Performance modeling and prediction for linear algebra algorithms
Iakymchuk, Roman
2012-01-01
This dissertation incorporates two research projects: performance modeling and prediction for dense linear algebra algorithms, and high-performance computing on clouds. The first project is focused on dense matrix computations, which are often used as computational kernels for numerous scientific applications. To solve a particular mathematical operation, linear algebra libraries provide a variety of algorithms. The algorithm of choice depends, obviously, on its performance. Performance of su...
Symplectic algebraic dynamics algorithm
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the algebraic dynamics solution of ordinary differential equations andintegration of ,the symplectic algebraic dynamics algorithm sn is designed,which preserves the local symplectic geometric structure of a Hamiltonian systemand possesses the same precision of the na ve algebraic dynamics algorithm n.Computer experiments for the 4th order algorithms are made for five test modelsand the numerical results are compared with the conventional symplectic geometric algorithm,indicating that sn has higher precision,the algorithm-inducedphase shift of the conventional symplectic geometric algorithm can be reduced,and the dynamical fidelity can be improved by one order of magnitude.
Redesigning linear algebra algorithms
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.
1983-01-01
Many of the standard algorithms in linear algebra as implemented in FORTRAN do not achieve maximum performance on today's large-scale vector computers. The author examines the problem and constructs alternative formulations of algorithms that do not lose the clarity of the original algorithm or sacrifice the FORTRAN portable environment, but do gain the performance attainable on these supercomputers. The resulting implementation not only performs well on vector computers but also increases performance on conventional sequential computers. 13 references.
Redesigning linear algebra algorithms
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.
1983-01-01
Many of the standard algorithms in linear algebra as implemented in FORTRAN do not achieve maximum performance on today's large-scale vector computers. In this paper we examine the problem and construct alternative formulations of algorithms that do not lose the clarity of the original algorithm or sacrifice the Fortran portable environment, but do gain the performance attainable on these supercomputers. The resulting implementation not only performs well on vector computers but also increases performance on conventional sequential computers.
Algebraic Approach to Algorithmic Logic
Directory of Open Access Journals (Sweden)
Bancerek Grzegorz
2014-09-01
Full Text Available We introduce algorithmic logic - an algebraic approach according to [25]. It is done in three stages: propositional calculus, quantifier calculus with equality, and finally proper algorithmic logic. For each stage appropriate signature and theory are defined. Propositional calculus and quantifier calculus with equality are explored according to [24]. A language is introduced with language signature including free variables, substitution, and equality. Algorithmic logic requires a bialgebra structure which is an extension of language signature and program algebra. While-if algebra of generator set and algebraic signature is bialgebra with appropriate properties and is used as basic type of algebraic logic.
Energy Technology Data Exchange (ETDEWEB)
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 {approximately} 2%) over a wide range of matrix sizes (10 {times} 10 through 200 {times} 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 dynamics solution and algebraic dynamics algorithm of Burgers equations
Institute of Scientific and Technical Information of China (English)
2008-01-01
Algebraic dynamics solution and algebraic dynamics algorithm of nonlinear partial differential evolution equations in the functional space are applied to Burgers equation. The results indicate that the approach is effective for analytical solutions to Burgers equation, and the algorithm for numerical solutions of Burgers equation is more stable, with higher precision than other existing finite difference algo-rithms.
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
Optimal Algorithm for Algebraic Factoring
Institute of Scientific and Technical Information of China (English)
支丽红
1997-01-01
This paper presents on optimized method for factoring multivariate polynomials over algebraic extension fields defined by an irreducible ascending set. The basic idea is to convert multivariate polynomials to univariate polynomials and algebraic extension fields to algebraic number fields by suitable integer substituteions.Then factorize the univariate polynomials over the algebraic number fields.Finally,construct mulativariate factors of the original polynomial by Hensel lemma and TRUEFACTOR test.Some examples with timing are included.
Linear algebra algorithms for divisors on an algebraic curve
Khuri-Makdisi, Kamal
2001-01-01
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and matrices of size $O(g^2)\\times O(g)$. When the base field $k$ is finite, or if $C$ has a rational point over $k$, these give algorithms for working on the Jacobian of $C$ that require $O(g^4)$ field operations, arising from the Gaussian elimination. Our point o...
Linear algebra algorithms for divisors on an algebraic curve
Khuri-Makdisi, Kamal
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and matrices of size $O(g^2)\\times O(g)$. When the base field $k$ is finite, or if $C$ has a rational point over $k$, these give algorithms for working on the Jacobian of $C$ that require $O(g^4)$ field operations, arising from the Gaussian elimination. Our point of view is strongly geometric, and our representation of points on the Jacobian is fairly simple to work with; in particular, none of our algorithms involves arithmetic with polynomials. We note that our algorithms have the same asymptotic complexity for general curves as the more algebraic algorithms in Hess' 1999 Ph.D. thesis, which works with function fields as extensions of $k[x]$. However, for special classes of curves, Hess' algorithms are asymptotically more efficient than ours, generalizing other known efficient algorithms for special classes of curves, such as hyperelliptic curves (Cantor), superelliptic curves (Galbraith, Paulus, and Smart), and $C_{ab}$ curves (Harasawa and Suzuki); in all those cases, one can attain a complexity of $O(g^2)$.
International Nuclear Information System (INIS)
In this paper, we begin the study of zero-dimensional field theories with fields taking values in a semistrict Lie 2-algebra. These theories contain the IKKT matrix model and various M-brane related models as special cases. They feature solutions that can be interpreted as quantized 2-plectic manifolds. In particular, we find solutions corresponding to quantizations of ℝ3, S3 and a five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie 2-algebra models around the solution corresponding to quantized ℝ3, we obtain higher BF-theory on this quantized space
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)
An Algebraic Hardware/Software Partitioning Algorithm
Institute of Scientific and Technical Information of China (English)
秦胜潮; 何积丰; 裘宗燕; 张乃孝
2002-01-01
Hardware and software co-design is a design technique which delivers computer systems comprising hardware and software components. A critical phase of the co-design process is to decompose a program into hardware and software. This paper proposes an algebraic partitioning algorithm whose correctness is verified in program algebra. The authors introduce a program analysis phase before program partitioning and develop a collection of syntax-based splitting rules. The former provides the information for moving operations from software to hardware and reducing the interaction between components, and the latter supports a compositional approach to program partitioning.
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....
Algebraic dynamics solution to and algebraic dynamics algorithm for nonlinear advection equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
Algebraic dynamics approach and algebraic dynamics algorithm for the solution of nonlinear partial differential equations are applied to the nonlinear advection equa-tion. The results show that the approach is effective for the exact analytical solu-tion and the algorithm has higher precision than other existing algorithms in nu-merical computation for the nonlinear advection equation.
Dimer models and Calabi-Yau algebras
Broomhead, Nathan
2008-01-01
In this thesis we study dimer models, as introduced in string theory, which give a way of writing down a class of non-commutative `superpotential' algebras. Some examples are 3-dimensional Calabi-Yau algebras, as defined by Ginzburg, and some are not. We consider two types of `consistency' condition on dimer models, and show that a `geometrically consistent' model is `algebraically consistent'. Finally we prove that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras.
Observable Algebra in Field Algebra of G-spin Models
Institute of Scientific and Technical Information of China (English)
蒋立宁
2003-01-01
Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observable algebra AH, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that AH is a C*-algebra. The correspondence between H and AH is strictly monotonic. Finally, a duality between D(H) and AH is given via an irreducible vacuum C*-representation of F.
Solving stochastic epidemiological models using computer algebra
Hincapie, Doracelly; Ospina, Juan
2011-06-01
Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.
FOUNDATION OF NUCLEAR ALGEBRAIC MODELS
Institute of Scientific and Technical Information of China (English)
周孝谦
1990-01-01
Based upon Tomonoga-Rowe's many body theory, we find that the algebraic models, including IBM and FDSM are simplest extension of Rowe-Rosensteel's sp(3R).Dynkin-Gruber's subalgebra embedding method is applied to find an appropriate algebra and it's reduction chains conforming to physical requirement. The separated cases sp(6) and so(8) now appear as two branches stemming from the same root D6-O(12). Transitional ease between sp(6) and so(8) is inherently include.
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...
Efficient computer algebra algorithms for polynomial matrices in control design
Baras, J. S.; Macenany, D. C.; Munach, R.
1989-01-01
The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.
A spatial operator algebra for manipulator modeling and control
Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.
1991-01-01
A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.
Impact of hierarchical memory systems on linear algebra algorithm design
Energy Technology Data Exchange (ETDEWEB)
Gallivan, K.; Jalby, W.; Meier, U.; Sameh, A.H.
1988-01-01
Linear algebra algorithms based on the BLAS or extended BLAS do not achieve high performance on multivector processors with a hierarchical memory system because of a lack of data locality. For such machines, block linear algebra algorithms must be implemented in terms of matrix-matrix primitives (BLAS3). Designing efficient linear algebra algorithms for these architectures requires analysis of the behavior of the matrix-matrix primitives and the resulting block algorithms as a function of certain system parameters. The analysis must identify the limits of performance improvement possible via blocking and any contradictory trends that require trade-off consideration. The authors propose a methodology that facilitates such an analysis and use it to analyze the performance of the BLAS3 primitives used in block methods. A similar analysis of the block size-performance relationship is also performed at the algorithm level for block versions of the LU decomposition and the Gram-Schmidt orthogonalization procedures.
Institute of Scientific and Technical Information of China (English)
WANG Shundin; ZHANG Hua
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.
Specific optimization of genetic algorithm on special algebras
Habiballa, Hashim; Novak, Vilem; Dyba, Martin; Schenk, Jiri
2016-06-01
Searching for complex finite algebras can be succesfully done by the means of genetic algorithm as we showed in former works. This genetic algorithm needs specific optimization of crossover and mutation. We present details about these optimizations which are already implemented in software application for this task - EQCreator.
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.
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
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...
An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications
Dougherty, Daniel J
2010-01-01
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.
An Improved Algorithm for Generating Database Transactions from Relational Algebra Specifications
Dougherty, Daniel J.
2010-01-01
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 transforma...
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.
Computing Small 1-Homological Models for Commutative Differential Graded Algebras
Alvarez, Victor; Armario, Jose Andres; Frau, Maria Dolores; Gonzalez-Diaz, Rocio; Jimenez, Maria Jose; Real, Pedro; Silva, Beatriz
2001-01-01
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the differential structure of a small 1--homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.
On the Model Properties of BCK Algebras
Institute of Scientific and Technical Information of China (English)
LIANGJun-qi
2004-01-01
This paper is devoted to the study of the logical properties of BCK algebras. For formalized BCK algebra theory T, it is proved that T is preserved under submodels and unions of chains; T is neither complete nor model complete, and hence there exist no builtin Skolem function. Moreover, the ultraproduct BCK algebras and the fuzzy ultraproduct of fuzzy subsets of BCK algebras were proposed by using the concept of ultrafilters with corresponding propertics of fuzzy ideals discussed.
Overview of parallel algorithms in numerical linear algebra
Energy Technology Data Exchange (ETDEWEB)
Sameh, A.
1983-01-01
The author gives a brief survey of the development of multiprocessor algorithms for: (i) the direct solution of linear systems, (ii) the algebraic eigenvalue problem, and (iii) the direct and iterative methods for solving the finite-difference or finite-element linear systems of equations arising from the discretization of linear partial differential equations. 66 references.
An Algorithm for the Decomposition of Semisimple Lie Algebras
Graaf, W.A. de
2001-01-01
We consider the problem of decomposing a semisimple Lie algebra dened over a eld of characteristic zero as a direct sum of its simple ideals The method is based on the decomposition of the action of a Cartan subalgebra An implementation of the algorithm in the system ELIAS is discussed at the end of
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158
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
HDL IMPLEMENTATION OF ALGEBRAIC SOFT DECISION ALGORITHM FOR RS CODES
M. Revathy; Saravanan, R.
2013-01-01
Reed Solomon (RS) codes are widely used to detect and correct data errors in transmission andstorage systems. Hence it is used in many digital communication and storage devices. In existing systemReformulated inversion less Burst error correcting (RiBC) algorithm is used. But it lacks in speed,throughput & area. To overcome this Algebraic Soft Decision (ASD) algorithm is proposed. This Proposedalgorithm is based on Unified VLSI architecture for correcting burst errors as well as random errors...
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
(Numerical algorithms for solving linear algebra problems). Final report
Energy Technology Data Exchange (ETDEWEB)
Golub, G.H.
1985-04-16
We have concentrated on developing and analyzing various numerical algorithms for solving problems arising in a linear algebra context. The papers and research fall into basically three categories: (1) iterative methods for solving linear equations arising from p.d.e.'s; (2) calculation of Gauss-type quadrature rules; and (3) solution of matrix and data problems arising in statistical computation. We summarize some of these results, highlighting those which are of most importance.
New parallel algorithms in linear algebra
Energy Technology Data Exchange (ETDEWEB)
Evans, D.J.
1983-01-01
The well-known and established techniques for deriving the numerical solution of linear systems of equations of the form ax=b are based on the following two basic strategies: (a) the factorisation of the coefficient matrix into easily inverted factors l and u leading to the class of direct methods, i.e. Gaussian elimination, Lu decomposition, Choleski, and (b) the splitting of the matrix a into convenient forms l and u which result in the iterative methods of Jacobi, Gauss Seidel and Sor. However, both these strategies essentially lead to algorithms more suitable for sequential computers and the question of a more convenient factorisation or splitting strategy for parallel processing is discussed leading to the formulation of new techniques based on the factorisation and splitting of the coefficient matrix a into components which are essentially interlocking matrix quadrants. It is shown that such a proposition leads to new parallel algorithms for both direct and iterative methods of solving linear equations and eigenvalue analysis. 15 references.
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
2012-06-01
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.
A Review of Algebraic Link Analysis Algorithms
Directory of Open Access Journals (Sweden)
Mini Singh Ahuja
2012-08-01
Full Text Available The World Wide Web is a system of interlinked hypertext documents accessed via the Internet. With a web browser, one can view web pages that may contain text, images, videos, and other multimedia and navigate between them by using hyperlinks. Navigation is the process through which the users can achieve their purposes in using Web site, such as to find the information that they need or to complete the transactions that they want to do. Web mining is the application of data mining techniques to extract knowledge from Web data, where at least one of structure (hyperlink or usage (Web log data is used in the mining process (with or without other types of Web data. In this paper we have briefly discussed the web mining technique with major stress to the link analysis algorithms.
An explicit algebraic reduced order algorithm for lithium ion cell voltage prediction
Senthil Kumar, V.; Gambhire, Priya; Hariharan, Krishnan S.; Khandelwal, Ashish; Kolake, Subramanya Mayya; Oh, Dukjin; Doo, Seokgwang
2014-02-01
The detailed isothermal electrochemical model for a lithium ion cell has ten coupled partial differential equations to describe the cell behavior. In an earlier publication [Journal of Power Sources, 222, 426 (2013)], a reduced order model (ROM) was developed by reducing the detailed model to a set of five linear ordinary differential equations and nonlinear algebraic expressions, using uniform reaction rate, volume averaging and profile based approximations. An arbitrary current profile, involving charge, rest and discharge, is broken down into constant current and linearly varying current periods. The linearly varying current period results are generic, since it includes the constant current period results as well. Hence, the linear ordinary differential equations in ROM are solved for a linearly varying current period and an explicit algebraic algorithm is developed for lithium ion cell voltage prediction. While the existing battery management system (BMS) algorithms are equivalent circuit based and ordinary differential equations, the proposed algorithm is an explicit algebraic algorithm. These results are useful to develop a BMS algorithm for on-board applications in electric or hybrid vehicles, smart phones etc. This algorithm is simple enough for a spread-sheet implementation and is useful for rapid analysis of laboratory data.
ALGEBRAIC GENERALIZATION OF THE CASH FLOW STATEMENT: REFLECTIONS BY MEANS OF AN ALGEBRAIC ALGORITHM
Directory of Open Access Journals (Sweden)
José Roberto Kassai
2012-09-01
Full Text Available Starting on January 1, 2008 it became mandatory for all Brazilian public companies and private companies with net worth greater than two million reais (about one million dollars as of this writing to publish a cash flow statement (CFS as part of their financial statements, making this statement another important source of information for investors. This article proposes an algebraic generalization for the CFS. Working papers can help fill in a gap in teaching about cash flow statements and produce an indirect method and a direct method, side by side with their equivalence highlighted, in a single matrix by means of algebraic algorithms. This study is normative in nature and stresses the transversal relationship between accounting and mathematics, showing that accounting reports and their structures can be seen as matrices and be subjected to algebraic deductions about the events recorded by double entries. As a result, we demonstrate a mathematical algorithm with matrices and submatrices and a script in the format of working papers, compatible with the normative orientations of the Federal Accounting Council (CFS and Brazilian legislation, permitting formulation of clear, reliable and effective cash flow statements.
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
Lagrangians for the W-Algebra Models
Gaite, J C
1994-01-01
The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams, which correspond to multicritical points with $D_n$ symmetry. In particular, it is shown that there is a perturbation for which the phase structure coincides with that of the IRF models of Jimbo et al.
An algebraic model of software evolution
Keller, Benjamin J.d
1990-01-01
A model of the software evolution process, called the Abstraction Refinement Model, is described which builds on the algebraic influence of the Laws of Programming and the transformational Draco Paradigm. The result is an algebraic structure consisting of the states of the software product (system descriptions) ordered by a relation of relative correctness with transformations defined between the system descriptions. This structure is interpreted as the software evolution space, ...
Parallelization for MIMD multiprocessors with applications to linear algebra algorithms
Energy Technology Data Exchange (ETDEWEB)
Nelken, I.H.
1989-01-01
In this thesis, the author considers the parallelization problem. Given a sequential algorithm and a target architecture, how can the sequential algorithm be converted into a parallel algorithm suitable for the target architecture The parallel algorithm must be correct and produce the same results as the sequential one. It must also utilize the resources of the target architecture efficiently. The parallelization problem can be divided into three main stages: identification of parallelism which includes dependency analysis, partitioning the statements into atomic tasks of granularity suitable to the target architecture and scheduling these tasks into the processors. The identification of parallelism is independent of the target architecture while the partitioning and scheduling stages are very dependent on it. For example, the partitioning for a machine with many small processors is very different than the partitioning for a machine with a few large ones. It is well known that the problems arising in the partitioning and scheduling stages are NP-complete. The thesis shows that for some algorithms arising in linear algebra, simple heuristics are sufficient to produce good solutions to the partitioning and scheduling problems. He considers the Gaussian elimination and Gauss-Jordan algorithms for general dense matrices and the Cholesky decomposition algorithms for symmetric positive definite matrices. In addition he studies algorithms for the solution of simultaneous triangular systems with the same coefficient matrix and different right hand sides and for the solution of the triangular Sylvester equation. Most of the results in this thesis are related to the more difficult problems of partitioning and scheduling for message passing architectures.
