of flat plate flow (APS meeting, 2016), we report here further applications of the model to the flow around airfoil, with significant improvement of the prediction accuracy of the lift (CL) and drag (CD) coefficients compared to other popular models (e.g. BL, SA, etc.). Two airfoils, namely RAE2822 airfoil and NACA0012 airfoil, are computed for over 50 cases. The results are compared to experimental data from AGARD report, which shows deviations of CL bounded within 2%, and CD within 2 counts (10-4) for RAE2822 and 6 counts for NACA0012 respectively (under a systematic adjustment of the flow conditions). In all these calculations, only one parameter (proportional to the Karmen constant) shows slight variation with Mach number. The most remarkable outcome is, for the first time, the accurate prediction of the drag coefficient. The other interesting outcome is the physical interpretation of the multi-layer parameters: they specify the corresponding multi-layer structure of turbulent boundary layer; when used together with simulation data, the SED-SL enables one to extract physical information from empirical data, and to understand the variation of the turbulent boundary layer.
A genetic algorithm for solving supply chain network design model
Firoozi, Z.; Ismail, N.; Ariafar, S. H.; Tang, S. H.; Ariffin, M. K. M. A.
2013-09-01
Network design is by nature costly and optimization models play significant role in reducing the unnecessary cost components of a distribution network. This study proposes a genetic algorithm to solve a distribution network design model. The structure of the chromosome in the proposed algorithm is defined in a novel way that in addition to producing feasible solutions, it also reduces the computational complexity of the algorithm. Computational results are presented to show the algorithm performance.
Rate-control algorithms testing by using video source model
DEFF Research Database (Denmark)
Belyaev, Evgeny; Turlikov, Andrey; Ukhanova, Anna
2008-01-01
In this paper the method of rate control algorithms testing by the use of video source model is suggested. The proposed method allows to significantly improve algorithms testing over the big test set.......In this paper the method of rate control algorithms testing by the use of video source model is suggested. The proposed method allows to significantly improve algorithms testing over the big test set....
Entropy correlation and entanglement for mixed states in an algebraic model
International Nuclear Information System (INIS)
Hou Xiwen; Chen Jinghua; Wan Mingfang; Ma Zhongqi
2009-01-01
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing
Yuan-Shyi Peter Chiu; Chien-Hua Lee; Nong Pan; Singa Wang Chiu
2013-01-01
This study uses mathematical modeling along with an algebraic technique to resolve the production-distribution policy for a single-producer multi-retailer integrated inventory system with scrap in production. We assume that a product is manufactured through an imperfect production process where all nonconforming items will be picked up and scrapped in each production cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in ...
Algebraic entropy for algebraic maps
International Nuclear Information System (INIS)
Hone, A N W; Ragnisco, Orlando; Zullo, Federico
2016-01-01
We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)
Galois Connections for Flow Algebras
DEFF Research Database (Denmark)
Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis
2011-01-01
to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...
Computations in finite-dimensional Lie algebras
Directory of Open Access Journals (Sweden)
A. M. Cohen
1997-12-01
Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.
Schilders, W.H.A.; Meijer, P.B.L.; Ciggaar, E.
2008-01-01
In this paper we discuss the use of the state-space modelling MOESP algorithm to generate precise information about the number of neurons and hidden layers in dynamic neural networks developed for the behavioural modelling of electronic circuits. The Bartels–Stewart algorithm is used to transform
Fusion rules of chiral algebras
International Nuclear Information System (INIS)
Gaberdiel, M.
1994-01-01
Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)
Generalized Jaynes-Cummings model as a quantum search algorithm
International Nuclear Information System (INIS)
Romanelli, A.
2009-01-01
We propose a continuous time quantum search algorithm using a generalization of the Jaynes-Cummings model. In this model the states of the atom are the elements among which the algorithm realizes the search, exciting resonances between the initial and the searched states. This algorithm behaves like Grover's algorithm; the optimal search time is proportional to the square root of the size of the search set and the probability to find the searched state oscillates periodically in time. In this frame, it is possible to reinterpret the usual Jaynes-Cummings model as a trivial case of the quantum search algorithm.
Aeon: Synthesizing Scheduling Algorithms from High-Level Models
Monette, Jean-Noël; Deville, Yves; van Hentenryck, Pascal
This paper describes the aeon system whose aim is to synthesize scheduling algorithms from high-level models. A eon, which is entirely written in comet, receives as input a high-level model for a scheduling application which is then analyzed to generate a dedicated scheduling algorithm exploiting the structure of the model. A eon provides a variety of synthesizers for generating complete or heuristic algorithms. Moreover, synthesizers are compositional, making it possible to generate complex hybrid algorithms naturally. Preliminary experimental results indicate that this approach may be competitive with state-of-the-art search algorithms.
Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA.
Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard
2012-01-01
Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting
Visualization of logistic algorithm in Wilson model
Glushchenko, A. S.; Rodin, V. A.; Sinegubov, S. V.
2018-05-01
Economic order quantity (EOQ), defined by the Wilson's model, is widely used at different stages of production and distribution of different products. It is useful for making decisions in the management of inventories, providing a more efficient business operation and thus bringing more economic benefits. There is a large amount of reference material and extensive computer shells that help solving various logistics problems. However, the use of large computer environments is not always justified and requires special user training. A tense supply schedule in a logistics model is optimal, if, and only if, the planning horizon coincides with the beginning of the next possible delivery. For all other possible planning horizons, this plan is not optimal. It is significant that when the planning horizon changes, the plan changes immediately throughout the entire supply chain. In this paper, an algorithm and a program for visualizing models of the optimal value of supplies and their number, depending on the magnitude of the planned horizon, have been obtained. The program allows one to trace (visually and quickly) all main parameters of the optimal plan on the charts. The results of the paper represent a part of the authors’ research work in the field of optimization of protection and support services of ports in the Russian North.
Algebraic Reconstruction of Current Dipoles and Quadrupoles in Three-Dimensional Space
Directory of Open Access Journals (Sweden)
Takaaki Nara
2013-01-01
Full Text Available This paper presents an algebraic method for an inverse source problem for the Poisson equation where the source consists of dipoles and quadrupoles. This source model is significant in the magnetoencephalography inverse problem. The proposed method identifies the source parameters directly and algebraically using data without requiring an initial parameter estimate or iterative computation of the forward solution. The obtained parameters could be used for the initial solution in an optimization-based algorithm for further refinement.
Applications of Computer Algebra Conference
Martínez-Moro, Edgar
2017-01-01
The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.
Applied matrix algebra in the statistical sciences
Basilevsky, Alexander
2005-01-01
This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.
Jafarizadeh, M. A.; Ranjbar, Z.; Fouladi, N.; Ghapanvari, M.
2018-01-01
In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE (4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE (4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE (2), BE (4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for 46 104 - 110Pd isotopes.
Continuous Time Dynamic Contraflow Models and Algorithms
Directory of Open Access Journals (Sweden)
Urmila Pyakurel
2016-01-01
Full Text Available The research on evacuation planning problem is promoted by the very challenging emergency issues due to large scale natural or man-created disasters. It is the process of shifting the maximum number of evacuees from the disastrous areas to the safe destinations as quickly and efficiently as possible. Contraflow is a widely accepted model for good solution of evacuation planning problem. It increases the outbound road capacity by reversing the direction of roads towards the safe destination. The continuous dynamic contraflow problem sends the maximum number of flow as a flow rate from the source to the sink in every moment of time unit. We propose the mathematical model for the continuous dynamic contraflow problem. We present efficient algorithms to solve the maximum continuous dynamic contraflow and quickest continuous contraflow problems on single source single sink arbitrary networks and continuous earliest arrival contraflow problem on single source single sink series-parallel networks with undefined supply and demand. We also introduce an approximation solution for continuous earliest arrival contraflow problem on two-terminal arbitrary networks.
Bouc–Wen hysteresis model identification using Modified Firefly Algorithm
International Nuclear Information System (INIS)
Zaman, Mohammad Asif; Sikder, Urmita
2015-01-01
The parameters of Bouc–Wen hysteresis model are identified using a Modified Firefly Algorithm. The proposed algorithm uses dynamic process control parameters to improve its performance. The algorithm is used to find the model parameter values that results in the least amount of error between a set of given data points and points obtained from the Bouc–Wen model. The performance of the algorithm is compared with the performance of conventional Firefly Algorithm, Genetic Algorithm and Differential Evolution algorithm in terms of convergence rate and accuracy. Compared to the other three optimization algorithms, the proposed algorithm is found to have good convergence rate with high degree of accuracy in identifying Bouc–Wen model parameters. Finally, the proposed method is used to find the Bouc–Wen model parameters from experimental data. The obtained model is found to be in good agreement with measured data. - Highlights: • We describe a new method to find the Bouc–Wen hysteresis model parameters. • We propose a Modified Firefly Algorithm. • We compare our method with existing methods to find that the proposed method performs better. • We use our model to fit experimental results. Good agreement is found
Bouc–Wen hysteresis model identification using Modified Firefly Algorithm
Energy Technology Data Exchange (ETDEWEB)
Zaman, Mohammad Asif, E-mail: zaman@stanford.edu [Department of Electrical Engineering, Stanford University (United States); Sikder, Urmita [Department of Electrical Engineering and Computer Sciences, University of California, Berkeley (United States)
2015-12-01
The parameters of Bouc–Wen hysteresis model are identified using a Modified Firefly Algorithm. The proposed algorithm uses dynamic process control parameters to improve its performance. The algorithm is used to find the model parameter values that results in the least amount of error between a set of given data points and points obtained from the Bouc–Wen model. The performance of the algorithm is compared with the performance of conventional Firefly Algorithm, Genetic Algorithm and Differential Evolution algorithm in terms of convergence rate and accuracy. Compared to the other three optimization algorithms, the proposed algorithm is found to have good convergence rate with high degree of accuracy in identifying Bouc–Wen model parameters. Finally, the proposed method is used to find the Bouc–Wen model parameters from experimental data. The obtained model is found to be in good agreement with measured data. - Highlights: • We describe a new method to find the Bouc–Wen hysteresis model parameters. • We propose a Modified Firefly Algorithm. • We compare our method with existing methods to find that the proposed method performs better. • We use our model to fit experimental results. Good agreement is found.
International Nuclear Information System (INIS)
MacCallum, M.A.H.
1990-01-01
The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one general relativity meeting and the next, despite which there have been significant changes in the period since the last report. The introductory remarks aim to give a brief survey of capabilities of the principal available systems and highlight one or two trends. The reference to the most recent full survey of computer algebra in relativity and brief descriptions of the Maple, REDUCE and SHEEP and other applications are given. (author)
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Jacobson, Nathan
2009-01-01
A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L
Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang
2016-01-01
A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively.
Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras
Andrade, Jefferson O.; Kameyama, Yukiyoshi
Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In this paper, we propose a novel, efficient algorithm for multi-valued bounded model checking. A notable feature of our algorithm is that it is not based on reduction of multi-values into two-values; instead, it generates a single formula which represents multi-valuedness by a suitable encoding, and asks a standard SAT solver to check its satisfiability. Our experimental results show a significant improvement in the number of variables and clauses and also in execution time compared with the reduction-based one.
Current and Future Tests of the Algebraic Cluster Model of12C
Gai, Moshe
2017-07-01
A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts, in12C, rotation-vibration structure with rotational bands of an oblate equilateral triangular symmetric spinning top with a D 3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with a degenerate 4+ and 4- (parity doublet) states. Our newly measured {2}2+ state in12C allows the first study of rotation-vibration structure in12C. The newly measured 5- state and 4- states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D 3h symmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of12C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in12C such as the (0+) Hoyle band and the (1-) bending mode with prediction of (“missing 3- and 4-”) states that may shed new light on clustering in12C and light nuclei. In particular, the observation (or non observation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in12C. We discuss proposed research programs at the Darmstadt S- DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon.
Risnawati; Khairinnisa, S.; Darwis, A. H.
2018-01-01
The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.
Djurfeldt, Mikael
2012-07-01
The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31-42, 2008b) and an implementation in Python has been publicly released.
Proposing and Testing a Model to Explain Traits of Algebra Preparedness
Venenciano, Linda; Heck, Ronald
2016-01-01
Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…
Developing Pre-Algebraic Thinking in Generalizing Repeating Pattern Using SOLO Model
Lian, Lim Hooi; Yew, Wun Thiam
2011-01-01
In this paper, researchers discussed the application of the generalization perspective in helping the primary school pupils to develop their pre-algebraic thinking in generalizing repeating pattern. There are two main stages of the generalization perspective had been adapted, namely investigating and generalizing the pattern. Since the Biggs and…
Indian Academy of Sciences (India)
polynomial) division have been found in Vedic Mathematics which are dated much before Euclid's algorithm. A programming language Is used to describe an algorithm for execution on a computer. An algorithm expressed using a programming.
Fast algorithms for transport models. Final report
International Nuclear Information System (INIS)
Manteuffel, T.A.
1994-01-01
This project has developed a multigrid in space algorithm for the solution of the S N equations with isotropic scattering in slab geometry. The algorithm was developed for the Modified Linear Discontinuous (MLD) discretization in space which is accurate in the thick diffusion limit. It uses a red/black two-cell μ-line relaxation. This relaxation solves for all angles on two adjacent spatial cells simultaneously. It takes advantage of the rank-one property of the coupling between angles and can perform this inversion in O(N) operations. A version of the multigrid in space algorithm was programmed on the Thinking Machines Inc. CM-200 located at LANL. It was discovered that on the CM-200 a block Jacobi type iteration was more efficient than the block red/black iteration. Given sufficient processors all two-cell block inversions can be carried out simultaneously with a small number of parallel steps. The bottleneck is the need for sums of N values, where N is the number of discrete angles, each from a different processor. These are carried out by machine intrinsic functions and are well optimized. The overall algorithm has computational complexity O(log(M)), where M is the number of spatial cells. The algorithm is very efficient and represents the state-of-the-art for isotropic problems in slab geometry. For anisotropic scattering in slab geometry, a multilevel in angle algorithm was developed. A parallel version of the multilevel in angle algorithm has also been developed. Upon first glance, the shifted transport sweep has limited parallelism. Once the right-hand-side has been computed, the sweep is completely parallel in angle, becoming N uncoupled initial value ODE's. The author has developed a cyclic reduction algorithm that renders it parallel with complexity O(log(M)). The multilevel in angle algorithm visits log(N) levels, where shifted transport sweeps are performed. The overall complexity is O(log(N)log(M))
Tracing a planar algebraic curve
International Nuclear Information System (INIS)
Chen Falai; Kozak, J.
1994-09-01
In this paper, an algorithm that determines a real algebraic curve is outlined. Its basic step is to divide the plane into subdomains that include only simple branches of the algebraic curve without singular points. Each of the branches is then stably and efficiently traced in the particular subdomain. Except for the tracing, the algorithm requires only a couple of simple operations on polynomials that can be carried out exactly if the coefficients are rational, and the determination of zeros of several polynomials of one variable. (author). 5 refs, 4 figs
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
Indian Academy of Sciences (India)
Deligne, Mumford and Artin [DM, Ar2]) and consider algebraic stacks, then we can cons- truct the 'moduli ... the moduli scheme and the moduli stack of vector bundles. First I will give ... 1–31. © Printed in India. 1 ...... Cultura, Spain. References.
Energy Technology Data Exchange (ETDEWEB)
Rossi, R., E-mail: riccardo.rossi12@unibo.i [Laboratorio di Termofluidodinamica Computazionale Seconda Facolta di Ingegneria di Forli, Universita di Bologna Via Fontanelle 40, 47100 Forli (Italy); Center for Turbulence Research Department of Mechanical Engineering Stanford University, CA 94305 (United States); Philips, D.A.; Iaccarino, G. [Center for Turbulence Research Department of Mechanical Engineering Stanford University, CA 94305 (United States)
2010-10-15
Research highlights: {yields} The computed DNS statistics indicate that a gradient-transport scheme can be applied to the vertical and spanwise scalar flux components. {yields} The streamwise scalar flux is characterized by a counter-gradient transport mechanism in the wake region close to the obstacle. {yields} The wake profiles of scalar fluctuations and the shape of probability density functions do not suggest a significant flapping movement of the scalar plume. {yields} The evaluation of scalar dispersion models must include a careful assessment of the computed mean velocity field and Reynolds stress tensor. {yields} Algebraic models provide an improved prediction of the mean concentration field as compared to the standard eddy-diffusivity model. -- Abstract: The dispersion of a passive scalar downstream of a wall-mounted cube is examined using direct numerical simulations and turbulence models applied to the Reynolds equations. The scalar is released from a circular source located on top of the obstacle, which is immersed in a developing boundary-layer flow. Direct simulations are performed to give insight into the mixing process and to provide a reference database for turbulence closures. Algebraic flux models are evaluated against the standard eddy-diffusivity representation. Coherent structures periodically released from the cube top are responsible for a counter-diffusion mechanism appearing in the streamwise scalar flux. Alternating vortex pairs form from the lateral edges of the cube, but the intensity profiles and probability density functions of scalar fluctuations suggest that they do not cause a significant flapping movement of the scalar plume. The gradient-transport scheme is consistent with the vertical and spanwise scalar flux components. From the comparative study with our direct simulations, we further stress that Reynolds stress predictions must be carefully evaluated along with scalar flux closures in order to establish the reliability of
International Nuclear Information System (INIS)
Rossi, R.; Philips, D.A.; Iaccarino, G.
2010-01-01
Research highlights: → The computed DNS statistics indicate that a gradient-transport scheme can be applied to the vertical and spanwise scalar flux components. → The streamwise scalar flux is characterized by a counter-gradient transport mechanism in the wake region close to the obstacle. → The wake profiles of scalar fluctuations and the shape of probability density functions do not suggest a significant flapping movement of the scalar plume. → The evaluation of scalar dispersion models must include a careful assessment of the computed mean velocity field and Reynolds stress tensor. → Algebraic models provide an improved prediction of the mean concentration field as compared to the standard eddy-diffusivity model. -- Abstract: The dispersion of a passive scalar downstream of a wall-mounted cube is examined using direct numerical simulations and turbulence models applied to the Reynolds equations. The scalar is released from a circular source located on top of the obstacle, which is immersed in a developing boundary-layer flow. Direct simulations are performed to give insight into the mixing process and to provide a reference database for turbulence closures. Algebraic flux models are evaluated against the standard eddy-diffusivity representation. Coherent structures periodically released from the cube top are responsible for a counter-diffusion mechanism appearing in the streamwise scalar flux. Alternating vortex pairs form from the lateral edges of the cube, but the intensity profiles and probability density functions of scalar fluctuations suggest that they do not cause a significant flapping movement of the scalar plume. The gradient-transport scheme is consistent with the vertical and spanwise scalar flux components. From the comparative study with our direct simulations, we further stress that Reynolds stress predictions must be carefully evaluated along with scalar flux closures in order to establish the reliability of Reynolds
Efficient Implementation Algorithms for Homogenized Energy Models
National Research Council Canada - National Science Library
Braun, Thomas R; Smith, Ralph C
2005-01-01
... for real-time control implementation. In this paper, we develop algorithms employing lookup tables which permit the high speed implementation of formulations which incorporate relaxation mechanisms and electromechanical coupling...
Computational linear and commutative algebra
Kreuzer, Martin
2016-01-01
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...
Characteristic Dynkin diagrams and W algebras
International Nuclear Information System (INIS)
Ragoucy, E.
1993-01-01
We present a classification of characteristic Dynkin diagrams for the A N , B N , C N and D N algebras. This classification is related to the classification of W(G, K) algebras arising from non-abelian Toda models, and we argue that it can give new insight on the structure of W algebras. (orig.)
The Das-Popowicz Moyal momentum algebra
International Nuclear Information System (INIS)
Boulahoual, A.; Sedra, M.B.
2002-08-01
We introduce in this short note some aspects of the Moyal momentum algebra that we call the Das-Popowicz Mm algebra. Our interest on this algebra is motivated by the central role that it can play in the formulation of integrable models and in higher conformal spin theories. (author)
On Elementary and Algebraic Cellular Automata
Gulak, Yuriy
In this paper we study elementary cellular automata from an algebraic viewpoint. The goal is to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures. We introduce algebraic cellular automata as a natural generalization of elementary ones and discuss their applications as generic models of complex systems.