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.
New Algebraic Soft Decision Decoding Algorithm for Reed-Solomon Code
Zhu, Yuan; Tang, Siyun
2014-01-01
In this paper, a new algebraic soft-decision decoding algorithm for Reed-Solomon code is presented. It is based on rational interpolation and the interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the traditional K{\\"o}tter-Vardy algorithm, new algorithm needs interpolation for two smaller multiplicity matrixes, due to the corresponding factorization algorithm for re-constructing codewords.
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Hinkelmann, Franziska; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2010-01-01
Motivation: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, bounded Petri nets, and agent-based models. Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone. Results: We convert discrete models into algebraic models and apply tools from computational algebra to analyze their dynamics. The key feature of biological systems that is exploited by our algorithms is their sparsity: while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes. In our experience with models arising in systems biology and random models, this structure leads to fast computations when using algebraic models, and thus efficient analysis. Availability: All algorithms and methods are available in our package Analysis of Dynamic Algebraic Models (ADAM), a user friendly web-interf...
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.
Tomino, Dan
2010-01-01
1-loop vacuum energies of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra are discussed. A_{2,2} algebra, Nambu-Poisson algebra in flat spacetime, and a Lorentzian 3-algebra are examined as 3-algebras.
Sigma-models and Homotopy Algebras
Zeitlin, Anton M
2015-01-01
We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein equations with extra fields, as generalized Maurer-Cartan equations.
Fusion algebras of logarithmic minimal models
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, Joergen; Pearce, Paul A [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)
2007-11-09
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 {ne} 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{sub p,p'} (minimal) models defined algebraically.
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...
AR quivers,exceptional sequences and algorithms in derived Hall algebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Consider the canonical isomorphism between the positive part U+ of the quantum group Uq(g) and the Hall algebra H(Λ),where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin diagram.Chen and Xiao have given two algorithms to decompose the root vectors into linear combinations of monomials of Chevalley generators of U+,respectively induced by the braid group action on the exceptional sequences of Λ-modules and the structure of the Auslander-Reiten quiver of Λ.In this paper,we obtain the corresponding algorithms for the derived Hall algebra DH(Λ),which was introduced by Toen.We show that both algorithms are applicable to the lattice algebra and Heisenberg double in the sense of Kapranov.All the new recursive formulae have the same flavor with the quantum Serre relations.
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.
Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
Nikolić, Zoran; Nguyen, Ha Thai; Frantz, Gene
2007-12-01
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.
Boundary algebras and Kac modules for logarithmic minimal models
Morin-Duchesne, Alexi; Rasmussen, Jørgen; Ridout, David
2015-10-01
Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be given by finitely generated submodules of Feigin-Fuchs modules. Additional evidence for this identification is obtained by comparing the formalism of lattice fusion with the fusion rules of the Virasoro Kac modules. These are obtained, at the character level, in complete generality by applying a Verlinde-like formula and, at the module level, in many explicit examples by applying the Nahm-Gaberdiel-Kausch fusion algorithm.
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 compo
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.
Graph model of the Heisenberg-Weyl algebra
Blasiak, P.; Horzela, A.; Duchamp, G. H. E.; Penson, K. A.; Solomon, A. I.
2007-01-01
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs. This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.
MODEL IDENTIFICATION AND COMPUTER ALGEBRA
Bollen, Kenneth A.; Bauldry, Shawn
2010-01-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local a...
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Through most of Greek history, mathematicians concentrated on geometry, although Euclid considered the theory of numbers. The Greek mathematician Diophantus (3rd century),however, presented problems that had to be solved by what we would today call algebra. His book is thus the first algebra text.
The impact of hierarchical memory systems on linear algebra algorithm design
Energy Technology Data Exchange (ETDEWEB)
Gallivan, K.; Jalby, W.; Meier, U.; Sameh, A.
1987-09-14
Performing an extremely detailed performance optimization analysis is counterproductive when the concern is performance behavior on a class of architecture, since general trends are obscured by the overwhelming number of machine-specific considerations required. Instead, in this paper, a methodology is used which identifies the effects of a hierarchical memory system on the performance of linear algebra algorithms on multivector processors; provides a means of producing a set of algorithm parameters, i.e., blocksizes, as functions of system parameters which yield near-optimal performance; and provides guidelines for algorithm designers which reduce the influence of the hierarchical memory system on algorithm performance to negligible levels and thereby allow them to concentrate on machine-specific optimizations. The remainder of this paper comprises five major discussions. First, the methodology and the attendant architectural model are discussed. Next, an analysis of the basic BLAS3 matrix-matrix primitive is presented. This is followed by a discussion of three block algorithms: a block LU decomposition, a block LDL/sup T/ decomposition and a block Gram-Schmidt algorithm. 22 refs., 9 figs.
Algebraic model of baryon resonances
Bijker, R
1997-01-01
We discuss recent calculations of electromagnetic form factors and strong decay widths of nucleon and delta resonances. The calculations are done in a collective constituent model of the nucleon, in which the baryons are interpreted as rotations and vibrations of an oblate top.
Algebraic model of baryon structure
Bijker, R
2000-01-01
We discuss properties of baryon resonances belonging to the Nucleon, Delta, Sigma, Lambda, Xi and Omega families in a collective string-like model for the nucleon, in which the radial excitations are interpreted as rotations and vibrations of the string configuration. We find good overall agreement with the available data. The main discrepancies are found for low lying S-wave states, in particular N(1535), N(1650), Sigma(1750), Lambda*(1405), Lambda(1670) and Lambda(1800).
Quantum spin models and extended conformal algebras
Honecker, A
1995-01-01
First, an algebraic criterion for integrability is discussed -the so-called `superintegrability'- and some results on the classification of superintegrable quantum spin Hamiltonians based on sl(2) are obtained. Next, the massive phases of the Z_n-chiral Potts quantum spin chain (a model that violates parity) are studied in detail. It is shown that the excitation spectrum of the massive high-temperature phase can be explained in terms of n-1 fundamental quasiparticles. We compute correlation functions from a perturbative and numerical evaluation of the groundstate for the Z_3-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general Z_n using a form factor expansion. Finally, we discuss several aspects of extended conformal algebras (W-algebras). We observe an analogy between boundary conditions for Z_n-spin chains ...
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
Algebraic model theory for languages without equality
Elgueta Montó, Raimon
1994-01-01
In our opinion, it is fair to distinguish two separate branches in the origins of model theory. The first one, the model theory of first-order logic, can be traced back to the pioneering work of L. Lowenheim, T. Skolem, K. Gödel, A. Tarski and A.I. MaI 'cev, published before the mid 30's. This branch was put forward during the 40s' and 50s’ by several authors, including A. Tarski, L. Henkin, A. Robinson, J. Los. Their contribution, however, was rather influenced by modern algebra, a disciplin...
Inverse-free Berlekamp-Massey-Sakata Algorithm and Small Decoders for Algebraic-Geometric Codes
Matsui, Hajime
2007-01-01
This paper proposes a novel algorithm for finding error-locators of algebraic-geometric codes that can eliminate the division-calculations of finite fields from the Berlekamp-Massey-Sakata algorithm. This inverse-free algorithm provides full performance in correcting a certain class of errors, generic errors, which includes most errors, and can decode codes on algebraic curves without the determination of unknown syndromes. Moreover, we propose three different kinds of architectures that our algorithm can be applied to, and we represent the control operation of shift-registers and switches at each clock-timing with numerical simulations. We estimate the performance in comparison of the total running time and the numbers of multipliers and shift-registers in three architectures with those of the conventional ones for codes on algebraic curves.
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...
The geometry of supersymmetric coset models and superconformal algebras
Papadopoulos, G
1993-01-01
An on-shell formulation of (p,q), 2\\leq p \\leq 4, 0\\leq q\\leq 4, supersymmetric coset models with target space the group G and gauge group a subgroup H of G is given. It is shown that there is a correspondence between the number of supersymmetries of a coset model and the geometry of the coset space G/H. The algebras of currents of supersymmetric coset models are superconformal algebras. In particular, the algebras of currents of (2,2) and (4,0) supersymmetric coset models are related to the N=2 Kazama-Suzuki and N=4 Van Proeyen superconformal algebras correspondingly.
Quantum Algorithms for Problems in Number Theory, Algebraic Geometry, and Group Theory
van Dam, Wim; Sasaki, Yoshitaka
2013-09-01
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same problem appears to be intractable on classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article will review the current state of quantum algorithms, focusing on algorithms for problems with an algebraic flavor that achieve an apparent superpolynomial speedup over classical computation.
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.
Matrix Algebra for Quantum Search Algorithm: Non Unitary Symmetries and Entanglement
Ellinas, Demosthenes; Konstandakis, Christos
2011-10-01
An algebraic reformulation of the quantum search algorithm associated to a k-valued oracle function, is introduced in terms of the so called oracle matrix algebra, by means of which a Bloch sphere like description of search is obtained. A parametric family of symmetric completely positive trace preserving (CPTP) maps, that formalize the presence of quantum noise but preserves the complexity of the algorithm, is determined. Dimensional reduction of representations of oracle Lie algebra is introduced in order to determine the reduced density matrix of subsets of qubits in database. The L1 vector-induced norm of reduced density matrix is employed to define an index function for the quantum entanglement between database qubits, in the presence of non invariant noise CPTP maps. Analytic investigations provide a causal relation between entanglement and fidelity of the algorithm, which is controlled by quantum noise parameter.
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.
Monotonic Property in Field Algebra of G-Spin Model
Institute of Scientific and Technical Information of China (English)
蒋立宁
2003-01-01
Let F be the field algebra of G-spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G. The paper builds a correspondence between D(H) and the D(H)-invariant sub-C*-algebra AH in F, and proves that the correspondence is strictly monotonic.
Symmetries of faces models and the double triangle algebra
Trinchero, R
2005-01-01
Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra isomorphic to the Ocneanu double triangle algebra(DTA).
A new algorithm for differential-algebraic equations based on HIDM
International Nuclear Information System (INIS)
A new algorithm is proposed to solve differential-algebraic equations. The algorithm is an extension of the algorithm of general purpose HIDM (higher order implicit difference method). A computer program named HDMTDV and based on the new algorithm is constructed and its high performance is proved numerically through several numerical computations, including index-2 problem of differential-algebraic equations and connected rigid pendulum equations. The new algorithm is also secular error free when applied to dissipationless dynamical systems. This nature is demonstrated numerically by computation of the Kepler motion. The new code can solve the initial value problem O = L { φ(x), [dφ(x)]/dx, [d2φ(x)]/dx2, x }, where L and φ are vectors of length N. The values of first or second derivatives of φ(x) are not always necessary in the equations. (author)
Models of stochastic gene expression and Weyl algebra
Vidal, Samuel,; Petitot, Michel; Boulier, François; Lemaire, François; Kuttler, Celine
2010-01-01
International audience; This paper presents a symbolic algorithm for computing the ODE systems which describe the evolution of the moments associated to a chemical reaction system, considered from a stochastic point of view. The algorithm, which is formulated in the Weyl algebra, seems more efficient than the corresponding method, based on partial derivatives. In particular, an efficient method for handling conservation laws is presented. The output of the algorithm can be used for a further ...
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Multiprocessing linear algebra algorithms on the CRAY X-MP-2: Experiences with small granularity
Energy Technology Data Exchange (ETDEWEB)
Chen, S.S.; Dongarra, J.J.; Hsiung, C.
1984-08-01
This paper gives a brief overview of the CRAY X-MP-2 general-purpose multiprocessor system and discusses how it can be used effectively to solve problems that have small granularity. An implementation is described for linear algebra algorithms that solve systems of linear equations when the matrix is general and when the matrix is symmetric and positive definite.
Topics in Randomized Algorithms for Numerical Linear Algebra
Holodnak, John T.
In this dissertation, we present results for three topics in randomized algorithms. Each topic is related to random sampling. We begin by studying a randomized algorithm for matrix multiplication that randomly samples outer products. We show that if a set of deterministic conditions is satisfied, then the algorithm can compute the exact product. In addition, we show probabilistic bounds on the two norm relative error of the algorithm. two norm relative error of the algorithm. In the second part, we discuss the sensitivity of leverage scores to perturbations. Leverage scores are scalar quantities that give a notion of importance to the rows of a matrix. They are used as sampling probabilities in many randomized algorithms. We show bounds on the difference between the leverage scores of a matrix and a perturbation of the matrix. In the last part, we approximate functions over an active subspace of parameters. To identify the active subspace, we apply an algorithm that relies on a random sampling scheme. We show bounds on the accuracy of the active subspace identification algorithm and construct an approximation to a function with 3556 parameters using a ten-dimensional active subspace.
L∞-algebra models and higher Chern-Simons theories
Ritter, Patricia; Sämann, Christian
2016-10-01
We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L∞-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie p-algebra extensions of 𝔰𝔬(p + 2). Finally, we study a number of L∞-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
Algebraic Jacobi-Perron algorithm for biquadratic numbers
Tamura, Jun-ichi; Yasutomi, Shin-ichi
2010-07-01
We introduced a new algorithm [6] which is something like the modified Jacobi-Perron algorithm and we conjectured that the expansion obtained by our algorithm for a¯ = (α1,…,as)∈Ks (with some natural conditions on a¯) becomes periodic for any real number field K as far as s+1 = degQ(K)≤4. We announce Theorem and some computer experiments for certain biquadratic real number fields K = Q(√m ,√n ) which support our conjecture.
Jain, A.; Man, G. K.
1993-01-01
This paper describes the Dynamics Algorithms for Real-Time Simulation (DARTS) real-time hardware-in-the-loop dynamics simulator for the National Aeronautics and Space Administration's Cassini spacecraft. The spacecraft model consists of a central flexible body with a number of articulated rigid-body appendages. The demanding performance requirements from the spacecraft control system require the use of a high fidelity simulator for control system design and testing. The DARTS algorithm provides a new algorithmic and hardware approach to the solution of this hardware-in-the-loop simulation problem. It is based upon the efficient spatial algebra dynamics for flexible multibody systems. A parallel and vectorized version of this algorithm is implemented on a low-cost, multiprocessor computer to meet the simulation timing requirements.
Fermi resonance-algebraic model for molecular vibrational spectra
Institute of Scientific and Technical Information of China (English)
侯喜文; 董世海; 谢汨; 马中骐
1999-01-01
A Fermi resonance-algebraic model is proposed for molecular vibrations, where a U(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent molecule XY2 and a molecule XY3 is successfully applied to fitting the recently observed vibrational spectrum of the water molecule and arsine (AsH3), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations.
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
An efficient algorithm for the contig ordering problem under algebraic rearrangement distance.
Lu, Chin Lung
2015-11-01
Assembling a genome from short reads currently obtained by next-generation sequencing techniques often results in a collection of contigs, whose relative position and orientation along the genome being sequenced are unknown. Given two sets of contigs, the contig ordering problem is to order and orient the contigs in each set such that the genome rearrangement distance between the resulting sets of ordered and oriented contigs is minimized. In this article, we utilize the permutation groups in algebra to propose a near-linear time algorithm for solving the contig ordering problem under algebraic rearrangement distance, where the algebraic rearrangement distance between two sets of ordered and oriented contigs is the minimum weight of applicable rearrangement operations required to transform one set into the other. PMID:26247343
Algebra model and security analysis for cryptographic protocols
Institute of Scientific and Technical Information of China (English)
HUAI Jinpeng; LI Xianxian
2004-01-01
More and more cryptographic protocols have been used to achieve various security requirements of distributed systems in the open network environment. However cryptographic protocols are very difficult to design and analyze due to the complexity of the cryptographic protocol execution, and a large number of problems are unsolved that range from the theory framework to the concrete analysis technique. In this paper, we build a new algebra called cryptographic protocol algebra (CPA) for describing the message operations with many cryptographic primitives, and proposed a new algebra model for cryptographic protocols based on the CPA. In the model, expanding processes of the participant's knowledge on the protocol runs are characterized with some algebraic notions such as subalgebra, free generator and polynomial algebra, and attack processes are modeled with a new notion similar to that of the exact sequence used in homological algebra. Then we develope a mathematical approach to the cryptographic protocol security analysis. By using algebraic techniques, we have shown that for those cryptographic protocols with some symmetric properties, the execution space generated by an arbitrary number of participants may boil down to a smaller space generated by several honest participants and attackers. Furthermore we discuss the composability problem of cryptographic protocols and give a sufficient condition under which the protocol composed of two correct cryptographic protocols is still correct, and we finally offer a counterexample to show that the statement may not be true when the condition is not met.
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.
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.
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. PMID:24135792
Pavelle, Richard; And Others
1981-01-01
Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)
Algebraic Modeling of Information Retrieval in XML Documents
Georgiev, Bozhidar; Georgieva, Adriana
2009-11-01
This paper presents an information retrieval approach in XML documents using tools, based on the linear algebra. The well-known transformation languages as XSLT (XPath) are grounded on the features of higher-order logic for manipulating hierarchical trees. The presented conception is compared to existing higher-order logic formalisms, where the queries are realized by both languages XSLT and XPath. The possibilities of the proposed linear algebraic model combined with hierarchy data models permit more efficient solutions for searching, extracting and manipulating semi-structured data with hierarchical structures avoiding the global navigation over the XML tree components. The main purpose of this algebraic model representation, applied to the hierarchical relationships in the XML data structures, is to make the implementation of linear algebra tools possible for XML data manipulations and to eliminate existing problems, related to regular grammars theory and also to avoid the difficulties, connected with higher -order logic (first-order logic, monadic second- order logic etc.).
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.
Implementing linear algebra algorithms for dense matrices on a vector pipeline machine
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.; Gustavson, F.G.; Karp, A.
1984-01-01
The authors examine common implementations of linear algebra algorithms, such as matrix-vector multiplication, matrix-matrix multiplication and the solution of linear equations. The different versions are examined for efficiency on a computer architecture which uses vector processing and has pipelined instruction execution. By using the advanced architectural features of such machines, one can usually achieve maximum performance, and tremendous improvements in terms of execution speed can be seen over conventional computers. 17 references.
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.
Boundary algebras and Kac modules for logarithmic minimal models
Morin-Duchesne, Alexi; Ridout, David
2015-01-01
Virasoro Kac modules were initially introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be...
Novel parallel architectures and algorithms for linear algebra processing. Semiannual report
Energy Technology Data Exchange (ETDEWEB)
Casasent, D.
1986-10-01
Advanced problems in computational fluid dynamics, finite element structural analysis, and related areas require the solution of large partial differential equations and matrices of large size and dynamic range. This project considers an advanced parallel linear algebra processor and associated novel parallel algorithms for such applications. Research on system fabrication, quantitative performance evaluation and new parallel algorithms are described and considered. Case studies in structural mechanics, dynamics and nonlinear systems, finite element methods, computational fluid dynamics, and partial differential equations are included. The novel utilization of an optical processor for the processing of such problems is the major research given attention.
An Algebraic Dexter-Based Hypertext Reference Model
Mattick, Volker
2009-01-01
We present the first formal algebraic specification of a hypertext reference model. It is based on the well-known Dexter Hypertext Reference Model and includes modifications with respect to the development of hypertext since the WWW came up. Our hypertext model was developed as a product model with the aim to automatically support the design process and is extended to a model of hypertext-systems in order to be able to describe the state transitions in this process. While the specification should be easy to read for non-experts in algebraic specification, it guarantees a unique understanding and enables a close connection to logic-based development and verification.
Algebraic model of an oblate top
Bijker, R
1996-01-01
We consider an algebraic treatment of a three-body system. In particular, we develop the formalism for a system of three identical objects and discuss an application to nonstrange baryon resonances which are interpreted as vibrational and rotational excitations of an oblate symmetric top. We derive closed expressions for a set of elementary form factors that appear in the calculation of both electromagnetic, strong and weak couplings of baryons.
A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures
Buttari, Alfredo; Kurzak, Jakub; Dongarra, Jack
2007-01-01
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be re- formulated or new algorithms have to be developed in order to take ad- vantage of the architectural features on these new processors. Fine grain parallelism becomes a major requirement and introduces the necessity of loose synchronization in the parallel execution of an operation. This paper presents an algorithm for the Cholesky, LU and QR factorization where the operations can be represented as a sequence of small tasks that operate on square blocks of data. These tasks can be dynamically scheduled for execution based on the dependencies among them and on the availability of computational resources. This may result in an out of order execution of the tasks which will completely hide the presence of intrinsically sequential tasks in the factorization. Performance com- parisons are presented with the LAPACK algorithms where parallelism can only be exploited at the level of the BLAS op...
A comparison between algebraic models of molecular spectroscopy
Bijker, R; Lemus, R; Arias, J M; Pérez-Bernal, F
1998-01-01
We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in previous versions of the vibron model, in which the Hamiltonian is expressed in terms of Casimir operators and their products. The inclusion of these new interactions leads to reliable spectroscopic predictions. As an example we study the vibrational excitations of the methane molecule, and compare our results with those obtained in other algebraic models.
Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
Directory of Open Access Journals (Sweden)
Xiaojian Zhou
2012-01-01
Full Text Available We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.
Towards P = NP via k-SAT: A k-SAT Algorithm Using Linear Algebra on Finite Fields
Groff, Matt
2011-01-01
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy understanding for many people and scientists from many diverse fields. In technical terms, a novel method for solving k-SAT is explained. This method is primarily based on linear algebra and finite fields. Evidence is given that this method may require only O(n^7) time and space for deterministic models. It's concluded that signi?cant evidence exists that P=NP. There is a forum devoted to this paper at http://482527.ForumRomanum.com. All are in- vited to correspond here and help with the anal- ysis of the algorithm.
Massierer, Maike
2014-01-01
The function field sieve, a subexponential algorithm of complexity L(1/3) that computes discrete logarithms in finite fields, has recently been improved to an algorithm of complexity L(1/4) and subsequently to a quasi-polynomial time algorithm. We investigate whether the new ideas also apply to index calculus algorithms for computing discrete logarithms in Jacobians of algebraic curves. While we do not give a final answer to the question, we discuss a number of ideas, experiments, and possibl...
Laser modeling a numerical approach with algebra and calculus
Csele, Mark Steven
2014-01-01
Offering a fresh take on laser engineering, Laser Modeling: A Numerical Approach with Algebra and Calculus presents algebraic models and traditional calculus-based methods in tandem to make concepts easier to digest and apply in the real world. Each technique is introduced alongside a practical, solved example based on a commercial laser. Assuming some knowledge of the nature of light, emission of radiation, and basic atomic physics, the text:Explains how to formulate an accurate gain threshold equation as well as determine small-signal gainDiscusses gain saturation and introduces a novel pass
An Algebraic Solution for the Kermack-McKendrick Model
Carvalho, Alexsandro M
2016-01-01
We present an algebraic solution for the Susceptible-Infective-Removed (SIR) model originally presented by Kermack-McKendrick in 1927. Starting from the differential equation for the removed subjects presented by them in the original paper, we re-write it in a slightly different form in order to derive formally the solution, unless one integration. Then, using algebraic techniques and some well justified numerical assumptions we obtain an analytic solution for the integral. Finally, we compare the numerical solution of the differential equations of the SIR model with the analytically solution here proposed, showing an excellent agreement.
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.
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…
Algebraic models of hadron structure I. Nonstrange baryons
Bijker, R; Leviatan, A
1994-01-01
We introduce an algebraic framework for the description of baryons. Within this framework we study a collective string-like model and show that this model gives a good overall description of the presently available data. We discuss in particular masses and electromagnetic couplings, including the transition form factors that can be measured at new electron facilities.
Sandryhaila, Aliaksei; Pueschel, Markus
2010-01-01
A polynomial transform is the multiplication of an input vector $x\\in\\C^n$ by a matrix $\\PT_{b,\\alpha}\\in\\C^{n\\times n},$ whose $(k,\\ell)$-th element is defined as $p_\\ell(\\alpha_k)$ for polynomials $p_\\ell(x)\\in\\C[x]$ from a list $b=\\{p_0(x),\\dots,p_{n-1}(x)\\}$ and sample points $\\alpha_k\\in\\C$ from a list $\\alpha=\\{\\alpha_0,\\dots,\\alpha_{n-1}\\}$. Such transforms find applications in the areas of signal processing, data compression, and function interpolation. Important examples include the discrete Fourier and cosine transforms. In this paper we introduce a novel technique to derive fast algorithms for polynomial transforms. The technique uses the relationship between polynomial transforms and the representation theory of polynomial algebras. Specifically, we derive algorithms by decomposing the regular modules of these algebras as a stepwise induction. As an application, we derive novel $O(n\\log{n})$ general-radix algorithms for the discrete Fourier transform and the discrete cosine transform of type 4.
An algebraic approach to modeling in software engineering
International Nuclear Information System (INIS)
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
An algebraic approach to modeling in software engineering
Energy Technology Data Exchange (ETDEWEB)
Loegel, G.J. [Superconducting Super Collider Lab., Dallas, TX (United States)]|[Michigan Univ., Ann Arbor, MI (United States); Ravishankar, C.V. [Michigan Univ., Ann Arbor, MI (United States)
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.
Indian Academy of Sciences (India)
Wen Debao; Liu Sanzhi
2010-08-01
For the limitation of the conventional multiplicative algebraic reconstruction technique (MART), a constrained MART (CMART) is proposed in this paper. In the new tomographic algorithm, a popular two-dimensional multi-point finite difference approximation of the second order Laplacian operator is used to smooth the electron density field. The feasibility and superiority of the new method are demonstrated by using the numerical simulation experiment. Finally, the CMART is used to reconstruct the regional electron density field by using the actual GNSS data under geomagnetic quiet and disturbed days. The available ionosonde data from Beijing station further validates the superiority of the new method.
Fully Analyzing an Algebraic Polya Urn Model
Morcrette, Basile
2012-01-01
This paper introduces and analyzes a particular class of Polya urns: balls are of two colors, can only be added (the urns are said to be additive) and at every step the same constant number of balls is added, thus only the color compositions varies (the urns are said to be balanced). These properties make this class of urns ideally suited for analysis from an "analytic combinatorics" point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006. Through an algebraic generating function to which we apply a multiple coalescing saddle-point method, we are able to give precise asymptotic results for the probability distribution of the composition of the urn, as well as local limit law and large deviation bounds.
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.
Weak quasitriangular Quasi-Hopf algebra structure of minimal models
Teschner, J. A.
1995-01-01
The chiral vertex operators for the minimal models are constructed and used to define a fusion product of representations. The existence of commutativity and associativity operations is proved. The matrix elements of the associativity operations are shown to be given in terms of the 6-j symbols of the weak quasitriangular quasi-Hopf algebra obtained by truncating $\\usl$ at roots of unity.
Form factors in an algebraic model of the nucleon
Bijker, R
1995-01-01
We study the electromagnetic form factors of the nucleon in a collective model of baryons. In an algebraic approach to hadron structure, we derive closed expressions for both elastic and transition form factors, and consequently for the helicity amplitudes that can be measured in electro- and photoproduction.
Algebraic Models of Hadron Structure; 2, Strange Baryons
Bijker, R; Leviatan, A
2000-01-01
The algebraic treatment of baryons is extended to strange resonances. Within this framework we study a collective string-like model in which the radial excitations are interpreted as rotations and vibrations of the strings. We derive a mass formula and closed expressions for strong and electromagnetic decay widths and use these to analyze the available experimental data.
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Directory of Open Access Journals (Sweden)
Blekherman Grigoriy
2011-07-01
Full Text Available Abstract Background 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. Results 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. Conclusions 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
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.
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...
An algorithm for identifying symmetric variables in the canonical OR-coincidence algebra system
Institute of Scientific and Technical Information of China (English)
Xiao-hua LI; Ji-zhong SHEN
2014-01-01
To simplify the process for identifying 12 types of symmetric variables in the canonical OR-coincidence (COC) algebra system, we propose a new symmetry detection algorithm based on OR-NXOR expansion. By analyzing the relationships between the coefficient matrices of sub-functions and the order coefficient subset matrices based on OR-NXOR expansion around two arbitrary logical variables, the constraint conditions of the order coefficient subset matrices are revealed for 12 types of symmetric variables. Based on the proposed constraints, the algorithm is realized by judging the order characteristic square value matrices. The proposed method avoids the transformation process from OR-NXOR expansion to AND-OR-NOT expansion, or to AND-XOR expansion, and solves the problem of completeness in the dj-map method. The application results show that, compared with traditional methods, the new algorithm is an optimal detection method in terms of applicability of the number of logical variables, detection type, and complexity of the identification process. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. Experimental results show that the proposed algorithm is convenient and efficient.
How algebraic Bethe ansatz works for integrable model
Fadeev, L
1996-01-01
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific details are given. Several parameters, appearing in these generalizations: spin s, anisotropy parameter \\ga, shift \\om in the alternating chain, allow to include in our treatment most known examples of soliton theory, including relativistic model of Quantum Field Theory.
Generalization of Richardson-Gaudin models to rank-2 algebras
Energy Technology Data Exchange (ETDEWEB)
Errea, B; Lerma, S; Dukelsky, J; Dimitrova, S S; Pittel, S; Van Isacker, P; Gueorguiev, V G
2006-07-20
A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained.
Algebraic turbulence modeling for unstructured and adaptive meshes
Mavriplis, Dimitri J.
1990-01-01
An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.
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.
An extended set of Fortran Basic Linear Algebra Subprograms: model implementation and test programs
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.; Du Croz, J.; Hammarling, S.; Hanson, R.J.
1987-01-01
This paper describes a model implementation and test software for the Level 2 Basic Linear Algebra Subprograms (Level 2 BLAS). The Level 2 BLAS are targeted at matrix-vector operations with the aim of providing more efficient, but portable, implementations of algorithms on high-performance computers. The model implementation provides a portable set of Fortran 77 Level 2 BLAS for machines where specialized implementations do not exist or are not required. The test software aims to verify that specialized implementations meet the specification of the Level 2 BLAS and that implementations are correctly installed.
Geometric Model of Topological Insulators from the Maxwell Algebra
Palumbo, Giandomenico
2016-01-01
We propose a novel geometric model of three-dimensional topological insulators in presence of an external electromagnetic field. The gapped boundary of these systems supports relativistic quantum Hall states and is described by a Chern-Simons theory with a gauge connection that takes values in the Maxwell algebra. This represents a non-central extension of the Poincar\\'e 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.
Free particles from Brauer algebras in complex matrix models
Kimura, Yusuke; Turton, David
2009-01-01
The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition. The Brauer algebra basis for complex matrix models developed earlier is useful in projecting to a sector which matches the state counting of N free fermions on a circle. The Brauer algebra projection is characterized by the vanishing of a scale invariant laplacian constructed from the complex matrix. The special case of N=2 is studied in detail: the ring of gauge invariant functions as well as a ring of scale and gauge invariant differential operators are characterized completely. The orthonormal basis of wavefunctions in this special case is completely characterized by a set of five commuting Hamiltonians, which display free particle structures. Applications to the reduced matrix quantum mechanics coming from radial quantization in N=4 SYM are described. We propose that th...
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.
Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua
2014-11-01
Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.
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.
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.; Hewitt, T.
1985-08-01
This note describes some experiments on simple, dense linear algebra algorithms. These experiments show that the CRAY X-MP is capable of small-grain multitasking arising from standard implementations of LU and Cholesky decomposition. The implementation described here provides the ''fastest'' execution rate for LU decomposition, 718 MFLOPS for a matrix of order 1000.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
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.
Karassiov, V. P.; A. A. Gusev; Vinitsky, S. I.
2001-01-01
We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.
Algebraic Turbulence-Chemistry Interaction Model
Norris, Andrew T.
2012-01-01
The results of a series of Perfectly Stirred Reactor (PSR) and Partially Stirred Reactor (PaSR) simulations are compared to each other over a wide range of operating conditions. It is found that the PaSR results can be simulated by a PSR solution with just an adjusted chemical reaction rate. A simple expression has been developed that gives the required change in reaction rate for a PSR solution to simulate the PaSR results. This expression is the basis of a simple turbulence-chemistry interaction model. The interaction model that has been developed is intended for use with simple one-step global reaction mechanisms and for steady-state flow simulations. Due to the simplicity of the model there is very little additional computational cost in adding it to existing CFD codes.
Algebraic spin liquid in an exactly solvable spin model
Energy Technology Data Exchange (ETDEWEB)
Yao, Hong; Zhang, Shou-Cheng; Kivelson, Steven A.; /Stanford U., Phys. Dept.
2010-03-25
We have proposed an exactly solvable quantum spin-3/2 model on a square lattice. Its ground state is a quantum spin liquid with a half integer spin per unit cell. The fermionic excitations are gapless with a linear dispersion, while the topological 'vison' excitations are gapped. Moreover, the massless Dirac fermions are stable. Thus, this model is, to the best of our knowledge, the first exactly solvable model of half-integer spins whose ground state is an 'algebraic spin liquid.'
An algebraic model of baryon spectroscopy
Bijker, R
1999-01-01
We discuss recent calculations of the mass spectrum, electromagnetic and strong couplings of baryon resonances. The calculations are done in a collective constituent model for the nucleon, in which the resonances are interpreted as rotations and vibrations of a symmetric top with a prescribed distribution of the charge and magnetization. We analyze recent data on eta-photo- and eta-electroproduction, and the tensor analyzing power in deuteron scattering.
A Multiple—Valued Algebra for Modeling MOS VLSI Circuits at Switch—Level
Institute of Scientific and Technical Information of China (English)
胡谋
1992-01-01
A multiple-valued algebra for modeling MOS VLSI circuits at switch-level is proposed in this paper,Its structure and properties are studied.This algebra can be used to transform a MOS digital circuit to a swith-level algebraic expression so as to generate the truth table for the circuit and to derive a Boolean expression for it.In the paper,methods to construct a switch-level algebraic expression for a circuit and methods to simplify expressions are given.This algebra provides a new tool for MOS VLSI circuit design and analysis.
Proceedings Second International Workshop on Algebraic Methods in Model-based Software Engineering
Durán, Francisco
2011-01-01
Over the past years there has been quite a lot of activity in the algebraic community about using algebraic methods for providing support to model-driven software engineering. The aim of this workshop is to gather researchers working on the development and application of algebraic methods to provide rigorous support to model-based software engineering. The topics relevant to the workshop are all those related to the use of algebraic methods in software engineering, including but not limited to: formally specifying and verifying model-based software engineering concepts and related ones (MDE, UML, OCL, MOF, DSLs, ...); tool support for the above; integration of formal and informal methods; and theoretical frameworks (algebraic, rewriting-based, category theory-based, ...). The workshop's main goal is to examine, discuss, and relate the existing projects within the algebraic community that address common open-issues in model-driven software engineering.
An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities
Pralet, C; Verfaillie, G; 10.1613/jair.2151
2011-01-01
Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we first adapt previous structures from Friedman, Chu and Halpern for representing uncertainty, utility, and expected utility in order to deal with generic forms of sequential decision making; (2) on these structures, we then introduce composite graphical models that express information via variables linked by "local" functions, thanks to conditional independence; (3) on these graphical models, we finally define a simple class ...
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
A U(1) Current Algebra Model Coupled to 2D-Gravity
Stoilov, M.; Zaikov, R.
1993-01-01
We consider a simple model of a scalar field with $U(1)$ current algebra gauge symmetry coupled to $2D$-gravity in order to clarify the origin of Stuckelberg symmetry in the $w_{\\infty}$-gravity theory. An analogous symmetry takes place in our model too. The possible central extension of the complete symmetry algebra and the corresponding critical dimension have been found. The analysis of the Hamiltonian and the constraints shows that the generators of the current algebra, the reparametrizat...
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
A New Algebraic Modelling Approach to Distributed Problem-Solving in MAS
Institute of Scientific and Technical Information of China (English)
帅典勋; 邓志东
2002-01-01
This paper is devoted to a new algebraic modelling approach to distributed problem-solving in multi-agent systems (MAS), which is featured by a unified framework for describing and treating social behaviors, social dynamics and social intelligence. A conceptual architecture of algebraic modelling is presented. The algebraic modelling of typical social behaviors, social situation and social dynamics is discussed in the context of distributed problemsolving in MAS. The comparison and simulation on distributed task allocations and resource assignments in MAS show more advantages of the algebraic approach than other conventional methods.
Clifford algebras geometric modelling and chain geometries with application in kinematics
Klawitter, Daniel
2015-01-01
After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework. Contents Models and representations of classical groups Clifford algebras, chain geometries over Clifford algebras Kinematic mappings for Pin and Spin groups Cayley-Klein geometries Target Groups Researchers and students in the field of mathematics, physics, and mechanical engineering About...
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
Energy Technology Data Exchange (ETDEWEB)
Gurau, Razvan, E-mail: rgurau@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo (Canada)
2012-12-01
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.