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Energy Technology Data Exchange (ETDEWEB)
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2010-01-01
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
An algebraic approach to the scattering equations
Energy Technology Data Exchange (ETDEWEB)
Huang, Rijun; Rao, Junjie [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Feng, Bo [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Center of Mathematical Science, Zhejiang University,Hangzhou, 310027 (China); He, Yang-Hui [School of Physics, NanKai University,Tianjin, 300071 (China); Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); Merton College, University of Oxford,Oxford, OX14JD (United Kingdom)
2015-12-10
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
An algebraic approach to the scattering equations
International Nuclear Information System (INIS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-01-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
Loop algorithms for quantum simulations of fermion models on lattices
International Nuclear Information System (INIS)
Kawashima, N.; Gubernatis, J.E.; Evertz, H.G.
1994-01-01
Two cluster algorithms, based on constructing and flipping loops, are presented for world-line quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip and loop-exchange algorithms. For these two algorithms and the standard world-line algorithm, we calculated the autocorrelation times for various physical quantities and found that the ordinary world-line algorithm, which uses only local moves, suffers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values themselves difficult. These difficulties are especially severe in the low-temperature, large-U regime. In contrast, we find that new algorithms, when used alone or in combinations with themselves and the standard algorithm, can have significantly smaller autocorrelation times, in some cases being smaller by three orders of magnitude. The new algorithms, which use nonlocal moves, are discussed from the point of view of a general prescription for developing cluster algorithms. The loop-flip algorithm is also shown to be ergodic and to belong to the grand canonical ensemble. Extensions to other models and higher dimensions are briefly discussed
Ernawati; Carnia, E.; Supriatna, A. K.
2018-03-01
Eigenvalues and eigenvectors in max-plus algebra have the same important role as eigenvalues and eigenvectors in conventional algebra. In max-plus algebra, eigenvalues and eigenvectors are useful for knowing dynamics of the system such as in train system scheduling, scheduling production systems and scheduling learning activities in moving classes. In the translation of proteins in which the ribosome move uni-directionally along the mRNA strand to recruit the amino acids that make up the protein, eigenvalues and eigenvectors are used to calculate protein production rates and density of ribosomes on the mRNA. Based on this, it is important to examine the eigenvalues and eigenvectors in the process of protein translation. In this paper an eigenvector formula is given for a ribosome dynamics during mRNA translation by using the Kleene star algorithm in which the resulting eigenvector formula is simpler and easier to apply to the system than that introduced elsewhere. This paper also discusses the properties of the matrix {B}λ \\otimes n of model. Among the important properties, it always has the same elements in the first column for n = 1, 2,… if the eigenvalue is the time of initiation, λ = τin , and the column is the eigenvector of the model corresponding to λ.
Algebraic characterizations of measure algebras
Czech Academy of Sciences Publication Activity Database
Jech, Thomas
2008-01-01
Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008
Comments on two-loop Kac-Moody algebras
Energy Technology Data Exchange (ETDEWEB)
Ferreira, L A; Gomes, J F; Zimerman, A H [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Schwimmer, A [Istituto Nazionale di Fisica Nucleare, Trieste (Italy)
1991-10-01
It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decouple {beta}-{gamma} system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity to versions of the corresponding ordinary models and decoupled Abelian fields. (author). 15 refs.
Quantum W-algebras and elliptic algebras
International Nuclear Information System (INIS)
Feigin, B.; Kyoto Univ.; Frenkel, E.
1996-01-01
We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)
Thinking Visually about Algebra
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
International Nuclear Information System (INIS)
Mohammad, N.; Siddiqui, A.H.
1987-11-01
The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs
Fireworks algorithm for mean-VaR/CVaR models
Zhang, Tingting; Liu, Zhifeng
2017-10-01
Intelligent algorithms have been widely applied to portfolio optimization problems. In this paper, we introduce a novel intelligent algorithm, named fireworks algorithm, to solve the mean-VaR/CVaR model for the first time. The results show that, compared with the classical genetic algorithm, fireworks algorithm not only improves the optimization accuracy and the optimization speed, but also makes the optimal solution more stable. We repeat our experiments at different confidence levels and different degrees of risk aversion, and the results are robust. It suggests that fireworks algorithm has more advantages than genetic algorithm in solving the portfolio optimization problem, and it is feasible and promising to apply it into this field.
Engineering of Algorithms for Hidden Markov models and Tree Distances
DEFF Research Database (Denmark)
Sand, Andreas
Bioinformatics is an interdisciplinary scientific field that combines biology with mathematics, statistics and computer science in an effort to develop computational methods for handling, analyzing and learning from biological data. In the recent decades, the amount of available biological data has...... speed up all the classical algorithms for analyses and training of hidden Markov models. And I show how two particularly important algorithms, the forward algorithm and the Viterbi algorithm, can be accelerated through a reformulation of the algorithms and a somewhat more complicated parallelization...... contribution to the theoretically fastest set of algorithms presently available to compute two closely related measures of tree distance, the triplet distance and the quartet distance. And I further demonstrate that they are also the fastest algorithms in almost all cases when tested in practice....
1983-03-01
Tic, equals to (NI/ Nic ) where Nic , defined as the net chemical production rate of i-th species, is in general the algebraic sum of terms which are...detailed analysis has shown that in preignition regions the chemical rates which make a significant contribution to any of the Nic are such that at least...Elkton Division Lab., Inc. ATTN. R. Biddle ATTN: M. Summeitield Tech Lib. 1041 US Hlighway One North P. 0. Box 241 Princeton, NJ 08540 Elkton, MD
Computers in nonassociative rings and algebras
Beck, Robert E
1977-01-01
Computers in Nonassociative Rings and Algebras provides information pertinent to the computational aspects of nonassociative rings and algebras. This book describes the algorithmic approaches for solving problems using a computer.Organized into 10 chapters, this book begins with an overview of the concept of a symmetrized power of a group representation. This text then presents data structures and other computational methods that may be useful in the field of computational algebra. Other chapters consider several mathematical ideas, including identity processing in nonassociative algebras, str
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Z2n Grading
International Nuclear Information System (INIS)
Ke San-Min; Li Xin-Ying; Wang Chun; Yue Rui-Hong
2011-01-01
The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Z 2n grading is derived using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution. When n = 2, our results coincide with the results given by Magro for the pure spinor description of AdS 5 × S 5 string theory (when the ghost terms are omitted). (the physics of elementary particles and fields)
International Nuclear Information System (INIS)
Fu Chuanji; Zhu Qinsheng; Wu Shaoyi
2010-01-01
Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external held. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external held. (general)
International Nuclear Information System (INIS)
Ribeiro, Rafael S.; Hermes, Christian J.L.
2014-01-01
In this study, the method of entropy generation minimization (i.e., design aimed at facilitating both heat, mass and fluid flows) is used to assess the evaporator design (aspect ratio and fin density) considering the thermodynamic losses due to heat and mass transfer, and viscous flow processes. A fully algebraic model was put forward to simulate the thermal-hydraulic behavior of tube-fin evaporator coils running under frosting conditions. The model predictions were validated against experimental data, showing a good agreement between calculated and measured counterparts. The optimization exercise has pointed out that high aspect ratio heat exchanger designs lead to lower entropy generation in cases of fixed cooling capacity and air flow rate constrained by the characteristic curve of the fan. - Highlights: • An algebraic model for frost accumulation on tube-fin heat exchangers was advanced. • Model predictions for cooling capacity and air flow rate were compared with experimental data, with errors within ±5% band. • Minimum entropy generation criterion was used to optimize the evaporator geometry. • Thermodynamic analysis led to slender designs for fixed cooling capacity and fan characteristics
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh, E-mail: far75m@yandex.ru, E-mail: farrukh.m@uaeu.ac.ae [International Islamic University Malaysia, Department of Computational and Theoretical Sciences, Faculty of Science (Malaysia); Barhoumi, Abdessatar, E-mail: abdessatar.barhoumi@ipein.rnu.tn [Carthage University, Department of Mathematics, Nabeul Preparatory Engineering Institute (Tunisia); Souissi, Abdessatar, E-mail: s.abdessatar@hotmail.fr [Carthage University, Department of Mathematics, Marsa Preparatory Institute for Scientific and Technical Studies (Tunisia)
2016-12-15
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains.
Availability Allocation of Networked Systems Using Markov Model and Heuristics Algorithm
Directory of Open Access Journals (Sweden)
Ruiying Li
2014-01-01
Full Text Available It is a common practice to allocate the system availability goal to reliability and maintainability goals of components in the early design phase. However, the networked system availability is difficult to be allocated due to its complex topology and multiple down states. To solve these problems, a practical availability allocation method is proposed. Network reliability algebraic methods are used to derive the availability expression of the networked topology on the system level, and Markov model is introduced to determine that on the component level. A heuristic algorithm is proposed to obtain the reliability and maintainability allocation values of components. The principles applied in the AGREE reliability allocation method, proposed by the Advisory Group on Reliability of Electronic Equipment, and failure rate-based maintainability allocation method persist in our allocation method. A series system is used to verify the new algorithm, and the result shows that the allocation based on the heuristic algorithm is quite accurate compared to the traditional one. Moreover, our case study of a signaling system number 7 shows that the proposed allocation method is quite efficient for networked systems.
International Nuclear Information System (INIS)
Jacob, M.
1967-01-01
The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( ΔI = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [fr
Algebraic classification of the conformal tensor
International Nuclear Information System (INIS)
Ares de Parga, Gonzalo; Chavoya, O.; Lopez B, J.L.; Ovando Z, Gerardo
1989-01-01
Starting from the Petrov matrix method, we deduce a new algorithm (adaptable to computers), within the Newman-Penrose formalism, to obtain the algebraic type of the Weyl tensor in general relativity. (author)
José, Marco V; Morgado, Eberto R; Govezensky, Tzipe
2011-07-01
Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The Extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. Since the dimensions of remarkable subsets of the Genetic Hotels are not necessarily integer numbers, we also introduce the concept of algebraic fractal dimension. A general decoding function which maps each codon to its corresponding amino acid or the stop signals is also derived. The Phenotypic Hotel of amino acids is also illustrated. The proposed evolutionary paths are discussed in terms of the existing theories of the evolution of the SGC. The adoption of 3-dimensional models of the Genetic and Phenotypic Hotels will facilitate the understanding of the biological properties of the SGC.