Fast algebra algorithm of shape-from-shading with specular reflectance
Institute of Scientific and Technical Information of China (English)
Lei Yang; Jiuqiang Han
2007-01-01
Shape-from-shading (SFS) is to reconstruct three-dimensional (3D) shape from a single gray image, which is an important problem in computer vision. We propose a novel SFS method based on hybrid reflection model which contains both diffuse reflectance and specular reflectance. The intensity gradient of image is in the direction that the shape of urface changes most, so we use directional derivative of the reflectance map as parts of objective function. When discrete characteristic of digital images is considered, finite difference approximates differential operator. So the reflectance map equation described by a partial differential equation (PDE) turns into an algebra equation about the nknown surface height correspondingly. Using iterative numeric computation, a new SFS method is gained. Experiments on synthesis and real images show that the proposed SFS method is accurate and fast.
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
Algebraic Traveling Wave Solutions of a Non-local Hydrodynamic-type Model
International Nuclear Information System (INIS)
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
The Galois Correspondence in Field Algebra of G-spin Model
Institute of Scientific and Technical Information of China (English)
Li Ning JIANG; Mao Zheng GUO
2005-01-01
Suppose that G is a finite group and D(G) the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D(G; H) of D(G). This paper gives the concrete construction of a D(G; H)-invariant subspace (A)H in field algebra of G-spin model and proves that if H is a normal subgroup of G, then (A)H is Galois closed.
Lie algebraic similarity transformed Hamiltonians for lattice model systems
Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.
2015-01-01
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.
Algebraic model for single-particle energies of $\\Lambda$ hypernuclei
Fortunato, L
2016-01-01
A model is proposed for the spectrum of $\\Lambda$ hypernuclei based on the $u(3)\\times u(2)$ Lie algebra, in which the internal degrees of freedom of the spin-1/2 $\\Lambda$ particle are treated in the Fermionic $u(2)$ scheme, while the motion of the hyperon inside a nucleus is described in the Bosonic $u(3)$ harmonic oscillator scheme. Within this model, a simple formula for single-particle energies of the $\\Lambda$ particle is obtained from the natural dynamical symmetry. The formula is applied to the experimental data on the reaction spectroscopy for the $^{89}_\\Lambda$Y and $^{51}_\\Lambda$V hypernuclei, providing a clear theoretical interpretation of the observed structures.
Infinite number of conserved quantities and extended conformal algebra in the Thirring model
Energy Technology Data Exchange (ETDEWEB)
Inoue, K.; Odaka, K.; Omote, M.
1988-02-01
It is shown that the Thirring model has an infinite number of local conserved quantities, explicit forms of which are presented. These quantities are shown to be expressed in terms of scattering parameters. It will be shown that in this model there exists an extended symmetry algebra that includes the Virasoro algebra as its subalgebra.
Algebraic models of deviant modal operators based on de Morgan and Kleene lattices
Cattaneo, G.; Ciucci, DE; Dubois, D.
2011-01-01
An algebraic model of a kind of modal extension of de Morgan logic is described under the name MDS5 algebra. The main properties of this algebra can be summarized as follows: (1) it is based on a de Morgan lattice, rather than a Boolean algebra; (2) a modal necessity operator that satisfies the axioms N, K, T, and 5 (and as a consequence also B and 4) of modal logic is introduced; it allows one to introduce a modal possibility by the usual combination of necessity operation and...
CUDA加速的地图代数并行算法%CUDA-Accelerated Parallel Algorithms for Map Algebra
Institute of Scientific and Technical Information of China (English)
张剑波; 周斯波; 张帅
2011-01-01
针对传统地图代数实现方法应用于海量栅格数据计算时效率低下的问题,在一种全新的GPU并行编程模型CUDA上,利用地图代数算子体现出来的基于栅格点集、处理流程相对固定、数据处理具有内在的并行性等特点,将传统的串行算法映射到GPU并行处理架构上,旨在从串行算法的并行化映射、计算机图形处理器资源的自适应参数调整等多角度来研究地图代数空间并行算法的实现机制,为空间分析算法的优化研究提供一种新的解决思路.%To improve the efficiency in traditional method of map algebra calculation for gigantic raster data, arithmetic operators characteristics are applied, including relatively fixed process flow and inherently parallel specialty, and a new GPU parallel programming model named CUDA is selectsed as technique supports. The realization mechanism surrounding parallel mapping of serial algorithms is discussed in adaptive parameter adjustments on computer graphic processor resources, thus providing a new solution for optimized research of spatial analytic algorithms.
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.
07071 Report on Dagstuhl Seminar -- Web Information Retrieval and Linear Algebra Algorithms
Frommer, Andreas; Mahoney, Michael W.; Szyld, Daniel B.
2007-01-01
A seminar concentrating on the intersection of the fields of information retrieval and other web-related aspects with numerical and applied linear algebra techniques was held with the attendance of scientists from industry and academia.
Re"modeling" College Algebra: An Active Learning Approach
Pinzon, D.; Pinzon, K.; Stackpole, M.
2016-01-01
In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…
Sigma-model Solutions and Intersecting p-Branes Related to Lie Algebras
Grebeniuk, M. A.; Ivashchuk, V. D.
1998-01-01
A family of Majumdar-Papapetrou type solutions in sigma-model of p-brane origin is obtained for all direct sums of finite-dimensional simple Lie algebras. Several examples of p-brane dyonic configurations in D=10 (IIA) and D=11 supergravities corresponding to the Lie algebra sl(3,C) are considered.
Algebraic structures generating reaction-diffusion models: the activator-substrate system
Palese, Marcella
2015-01-01
We shall construct a class of nonlinear reaction-diffusion equations starting from an infinitesimal algebraic skeleton. Our aim is to explore the possibility of an algebraic foundation of integrability properties and of stability of equilibrium states associated with nonlinear models describing patterns formation.
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
Index-aware model order reduction methods applications to differential-algebraic equations
Banagaaya, N; Schilders, W H A
2016-01-01
The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.
Energy Technology Data Exchange (ETDEWEB)
Bracken, Anthony J.; Ge Xiangyu; Gould, Mark D.; Links, Jon; Zhou Huanqiang [Centre for Mathematical Physics, University of Queensland, Brisbane, QLD (Australia)
2001-06-01
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method. (author)
Liu, Jianzhou; Zhang, Juan
2011-08-01
In this article, applying the properties of M-matrix and non-negative matrix, utilising eigenvalue inequalities of matrix's sum and product, we firstly develop new upper and lower matrix bounds of the solution for discrete coupled algebraic Riccati equation (DCARE). Secondly, we discuss the solution existence uniqueness condition of the DCARE using the developed upper and lower matrix bounds and a fixed point theorem. Thirdly, a new fixed iterative algorithm of the solution for the DCARE is shown. Finally, the corresponding numerical examples are given to illustrate the effectiveness of the developed results.
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.
Analysis of DIRAC's behavior using model checking with process algebra
International Nuclear Information System (INIS)
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.
Y(sl(2)) Algebra Application in Extended Hydrogen Atom and Monopole Models
Institute of Scientific and Technical Information of China (English)
TIAN Li-Jun; ZHANG Hong-Biao; JIN Shuo; XUE Kang
2004-01-01
We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y (sl(2) ) algebras are realized. We derive the Hamiltonians of the two models based on the Y(sl(2) ) and the generalized Pauli equation. The energy spectra of the systems are also given in terms of Yangian algebra and quantum mechanics.
The Standard Model as an extension of the noncommutative algebra of forms
Brouder, Christian; Besnard, Fabien
2015-01-01
The Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra extension in the sense of Eilenberg. By doing so, they could deduce three axioms of the NCG Standard Model (i.e. order zero, order one and massless photon) from the single requirement that the extended algebra be associative. However, their approach was only applied to the finite part of the model because it fails for the full model. By taking into account the differential graded structure of the algebra of noncommutative differential forms, we obtain a formulation where the same three axioms are deduced from the associativity of the extended differential graded algebra, but which is now compatible with the full Standard Model.
Quasi-exactly solvable models derived from the quasi-Gaudin algebra
Energy Technology Data Exchange (ETDEWEB)
Lee, Yuan-Harng; Links, Jon; Zhang Yaozhong, E-mail: jrl@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, Qld 4072 (Australia)
2011-12-02
The quasi-Gaudin algebra was introduced to construct integrable systems which are only quasi-exactly solvable. Using a suitable representation of the quasi-Gaudin algebra, we obtain a class of bosonic models which exhibit this curious property. These models have the notable feature that they do not preserve U(1) symmetry, which is typically associated with a non-conservation of particle number. An exact solution for the eigenvalues within the quasi-exactly solvable sector is obtained via the algebraic Bethe ansatz formalism. (fast track communication)
Currents algebra for an atom-molecule Bose-Einstein condensate model
Filho, Gilberto N. Santos
2016-01-01
I present an interconversion currents algebra for an atom-molecule Bose-Einstein condensate model and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters I get different currents dynamics.
Institute of Scientific and Technical Information of China (English)
李宝; 周林芳; 肖国镇
1999-01-01
For a class of algebraic-geometric codes, a type of recurring relation is introduced on the syndrome sequence of an error vector. Then, a new majority yoting scheme is developed. By applying the generalized Berlekamp-Massey algorithm, and incorporating the majority voting scheme, an efficient decoding algorithm up to half the Feng-Rao bound is developed for a class of algebraic-geometric codes, the complexity of which is O （ γo1n2）, where n is the code length, and γ is the genus of curve. On different algebraic curves, the complexity of the algorithm can be lowered by choosing base functions suitably. For example, on Hermitian curves the complexity is O(n7/3.
Lie algebra solution of population models based on time-inhomogeneous Markov chains
House, Thomas
2011-01-01
Many natural populations are well modelled through time-inhomogeneous stochastic processes. Such processes have been analysed in the physical sciences using a method based on Lie algebras, but this methodology is not widely used for models with ecological, medical and social applications. This paper presents the Lie algebraic method, and applies it to three biologically well motivated examples. The result of this is a solution form that is often highly computationally advantageous.
Off-critical W∞ and Virasoro algebras as dynamical symmetries of the integrable models
International Nuclear Information System (INIS)
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)
Ahmadi, Amir Ali; Parrilo, Pablo A.
2014-01-01
Exciting recent developments at the interface of optimization and control have shown that several fundamental problems in dynamics and control, such as stability, collision avoidance, robust performance, and controller synthesis can be addressed by a synergy of classical tools from Lyapunov theory and modern computational techniques from algebraic optimization. In this paper, we give a brief overview of our recent research efforts (with various coauthors) to (i) enhance the scalability of the...
A novel hybrid optimization algorithm for diferential-algebraic control problems
Directory of Open Access Journals (Sweden)
F. S. Lobato
2007-09-01
Full Text Available Dynamic optimization problems can be numerically solved by direct, indirect and Hamilton-Jacobi-Bellman methods. In this paper, the differential-algebraic approach is incorporated into a hybrid method, extending the concepts of structural and differential indexes, consistent initialization analysis, index reduction and dynamic degrees of freedom to the optimal control problem. The resultant differential-algebraic optimal control problem is solved in the following steps: transformation of the original problem into a standard nonlinear programming problem that provides control and state variables, switching time estimates and costate variables profiles with the DIRCOL code; definition of the switching function and the automatically generated sequence of index-1 differential-algebraic boundary value problems from Pontryagin’s minimum principle by using the developed Otima code; and finally, application of the COLDAE code with the results of the direct method as an initial guess. The proposed hybrid method is illustrated with a pressure-constrained batch reactor optimization problem associated with the slack variable method.
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...
On the minimum weight states of the Lipkin model obeying the su(n)-algebra
Tsue, Yasuhiko; da Providencia, Joao; Yamamura, Masatoshi
2015-01-01
The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the su(n)-algebra are investigated systematically. The basic idea is to use the su(2)-algebra which is independent of the su(n)-algebra. This idea has been already presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the su(2)-algebra. If following this idea, the minimum weight states are determined for any fermion number occupying appropriately n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction.
The classical origin of quantum affine algebra in squashed sigma models
Kawaguchi, Io; Matsumoto, Takuya; Yoshida, Kentaroh
2012-01-01
We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassic...
International Nuclear Information System (INIS)
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)
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'…
On Derivations Of Genetic Algebras
International Nuclear Information System (INIS)
A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two
Symmetric structure of field algebra of G-spin models determined by a normal subgroup
Energy Technology Data Exchange (ETDEWEB)
Xin, Qiaoling, E-mail: xinqiaoling0923@163.com; Jiang, Lining, E-mail: jianglining@bit.edu.cn [School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081 (China)
2014-09-15
Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra F{sub H} of the field algebra F of G-spin models, so that F{sub H} is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A{sub (H,G)} is obtained as the D(H; G)-invariant subalgebra of F{sub H}, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A{sub (H,G)} are commutants with each other.
Numerical algorithms in chemistry: algebraic methods. [Workshop, August 9-11, 1978
Energy Technology Data Exchange (ETDEWEB)
Moler, C.; Shavitt, I. (eds.)
1978-08-09
The National Resource for Computation in Chemistry was established to make information on existing and developing computational methodologies available to all segments of the chemistry community, to make state-of-the-art computation facilities accessible to the chemistry community, and to foster research and development of new computational methods for application to chemical problems. Attention was directed to algebraic methods because of their continuing importance in chemical applications. This volume contains digests of the contributions to the workshop of August 9--11, 1978. Presentations were given on eigenvalue problems, linear systems of equations, and integral transformations. One of the papers in this volume was abstracted and indexed separately. (RWR)
Investigating modularity in the analysis of process algebra models of biochemical systems
Ciocchetta, Federica; Hillston, Jane; 10.4204/EPTCS.19.4
2010-01-01
Compositionality is a key feature of process algebras which is often cited as one of their advantages as a modelling technique. It is certainly true that in biochemical systems, as in many other systems, model construction is made easier in a formalism which allows the problem to be tackled compositionally. In this paper we consider the extent to which the compositional structure which is inherent in process algebra models of biochemical systems can be exploited during model solution. In essence this means using the compositional structure to guide decomposed solution and analysis. Unfortunately the dynamic behaviour of biochemical systems exhibits strong interdependencies between the components of the model making decomposed solution a difficult task. Nevertheless we believe that if such decomposition based on process algebras could be established it would demonstrate substantial benefits for systems biology modelling. In this paper we present our preliminary investigations based on a case study of the phero...
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.
Rigidification of algebras over essentially algebraic theories
Rosicky, J
2012-01-01
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result can be extended from algebraic theories to finite limit theories and from simplicial sets to more general monoidal model categories. We will present some answers to this question.
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.
Galois Correspondence in Field Algebra of G-spin Model
Institute of Scientific and Technical Information of China (English)
蒋立宁; 郭懋正
2003-01-01
@@ A C*-system is a pair (B, G) consisting of a unital C*-algebra B and a continuous group homomorphism α: G → Aut(B) where G is a compact group and Aut(B) the group of automor-phisms of B. If K is a normal subgroup of G and BK = {B∈ B: k(B) = B, k ∈ K}, then BK is a G-invariant C*-subalgebra of B. On the other hand, if A is a G-invariant C*-algebra with BG A B, set G (A) = {g ∈ G: g(A) = A, A ∈ A}, G (A) is a normal subgroup of G. Clearly K G(BK) and we call K Galois closed ifK = G(BK). Similarly, A BG(A) and we call A Galois closed if A = BG(A).
Patenting mathematical algorithms : What's the harm? A thought experiment in algebra
de Laat, P.B.
2000-01-01
The patenting of software-related inventions is on the increase, especially in the United States. Mathematical formulas and algorithms, though, are still sacrosanct. Only under special conditions may algorithms qualify as statutory matter: if they are not solely a mathematical exercise, but if they
Reachability for Finite-state Process Algebras Using Horn Clauses
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya; Nielson, Flemming
2013-01-01
In this work we present an algorithm for solving the reachability problem in finite systems that are modelled with process algebras. Our method is based on Static Analysis, in particular, Data Flow Analysis, of the syntax of a process algebraic system with multi-way synchronisation. The results...
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.
Direct Model Checking Matrix Algorithm
Institute of Scientific and Technical Information of China (English)
Zhi-Hong Tao; Hans Kleine Büning; Li-Fu Wang
2006-01-01
During the last decade, Model Checking has proven its efficacy and power in circuit design, network protocol analysis and bug hunting. Recent research on automatic verification has shown that no single model-checking technique has the edge over all others in all application areas. So, it is very difficult to determine which technique is the most suitable for a given model. It is thus sensible to apply different techniques to the same model. However, this is a very tedious and time-consuming task, for each algorithm uses its own description language. Applying Model Checking in software design and verification has been proved very difficult. Software architectures (SA) are engineering artifacts that provide high-level and abstract descriptions of complex software systems. In this paper a Direct Model Checking (DMC) method based on Kripke Structure and Matrix Algorithm is provided. Combined and integrated with domain specific software architecture description languages (ADLs), DMC can be used for computing consistency and other critical properties.
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.
Universal Algebras of Hurwitz Numbers
A. Mironov; Morozov, A; Natanzon, S.
2009-01-01
Infinite-dimensional universal Cardy-Frobenius algebra is constructed, which unifies all particular algebras of closed and open Hurwitz numbers and is closely related to the algebra of differential operators, familiar from the theory of Generalized Kontsevich Model.
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.
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
, urgentness and resource usage over a dense-time model. The semantic interpretation of PACoR is defined in the form of a timed transition system expressing the timed behavior and dynamic creation of processes. We define a translation of PACoR systems to Parameterized Stopwatch Automata (PSA). The translation...... preserves the original semantics of PACoR and enables the verification of PACoR systems using symbolic model checking in Uppaal and statistical model checking UppaalSMC. Finally we provide an example to illustrate system specification in PACoR, translation and verification.......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...
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
and resource usage over a dense-time model. The semantic interpretation of PACOR is defined in the form of a timed transition system expressing the timed behavior and dynamic creation of processes. We define a translation of PACOR systems to Parameterized Stopwatch Automata (PSA). The translation preserves...... the original semantics of PACOR and enables the verification of PACOR systems using symbolic model checking in UPPAAL and statistical model checking UPPAAL SMC. Finally we provide an example to illustrate system specification in PACOR, translation and verification.......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...
The algebraic Bethe ansatz for rational braid-monoid lattice models
Martins, M J
1997-01-01
In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the superalgebra Osp(n|2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B_n, C_n, D_n, Osp(2n-1|2), Osp(2|2n-2), Osp(2n-2|2) and Osp(1|2n) models. The corresponding Bethe Ansatz equations can be formulated in terms of the root structure of the underlying algebra.