Computationally efficient model predictive control algorithms a neural network approach
Ławryńczuk, Maciej
2014-01-01
This book thoroughly discusses computationally efficient (suboptimal) Model Predictive Control (MPC) techniques based on neural models. The subjects treated include: · A few types of suboptimal MPC algorithms in which a linear approximation of the model or of the predicted trajectory is successively calculated on-line and used for prediction. · Implementation details of the MPC algorithms for feedforward perceptron neural models, neural Hammerstein models, neural Wiener models and state-space neural models. · The MPC algorithms based on neural multi-models (inspired by the idea of predictive control). · The MPC algorithms with neural approximation with no on-line linearization. · The MPC algorithms with guaranteed stability and robustness. · Cooperation between the MPC algorithms and set-point optimization. Thanks to linearization (or neural approximation), the presented suboptimal algorithms do not require d...
International Nuclear Information System (INIS)
Gulshani, P.; So, C.B.
1986-10-01
In a number of postulated accident scenarios in a CANDU reactor, some of the horizontal fuel channels are predicted to experience periods of stratified channel coolant condition which can lead to a circumferential temperature gradient around the pressure tube. To study pressure tube strain and integrity under stratified flow channel conditions, it is, necessary to determine the pressure tube circumferential temperature distribution. This paper presents an algebraic model, called AMPTRACT (Algebraic Model for Pressure Tube TRAnsient Circumferential Temperature), developed to give the transient temperature distribution in a closed form. AMPTRACT models the following modes of heat transfer: radiation from the outermost elements to the pressure tube and from the pressure to calandria tube, convection between the fuel elements and the pressure tube and superheated steam, and circumferential conduction from the exposed to submerged part of the pressure tube. An iterative procedure is used to solve the mass and energy equations in closed form for axial steam and fuel-sheath transient temperature distributions. The one-dimensional conduction equation is then solved to obtain the pressure tube circumferential transient temperature distribution in a cosine series expansion. In the limit of large times and in the absence of convection and radiation to the calandria tube, the predicted pressure tube temperature distribution reduces identically to a parabolic profile. In this limit, however, radiation cannot be ignored because the temperatures are generally high. Convection and radiation tend to flatten the parabolic distribution
Kleyn, Aleks
2007-01-01
The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.
Indian Academy of Sciences (India)
to as 'divide-and-conquer'. Although there has been a large effort in realizing efficient algorithms, there are not many universally accepted algorithm design paradigms. In this article, we illustrate algorithm design techniques such as balancing, greedy strategy, dynamic programming strategy, and backtracking or traversal of ...
DEVELOPMENT OF 2D HUMAN BODY MODELING USING THINNING ALGORITHM
Directory of Open Access Journals (Sweden)
K. Srinivasan
2010-11-01
Full Text Available Monitoring the behavior and activities of people in Video surveillance has gained more applications in Computer vision. This paper proposes a new approach to model the human body in 2D view for the activity analysis using Thinning algorithm. The first step of this work is Background subtraction which is achieved by the frame differencing algorithm. Thinning algorithm has been used to find the skeleton of the human body. After thinning, the thirteen feature points like terminating points, intersecting points, shoulder, elbow, and knee points have been extracted. Here, this research work attempts to represent the body model in three different ways such as Stick figure model, Patch model and Rectangle body model. The activities of humans have been analyzed with the help of 2D model for the pre-defined poses from the monocular video data. Finally, the time consumption and efficiency of our proposed algorithm have been evaluated.
Model-Free Adaptive Control Algorithm with Data Dropout Compensation
Directory of Open Access Journals (Sweden)
Xuhui Bu
2012-01-01
Full Text Available The convergence of model-free adaptive control (MFAC algorithm can be guaranteed when the system is subject to measurement data dropout. The system output convergent speed gets slower as dropout rate increases. This paper proposes a MFAC algorithm with data compensation. The missing data is first estimated using the dynamical linearization method, and then the estimated value is introduced to update control input. The convergence analysis of the proposed MFAC algorithm is given, and the effectiveness is also validated by simulations. It is shown that the proposed algorithm can compensate the effect of the data dropout, and the better output performance can be obtained.
Evaluation of models generated via hybrid evolutionary algorithms ...
African Journals Online (AJOL)
2016-04-02
Apr 2, 2016 ... Evaluation of models generated via hybrid evolutionary algorithms for the prediction of Microcystis ... evolutionary algorithms (HEA) proved to be highly applica- ble to the hypertrophic reservoirs of South Africa. .... discovered and optimised using a large-scale parallel computational device and relevant soft-.
Fast Algorithms for Fitting Active Appearance Models to Unconstrained Images
Tzimiropoulos, Georgios; Pantic, Maja
2016-01-01
Fitting algorithms for Active Appearance Models (AAMs) are usually considered to be robust but slow or fast but less able to generalize well to unseen variations. In this paper, we look into AAM fitting algorithms and make the following orthogonal contributions: We present a simple “project-out‿
Models and algorithms for biomolecules and molecular networks
DasGupta, Bhaskar
2016-01-01
By providing expositions to modeling principles, theories, computational solutions, and open problems, this reference presents a full scope on relevant biological phenomena, modeling frameworks, technical challenges, and algorithms. * Up-to-date developments of structures of biomolecules, systems biology, advanced models, and algorithms * Sampling techniques for estimating evolutionary rates and generating molecular structures * Accurate computation of probability landscape of stochastic networks, solving discrete chemical master equations * End-of-chapter exercises
Optimization algorithms intended for self-tuning feedwater heater model
International Nuclear Information System (INIS)
Czop, P; Barszcz, T; Bednarz, J
2013-01-01
This work presents a self-tuning feedwater heater model. This work continues the work on first-principle gray-box methodology applied to diagnostics and condition assessment of power plant components. The objective of this work is to review and benchmark the optimization algorithms regarding the time required to achieve the best model fit to operational power plant data. The paper recommends the most effective algorithm to be used in the model adjustment process.
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
1998-01-01
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Insertion algorithms for network model database management systems
Mamadolimov, Abdurashid; Khikmat, Saburov
2017-12-01
The network model is a database model conceived as a flexible way of representing objects and their relationships. Its distinguishing feature is that the schema, viewed as a graph in which object types are nodes and relationship types are arcs, forms partial order. When a database is large and a query comparison is expensive then the efficiency requirement of managing algorithms is minimizing the number of query comparisons. We consider updating operation for network model database management systems. We develop a new sequantial algorithm for updating operation. Also we suggest a distributed version of the algorithm.
International Nuclear Information System (INIS)
Sugiyama, Hitoshi; Akiyama, Mitsunobu; Shinohara, Yasunori; Hitomi, Daisuke
1997-01-01
A numerical analysis has been performed for three dimensional developing turbulent flow in a 90deg bent tube with straight inlet and outlet sections by an algebraic Reynolds stress model. To our knowledge, very little has been reported about detailed comparison between calculated results and experimental data containing Reynolds stresses. In calculation, an algebraic Reynolds stress model together with a boundary-fitted coordinate system is applied to a 90deg bent tube in order to solve anisotropic turbulent flow precisely. The calculated results display comparatively good agreement with the experimental data of time averaged velocity and secondary vectors. In addition, the present method predicts as a characteristic feature that the intensity of secondary flow near the inner wall is increased immediately downstream from the bend outlet by the pressure gradient. With regard to comparison of Reynolds stresses, the present method is able to reproduce well the distributions of streamwise normal stress and shear stress defined streamwise and radial velocity fluctuation except for the shear stress defined streamwise and circumferential velocity fluctuation. The present calculation has been found to simulate many features of the developing flow in bent tube satisfactorily, but it has a tendency to underpredict the Reynolds stresses. (author)
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Directory of Open Access Journals (Sweden)
Samuel Belliard
2013-11-01
Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.
An Ada Linear-Algebra Software Package Modeled After HAL/S
Klumpp, Allan R.; Lawson, Charles L.
1990-01-01
New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.
Lie algebra in quantum physics by means of computer algebra
Kikuchi, Ichio; Kikuchi, Akihito
2017-01-01
This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...
Algorithmic detectability threshold of the stochastic block model
Kawamoto, Tatsuro
2018-03-01
The assumption that the values of model parameters are known or correctly learned, i.e., the Nishimori condition, is one of the requirements for the detectability analysis of the stochastic block model in statistical inference. In practice, however, there is no example demonstrating that we can know the model parameters beforehand, and there is no guarantee that the model parameters can be learned accurately. In this study, we consider the expectation-maximization (EM) algorithm with belief propagation (BP) and derive its algorithmic detectability threshold. Our analysis is not restricted to the community structure but includes general modular structures. Because the algorithm cannot always learn the planted model parameters correctly, the algorithmic detectability threshold is qualitatively different from the one with the Nishimori condition.
Vertex algebras and mirror symmetry
International Nuclear Information System (INIS)
Borisov, L.A.
2001-01-01
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)
International Nuclear Information System (INIS)
Dragon, N.
1979-01-01
The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)
International Nuclear Information System (INIS)
Yau, Donald
2011-01-01
We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.
Bliss, Gilbert Ames
1933-01-01
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t
Concurrent algorithms for nuclear shell model calculations
International Nuclear Information System (INIS)
Mackenzie, L.M.; Macleod, A.M.; Berry, D.J.; Whitehead, R.R.
1988-01-01
The calculation of nuclear properties has proved very successful for light nuclei, but is limited by the power of the present generation of computers. Starting with an analysis of current techniques, this paper discusses how these can be modified to map parallelism inherent in the mathematics onto appropriate parallel machines. A prototype dedicated multiprocessor for nuclear structure calculations, designed and constructed by the authors, is described and evaluated. The approach adopted is discussed in the context of a number of generically similar algorithms. (orig.)
Iterated Leavitt Path Algebras
International Nuclear Information System (INIS)
Hazrat, R.
2009-11-01
Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k). In this note, we introduce iterated Leavitt path algebras associated to directed weighted graphs which have natural ± Z grading and in their simplest form recover the Leavitt algebras L(n,k). We also characterize Leavitt path algebras which are strongly graded. (author)
A Developed Artificial Bee Colony Algorithm Based on Cloud Model
Directory of Open Access Journals (Sweden)
Ye Jin
2018-04-01
Full Text Available The Artificial Bee Colony (ABC algorithm is a bionic intelligent optimization method. The cloud model is a kind of uncertainty conversion model between a qualitative concept T ˜ that is presented by nature language and its quantitative expression, which integrates probability theory and the fuzzy mathematics. A developed ABC algorithm based on cloud model is proposed to enhance accuracy of the basic ABC algorithm and avoid getting trapped into local optima by introducing a new select mechanism, replacing the onlooker bees’ search formula and changing the scout bees’ updating formula. Experiments on CEC15 show that the new algorithm has a faster convergence speed and higher accuracy than the basic ABC and some cloud model based ABC variants.
PM Synchronous Motor Dynamic Modeling with Genetic Algorithm ...
African Journals Online (AJOL)
Adel
This paper proposes dynamic modeling simulation for ac Surface Permanent Magnet Synchronous ... Simulations are implemented using MATLAB with its genetic algorithm toolbox. .... selection, the process that drives biological evolution.
Quantum affine algebras and deformations of the virasoro and W-algebras
International Nuclear Information System (INIS)
Frenkel, E.; Reshetikhin, N.
1996-01-01
Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which are q-deformations of the classical W-algebras. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method. (orig.)
A Mining Algorithm for Extracting Decision Process Data Models
Directory of Open Access Journals (Sweden)
Cristina-Claudia DOLEAN
2011-01-01
Full Text Available The paper introduces an algorithm that mines logs of user interaction with simulation software. It outputs a model that explicitly shows the data perspective of the decision process, namely the Decision Data Model (DDM. In the first part of the paper we focus on how the DDM is extracted by our mining algorithm. We introduce it as pseudo-code and, then, provide explanations and examples of how it actually works. In the second part of the paper, we use a series of small case studies to prove the robustness of the mining algorithm and how it deals with the most common patterns we found in real logs.
Seismotectonic models and CN algorithm: The case of Italy
International Nuclear Information System (INIS)
Costa, G.; Orozova Stanishkova, I.; Panza, G.F.; Rotwain, I.M.
1995-07-01
The CN algorithm is here utilized both for the intermediate term earthquake prediction and to validate the seismotectonic model of the Italian territory. Using the results of the analysis, made through the CN algorithm and taking into account the seismotectonic model, three areas, one for Northern Italy, one for Central Italy and one for Southern Italy, are defined. Two transition areas, between the three main areas are delineated. The earthquakes which occurred in these two areas contribute to the precursor phenomena identified by the CN algorithm in each main area. (author). 26 refs, 6 figs, 2 tabs
Grätzer, George
1979-01-01
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...
Filiform Lie algebras of order 3
International Nuclear Information System (INIS)
Navarro, R. M.
2014-01-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...
The bubble algebra: structure of a two-colour Temperley-Lieb Algebra
International Nuclear Information System (INIS)
Grimm, Uwe; Martin, Paul P
2003-01-01
We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations
Quantitative Methods in Supply Chain Management Models and Algorithms
Christou, Ioannis T
2012-01-01
Quantitative Methods in Supply Chain Management presents some of the most important methods and tools available for modeling and solving problems arising in the context of supply chain management. In the context of this book, “solving problems” usually means designing efficient algorithms for obtaining high-quality solutions. The first chapter is an extensive optimization review covering continuous unconstrained and constrained linear and nonlinear optimization algorithms, as well as dynamic programming and discrete optimization exact methods and heuristics. The second chapter presents time-series forecasting methods together with prediction market techniques for demand forecasting of new products and services. The third chapter details models and algorithms for planning and scheduling with an emphasis on production planning and personnel scheduling. The fourth chapter presents deterministic and stochastic models for inventory control with a detailed analysis on periodic review systems and algorithmic dev...
Miyanishi, Masayoshi
2000-01-01
Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...
A linear time layout algorithm for business process models
Gschwind, T.; Pinggera, J.; Zugal, S.; Reijers, H.A.; Weber, B.
2014-01-01
The layout of a business process model influences how easily it can beunderstood. Existing layout features in process modeling tools often rely on graph representations, but do not take the specific properties of business process models into account. In this paper, we propose an algorithm that is
DiamondTorre Algorithm for High-Performance Wave Modeling
Directory of Open Access Journals (Sweden)
Vadim Levchenko
2016-08-01
Full Text Available Effective algorithms of physical media numerical modeling problems’ solution are discussed. The computation rate of such problems is limited by memory bandwidth if implemented with traditional algorithms. The numerical solution of the wave equation is considered. A finite difference scheme with a cross stencil and a high order of approximation is used. The DiamondTorre algorithm is constructed, with regard to the specifics of the GPGPU’s (general purpose graphical processing unit memory hierarchy and parallelism. The advantages of these algorithms are a high level of data localization, as well as the property of asynchrony, which allows one to effectively utilize all levels of GPGPU parallelism. The computational intensity of the algorithm is greater than the one for the best traditional algorithms with stepwise synchronization. As a consequence, it becomes possible to overcome the above-mentioned limitation. The algorithm is implemented with CUDA. For the scheme with the second order of approximation, the calculation performance of 50 billion cells per second is achieved. This exceeds the result of the best traditional algorithm by a factor of five.
Collaborative filtering recommendation model based on fuzzy clustering algorithm
Yang, Ye; Zhang, Yunhua
2018-05-01
As one of the most widely used algorithms in recommender systems, collaborative filtering algorithm faces two serious problems, which are the sparsity of data and poor recommendation effect in big data environment. In traditional clustering analysis, the object is strictly divided into several classes and the boundary of this division is very clear. However, for most objects in real life, there is no strict definition of their forms and attributes of their class. Concerning the problems above, this paper proposes to improve the traditional collaborative filtering model through the hybrid optimization of implicit semantic algorithm and fuzzy clustering algorithm, meanwhile, cooperating with collaborative filtering algorithm. In this paper, the fuzzy clustering algorithm is introduced to fuzzy clustering the information of project attribute, which makes the project belong to different project categories with different membership degrees, and increases the density of data, effectively reduces the sparsity of data, and solves the problem of low accuracy which is resulted from the inaccuracy of similarity calculation. Finally, this paper carries out empirical analysis on the MovieLens dataset, and compares it with the traditional user-based collaborative filtering algorithm. The proposed algorithm has greatly improved the recommendation accuracy.
Applicability of genetic algorithms to parameter estimation of economic models
Directory of Open Access Journals (Sweden)
Marcel Ševela
2004-01-01
Full Text Available The paper concentrates on capability of genetic algorithms for parameter estimation of non-linear economic models. In the paper we test the ability of genetic algorithms to estimate of parameters of demand function for durable goods and simultaneously search for parameters of genetic algorithm that lead to maximum effectiveness of the computation algorithm. The genetic algorithms connect deterministic iterative computation methods with stochastic methods. In the genteic aůgorithm approach each possible solution is represented by one individual, those life and lifes of all generations of individuals run under a few parameter of genetic algorithm. Our simulations resulted in optimal mutation rate of 15% of all bits in chromosomes, optimal elitism rate 20%. We can not set the optimal extend of generation, because it proves positive correlation with effectiveness of genetic algorithm in all range under research, but its impact is degreasing. The used genetic algorithm was sensitive to mutation rate at most, than to extend of generation. The sensitivity to elitism rate is not so strong.
Hopf algebras and topological recursion
International Nuclear Information System (INIS)
Esteves, João N
2015-01-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Approximation Algorithms for Model-Based Diagnosis
Feldman, A.B.
2010-01-01
Model-based diagnosis is an area of abductive inference that uses a system model, together with observations about system behavior, to isolate sets of faulty components (diagnoses) that explain the observed behavior, according to some minimality criterion. This thesis presents greedy approximation
Basic Research on Adaptive Model Algorithmic Control
1985-12-01
Control Conference. Richalet, J., A. Rault, J.L. Testud and J. Papon (1978). Model predictive heuristic control: applications to industrial...pp.977-982. Richalet, J., A. Rault, J. L. Testud and J. Papon (1978). Model predictive heuristic control: applications to industrial processes
Implementing Modifed Burg Algorithms in Multivariate Subset Autoregressive Modeling
Directory of Open Access Journals (Sweden)
A. Alexandre Trindade
2003-02-01
Full Text Available The large number of parameters in subset vector autoregressive models often leads one to procure fast, simple, and efficient alternatives or precursors to maximum likelihood estimation. We present the solution of the multivariate subset Yule-Walker equations as one such alternative. In recent work, Brockwell, Dahlhaus, and Trindade (2002, show that the Yule-Walker estimators can actually be obtained as a special case of a general recursive Burg-type algorithm. We illustrate the structure of this Algorithm, and discuss its implementation in a high-level programming language. Applications of the Algorithm in univariate and bivariate modeling are showcased in examples. Univariate and bivariate versions of the Algorithm written in Fortran 90 are included in the appendix, and their use illustrated.
Stochastic cluster algorithms for discrete Gaussian (SOS) models
International Nuclear Information System (INIS)
Evertz, H.G.; Hamburg Univ.; Hasenbusch, M.; Marcu, M.; Tel Aviv Univ.; Pinn, K.; Muenster Univ.; Solomon, S.
1990-10-01
We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete Gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z. Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm. (orig.)
Algorithms and procedures in the model based control of accelerators
International Nuclear Information System (INIS)
Bozoki, E.