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.
The Algebraic Cluster Model: Structure of 16O
Bijker, R
2016-01-01
We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with T(d) symmetry are analyzed with respect to the energy spectrum, transition form factors and B(EL) values. It is concluded that the low-lying spectrum of 16O can be described by four alpha-particles at the vertices of a regular tetrahedron, not as a rigid structure but rather a more floppy structure with relatively large rotation-vibration interactions and Coriolis forces.
An algebraic model of Coulomb scattering with spin
Energy Technology Data Exchange (ETDEWEB)
Levay, P. [School of Physics, University of Melbourne, Parkville (Australia); Department of Theoretical Physics, Institute of Physics, Technical University, Budapest (Hungary); Amos, K. [School of Physics, University of Melbourne, Parkville (Australia)
2001-05-11
A new matrix-valued realization for the so(3,1) algebra leads to a natural generalization of the Coulomb scattering problem of a particle with spin. The underlying su(2) gauge structure of this realization recasts the scattering problem into a familiar form, namely, the Coulomb scattering problem of a collection of dyons (particles having both electric and magnetic charges). Using this equivalent form and the results of Zwanziger for such systems, the scattering matrix can be calculated in the helicity formalism. (author)
Shafarevich, I
1994-01-01
This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.
de Brito, G P; Gomes, Y M P; Junior, J T Guaitolini; Nikoofard, V
2016-01-01
In this paper we introduce a modified covariant quantum algebra based in the so-called Quesne-Tkachuk algebra. By means of a deformation procedure we arrive at a class of higher derivative models of gravity. The study of the particle spectra of these models reveals an equivalence with the physical content of the well-known renormalizable and super-renormalizable higher derivative gravities. The particle spectrum exhibits the presence of spurious complex ghosts and, in light of this problem, we suggest an interesting interpretation in the context of minimal length theories. Also, a discussion regarding the non-relativistic potential energy is proposed.
Algebraic Specifications, Higher-order Types and Set-theoretic Models
DEFF Research Database (Denmark)
Kirchner, Hélène; Mosses, Peter David
2001-01-01
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......, 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...
Construction of the Model of the Lambda Calculus System with Algebraic Operators
Institute of Scientific and Technical Information of China (English)
陆汝占; 张政; 等
1991-01-01
A lambda system with algebraic operators,Lambda-plus system,is introduced.After giving the definitions of the system,we present a sufficient condition for formulating a model of the system.Finally,a model of such system is constructed.
Hopf Algebra Structure of a Model Quantum Field Theory
Solomon, A I; Blasiak, P; Horzela, A; Penson, K A
2006-01-01
Recent elegant work on the structure of Perturbative Quantum Field Theory (PQFT) has revealed an astonishing interplay between analysis(Riemann Zeta functions), topology (Knot theory), combinatorial graph theory (Feynman Diagrams) and algebra (Hopf structure). The difficulty inherent in the complexities of a fully-fledged field theory such as PQFT means that the essential beauty of the relationships between these areas can be somewhat obscured. Our intention is to display some, although not all, of these structures in the context of a simple zero-dimensional field theory; i.e. a quantum theory of non-commuting operators which do not depend on spacetime. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs, analogous to the Feynman diagrams of PQFT, which we show possess a Hopf algebra structure. Our approach is based on the partition function for a boson gas. In a subsequent note in these Proceedings we sketch the relationship...
Mathematical modelling in engineering: an alternative way to teach Linear Algebra
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-10-01
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 classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).
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.
Left Artinian Algebraic Algebras
Institute of Scientific and Technical Information of China (English)
S. Akbari; M. Arian-Nejad
2001-01-01
Let R be a left artinian central F-algebra, T(R) = J(R) + [R, R],and U(R) the group of units of R. As one of our results, we show that, if R is algebraic and char F = 0, then the number of simple components of -R = R/J(R)is greater than or equal to dimF R/T(R). We show that, when char F = 0 or F is uncountable, R is algebraic over F if and only if [R, R] is algebraic over F. As another approach, we prove that R is algebraic over F if and only if the derived subgroup of U(R) is algebraic over F. Also, we present an elementary proof for a special case of an old question due to Jacobson.
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.
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…
Institute of Scientific and Technical Information of China (English)
JIN Shuo; XIE Bing-Hao; ZHANG Hong-Biao; GE Mo-Lin
2004-01-01
Some analytical solutions of generalized two-mode harmonic oscillators model are obtained by utilizing an algebraic diagonalization method. We find two types of eigenstates which are formulated as extended SU(1,1), SU(2)squeezed number states respectively. Some statistical properties of these states are also discussed.
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
Kink states in P(φ)2-models. (An algebraic approach)
International Nuclear Information System (INIS)
Several two-dimensional quantum field theory models have more than one vacuum state. Familiar examples are the Sine-Gordon and the φ24-model. It is known that in these models there are also states, called kink states, which interpolate different vacua. A general construction scheme for kink states in the framework of algebraic quantum field theory is developed in a previous paper. However, for the application of this method, the crucial condition is the split property for wedge algebras in the vacuum representations of the considered models. It is believed that the vacuum representations of P(φ)2-models fulfill this condition, but a rigorous proof is only known for the massive free scalar field. Therefore, we investigate in a construction of kink states which can directly be applied to P(φ)2-model, by making use of the properties of the dynamic of a P(φ)2-model. (orig.)
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.
Deskins, W E
1996-01-01
This excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. These systems, which consist of sets of elements, operations, and relations among the elements, and prescriptive axioms, are abstractions and generalizations of various models which evolved from efforts to explain or discuss physical phenomena.In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diop
Combinatorics of solvable lattice models, and modular representations of Hecke algebras
Foda, O E; Okado, M; Thibon, J Y; Welsh, Trevor A; Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
We review and motivate recently-observed relationships between exactly solvable lattice models and modular representations of Hecke algebras. Firstly, we describe how the set of $n$-regular partitions label both of the following classes of objects: 1. The spectrum of unrestricted solid-on-solid lattice models based on level-1 representations of the affine algebras $\\sl_n$, 2. The irreducible representations of type-A Hecke algebras at roots of unity: $H_m(\\sqrt[n]{1})$. Secondly, we show that a certain subset of the $n$-regular partitions label both of the following classes of objects: 1. The spectrum of restricted solid-on-solid lattice models based on cosets of affine algebras $(sl(n)^_1 \\times sl(n)^_1)/ sl(n)^_2$. 2. Jantzen-Seitz (JS) representations of $H_m(\\sqrt[n]{1})$: irreducible representations that remain irreducible under restriction to $H_{m-1}(\\sqrt[n]{1})$. Using the above relationships, we characterise the JS representations of $H_m(\\sqrt[n]{1})$ and show that the generating series that count...
Performance of parallel linear algebra algorithms on an interleaved array processor
Energy Technology Data Exchange (ETDEWEB)
Wolf, G.
1986-01-01
This thesis investigates the performance of numerical algorithms that take advantage of the unique properties of a new type of array processor. This processor, called an Interleaved Array Processor (IAP), is characterized by its ability to use multiple Programmable Functional Units (PFU's) with local data and instruction memories. Unlike conventional array processors, which can only execute simple arithmetic vector operations such as addition and multiplication, the IAP can execute complex vector operations defined by the user. These operations are specified by small programs that can contain conditional branching as well as arithmetic and data movement instructions in each processor. The author calls these programs High-Level Vector Operations (HLVO's). Ways to partition the algorithms and the data among the processing units in the system are presented so that in such a way that the computation time in every processing unit is increased, and at the same time the data movement on the system bus, is reduced. In this way the bus can be timeshared among several functional units, allowing several operations on different vector components to be executed simultaneously and overlapped with the transfer of operands and results.
Optical systolic solutions of linear algebraic equations
Neuman, C. P.; Casasent, D.
1984-01-01
The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.
Deformable target tracking method based on Lie algebra
Liu, Yunpeng; Shi, Zelin; Li, Guangwei
2007-11-01
Conventional approaches to object tracking use area correlation, but they are difficult to solve the problem of deformation of object region during tracking. A novel target tracking method based on Lie algebra is presented. We use Gabor feature as target token, model deformation using affine Lie group, and optimize parameters directly on manifold, which can be solved by exponential mapping between Lie Group and its Lie algebra. We analyze the essence of our method and test the algorithm using real image sequences. The experimental results demonstrate that Lie algebra method outperforms other traditional algorithms in efficiency, stabilization and accuracy.
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
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....
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.
A computer code for calculations in the algebraic collective model of the atomic nucleus
Welsh, T A
2016-01-01
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x SO(5) dynamical group. This, in particular, obviates the use of coefficients of fractional parentage. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [pi x q x pi]_0 and [pi x pi]_{LM}, where q_M are the model's quadrupole moments, and pi_N are corresponding conjugate momenta (-2>=M,N<=2). The code also provides ready access to SO(3)-reduced SO(5) Clebsch-Gordan coefficients through data files provided with the code.
Composing Scalable Nonlinear Algebraic Solvers
Brune, Peter R.; Knepley, Matthew G.; Smith, Barry F.; Tu, Xuemin
2016-01-01
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial diff...
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.
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
2012-01-01
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)
Recent developments and applications of an algebraic version of Bohr's collective model, known as the algebraic collective model (ACM), have shown that fully converged calculations can be performed for a large range of Hamiltonians. Examining the algebraic structure underlying the Bohr model (BM) has also clarified its relationship with the interacting boson model (IBM), with which it has related solvable limits and corresponding dynamical symmetries. In particular, the algebraic structure of the IBM is obtained as a compactification of the BM and conversely the BM is regained in various contraction limits of the IBM. In a previous paper, corresponding contractions were identified and confirmed numerically for axially-symmetric states of relatively small deformation. In this paper, we extend the comparisons to realistic deformations and compare results of the two models in the rotor-vibrator limit. These models describe rotations and vibrations about an axially symmetric prolate or oblate rotor, and rotations and vibrations of a triaxial rotor. It is determined that most of the standard results of the BM can be obtained as contraction limits of the IBM in its U(5)-SO(6) dynamical symmetries.
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...
Meadow enriched ACP process algebras
J.A. Bergstra; Middelburg, C.A.
2009-01-01
We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization of the notion of an ACP process algebra to processes in which data are involved. In meadow enriched ACP process algebras, the mathematical structure for data is a meadow.
Algebraic and relational models for a system based on a poset of two elements
Iturrioz, Luisa
2014-01-01
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal system and we elaborate suitable semantic models in order to derive information from the poset. The system is related to three-valued Heyting algebras with Boolean operators.
On the algebraic structure of self-dual gauge fields and sigma models
International Nuclear Information System (INIS)
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 nonlinear 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. (author)
Another algebraic variational principle for the spectral curve of matrix models
Eynard, B
2014-01-01
We propose an alternative variational principle whose critical point is the algebraic plane curve associated to a matrix model (the spectral curve, i.e. the large $N$ limit of the resolvent). More generally, we consider a variational principle that is equivalent to the problem of finding a plane curve with given asymptotics and given cycle integrals. This variational principle is not given by extremization of the energy, but by the extremization of an "entropy".
RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity
Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
A special family of partitions occurs in two apparently unrelated contexts: the evaluation of 1-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras $H_m$. We provide an explanation of this coincidence by showing how the irreducible $H_m$-modules which remain irreducible under restriction to $H_{m-1}$ (Jantzen-Seitz modules) can be determined from the decomposition of a tensor product of representations of aff...
Svetoslav Markov
2005-01-01
This survey paper aims to promote certain novel mathematical tools, such as computer algebra systems, enclosure methods and interval analysis, to the mathematical modelling and optimization of biotechnological processes.
Directory of Open Access Journals (Sweden)
Svetoslav Markov
2005-12-01
Full Text Available This survey paper aims to promote certain novel mathematical tools, such as computer algebra systems, enclosure methods and interval analysis, to the mathematical modelling and optimization of biotechnological processes.
Vibrational spectrum of CF4 isotopes in an algebraic model
Indian Academy of Sciences (India)
Joydeep Choudhury; Srinivasa Rao Karumuri; Nirmal Kumar Sarkar; Ramendu Bhattacharjee
2009-11-01
n this paper the stretching vibrational modes of CF4 isotopes are calculated up to first overtone using the one-dimensional vibron model for the first time. The model Hamiltonian so constructed seems to describe the C–F stretching modes accurately using a relatively small set of well-defined parameters.
From Clifford Algebra of Nonrelativistic Phase Space to Quarks and Leptons of the Standard Model
Żenczykowski, Piotr
2015-01-01
We review a recently proposed Clifford-algebra approach to elementary particles. We start with: (1) a philosophical background that motivates a maximally symmetric treatment of position and momentum variables, and: (2) an analysis of the minimal conceptual assumptions needed in quark mass extraction procedures. With these points in mind, a variation on Born's reciprocity argument provides us with an unorthodox view on the problem of mass. The idea of space quantization suggests then the linearization of the nonrelativistic quadratic form ${\\bf p}^2 +{\\bf x}^2$ with position and momentum satisfying standard commutation relations. This leads to the 64-dimensional Clifford algebra ${Cl}_{6,0}$ of nonrelativistic phase space within which one identifies the internal quantum numbers of a single Standard Model generation of elementary particles (i.e. weak isospin, hypercharge, and color). The relevant quantum numbers are naturally linked to the symmetries of macroscopic phase space. It is shown that the obtained pha...
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.
Algebraic nonlinear collective motion
Troupe, J.; Rosensteel, G.
1999-01-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real number $\\Lambda$. The $\\Lambda=0$ solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear g...
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
A new algebraic structure in the standard model of particle physics
Boyle, Latham
2016-01-01
We introduce a new formulation of non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to represent $A$ (the algebra of differential forms on some possibly-noncommutative space) on $H$ (the Hilbert space of spinors on that space); and to reinterpret this representation as a simple super-algebra $B=A\\oplus H$ with even part $A$ and odd part $H$. $B$ is the fundamental object in our approach: we show that (nearly) all of the basic axioms and assumptions of the traditional ("spectral triple") formulation of NCG are elegantly recovered from the simple requirement that $B$ should be a differential graded $\\ast$-algebra (or "$\\ast$-DGA"). But this requirement also yields other, new, geometrical constraints. When we apply our formalism to the NCG traditionally used to describe the standard model of particle physics, we find that these new constraints are physically meaningful and phenomenolo...
Cellular modelling using P systems and process algebra
Institute of Scientific and Technical Information of China (English)
Francisco J.Romero-Campero; Marian Gheorghe; Gabriel Ciobanu; John M. Auld; Mario J. Pérez-Jiménez
2007-01-01
In this paper various molecular chemical interactions are modelled under different computational paradigms. P systems and π-calculus are used to describe intra-cellular reactions like protein-protein interactions and gene regulation control.
Algebraic statistics computational commutative algebra in statistics
Pistone, Giovanni; Wynn, Henry P
2000-01-01
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
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...
LCD motion blur: modeling, analysis, and algorithm.
Chan, Stanley H; Nguyen, Truong Q
2011-08-01
Liquid crystal display (LCD) devices are well known for their slow responses due to the physical limitations of liquid crystals. Therefore, fast moving objects in a scene are often perceived as blurred. This effect is known as the LCD motion blur. In order to reduce LCD motion blur, an accurate LCD model and an efficient deblurring algorithm are needed. However, existing LCD motion blur models are insufficient to reflect the limitation of human-eye-tracking system. Also, the spatiotemporal equivalence in LCD motion blur models has not been proven directly in the discrete 2-D spatial domain, although it is widely used. There are three main contributions of this paper: modeling, analysis, and algorithm. First, a comprehensive LCD motion blur model is presented, in which human-eye-tracking limits are taken into consideration. Second, a complete analysis of spatiotemporal equivalence is provided and verified using real video sequences. Third, an LCD motion blur reduction algorithm is proposed. The proposed algorithm solves an l(1)-norm regularized least-squares minimization problem using a subgradient projection method. Numerical results show that the proposed algorithm gives higher peak SNR, lower temporal error, and lower spatial error than motion-compensated inverse filtering and Lucy-Richardson deconvolution algorithm, which are two state-of-the-art LCD deblurring algorithms.
The standard model of quantum physics in Clifford algebra
Daviau, Claude
2016-01-01
We extend to gravitation our previous study of a quantum wave for all particles and antiparticles of each generation (electron + neutrino + u and d quarks for instance). This wave equation is form invariant under Cl3*, then relativistic invariant. It is gauge invariant under the gauge group of the standard model, with a mass term: this was impossible before, and the consequence was an impossibility to link gauge interactions and gravitation.
Safety properties test data selection from an algebraic model of Lustre programs
International Nuclear Information System (INIS)
In the context to validate an industrial software, which is a set of reactive programs, we are confronted with the safety properties verification problem. This thesis reports an experience in which our goal is to generate the test data satisfying a safety property. The software to be validated is designed with the SAGA tool, in which a view can be regarded as a program of a programming language called LUSTRE. We adapt a test data generation tool called LOFT to this kind of programs. In this way, we consider the functional testing method on which the LOFT tool is based. Given any LUSTRE program, we try to give it an algebraic model because LOFT treats algebraic specifications. So, our task consists In defining a formal framework in which any LUSTRE program can be translated into a LOFT module: based on an operational semantics of the LUSTRE language, the flow types 'T-flow' are specified with the constructive algebraic formalism, then implemented in a LOFT modules base. Next, in a test selection process assisted by LOFT, a safety property Is expressed by an equation to join other control hypotheses, and to guide the test data selection. Some concrete test data set are generated in this way on some significant examples. This experience confirm the feasibility of formal method on test data selection for the reactive programs. (author)
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.
THE ALGEBRAIC METHOD OF RATIONAL INTERPOLATION
Institute of Scientific and Technical Information of China (English)
Cai Shoufeng; Zhang Shugong
2005-01-01
This paper deals with rational interpolation. From algebraic viewpoint, we present an algebraic formulation of rational interpolation and discuss the existence of the interpolation function. Finally an algorithm for univariate case and an example are presented.
Asymptotic Solutions of Algebraic Reynolds Stress Model Applied to Rough Bottom Open Channel Flow
Directory of Open Access Journals (Sweden)
Soualmia Amel
2014-05-01
Full Text Available We interpret experimental results on the structure of an open channel flow with a strong transverse variation of the bottom roughness. Knowing the wall parameters, we analyze the behavior of Reynolds stress components by using asymptotic solutions of an algebraic stress model developed in the wall and free surface regions. This analysis allowed us to emphasize effects of secondary flows on the production of turbulence near the wall, and the capability of this model to predict the normal components of the Reynolds tensor in the wall and free surface regions when the turbulent shear stresses are well predicted.