1987-10-01
The overall design of a Model Based Control system was presented. The system consists of PLUG-IN MODULES, governed by a SUPERVISORY PROGRAM and communicating via SHARED DATA FILES. Models can be ladded or replaced without affecting the oveall system. There can be more then one module (algorithm) to perform the same task. The user can choose the most appropriate algorithm or can compare the results using different algorithms. Calculations, algorithms, file read and write, etc. which are used in more than one module, will be in a subroutine library. This feature will simplify the maintenance of the system. A partial list of modules is presented, specifying the task they perform. 19 refs., 1 fig
The Yoneda algebra of a K2 algebra need not be another K2 algebra
Cassidy, T.; Phan, C.; Shelton, B.
2010-01-01
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.
An Improved Nested Sampling Algorithm for Model Selection and Assessment
Zeng, X.; Ye, M.; Wu, J.; WANG, D.
2017-12-01
Multimodel strategy is a general approach for treating model structure uncertainty in recent researches. The unknown groundwater system is represented by several plausible conceptual models. Each alternative conceptual model is attached with a weight which represents the possibility of this model. In Bayesian framework, the posterior model weight is computed as the product of model prior weight and marginal likelihood (or termed as model evidence). As a result, estimating marginal likelihoods is crucial for reliable model selection and assessment in multimodel analysis. Nested sampling estimator (NSE) is a new proposed algorithm for marginal likelihood estimation. The implementation of NSE comprises searching the parameters' space from low likelihood area to high likelihood area gradually, and this evolution is finished iteratively via local sampling procedure. Thus, the efficiency of NSE is dominated by the strength of local sampling procedure. Currently, Metropolis-Hasting (M-H) algorithm and its variants are often used for local sampling in NSE. However, M-H is not an efficient sampling algorithm for high-dimensional or complex likelihood function. For improving the performance of NSE, it could be feasible to integrate more efficient and elaborated sampling algorithm - DREAMzs into the local sampling. In addition, in order to overcome the computation burden problem of large quantity of repeating model executions in marginal likelihood estimation, an adaptive sparse grid stochastic collocation method is used to build the surrogates for original groundwater model.
Indian Academy of Sciences (India)
ticians but also forms the foundation of computer science. Two ... with methods of developing algorithms for solving a variety of problems but ... applications of computers in science and engineer- ... numerical calculus are as important. We will ...
Dzhumadil'daev, A. S.
2002-01-01
Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.
International Nuclear Information System (INIS)
Ke Sanmin; Yang Wenli; Shi Kangjie; Wang Chun; Jiang Kexia
2011-01-01
We investigate the classical exchange algebra of the monodromy matrix for a Green-Schwarz sigma model on supercoset target space with Z 4m grading by using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution in the Poisson bracket sense. Our calculation is based on a general world-sheet metric. Taking a particular case of m= 1 (and a particular choice of supergroup), our results coincide with those of the Green-Schwarz superstring theory in AdS 5 xS 5 background obtained by Magro [J. High Energy Phys. 0901, 021 (2009)].
International Nuclear Information System (INIS)
Rahmouni, Adib N.
2004-01-01
In 1994, Berenger [Journal of Computational Physics 114 (1994) 185] proposed a new layer method: perfectly matched layer, PML, for electromagnetism. This new method is based on the truncation of the computational domain by a layer which absorbs waves regardless of their frequency and angle of incidence. Unfortunately, the technique proposed by Berenger (loc. cit.) leads to a system which has lost the most important properties of the original one: strong hyperbolicity and symmetry. We present in this paper an algebraic technique leading to well-known PML model [IEEE Transactions on Antennas and Propagation 44 (1996) 1630] for the linearized Euler equations, strongly well-posed, preserving the advantages of the initial method, and retaining symmetry. The technique proposed in this paper can be extended to various hyperbolic problems
Study of phase transition of even and odd nuclei based on q-deforme SU(1,1) algebraic model
Jafarizadeh, M. A.; Amiri, N.; Fouladi, N.; Ghapanvari, M.; Ranjbar, Z.
2018-04-01
The q-deformed Hamiltonian for the SO (6) ↔ U (5) transitional case in s, d interaction boson model (IBM) can be constructed by using affine SUq (1 , 1) Lie algebra in the both IBM-1 and 2 versions and IBFM. In this research paper, we have studied the energy spectra of 120-128Xe isotopes and 123-131Xe isotopes and B(E2) transition probabilities of 120-128Xe isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes of the theory of quantum deformation. The theoretical results agree with the experimental data fairly well. It is shown that the q-deformed SO (6) ↔ U (5) transitional dynamical symmetry remains after deformation.
Joux, Antoine
2009-01-01
Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applic
Introduction to relation algebras relation algebras
Givant, Steven
2017-01-01
The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...
Algebraic structure of chiral anomalies
International Nuclear Information System (INIS)
Stora, R.
1985-09-01
I will describe first the algebraic aspects of chiral anomalies, exercising however due care about the topological delicacies. I will illustrate the structure and methods in the context of gauge anomalies and will eventually make contact with results obtained from index theory. I will go into two sorts of generalizations: on the one hand, generalizing the algebraic set up yields e.g. gravitational and mixed gauge anomalies, supersymmetric gauge anomalies, anomalies in supergravity theories; on the other hand most constructions applied to the cohomologies which characterize anomalies easily extend to higher cohomologies. Section II is devoted to a description of the general set up as it applies to gauge anomalies. Section III deals with a number of algebraic set ups which characterize more general types of anomalies: gravitational and mixed gauge anomalies, supersymmetric gauge anomalies, anomalies in supergravity theories. It also includes brief remarks on σ models and a reminder on the full BRST algebra of quantized gauge theories
A Parallel Algebraic Multigrid Solver on Graphics Processing Units
Haase, Gundolf
2010-01-01
The paper presents a multi-GPU implementation of the preconditioned conjugate gradient algorithm with an algebraic multigrid preconditioner (PCG-AMG) for an elliptic model problem on a 3D unstructured grid. An efficient parallel sparse matrix-vector multiplication scheme underlying the PCG-AMG algorithm is presented for the many-core GPU architecture. A performance comparison of the parallel solver shows that a singe Nvidia Tesla C1060 GPU board delivers the performance of a sixteen node Infiniband cluster and a multi-GPU configuration with eight GPUs is about 100 times faster than a typical server CPU core. © 2010 Springer-Verlag.
International Nuclear Information System (INIS)
Ludu, A.; Greiner, M.
1995-09-01
A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs
Foulis, David J.; Pulmannov, Sylvia
2018-04-01
Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.
International Nuclear Information System (INIS)
Eynard, B; Orantin, N
2008-01-01
We compute expectation values of mixed traces containing both matrices in a two matrix model, i.e. a generating function for counting bicolored discrete surfaces with non-uniform boundary conditions. As an application, we prove the x-y symmetry of Eynard and Orantin (2007 Invariants of algebraic curves and topological expansion Preprint math-ph/0702045)
International Nuclear Information System (INIS)
Grimm, Uwe; Schuetz, Gunter
1992-09-01
The finite-size spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with central charge c q [sl(2)] quantum algebra transformations. (author)
Quantum complexity of graph and algebraic problems
International Nuclear Information System (INIS)
Doern, Sebastian
2008-01-01
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Quantum complexity of graph and algebraic problems
Energy Technology Data Exchange (ETDEWEB)
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Co-clustering models, algorithms and applications
Govaert, Gérard
2013-01-01
Cluster or co-cluster analyses are important tools in a variety of scientific areas. The introduction of this book presents a state of the art of already well-established, as well as more recent methods of co-clustering. The authors mainly deal with the two-mode partitioning under different approaches, but pay particular attention to a probabilistic approach. Chapter 1 concerns clustering in general and the model-based clustering in particular. The authors briefly review the classical clustering methods and focus on the mixture model. They present and discuss the use of different mixture
Comparison of parameter estimation algorithms in hydrological modelling
DEFF Research Database (Denmark)
Blasone, Roberta-Serena; Madsen, Henrik; Rosbjerg, Dan
2006-01-01
Local search methods have been applied successfully in calibration of simple groundwater models, but might fail in locating the optimum for models of increased complexity, due to the more complex shape of the response surface. Global search algorithms have been demonstrated to perform well......-Marquardt-Levenberg algorithm (implemented in the PEST software), when applied to a steady-state and a transient groundwater model. The results show that PEST can have severe problems in locating the global optimum and in being trapped in local regions of attractions. The global SCE procedure is, in general, more effective...... and provides a better coverage of the Pareto optimal solutions at a lower computational cost....
Applied economic model development algorithm for electronics company
Directory of Open Access Journals (Sweden)
Mikhailov I.
2017-01-01
Full Text Available The purpose of this paper is to report about received experience in the field of creating the actual methods and algorithms that help to simplify development of applied decision support systems. It reports about an algorithm, which is a result of two years research and have more than one-year practical verification. In a case of testing electronic components, the time of the contract conclusion is crucial point to make the greatest managerial mistake. At this stage, it is difficult to achieve a realistic assessment of time-limit and of wage-fund for future work. The creation of estimating model is possible way to solve this problem. In the article is represented an algorithm for creation of those models. The algorithm is based on example of the analytical model development that serves for amount of work estimation. The paper lists the algorithm’s stages and explains their meanings with participants’ goals. The implementation of the algorithm have made possible twofold acceleration of these models development and fulfilment of management’s requirements. The resulting models have made a significant economic effect. A new set of tasks was identified to be further theoretical study.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Economic Models and Algorithms for Distributed Systems
Neumann, Dirk; Altmann, Jorn; Rana, Omer F
2009-01-01
Distributed computing models for sharing resources such as Grids, Peer-to-Peer systems, or voluntary computing are becoming increasingly popular. This book intends to discover fresh avenues of research and amendments to existing technologies, aiming at the successful deployment of commercial distributed systems
Robust Return Algorithm for Anisotropic Plasticity Models
DEFF Research Database (Denmark)
Tidemann, L.; Krenk, Steen
2017-01-01
Plasticity models can be defined by an energy potential, a plastic flow potential and a yield surface. The energy potential defines the relation between the observable elastic strains ϒe and the energy conjugate stresses Τe and between the non-observable internal strains i and the energy conjugat...
A tractable algorithm for the wellfounded model
Jonker, C.M.; Renardel de Lavalette, G.R.