Generalized model of double random phase encoding based on linear algebra
Nakano, Kazuya; Takeda, Masafumi; Suzuki, Hiroyuki; Yamaguchi, Masahiro
2013-01-01
We propose a generalized model for double random phase encoding (DRPE) based on linear algebra. We defined the DRPE procedure in six steps. The first three steps form an encryption procedure, while the later three steps make up a decryption procedure. We noted that the first (mapping) and second (transform) steps can be generalized. As an example of this generalization, we used 3D mapping and a transform matrix, which is a combination of a discrete cosine transform and two permutation matrices. Finally, we investigated the sensitivity of the proposed model to errors in the decryption key.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept-wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
On the numerical simulation of active scalar,a new explicit algebraic expression on active scalar flux was derived based on Wikstrm,Wallin and Johansson model (aWWJ model). Reynolds stress algebraic expressions were added by a term to account for the buoyancy effect. The new explicit Reynolds stress and active scalar flux model was then established. Governing equations of this model were solved by finite volume method with unstructured grids. The thermal shear stratified cylinder wake flow was computed by this new model. The computational results are in good agreement with laboratorial measurements. This work is the development on modeling of explicit algebraic Reynolds stress and scalar flux,and is also a further modification of the aWWJ model for complex situations such as a shear stratified flow.
Institute of Scientific and Technical Information of China (English)
HUA ZuLin; GU Li; XING LingHang; DAI WenHong
2009-01-01
On the numerical simulation of active scalar, a new explicit algebraic expression on active scalar flux was derived based on Wikstrom, Wallin and Johansson model (aWWJ model). Reynolds stress algebraic expressions were added by a term to account for the buoyancy effect. The new explicit Reynolds stress and active scalar flux model was then established. Governing equations of this model were solved by finite volume method with unstructured grids. The thermal shear stratified cylinder wake flow was computed by this new model. The computational results are in good agreement with Laboratorial measurements. This work is the development on modeling of explicit algebraic Reynolds stress and scalar flux, and is also a further modification of the aWWJ model for complex situations such as a shear stratified flow.
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.
A computer code for calculations in the algebraic collective model of the atomic nucleus
Welsh, T. A.; Rowe, D. J.
2016-03-01
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.
Adaptive Genetic Algorithm Model for Intrusion Detection
Directory of Open Access Journals (Sweden)
K. S. Anil Kumar
2012-09-01
Full Text Available Intrusion detection systems are intelligent systems designed to identify and prevent the misuse of computer networks and systems. Various approaches to Intrusion Detection are currently being used, but they are relatively ineffective. Thus the emerging network security systems need be part of the life system and this ispossible only by embedding knowledge into the network. The Adaptive Genetic Algorithm Model - IDS comprising of K-Means clustering Algorithm, Genetic Algorithm and Neural Network techniques. Thetechnique is tested using multitude of background knowledge sets in DARPA network traffic datasets.
A Feedback Control in Max-Algebra
Menguy, Eric; Boimond, Jean-Louis; Hardouin, Laurent
1997-01-01
International audience For timed event graphs, linear models were obtained using Max-Algebra. This paper presents a method to control such systems. After describing the optimal solution of a model tracking problem, we propose a feedback control structure in order to take into account a possible modeling error. We present its construction, its main properties and an algorithm for its practical implementation. An illustrative example is provided.
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.
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.
Modeling boyciana-fish-human interaction with partial differential algebraic equations.
Jiang, Yushan; Zhang, Qingling; Wang, Haiyan
2016-07-01
Under the influence of human population distribution, the boyciana-fish ecological system is considered. First, the system can be described as a nonlinear partial differential algebraic equations system (PDAEs) with Neumann boundary conditions and ratio-dependent functional response. Second, we examine the system's persistence properties: the loacl stabilities of positive steady states, the absorbtion region and the global stability. And the proposed approach is illustrated by numerical simulation. Finally, by using the realistic data collected in the past fourteen years, the PDAEs parameter optimization model is built to predict the boyciana population. PMID:27155570
RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity
Foda, O E; Okado, M; Thibon, J Y; Welsh, Trevor A; Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
A special family of partitions occurs in two apparently unrelated contexts: the evaluation of 1-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras $H_m$. We provide an explanation of this coincidence by showing how the irreducible $H_m$-modules which remain irreducible under restriction to $H_{m-1}$ (Jantzen-Seitz modules) can be determined from the decomposition of a tensor product of representations of affine $\\sl_n$.
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.
Graphical model construction based on evolutionary algorithms
Institute of Scientific and Technical Information of China (English)
Youlong YANG; Yan WU; Sanyang LIU
2006-01-01
Using Bayesian networks to model promising solutions from the current population of the evolutionary algorithms can ensure efficiency and intelligence search for the optimum. However, to construct a Bayesian network that fits a given dataset is a NP-hard problem, and it also needs consuming mass computational resources. This paper develops a methodology for constructing a graphical model based on Bayesian Dirichlet metric. Our approach is derived from a set of propositions and theorems by researching the local metric relationship of networks matching dataset. This paper presents the algorithm to construct a tree model from a set of potential solutions using above approach. This method is important not only for evolutionary algorithms based on graphical models, but also for machine learning and data mining.The experimental results show that the exact theoretical results and the approximations match very well.
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...
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.
Models and Algorithm for Stochastic Network Designs
Institute of Scientific and Technical Information of China (English)
Anthony Chen; Juyoung Kim; Seungjae Lee; Jaisung Choi
2009-01-01
The network design problem (NDP) is one of the most difficult and challenging problems in trans-portation. Traditional NDP models are often posed as a deterministic bilevel program assuming that all rele-vant inputs are known with certainty. This paper presents three stochastic models for designing transporta-tion networks with demand uncertainty. These three stochastic NDP models were formulated as the ex-pected value model, chance-constrained model, and dependent-chance model in a bilevel programming framework using different criteria to hedge against demand uncertainty. Solution procedures based on the traffic assignment algorithm, genetic algorithm, and Monte-Cado simulations were developed to solve these stochastic NDP models. The nonlinear and nonconvex nature of the bilevel program was handled by the genetic algorithm and traffic assignment algorithm, whereas the stochastic nature was addressed through simulations. Numerical experiments were conducted to evaluate the applicability of the stochastic NDP models and the solution procedure. Results from the three experiments show that the solution procedures are quite robust to different parameter settings.
Izhakian, Zur; Rowen, Louis
2008-01-01
We develop the algebraic polynomial theory for "supertropical algebra," as initiated earlier over the real numbers by the first author. The main innovation there was the introduction of "ghost elements," which also play the key role in our structure theory. Here, we work somewhat more generally over an ordered monoid, and develop a theory which contains the analogs of several basic theorems of classical commutative algebra. This structure enables one to develop a Zariski-type algebraic geomet...
Nissen, Edward W.
2011-12-01
The future of particle accelerators is moving towards the intensity frontier; the need to place more particles into a smaller space is a common requirement of nearly all applications of particle accelerators. Putting large numbers of particles in a small space means that the mutual repulsion of these charged particles becomes a significant factor, this effect is called space charge. In this work we develop a series of differential algebra based methods to simulate the effects of space charge in particle accelerators. These methods were used to model the University of Maryland Electron Ring, a small 3.8 meter diameter 10 KeV electron storage ring designed to observe the effects of space charge in a safe, cost effective manner. The methods developed here are designed to not only simulate the effects of space charge on the motions of the test particles in the system but to add their effects to the transfer map of the system. Once they have been added useful information about the beam, such as tune shifts and chromaticities, can be extracted directly from the map. In order to make the simulation self consistent, the statistical moments of the distribution are used to create a self consistent Taylor series representing the distribution function, which is combined with pre-stored integrals solved using a Duffy transformation to find the potential. This method can not only find the map of the system, but also advance the particles under most conditions. For conditions where it cannot be used to accurately advance the particles a differential algebra based fast multipole method is implemented. By using differential algebras to create local expansions, noticeable time savings are found.
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)
Algebraic solutions for two-level pairing model in IBM-2 and IVBM
Jalili-Majarshin, A.; Jafarizadeh, M. A.; Fouladi, N.
2016-09-01
In this paper the affine SU(1,1) approach is applied to numerically solve two pairing problems. A dynamical symmetry limit of the two-fluid interacting boson model-2 (IBM-2) and of the interacting vector boson model (IVBM) defined through the chains U_{π}(6) ⊗ U_{ν}(6) supset SO_{π}(5)⊗ SO_{ν}(5) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) and U(6) supset U_{π}(3) ⊗ U_{ν}(3) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) are introduced, respectively. The quantum phase transition between spherical and γ-soft shapes in medium-mass nuclei is analyzed using U(5) leftrightarrow SO(6) transitional nuclei in IBM-2 and one case U_{π}(3) ⊗ U_{ν}(3) leftrightarrow SO(6) transitional nuclei in IVBM found by using an infinite dimensional algebraic method based on affine SU(1,1) Lie algebra. The calculated energy spectra, energy ratio and energy staggering of Mo isotopes are compared with experimental results. The interplay between phase transitions and configuration mixing of intruder excitations between spherical vibrations and the γ-soft shapes in Mo isotopes is succinctly addressed and displays fingerprints of the transitional dynamical symmetry E(5).
A note on the "logarithmic-W_3" octuplet algebra and its Nichols algebra
Semikhatov, A M
2013-01-01
We describe a Nichols-algebra-motivated construction of an octuplet chiral algebra that is a "W_3-counterpart" of the triplet algebra of (p,1) logarithmic models of two-dimensional conformal field theory.
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.
Meadow enriched ACP process algebras
J.A. Bergstra; C.A. Middelburg
2009-01-01
We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization o
A Generic Design Model for Evolutionary Algorithms
Institute of Scientific and Technical Information of China (English)
He Feng; Kang Li-shan; Chen Yu-ping
2003-01-01
A generic design model for evolutionary algo rithms is proposed in this paper. The model, which was described by UML in details, focuses on the key concepts and mechanisms in evolutionary algorithms. The model not only achieves separation of concerns and encapsulation of implementations by classification and abstraction of those concepts,it also has a flexible architecture due to the application of design patterns. As a result, the model is reusable, extendible,easy to understand, easy to use, and easy to test. A large number of experiments applying the model to solve many different problems adequately illustrate the generality and effectivity of the model.
Compatible Relaxation and Coarsening in Algebraic Multigrid
Energy Technology Data Exchange (ETDEWEB)
Brannick, J J; Falgout, R D
2009-09-22
We introduce a coarsening algorithm for algebraic multigrid (AMG) based on the concept of compatible relaxation (CR). The algorithm is significantly different from standard methods, most notably because it does not rely on any notion of strength of connection. We study its behavior on a number of model problems, and evaluate the performance of an AMG algorithm that incorporates the coarsening approach. Lastly, we introduce a variant of CR that provides a sharper metric of coarse-grid quality and demonstrate its potential with two simple examples.
Templates for Linear Algebra Problems
Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der
2001-01-01
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 eig
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 ...
Algebraic turbulent heat flux model for prediction of thermal stratification in piping system
International Nuclear Information System (INIS)
The effect of stratification on the flow in bounded geometries is studied through computational fluid dynamics (CFD) and two different modeling of the turbulent heat flux, namely constant turbulent Prandtl number and Algebraic Heat Flux Model (AHFM). The main feature of the work is the evaluation of the effect of buoyancy on the thermal quantities, velocity field and related pressure drop. It has been stated the superiority of the AHFM for the evaluation of turbulent heat flux and temperature field together with a correct evaluation of the thickness of the thermal layer (i.e stratification persistence), in comparison with the simple eddy diffusivity approach. However the adopted model shows over-prediction of the momentum transport in the vertical direction in comparison with the experimental data introducing higher uncertainties for the obtained pressure drop and related Fanning friction factor. (author)
New solutions from algebraic equations for the Skyrme model coupled to a scalar meson
Energy Technology Data Exchange (ETDEWEB)
Braghin, Fabio L. [Universidade Federal do Rio Grande do Norte (IIF/UFRN), Natal, RN (Brazil). Inst. Internacional de Fisica
2010-07-01
Full text: In this work a modified Skyrme model is considered such as to incorporate the interaction of the hedgehog with a scalar field, based on a previous work. The Skyrme model is a model of the nucleon in which the baryon emerges as a topological soliton and its coupling to a scalar field can either correspond to the coupling to the lightest scalar isoscalar meson sigma and also to implement the spontaneous breakdown of chiral symmetry in a consistent way. Therefore it can be related to modifications of a dense interacting medium and it becomes suitable for investigating the role of the symmetry breaking and its restoration. A transcendental algebraic equation is found to be enough to extract a new class of profile solutions of the skyrmion in a constant background. The mass of the corresponding topological soliton was found to decrease considerably in the case small masses are associated to the scalar field. (author)
Tsue, Yasuhiko; Providência, Constança; Providência, João da; Yamamura, Masatoshi
2016-08-01
The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the SU(n) algebra are investigated systematically. The basic idea is to use the SU(2) algebra, which is independent of the SU(n) algebra. This idea has already been presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the SU(2) algebra. If this idea is followed, the minimum weight states are determined for any fermion number appropriately occupying n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n=2, 3, 4, and 5 are discussed in some detail.
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…
Computations in finite-dimensional Lie algebras
Cohen, A.M.; Graaf, W.A. de; Rónyai, L.
2001-01-01
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 packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative
Weekly Fleet Assignment Model and Algorithm
Institute of Scientific and Technical Information of China (English)
ZHU Xing-hui; ZHU Jin-fu; GONG Zai-wu
2007-01-01
A 0-1 integer programming model for weekly fleet assignment was put forward based on linear network and weekly flight scheduling in China. In this model, the objective function is to maximize the total profit of fleet assignment, subject to the constraints of coverage, aircraft flow balance, fleet size, aircraft availability, aircraft usage, flight restriction, aircraft seat capacity,and stopover. Then the branch-and-bound algorithm based on special ordered set was applied to solve the model. At last, a realworld case study on an airline with 5 fleets, 48 aircrafts and 1 786 flight legs indicated that the profit increase was $1591276 one week and the running time was no more than 4 min, which shows that the model and algorithm are fairly good for domestic airline.
Analysis of an algebraic model for the chromophore vibrations of CF$_3$CHFI
Jung, C; Taylor, H S
2004-01-01
We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the hydrogen chromophore's vibrational motion in the molecule $CF_3CHFI$. The original model has 4 degrees of freedom, three positions and one representing interbond couplings. A conserved polyad allows the reduction to 3 degrees of freedom. For most quantum states we can identify the underlying motion that when quantized gives the said state. Most of the classifications, identifications and assignments are done by visual inspection of the already available wave function semiclassically transformed from the number representation to a representation on the reduced dimension toroidal configuration space corresponding to the classical action and angle variables. The concentration of the wave function density to lower dimensional subsets centered on idealized simple lower dimensional organizing structures and the behavior of the phase along such organizing centers already reveals the atomic motion. Extremely little computational work is...
Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry
Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.
2016-09-01
The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.
Two types of loop algebras and their expanding Lax integrable models
Institute of Scientific and Technical Information of China (English)
Yue Chao; Zhang Yu-Feng; Wei Yuan
2007-01-01
Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation Ut-Vx+[U,V]=0,but in this paper,a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials.Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator (J) is presented by constructing a subalgebra (G) of the loop algebra (A)2.As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers,their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.
Structure of $^{23}$Al from a multi-channel algebraic scattering model based on mirror symmetry
Fraser, P R; Massen-Hane, K; Amos, K; Canton, L; Karataglidis, S; van der Knijff, D; Bray, I
2016-01-01
The proton-rich nucleus $^{23}$Al has a ground state just 123 keV below the proton drip-line, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering (MCAS) method to describe states as resonances of a valence proton coupled to a $^{22}$Mg rotor core. Six states with low-excitation energies and defined $J^\\pi$ are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.
Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
Chamseddine, Ali H.; Connes, Alain
2007-11-01
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.
Conceptual explanation for the algebra in the noncommutative approach to the standard model.
Chamseddine, Ali H; Connes, Alain
2007-11-01
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.
Models and Algorithms for Crowdsourcing Discovery
Faridani, Siamak
2012-01-01
The internet enables us to collect and store unprecedented amounts of data. We need better models for processing, analyzing, and making conclusions from the data. In this work, crowdsourcing is presented as a viable option for collecting data, extracting patterns and insights from big data. Humans in collaboration, when provided with appropriate tools, can collectively see patterns, extract insights and draw conclusions from data. We study different models and algorithms for crowdsourcing dis...
Stream Processing Algorithms that model behavior changes
Capponi, Agostino; Chandy, Mani
2005-01-01
This paper presents algorithms that fuse information in multiple event streams to update models that represent system behavior. System behaviors vary over time; for example, an information network varies from heavily loaded to lightly loaded conditions; patterns of incidence of disease change at the onset of pandemics; file access patterns change from proper usage to improper use that may signify insider threat. The models that represent behavior must be updated frequently to adapt to chan...
Efficient Algorithms for Parsing the DOP Model
Goodman, J
1996-01-01
Excellent results have been reported for Data-Oriented Parsing (DOP) of natural language texts (Bod, 1993). Unfortunately, existing algorithms are both computationally intensive and difficult to implement. Previous algorithms are expensive due to two factors: the exponential number of rules that must be generated and the use of a Monte Carlo parsing algorithm. In this paper we solve the first problem by a novel reduction of the DOP model to a small, equivalent probabilistic context-free grammar. We solve the second problem by a novel deterministic parsing strategy that maximizes the expected number of correct constituents, rather than the probability of a correct parse tree. Using the optimizations, experiments yield a 97% crossing brackets rate and 88% zero crossing brackets rate. This differs significantly from the results reported by Bod, and is comparable to results from a duplication of Pereira and Schabes's (1992) experiment on the same data. We show that Bod's results are at least partially due to an e...
Computational Granular Dynamics Models and Algorithms
Pöschel, Thorsten
2005-01-01
Computer simulations not only belong to the most important methods for the theoretical investigation of granular materials, but also provide the tools that have enabled much of the expanding research by physicists and engineers. The present book is intended to serve as an introduction to the application of numerical methods to systems of granular particles. Accordingly, emphasis is placed on a general understanding of the subject rather than on the presentation of the latest advances in numerical algorithms. Although a basic knowledge of C++ is needed for the understanding of the numerical methods and algorithms in the book, it avoids usage of elegant but complicated algorithms to remain accessible for those who prefer to use a different programming language. While the book focuses more on models than on the physics of granular material, many applications to real systems are presented.
Energy Technology Data Exchange (ETDEWEB)
Lashkevich, Michael; Pugai, Yaroslav [Landau Institute for Theoretical Physics, 142432 Chernogolovka, Moscow Region (Russian Federation); Moscow Institute of Physics and Technology, 141707 Dolgoprudny, Moscow Region (Russian Federation)
2013-12-11
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.
Reachability for Finite-State Process Algebras Using Static Analysis
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya; Nielson, Flemming
2011-01-01
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...... 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...
Jorgensen, PET
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
W-algebras, new rational models and completeness of the c=1 classification
International Nuclear Information System (INIS)
Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If c=1-24k, there exists a W(2,3k) algebra for k element of Z+/2 and a W(2,8k) algebra for k element of Z+/4. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these theories are rational. It is shown, that these non-unitary theories complete the classification of all rational theories with effective central charge ceff=1. The results are generalized to the case of extended supersymmetric conformal algebras. (orig.)
W-algebras, new rational models and completeness of the c=1 classification
International Nuclear Information System (INIS)
Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If c = 1 - 24 k, there exists a W(2,3k) algebra for kelement of Z+/2 and a W (2,8k) algebra for k element of Z+/4. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these therories are rational. It is shown, that these non-unitary theories complete the classification of all rational therories with effective central charge ceff = 1. The results are generalized to the case of extended supersymmetric conformal algebras. (orig.)
International Nuclear Information System (INIS)
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 φ42-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 Yukawa2-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.)
Poisson bracket algebra for chiral group elements in the WZNW model
Bimonte, G; Simoni, A; Stern, A
1992-01-01
We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left and right moving chiral group elements. Our computations apply for arbitrary groups and boundary conditions, the latter being characterized by the monodromy matrix. Unlike in previous treatments, they do not require specifying a particular parametrization of the group valued fields in terms of angles spanning the group. We do however find it necessary to make a gauge choice, as the chiral group elements are not gauge invariant observables. (On the other hand, the quadratic form of the Poisson brackets may be defined independent of a gauge fixing.) Gauge invariant observables can be formed from the monodromy matrix and these observables are seen to commute in the quantum theory.
Approach method of the solutions of algebraic models of the N body problem
International Nuclear Information System (INIS)
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
Algebraic geometry methods associated to the one-dimensional Hubbard model
Martins, M. J.
2016-06-01
In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
Directory of Open Access Journals (Sweden)
Shogo Aoyama
2014-10-01
Full Text Available 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.
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
Energy Technology Data Exchange (ETDEWEB)
Aoyama, Shogo, E-mail: spsaoya@ipc.shizuoka.ac.jp
2014-10-07
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.
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
Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models
Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.
2016-10-01
We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.
Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models
Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.
2016-08-01
We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.
Energy Technology Data Exchange (ETDEWEB)
Odesskii, A V [L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow (Russian Federation)
2002-12-31
This survey is devoted to associative Z{sub {>=}}{sub 0}-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations.
Splitting full matrix algebras over algebraic number fields
Ivanyos, Gábor; Schicho, Joseph
2011-01-01
Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is siomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.) As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K.
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.
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.
Evolutionary algorithms in genetic regulatory networks model
Raza, Khalid
2012-01-01
Genetic Regulatory Networks (GRNs) plays a vital role in the understanding of complex biological processes. Modeling GRNs is significantly important in order to reveal fundamental cellular processes, examine gene functions and understanding their complex relationships. Understanding the interactions between genes gives rise to develop better method for drug discovery and diagnosis of the disease since many diseases are characterized by abnormal behaviour of the genes. In this paper we have reviewed various evolutionary algorithms-based approach for modeling GRNs and discussed various opportunities and challenges.
Sparse modeling theory, algorithms, and applications
Rish, Irina
2014-01-01
""A comprehensive, clear, and well-articulated book on sparse modeling. This book will stand as a prime reference to the research community for many years to come.""-Ricardo Vilalta, Department of Computer Science, University of Houston""This book provides a modern introduction to sparse methods for machine learning and signal processing, with a comprehensive treatment of both theory and algorithms. Sparse Modeling is an ideal book for a first-year graduate course.""-Francis Bach, INRIA - École Normale Supřieure, Paris
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 ve...
Institute of Scientific and Technical Information of China (English)
Xianbin Wen; Hua Zhang; Jianguang Zhang; Xu Jiao; Lei Wang
2009-01-01
A novel method that hybridizes genetic algorithm (GA) and expectation maximization (EM) algorithm for the classification of syn-thetic aperture radar (SAR) imagery is proposed by the finite Gaussian mixtures model (GMM) and multiscale autoregressive (MAR)model. This algorithm is capable of improving the global optimality and consistency of the classification performance. The experiments on the SAR images show that the proposed algorithm outperforms the standard EM method significantly in classification accuracy.
Wei, Hui; Ren, Yuan; Wang, Zi Yan
2013-10-01
The implementation of Hubel-Wiesel hypothesis that orientation selectivity of a simple cell is based on ordered arrangement of its afferent cells has some difficulties. It requires the receptive fields (RFs) of those ganglion cells (GCs) and LGN cells to be similar in size and sub-structure and highly arranged in a perfect order. It also requires an adequate number of regularly distributed simple cells to match ubiquitous edges. However, the anatomical and electrophysiological evidence is not strong enough to support this geometry-based model. These strict regularities also make the model very uneconomical in both evolution and neural computation. We propose a new neural model based on an algebraic method to estimate orientations. This approach synthesizes the guesses made by multiple GCs or LGN cells and calculates local orientation information subject to a group of constraints. This algebraic model need not obey the constraints of Hubel-Wiesel hypothesis, and is easily implemented with a neural network. By using the idea of a satisfiability problem with constraints, we also prove that the precision and efficiency of this model are mathematically practicable. The proposed model makes clear several major questions which Hubel-Wiesel model does not account for. Image-rebuilding experiments are conducted to check whether this model misses any important boundary in the visual field because of the estimation strategy. This study is significant in terms of explaining the neural mechanism of orientation detection, and finding the circuit structure and computational route in neural networks. For engineering applications, our model can be used in orientation detection and as a simulation platform for cell-to-cell communications to develop bio-inspired eye chips. PMID:24427212
Algebra-Geometry of Piecewise Algebraic Varieties
Institute of Scientific and Technical Information of China (English)
Chun Gang ZHU; Ren Hong WANG
2012-01-01
Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
The algebraic structure of the Onsager algebra
DATE, ETSURO; Roan, Shi-shyr
2000-01-01
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also discuss the solvable algebra aspect of the Onsager algebra through the formal Lie algebra theory.
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. PMID:27289536
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
Energy Technology Data Exchange (ETDEWEB)
Okuda, Satoshi [Department of Physics, Rikkyo University,Toshima, Tokyo 171-8501 (Japan); Yoshida, Yutaka [High Energy Accelerator Research Organization (KEK),Tsukuba, Ibaraki 305-0801 (Japan)
2014-03-03
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.
Constrained WZWN models on G/{S⊗U(1)"n} and exchange algebra of G-primaries
Energy Technology Data Exchange (ETDEWEB)
Aoyama, Shogo, E-mail: spsaoya@ipc.shizuoka.ac.jp; Ishii, Katsuyuki
2013-11-11
Consistently constrained WZWN models on G/{S⊗U(1)"n} is given by constraining currents of the WZWN models with G. Poisson brackets are set up on the light-like plane. Using them we show the Virasoro algebra for the energy–momentum tensor of constrained WZWN models. We find a G-primary which satisfies a classical exchange algebra in an arbitrary representation of G. The G-primary and the constrained currents are also shown to obey the conformal transformation with respect to the energy–momentum tensor. It is checked that conformal weight of the constrained currents is 0. This is necessary for the consistency for our formulation of constrained WZWN models.
Algebraic stress model for axial flow in a bare rod-bundle
International Nuclear Information System (INIS)
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
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.
Energy Technology Data Exchange (ETDEWEB)
Choudhury, A.G.; Chowdhury, A.R. [Jadavpur Univ., Calcutta (India)
1996-08-01
Intertwining relations for the quantum R-matrix of the SU{sub p,q}(2) invariant spin chain are obtained and the corresponding face model is deduced. An important difference is seen to arise due to the asymmetry generated by the parameters p and q, which leads to a asymmetric face model. An algebraic Bethe ansatz is set up and solved with the help of these intertwining vectors.
Zhang, Yue; Zheng, Yan; Liu, Xi; Zhang, Qingling; Li, Aihua
2016-11-01
This study considers a class of differential algebraic stage-structured bio-economic models with stochastic fluctuations. The stochastic bio-economic model is simplified to an Itô equation using the stochastic averaging method. The stochastic stability, Hopf bifurcation, and P-bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems. Numerical simulations are presented to illustrate our main results.
Robot Control Based On Spatial-Operator Algebra
Rodriguez, Guillermo; Kreutz, Kenneth K.; Jain, Abhinandan
1992-01-01
Method for mathematical modeling and control of robotic manipulators based on spatial-operator algebra providing concise representation and simple, high-level theoretical frame-work for solution of kinematical and dynamical problems involving complicated temporal and spatial relationships. Recursive algorithms derived immediately from abstract spatial-operator expressions by inspection. Transition from abstract formulation through abstract solution to detailed implementation of specific algorithms to compute solution greatly simplified. Complicated dynamical problems like two cooperating robot arms solved more easily.
A Clifford Algebra approach to the Discretizable Molecular Distance Geometry Problem
Andrioni, Alessandro
2013-01-01
The Discretizable Molecular Distance Geometry Problem (DMDGP) consists in a subclass of the Molecular Distance Geometry Problem for which an embedding in ${\\mathbb{R}^3}$ can be found using a Branch & Prune (BP) algorithm in a discrete search space. We propose a Clifford Algebra model of the DMDGP with an accompanying version of the BP algorithm.
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.
Link mining models, algorithms, and applications
Yu, Philip S; Faloutsos, Christos
2010-01-01
This book presents in-depth surveys and systematic discussions on models, algorithms and applications for link mining. Link mining is an important field of data mining. Traditional data mining focuses on 'flat' data in which each data object is represented as a fixed-length attribute vector. However, many real-world data sets are much richer in structure, involving objects of multiple types that are related to each other. Hence, recently link mining has become an emerging field of data mining, which has a high impact in various important applications such as text mining, social network analysi
Coherent States and Schwinger Models for Pseudo Generalization of the Heisenberg Algebra
Fakhri, H.; Mojaveri, B.; Dehghani, A.
We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with {PT} and {C} symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are {T}-pseudo-Hermiticity and {P}-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.
C*-index of observable algebras in G-spin model
Institute of Scientific and Technical Information of China (English)
JIANG; Lining
2005-01-01
In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action of D(G; H),which is a subalgebra of D(G) determined by a subgroup H of G,so that F becomes a modular algebra.The concrete construction of D(G; H)-invariant subspace AH in F is given.By constructing the quasi-basis of conditional expectation γG of AH onto AG,the C*-index of γG is exactly the index of H in G.
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.
Chisolm, Eric
2012-01-01
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) and includes it as a subset. Over the years, various parts of Clifford algebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that geometric algebra, not the reduced version we use today, deserves to be the standard "vector algebra." My goal in these notes is to describe geometric al...
Mokler, Claus
2009-01-01
The face monoid described in [M1] acts on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group. We found in [M5] two natural extensions of the action of the Kac-Moody group on its building to actions of the face monoid on the building. Now we give an algebraic geometric model of one of these actions of the face monoid. The building is obtained as a part of the spectrum of homogeneous prime ideals of the Cartan algebra of the Kac-Moody group. We describe the full spectrum of homogeneous prime ideals of the Cartan algebra.
Issa, A. Nourou
2010-01-01
Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra (i.e. a Hom-nonassociative algebra) is a Hom-Akivis algebra. It is shown that non-Hom-associative algebras can be obtained from nonassociative algebras by twisting along algebra automorphisms while Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms. It is pointed out that a Hom-Akivis algebra associated to a Hom-alternative algebra is a Hom-M...
Elements of algebraic coding systems
Cardoso da Rocha, Jr, Valdemar
2014-01-01
Elements of Algebraic Coding Systems is an introductory textto algebraic coding theory. In the first chapter, you'll gain insideknowledge of coding fundamentals, which is essential for a deeperunderstanding of state-of-the-art coding systems.This book is a quick reference for those who are unfamiliar withthis topic, as well as for use with specific applications such as cryptographyand communication. Linear error-correcting block codesthrough elementary principles span eleven chapters of the text.Cyclic codes, some finite field algebra, Goppa codes, algebraic decodingalgorithms, and applications in public-key cryptography andsecret-key cryptography are discussed, including problems and solutionsat the end of each chapter. Three appendices cover the Gilbertbound 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 finitefield Fourier transform and the Euclidean algorithm for polynomials.
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
Holtz, Olga; Ron, Amos
2007-01-01
A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\\cal H}(X)$. This well-known line of study is particularly interesting in case $n\\eqbd\\rank X \\ll N$. We enhance this study to an algebraic level, and associate $X$ with three algebraic structures, referred herein as {\\it external, central, and internal.} Each algebraic structure is ...
A Multiple Model Approach to Modeling Based on LPF Algorithm
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Input-output data fitting methods are often used for unknown-structure nonlinear system modeling. Based on model-on-demand tactics, a multiple model approach to modeling for nonlinear systems is presented. The basic idea is to find out, from vast historical system input-output data sets, some data sets matching with the current working point, then to develop a local model using Local Polynomial Fitting (LPF) algorithm. With the change of working points, multiple local models are built, which realize the exact modeling for the global system. By comparing to other methods, the simulation results show good performance for its simple, effective and reliable estimation.``
Institute of Scientific and Technical Information of China (English)
XIEBing_Hao; ZHANGHong－Biao; 等
2002-01-01
An algebraic diagonalization method is proposed.As two examples,the Hamiltonians of BCS ground state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2),SU(1,1) Lie algebraic method,respectively.Meanwhile,the eignenstates of the above two models are revealed to be SU(2),SU(1,1) coherent states,respectively,The relation between the usual Bogoliubov-Valatin transformation and the algebraic method in a special case is also discussed.
几何模型在线性代数教学中的应用%Application of Geometric Model in Linear Algebra Teaching
Institute of Scientific and Technical Information of China (English)
席政军
2013-01-01
Through analyzing the relationship between geometric model and linear algebra, this article focuses on the application of geometric model in linear algebra, and discusses the classroom teaching of linear algebra.%本文通过几何模型与线性代数之间的关系，重点讨论几何模型在线性代数中的应用，并对线性代数课堂教学进行了初步探讨。
Directory of Open Access Journals (Sweden)
Murali Bosukonda
2011-01-01
Full Text Available This paper reveals mathematical models of the simplest Mamdani PI/PD controllers which employ two fuzzy sets (N: negative and P: positive on the universe of discourse (UoD of each of two input variables (displacement and velocity and three fuzzy sets (N: negative, Z: zero, and P: positive on the UoD of output variable (control output in the case of PD, and incremental control output in the case of PI. The basic constituents of these models are algebraic product/minimum AND, bounded sum/algebraic sum/maximum OR, algebraic product inference, three linear fuzzy control rules, and Center of Sums (CoS defuzzification. Properties of all these models are investigated. It is shown that all these controllers are different nonlinear PI/PD controllers with their proportional and derivative gains changing with the inputs. The proposed models are significant and useful to control community as they are completely new and qualitatively different from those reported in the literature.
Super Lie n-algebra extensions, higher WZW models, and super p-branes with tensor multiplet fields
Fiorenza, Domenico; Schreiber, Urs
2013-01-01
We formalize higher dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type sigma-model branes (open brane ending on background brane) are encoded precisely in (super-) L-infinity-extension theory and how the resulting "extended (super-)spacetimes" formalize spacetimes containing sigma model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super p-brane spectrum of superstring/M-theory is realized this way, including the pure sigma-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional spacetime with an M2-brane condensate turns out to be the ...
Warehouse Optimization Model Based on Genetic Algorithm
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Guofeng Qin
2013-01-01
Full Text Available This paper takes Bao Steel logistics automated warehouse system as an example. The premise is to maintain the focus of the shelf below half of the height of the shelf. As a result, the cost time of getting or putting goods on the shelf is reduced, and the distance of the same kind of goods is also reduced. Construct a multiobjective optimization model, using genetic algorithm to optimize problem. At last, we get a local optimal solution. Before optimization, the average cost time of getting or putting goods is 4.52996 s, and the average distance of the same kinds of goods is 2.35318 m. After optimization, the average cost time is 4.28859 s, and the average distance is 1.97366 m. After analysis, we can draw the conclusion that this model can improve the efficiency of cargo storage.
Institute of Scientific and Technical Information of China (English)
ZHAO xiao-Song; L(U) Jian-Qin
2009-01-01
Both the PIC(Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams.The PIC model is to calculate the space charge field,which is blended into the external field,and then simulate the trajectories of particles in the total field;the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes.Two simulation codes based on the two methods are developed respectively,and the simulated results of transport in a set of electrostatic lenses are compared.It is found that the results from the two codes are in agreement with each other.and both approaches have their own merits.
Surfaces immersed in su(N+1) Lie algebras obtained from the CP{sup N} sigma models
Energy Technology Data Exchange (ETDEWEB)
Grundland, A M [Centre de Recherches Mathematiques, Universite de Montreal, CP 6128, Succ. Centre-ville, Montreal (Ciheam) H3C 3J7 (Canada) Universite du Quebec, Trois-Rivieres CP500 (QC) G9A 5H7 (Canada); Strasburger, A [Department of Mathematical Economics, Warsaw Agricultural University, ul. Nowoursynowska 166, 02-787 Warsaw (Poland); Zakrzewski, W J [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)
2006-07-21
We study some geometrical aspects of two-dimensional orientable surfaces arising from the study of CP{sup N} sigma models. To this aim we employ an identification of R{sup N(N+2)} with the Lie algebra su(N+1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CP{sup N} model defining it. Further, the first and second fundamental forms, the Gaussian curvature, the mean curvature vector, the Willmore functional and the topological charge of surfaces are expressed in terms of this solution. We present detailed implementation of these results for surfaces immersed in su(2) and su(3) Lie algebras.
Computer algebra in spacetime embedding
Roque, Waldir L
2014-01-01
In this paper we describe an algorithm to determine the vectors normal to a space-time V4 embedded in a pseudo-Euclidean manifold M4+n. An application of this algorithm is given considering the Schwarzchild space-time geometry embedded in a 6 dimensional pseudo-Euclidean manifold, using the algebraic computing system REDUCE.