In the area of general logic programming (negated atoms allowed in the bodies of rules) and reason maintenance systems, the wellfounded model (first defined by Van Gelder, Ross and Schlipf in 1988) is generally considered to be the declarative semantics of the program. In this paper we present
Rationality problem for algebraic tori
Hoshi, Akinari
2017-01-01
The authors give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. The authors show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. The authors make a procedure to compute a flabby resolution of a G-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a G-lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby G-lattices of rank up to 6 and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for G-...
International Nuclear Information System (INIS)
Yan Qingyou; Zhang Yufeng; Wei Xiaopeng
2004-01-01
A new subalgebra G of the Lie algebra A 2 is first constructed. Then two loop algebra G-bar 1 , G-bar 2 are presented in terms of different definitions of gradations. Using G-bar 1 , G-bar 2 designs two isospectral problems, respectively. Again utilizing Tu-pattern obtains two types of various integrable Hamiltonian hierarchies of evolution equations. As reduction cases, the well-known Schroedinger equation and MKdV equation are obtained. At last, we turn the subalgebras G-bar 1 , G-bar 2 of the loop algebra A-bar 2 into equivalent subalgebras of the loop algebra A-bar 1 by making a suitable linear transformation so that the two types of 5-dimensional loop algebras are constructed. Two kinds of integrable couplings of the obtained hierarchies are showed. Specially, the integrable couplings of Schroedinger equation and MKdV equation are obtained, respectively
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Differential Evolution algorithm applied to FSW model calibration
Idagawa, H. S.; Santos, T. F. A.; Ramirez, A. J.
2014-03-01
Friction Stir Welding (FSW) is a solid state welding process that can be modelled using a Computational Fluid Dynamics (CFD) approach. These models use adjustable parameters to control the heat transfer and the heat input to the weld. These parameters are used to calibrate the model and they are generally determined using the conventional trial and error approach. Since this method is not very efficient, we used the Differential Evolution (DE) algorithm to successfully determine these parameters. In order to improve the success rate and to reduce the computational cost of the method, this work studied different characteristics of the DE algorithm, such as the evolution strategy, the objective function, the mutation scaling factor and the crossover rate. The DE algorithm was tested using a friction stir weld performed on a UNS S32205 Duplex Stainless Steel.
Numerical linear algebra theory and applications
Beilina, Larisa; Karchevskii, Mikhail
2017-01-01
This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.
Commutative algebra constructive methods finite projective modules
Lombardi, Henri
2015-01-01
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside several abstract classical theories. Indeed, it revisits these traditional topics with a new and simplifying manner, making the subject both accessible and innovative. The algorithmic aspects of such naturally abstract topics as Galois theory, Dedekind rings, Prüfer rings, finitely generated projective modules, dimension theory of commutative rings, and others in the current treatise, are all analysed in the spirit of the great developers of constructive algebra in the nineteenth century. This updated and revised edition contains over 350 well-arranged exercises, together with their helpful hints for solution. A basic knowledge of linear algebra, group theory, elementary number theory as well as the fundamentals of ring and module theory is r...
Elsheikh, Ahmed H.; Wheeler, Mary Fanett; Hoteit, Ibrahim
2014-01-01
A Hybrid Nested Sampling (HNS) algorithm is proposed for efficient Bayesian model calibration and prior model selection. The proposed algorithm combines, Nested Sampling (NS) algorithm, Hybrid Monte Carlo (HMC) sampling and gradient estimation using
Coset realization of unifying W-algebras
International Nuclear Information System (INIS)
Blumenhagen, R.; Huebel, R.
1994-06-01
We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R)/sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras. We show that it is possible to give coset realizations of various types of unifying W-algebras, e.g. the diagonal cosets based on the symplectic Lie algebras sp(2n) realize the unifying W-algebras which have previously been introduced as 'WD -n '. In addition, minimal models of WD -n are studied. The coset realizations provide a generalization of level-rank-duality of dual coset pairs. As further examples of finitely nonfreely generated quantum W-algebras we discuss orbifolding of W-algebras which on the quantum level has different properties than in the classical case. We demonstrate in some examples that the classical limit according to Bowcock and Watts of these nonfreely finitely generated quantum W-algebras probably yields infinitely nonfreely generated classical W-algebras. (orig.)
The algebras of large N matrix mechanics
Energy Technology Data Exchange (ETDEWEB)
Halpern, M.B.; Schwartz, C.
1999-09-16
Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
Directory of Open Access Journals (Sweden)
Zhe Dong
2015-01-01
Full Text Available Small modular reactors (SMRs are those fission reactors whose electrical output power is no more than 300 MWe. SMRs usually have the inherent safety feature that can be applicable to power plants of any desired power rating by applying the multimodular operation scheme. Due to its strong inherent safety feature, the modular high temperature gas-cooled reactor (MHTGR, which uses helium as coolant and graphite as moderator and structural material, is a typical SMR for building the next generation of nuclear plants (NGNPs. The once-through steam generator (OTSG is the basis of realizing the multimodular scheme, and modeling of the OTSG is meaningful to study the dynamic behavior of the multimodular plants and to design the operation and control strategy. In this paper, based upon the conservation laws of mass, energy, and momentum, a new differential-algebraic model for the OTSGs of the MHTGR-based multimodular nuclear plants is given. This newly-built model can describe the dynamic behavior of the OTSG in both the cases of providing superheated steam and generating saturated steam. Numerical simulation results show the feasibility and satisfactory performance of this model. Moreover, this model has been applied to develop the real-time simulation software for the operation and regulation features of the world first underconstructed MHTGR-based commercial nuclear plant—HTR-PM.
Cluster algebras in mathematical physics
International Nuclear Information System (INIS)
Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-01-01
identities in conformal field theory and so forth. It is remarkable that the key ingredients in such a variety of theories and models are captured and described universally in the common language of cluster algebras. This special issue provides a bird's-eye view of the known and latest results in various topics in mathematical physics where cluster algebras have played an essential role. The contributed articles are themselves an eloquent illustration of the breadth and depth of the subject of cluster algebras. We are confident that the issue will stimulate both newcomers and experts, since the applications to physics still seem to be growing
Methodology, models and algorithms in thermographic diagnostics
Živčák, Jozef; Madarász, Ladislav; Rudas, Imre J
2013-01-01
This book presents the methodology and techniques of thermographic applications with focus primarily on medical thermography implemented for parametrizing the diagnostics of the human body. The first part of the book describes the basics of infrared thermography, the possibilities of thermographic diagnostics and the physical nature of thermography. The second half includes tools of intelligent engineering applied for the solving of selected applications and projects. Thermographic diagnostics was applied to problematics of paraplegia and tetraplegia and carpal tunnel syndrome (CTS). The results of the research activities were created with the cooperation of the four projects within the Ministry of Education, Science, Research and Sport of the Slovak Republic entitled Digital control of complex systems with two degrees of freedom, Progressive methods of education in the area of control and modeling of complex object oriented systems on aircraft turbocompressor engines, Center for research of control of te...
Classification and identification of Lie algebras
Snobl, Libor
2014-01-01
The purpose of this book is to serve as a tool for researchers and practitioners who apply Lie algebras and Lie groups to solve problems arising in science and engineering. The authors address the problem of expressing a Lie algebra obtained in some arbitrary basis in a more suitable basis in which all essential features of the Lie algebra are directly visible. This includes algorithms accomplishing decomposition into a direct sum, identification of the radical and the Levi decomposition, and the computation of the nilradical and of the Casimir invariants. Examples are given for each algorithm. For low-dimensional Lie algebras this makes it possible to identify the given Lie algebra completely. The authors provide a representative list of all Lie algebras of dimension less or equal to 6 together with their important properties, including their Casimir invariants. The list is ordered in a way to make identification easy, using only basis independent properties of the Lie algebras. They also describe certain cl...
A division algebra classification of generalized supersymmetries
International Nuclear Information System (INIS)
Toppan, Francesco
2004-10-01
Generalized supersymmetries admitting bosonic tensor central charges are classified in accordance with their division algebra properties. Division algebra consistent constraints lead (in the complex and quaternionic cases) to the classes of hermitian and holomorphic generalized supersymmetries. Applications to the analytic continuation of the M-algebra to the Euclidean and the systematic investigation of certain classes of models in generic space-times are briefly mentioned. (author)
International Nuclear Information System (INIS)
Finch, P.E.; Dancer, K.A.; Isaac, P.S.; Links, J.
2011-01-01
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the two-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.
Modeling Algorithms in SystemC and ACL2
Directory of Open Access Journals (Sweden)
John W. O'Leary
2014-06-01
Full Text Available We describe the formal language MASC, based on a subset of SystemC and intended for modeling algorithms to be implemented in hardware. By means of a special-purpose parser, an algorithm coded in SystemC is converted to a MASC model for the purpose of documentation, which in turn is translated to ACL2 for formal verification. The parser also generates a SystemC variant that is suitable as input to a high-level synthesis tool. As an illustration of this methodology, we describe a proof of correctness of a simple 32-bit radix-4 multiplier.
Algorithmic fault tree construction by component-based system modeling
International Nuclear Information System (INIS)
Majdara, Aref; Wakabayashi, Toshio
2008-01-01
Computer-aided fault tree generation can be easier, faster and less vulnerable to errors than the conventional manual fault tree construction. In this paper, a new approach for algorithmic fault tree generation is presented. The method mainly consists of a component-based system modeling procedure an a trace-back algorithm for fault tree synthesis. Components, as the building blocks of systems, are modeled using function tables and state transition tables. The proposed method can be used for a wide range of systems with various kinds of components, if an inclusive component database is developed. (author)
Algorithm of Dynamic Model Structural Identification of the Multivariable Plant
Directory of Open Access Journals (Sweden)
Л.М. Блохін
2004-02-01
Full Text Available The new algorithm of dynamic model structural identification of the multivariable stabilized plant with observable and unobservable disturbances in the regular operating modes is offered in this paper. With the help of the offered algorithm it is possible to define the “perturbed” models of dynamics not only of the plant, but also the dynamics characteristics of observable and unobservable casual disturbances taking into account the absence of correlation between themselves and control inputs with the unobservable perturbations.
Numerical linear algebra with applications using Matlab
Ford, William
2014-01-01
Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for
DEFF Research Database (Denmark)
Schmidt, Thomas Lundsgaard; Thomsen, Klaus
2015-01-01
We consider a construction of $C^*$-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and Anantharaman-Delaroche for local homeomorphisms. Assuming that the map...... is surjective and not locally injective we give necessary and sufficient conditions for the simplicity of the $C^*$-algebra and show that it is then a Kirchberg algebra. We provide tools for the calculation of the K-theory groups and turn them into an algorithmic method for Markov maps....
Introduction to genetic algorithms as a modeling tool
International Nuclear Information System (INIS)
Wildberger, A.M.; Hickok, K.A.
1990-01-01
Genetic algorithms are search and classification techniques modeled on natural adaptive systems. This is an introduction to their use as a modeling tool with emphasis on prospects for their application in the power industry. It is intended to provide enough background information for its audience to begin to follow technical developments in genetic algorithms and to recognize those which might impact on electric power engineering. Beginning with a discussion of genetic algorithms and their origin as a model of biological adaptation, their advantages and disadvantages are described in comparison with other modeling tools such as simulation and neural networks in order to provide guidance in selecting appropriate applications. In particular, their use is described for improving expert systems from actual data and they are suggested as an aid in building mathematical models. Using the Thermal Performance Advisor as an example, it is suggested how genetic algorithms might be used to make a conventional expert system and mathematical model of a power plant adapt automatically to changes in the plant's characteristics
Gauss Elimination: Workhorse of Linear Algebra.
1995-08-05
linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also
Indian Academy of Sciences (India)
algorithm design technique called 'divide-and-conquer'. One of ... Turtle graphics, September. 1996. 5. ... whole list named 'PO' is a pointer to the first element of the list; ..... Program for computing matrices X and Y and placing the result in C *).
Indian Academy of Sciences (India)
algorithm that it is implicitly understood that we know how to generate the next natural ..... Explicit comparisons are made in line (1) where maximum and minimum is ... It can be shown that the function T(n) = 3/2n -2 is the solution to the above ...
ABC Algorithm based Fuzzy Modeling of Optical Glucose Detection
Directory of Open Access Journals (Sweden)
SARACOGLU, O. G.
2016-08-01
Full Text Available This paper presents a modeling approach based on the use of fuzzy reasoning mechanism to define a measured data set obtained from an optical sensing circuit. For this purpose, we implemented a simple but effective an in vitro optical sensor to measure glucose content of an aqueous solution. Measured data contain analog voltages representing the absorbance values of three wavelengths measured from an RGB LED in different glucose concentrations. To achieve a desired model performance, the parameters of the fuzzy models are optimized by using the artificial bee colony (ABC algorithm. The modeling results presented in this paper indicate that the fuzzy model optimized by the algorithm provide a successful modeling performance having the minimum mean squared error (MSE of 0.0013 which are in clearly good agreement with the measurements.
Abrams, Gene; Siles Molina, Mercedes
2017-01-01
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...
Quantum algebras in nuclear structure
International Nuclear Information System (INIS)
Bonatsos, D.; Daskaloyannis, C.
1995-01-01
Quantum algebras is a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction through the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underline the structure of superdeformed and hyperdeformed nuclei are discussed in some details. A brief description of similar applications to molecular structure and an outlook are also given. (author) 2 Tabs., 324 Refs
Samuel, Pierre
2008-01-01
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal
Boicescu, V; Georgescu, G; Rudeanu, S
1991-01-01
The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.
Introduction to quantum algebras
International Nuclear Information System (INIS)
Kibler, M.R.
1992-09-01
The concept of a quantum algebra is made easy through the investigation of the prototype algebras u qp (2), su q (2) and u qp (1,1). The latter quantum algebras are introduced as deformations of the corresponding Lie algebras; this is achieved in a simple way by means of qp-bosons. The Hopf algebraic structure of u qp (2) is also discussed. The basic ingredients for the representation theory of u qp (2) are given. Finally, in connection with the quantum algebra u qp (2), the qp-analogues of the harmonic oscillator are discussed and of the (spherical and hyperbolical) angular momenta. (author) 50 refs
An Interactive Personalized Recommendation System Using the Hybrid Algorithm Model
Directory of Open Access Journals (Sweden)
Yan Guo
2017-10-01
Full Text Available With the rapid development of e-commerce, the contradiction between the disorder of business information and customer demand is increasingly prominent. This study aims to make e-commerce shopping more convenient, and avoid information overload, by an interactive personalized recommendation system using the hybrid algorithm model. The proposed model first uses various recommendation algorithms to get a list of original recommendation results. Combined with the customer’s feedback in an interactive manner, it then establishes the weights of corresponding recommendation algorithms. Finally, the synthetic formula of evidence theory is used to fuse the original results to obtain the final recommendation products. The recommendation performance of the proposed method is compared with that of traditional methods. The results of the experimental study through a Taobao online dress shop clearly show that the proposed method increases the efficiency of data mining in the consumer coverage, the consumer discovery accuracy and the recommendation recall. The hybrid recommendation algorithm complements the advantages of the existing recommendation algorithms in data mining. The interactive assigned-weight method meets consumer demand better and solves the problem of information overload. Meanwhile, our study offers important implications for e-commerce platform providers regarding the design of product recommendation systems.
Homotopy Theory of C*-Algebras
Ostvaer, Paul Arne
2010-01-01
Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It
Indian Academy of Sciences (India)
will become clear in the next article when we discuss a simple logo like programming language. ... Rod B may be used as an auxiliary store. The problem is to find an algorithm which performs this task. ... No disks are moved from A to Busing C as auxiliary rod. • move _disk (A, C);. (No + l)th disk is moved from A to C directly ...
International Nuclear Information System (INIS)
Bataille, F.; Younis, B.A.; Bellettre, J.; Lallemand, A.
2003-01-01
The paper reports on the prediction of the effects of blowing on the evolution of the thermal and velocity fields in a flat-plate turbulent boundary layer developing over a porous surface. Closure of the time-averaged equations governing the transport of momentum and thermal energy is achieved using a complete Reynolds-stress transport model for the turbulent stresses and a non-linear, algebraic and explicit model for the turbulent heat fluxes. The latter model accounts explicitly for the dependence of the turbulent heat fluxes on the gradients of mean velocity. Results are reported for the case of a heated boundary layer which is first developed into equilibrium over a smooth impervious wall before encountering a porous section through which cooler fluid is continuously injected. Comparisons are made with LDA measurements for an injection rate of 1%. The reduction of the wall shear stress with increase in injection rate is obtained in the calculations, and the computed rates of heat transfer between the hot flow and the wall are found to agree well with the published data
Icardi, Matteo; Ronco, Gianni; Marchisio, Daniele Luca; Labois, Mathieu
2014-01-01
The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier-Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries. © 2014 Elsevier Inc.
Icardi, Matteo
2014-09-01
The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier-Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries. © 2014 Elsevier Inc.
Epidemic Processes on Complex Networks : Modelling, Simulation and Algorithms
Van de Bovenkamp, R.
2015-01-01
Local interactions on a graph will lead to global dynamic behaviour. In this thesis we focus on two types of dynamic processes on graphs: the Susceptible-Infected-Susceptilbe (SIS) virus spreading model, and gossip style epidemic algorithms. The largest part of this thesis is devoted to the SIS
Worm Algorithm for CP(N-1) Model
Rindlisbacher, Tobias
2017-01-01
The CP(N-1) model in 2D is an interesting toy model for 4D QCD as it possesses confinement, asymptotic freedom and a non-trivial vacuum structure. Due to the lower dimensionality and the absence of fermions, the computational cost for simulating 2D CP(N-1) on the lattice is much lower than that for simulating 4D QCD. However, to our knowledge, no efficient algorithm for simulating the lattice CP(N-1) model has been tested so far, which also works at finite density. To this end we propose a new type of worm algorithm which is appropriate to simulate the lattice CP(N-1) model in a dual, flux-variables based representation, in which the introduction of a chemical potential does not give rise to any complications. In addition to the usual worm moves where a defect is just moved from one lattice site to the next, our algorithm additionally allows for worm-type moves in the internal variable space of single links, which accelerates the Monte Carlo evolution. We use our algorithm to compare the two popular CP(N-1) l...
Optimisation of Hidden Markov Model using Baum–Welch algorithm
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 126; Issue 1. Optimisation of Hidden Markov Model using Baum–Welch algorithm for prediction of maximum and minimum temperature over Indian Himalaya. J C Joshi Tankeshwar Kumar Sunita Srivastava Divya Sachdeva. Volume 126 Issue 1 February 2017 ...
Heterogenous Agents Model with the Worst Out Algorithm
Czech Academy of Sciences Publication Activity Database
Vácha, Lukáš; Vošvrda, Miloslav
-, č. 8 (2006), s. 3-19 ISSN 1801-5999 Institutional research plan: CEZ:AV0Z10750506 Keywords : efficient market hypothesis * fractal market hypothesis * agents' investment horizons * agents' trading strategies * technical trading rules * heterogeneous agent model with stochastic memory * Worst out algorithm Subject RIV: AH - Economics
INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS
KUIJPER, M; SCHUMACHER, JM
Systems of linear differential and algebraic equations occur in various ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics and exact model matching. Differential/algebraic systems may represent an input-output
Boundary Lax pairs from non-ultra-local Poisson algebras
International Nuclear Information System (INIS)
Avan, Jean; Doikou, Anastasia
2009-01-01
We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.
Application of genetic algorithm in radio ecological models parameter determination
Energy Technology Data Exchange (ETDEWEB)
Pantelic, G. [Institute of Occupatioanl Health and Radiological Protection ' Dr Dragomir Karajovic' , Belgrade (Serbia)
2006-07-01
The method of genetic algorithms was used to determine the biological half-life of 137 Cs in cow milk after the accident in Chernobyl. Methodologically genetic algorithms are based on the fact that natural processes tend to optimize themselves and therefore this method should be more efficient in providing optimal solutions in the modeling of radio ecological and environmental events. The calculated biological half-life of 137 Cs in milk is (32 {+-} 3) days and transfer coefficient from grass to milk is (0.019 {+-} 0.005). (authors)