On some spurious mode issues in shallow-water models using a linear algebra approach
Le Roux, D. Y.; Sène, A.; Rostand, V.; Hanert, E.
Numerical methods that are usually employed in ocean modelling are typically finite-difference, finite and spectral-element techniques. For most of these methods the coupling between the momentum and continuity equations is a delicate problem and it usually leads to spurious solutions in the representation of inertia-gravity waves. The spurious modes have a wide range of characteristics and may take the form of pressure (surface-elevation), velocity and/or Coriolis modes. The modes usually cause aliasing and an accumulation of energy in the smallest-resolvable scale, leading to noisy solutions. The Fourier analysis has proven practical and beneficial to describe the spurious solutions of several classical schemes. However it is restricted to uniform meshes on which the variables are regularly distributed. In this paper, a linear algebra approach is proposed to study the existence and the behaviour of stationary spurious modes associated with zero frequency, for some popular finite-difference and finite-element grids. The present approach is performed on uniform meshes but it applies equally well to regular as well as unstructured meshes with irregular geometry for the finite-element schemes.
Tze, Chia-Hsiung; Nam, Soonkeon
1989-08-01
Exploiting the unique connection between the division algebras of the complex numbers ( C), quaternions ( H), octonions ( Ω) and the essential Hopf maps S2 n - 1 → Sn with n = 2, 4, 8, we study Sn - 2 -membrane solitons in three D-dimensional KP(1) σ-models with a Hopf term, (D, K) = (3, C), (7, H), and (15, Ω). We present a comprehensive analysis of their topological phase entanglements. Extending Polyakov's approach to Fermi-Bose transmutations to higher dimensions, we detail a geometric regularization of Gauss' linking coefficient, its connections to the self-linking, twisting, writhing numbers of the Feynman paths of the solitons in their thin membrane limit. Alternative forms of the Hopf invariant show the latter as an Aharonov-Bohm-Berry phase of topologically massive, rank ( n - 1) antisymmetric tensor U(1) gauge fields coupled to the Sn - 2 -membranes. Via a K-bundle formulation of the dynamics of electrically and magnetically charged extended objects these phases are shown to induce a dyon-like structure on these membranes. We briefly discuss the connections to harmonic mappings, higher dimensional monopoles and instantons. We point out the relevance of the Gauss-Bonnet-Chern theorem on the connection between spin and statistics. By way of the topology of the infinite groups of sphere mappings Sn → Sn, n = 2, 4, 8, we also analyze the implications of the Hopf phases on the fractional spin and statistics of the membranes.
$\\eta_{c}$ Elastic and Transition Form Factors: Contact Interaction and Algebraic Model
Bedolla, Marco A; Cobos-Martínez, J J; Bashir, Adnan
2016-01-01
For the flavor-singlet heavy quark system of charmonia in the pseudoscalar ($\\eta_c(1S)$) channel, we calculate the elastic (EFF) and transition form factors (TFF) ($\\eta_c(1S) \\rightarrow \\gamma \\gamma^*$) for a wide range of photon momentum transfer squared ($Q^2$). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDE) and Bethe-Salpeter equation (BSE) treatment of a vector$\\times$vector contact interaction (CI). We also employ an algebraic model (AM), developed earlier to describe the light quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The CI results agree with the lattice data for low $Q^2$. For $Q^2 \\geqslant Q_0^2$, the results start deviating from the lattice results by more than $20 \\%$. $Q_0^2 \\thickapprox 2.5 {\\rm GeV}^2$ for the EFF and $\\thickapprox 25 {\\rm GeV}^2$ for the TFF. We also present the results for the EFF, TFF as well as $\\eta_c(1S)$ parton distribution amplitude for the AM. Wherev...
McKeague, Charles P
1986-01-01
Elementary Algebra, Third Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first ponders on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the elimination method, solving linear systems by graphing, word problems, addition property of equality, solving linear equations, linear inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then takes a look at exponents and polynomials, factoring, and rational expressions. Topics include reducing ra
McKeague, Charles P
1981-01-01
Elementary Algebra 2e, Second Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first tackles the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the substitution method, solving linear systems by graphing, solutions to linear equations in two variables, multiplication property of equality, word problems, addition property of equality, and subtraction, addition, multiplication, and division of real numbers. The manuscript then examines exponents and polynomials, factoring, and rational e
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.
Which multiplier algebras are $W^*$-algebras?
Akemann, Charles A.; Amini, Massoud; Asadi, Mohammad B.
2013-01-01
We consider the question of when the multiplier algebra $M(\\mathcal{A})$ of a $C^*$-algebra $\\mathcal{A}$ is a $ W^*$-algebra, and show that it holds for a stable $C^*$-algebra exactly when it is a $C^*$-algebra of compact operators. This implies that if for every Hilbert $C^*$-module $E$ over a $C^*$-algebra $\\mathcal{A}$, the algebra $B(E)$ of adjointable operators on $E$ is a $ W^*$-algebra, then $\\mathcal{A}$ is a $C^*$-algebra of compact operators. Also we show that a unital $C^*$-algebr...
A new model for algebraic Rossby solitary waves in rotation fluid and its solution
Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru
2015-09-01
A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.
Genetic Algorithm Approaches to Prebiobiotic Chemistry Modeling
Lohn, Jason; Colombano, Silvano
1997-01-01
We model an artificial chemistry comprised of interacting polymers by specifying two initial conditions: a distribution of polymers and a fixed set of reversible catalytic reactions. A genetic algorithm is used to find a set of reactions that exhibit a desired dynamical behavior. Such a technique is useful because it allows an investigator to determine whether a specific pattern of dynamics can be produced, and if it can, the reaction network found can be then analyzed. We present our results in the context of studying simplified chemical dynamics in theorized protocells - hypothesized precursors of the first living organisms. Our results show that given a small sample of plausible protocell reaction dynamics, catalytic reaction sets can be found. We present cases where this is not possible and also analyze the evolved reaction sets.
Directory of Open Access Journals (Sweden)
Yuan-Shyi Peter Chiu
2013-02-01
Full Text Available 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 each cycle. The objective is to determine the optimal replenishment lot size and optimal number of shipments that minimizes total expected costs for such a specific supply chains system. Conventional method is by the use of differential calculus on system cost function to derive the optimal policy (Chiu et al al., 2012c, whereas the proposed algebraic approach is a straightforward method that enables practitioners who may not have sufficient knowledge of calculus to understand and manage more effectively the real-life systems.
Zhang, Tian; Zhang, Daijun; Li, Zhenliang; Cai, Qing
2010-05-01
The calibration of ASMs is a prerequisite for their application to simulation of a wastewater treatment plant. This work should be made based on the evaluation of structural identifiability of model parameters. An EBPR sub-model including denitrification phosphorus removal has been incorporated in ASM2d. Yet no report is presented on the structural identifiability of the parameters in the EBPR sub-model. In this paper, the differential algebra approach was used to address this issue. The results showed that the structural identifiability of parameters in the EBPR sub-model could be improved by increasing the measured variables. The reduction factor eta(NO)(3) was identifiable when combined data of aerobic process and anoxic process were assumed. For K(PP), X(PAO) and q(PHA) of the anaerobic process to be uniquely identifiable, one of them is needed to be determined by other ways. Likewise, if prior information on one of the parameters, K(PHA), X(PAO) and q(PP) of the aerobic process, is known, all the parameters are identifiable. The above results could be of interest to the parameter estimation of the EBPR sub-model. The algorithm proposed in the paper is also suitable for other sub-models of ASMs.
Algebraic totality, towards completeness
Tasson, Christine
2009-01-01
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans ${\\mathcal{B}}$ and a conditional operator, which can be interpreted in this model. We prove completeness at type ${\\mathcal{B}}^n\\to{\\mathcal{B}}$ for every n by an algebraic metho...
Lazeroms, W. M.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.; Svensson, G.
2014-12-01
Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer (ABL). Explicit algebraic turbulence models are a class of parametrizations that, on the one hand, are more advanced than standard eddy-diffusivity relations. On the other hand, they are signficantly easier to handle numerically than models that require the solution of the full flux-budget equations. To derive the algebraic model, we apply the assumption that transport terms of dimensionless fluxes can be neglected. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux, which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow. Recent work has been aimed at testing the model in an atmospheric context. The first of these tests makes use of the GABLS1 case, in which a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES (see attached figure). Interestingly, the results are very close to the outcome of the recently developed Energy-Flux-Budget (EFB) closure by Zilitinkevich et al. (2013). A detailed discussion of the similarities and differences between these models will be given, which can give insight in the more general gap between engineering and
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. PMID:27186457
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...... model being correct is computed through a likelihood function for each model. The study presented a simple technique to introduce additional models into the system using deterministic acceleration which basically defines the dynamics of the system. Therefore, based on this value more motion models can...... be employed to increase the coverage. Finally, the combined estimate is obtained using posteriori probabilities from different filter models. The implemented approach provides an adaptive scheme for selecting various number of motion models. Motion model description is important as it defines the kind...
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.
Energy Technology Data Exchange (ETDEWEB)
Casasent, D.; Ghosh, A.
1983-01-01
Many of the linear algebra operations and algorithms possible on optical matrix-vector processors are reviewed. Emphasis is given to the use of direct solutions and their realization on systolic optical processors. As an example, implicit and explicit solutions to partial differential equations are considered. The matrix-decomposition required is found to be the major operation recommended for optical realization. The pipelining and flow of data and operations are noted to be key issues in the realization of any algorithm on an optical systolic array processor. A realization of the direct solution by householder qr decomposition is provided as a specific case study. 19 references.
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic variety is a generalization of the classical algebraic variety. This paper discusses some properties of piecewise algebraic varieties and their coordinate rings based on the knowledge of algebraic geometry.
Algebras, dialgebras, and polynomial identities
Bremner, Murray R
2012-01-01
This is a survey of some recent developments in the theory of associative and nonassociative dialgebras, with an emphasis on polynomial identities and multilinear operations. We discuss associative, Lie, Jordan, and alternative algebras, and the corresponding dialgebras; the KP algorithm for converting identities for algebras into identities for dialgebras; the BSO algorithm for converting operations in algebras into operations in dialgebras; Lie and Jordan triple systems, and the corresponding disystems; and a noncommutative version of Lie triple systems based on the trilinear operation abc-bca. The paper concludes with a conjecture relating the KP and BSO algorithms, and some suggestions for further research. Most of the original results are joint work with Raul Felipe, Luiz A. Peresi, and Juana Sanchez-Ortega.
A Deductive Approach towards Reasoning about Algebraic Transition Systems
Jun Fu; Jinzhao Wu; Hongyan Tan
2015-01-01
Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semanti...
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.
Algorithm for Realistic Modeling of Graphitic Systems
Directory of Open Access Journals (Sweden)
A.V. Khomenko
2011-01-01
Full Text Available An algorithm for molecular dynamics simulations of graphitic systems using realistic semiempirical interaction potentials of carbon atoms taking into account both short-range and long-range contributions is proposed. Results of the use of the algorithm for a graphite sample are presented. The scalability of the algorithm depending on the system size and the number of processor cores involved in the calculations is analyzed.
Dimensionally Distributed Learning: Models and Algorithm
Zheng, Haipeng; Kulkarni, Sanjeev R.; Poor, H. Vincent
2008-01-01
This paper introduces a framework for regression with dimensionally distributed data with a fusion center. A cooperative learning algorithm, the iterative conditional expectation algorithm (ICEA), is designed within this framework. The algorithm can effectively discover linear combinations of individual estimators trained by each agent without transferring and storing large amount of data amongst the agents and the fusion center. The convergence of ICEA is explored. Specifically, for a two ag...
Hazewinkel, Michiel
2004-01-01
Two important generalizations of the Hopf algebra of symmetric functions are the Hopf algebra of noncommutative symmetric functions and its graded dual the Hopf algebra of quasisymmetric functions. A common generalization of the latter is the selfdual Hopf algebra of permutations (MPR Hopf algebra). This latter Hopf algebra can be seen as a Hopf algebra of endomorphisms of a Hopf algebra. That turns out to be a fruitful way of looking at things and gives rise to wide ranging further generaliz...
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...
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…
Caglayan, Günhan
2013-01-01
This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…
Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations
Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie
2015-01-01
The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…
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…
Algebraic Squares: Complete and Incomplete.
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
RSA算法中Z*(φ)(n)的代数结构研究%Study on Algebraic Structure of Z*(φ)(n) in RSA Algorithm
Institute of Scientific and Technical Information of China (English)
裴东林; 胡建军; 李旭
2013-01-01
[Abstract] Based on the theory of quadratic residues, this paper considers the algebraic structure of Z*φ(n) in the two order strong RSA algorithm. It is proved that the element α of Z*φ(n) gets maximal order if and only if gcd(α±l,n1) = 1, and the numbers of quadratic residues in the group Z*φ(n) is φ(φ(n))/8 .Z*φ(n) is divided up by the group which is composed of all quadratic residues, and all cosets form a Klein eight-group. It proves that the group Z*φ(n) can be generated by seven elements of quadratic non-residues.%应用二次剩余理论,对二阶强RSA算法中Z*(φ)(n)的代数结构进行研究,证明Z*(φ)(n)中元素a取最大阶的充要条件为gcd(a±1,n1)=1,以及任意元素的阶Z*(φ)(n)中模(φ)(n)的二次剩余个数为(φ)(φ)(n))/8,以所有二次剩余构成的群对Z*(φ)(n)进行分割,利用所有陪集构成一个Klein八元群,在此基础上证明Z*(φ)(n)可由7个二次非剩余元素生成.
International Nuclear Information System (INIS)
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
GOLDMAN ALGEBRA, OPERS AND THE SWAPPING ALGEBRA
Labourie, François
2012-01-01
We define a Poisson Algebra called the {\\em swapping algebra} using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra -- called the {\\em algebra of multifractions} -- as an algebra of functions on the space of cross ratios and thus as an algebra of functions on the Hitchin component as well as on the space of $\\mathsf{SL}_n(\\mathbb R)$-opers with trivial holonomy. We relate this Poisson algebra to the Atiyah--Bott--Goldman symple...
Directory of Open Access Journals (Sweden)
G.C. Rao
2012-11-01
Full Text Available A C- algebra is the algebraic form of the 3-valued conditional logic, which was introduced by F. Guzman and C. C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra in terms of congruences are given. It is proved that the set of all central elements B(A is isomorphic to the Boolean algebra of all C-algebras Sa, where a B(A. It is also proved that B(A is isomorphic to the Boolean algebra of all C-algebras Aa, where a B(A.
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
Allenby, Reg
1995-01-01
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.Solutions to the exercises are available onlin
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
Evrendilek, Fatih
2007-01-01
This study aims at quantifying spatio-temporal dynamics of monthly mean daily incident photosynthetically active radiation (PAR) over a vast and complex terrain such as Turkey. The spatial interpolation method of universal kriging, and the combination of multiple linear regression (MLR) models and map algebra techniques were implemented to generate surface maps of PAR with a grid resolution of 500 × 500 m as a function of five geographical and 14 climatic variables. Performance of the geostatistical and MLR models was compared using mean prediction error (MPE), root-mean-square prediction error (RMSPE), average standard prediction error (ASE), mean standardized prediction error (MSPE), root-mean-square standardized prediction error (RMSSPE), and adjusted coefficient of determination (R2adj.). The best-fit MLR- and universal kriging-generated models of monthly mean daily PAR were validated against an independent 37-year observed dataset of 35 climate stations derived from 160 stations across Turkey by the Jackknifing method. The spatial variability patterns of monthly mean daily incident PAR were more accurately reflected in the surface maps created by the MLR-based models than in those created by the universal kriging method, in particular, for spring (May) and autumn (November). The MLR-based spatial interpolation algorithms of PAR described in this study indicated the significance of the multifactor approach to understanding and mapping spatio-temporal dynamics of PAR for a complex terrain over meso-scales.
D. Haritha; K. Srinivasa Rao; Ch.Satyanarayana
2012-01-01
A robust and efficient face recognition system was developed and evaluated. The each individual face is characterized by 2D-DCT coefficients which follows a finite mixture of doubly truncated Gaussian distribution. In modelling the features vector of the face the number of components (in the mixture model) are determined by hierarchical clustering. The model parameters are estimated using EM algorithm. The face recognition algorithm is developed by maximum likelihood under Baysian frame. The ...
Spatial-Operator Algebra For Robotic Manipulators
Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.
1991-01-01
Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.
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...
Indian Academy of Sciences (India)
Tomás L Gómez
2001-02-01
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector bundles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory.
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Fast algorithms for transport models. Final report
International Nuclear Information System (INIS)
This project has developed a multigrid in space algorithm for the solution of the SN 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))
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.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2009-01-01
Property testing was initially studied from various motivations in 1990's.A code C (∩)GF(r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector's coordinates.The problem of testing codes was firstly studied by Blum,Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs).How to characterize locally testable codes is a complex and challenge problem.The local tests have been studied for Reed-Solomon (RS),Reed-Muller (RM),cyclic,dual of BCH and the trace subcode of algebraicgeometric codes.In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions).We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Homological Dimensions of the Extension Algebras of Monomial Algebras
Institute of Scientific and Technical Information of China (English)
Hong Bo SHI
2015-01-01
The main objective of this paper is to study the dimension trees and further the homo-logical dimensions of the extension algebras — dual and trivially twisted extensions — with a unified combinatorial approach using the two combinatorial algorithms — Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden sub-tle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more eﬃ cient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras.
Wang, Dan; Wang, Linxiang; Melnik, Roderick
2016-07-01
In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature.
Institute of Scientific and Technical Information of China (English)
O.G.Martynenko; V.N.Korovkin
1992-01-01
An algebraic model of turbulence,involving buyancy forces,is used for calculating velocity and temperature fields in plane turbulent vertical jets in a non-homogeneous stagnant medium,A new approach to the solution of the governing system of partial differential differental equations (Continuity ,Conservation of momentum,heat (buoyancy),turbulent kinetic energy,dissipation rate and mean quadratic temperature fluctuation)is suggested which is based on the intrduction of mathematical variables.Comparison is made between the results of the present calculations with experimental and numerical data of ther authors.
Performance analysis of FXLMS algorithm with secondary path modeling error
Institute of Scientific and Technical Information of China (English)
SUN Xu; CHEN Duanshi
2003-01-01
Performance analysis of filtered-X LMS (FXLMS) algorithm with secondary path modeling error is carried out in both time and frequency domain. It is shown firstly that the effects of secondary path modeling error on the performance of FXLMS algorithm are determined by the distribution of the relative error of secondary path model along with frequency.In case of that the distribution of relative error is uniform the modeling error of secondary path will have no effects on the performance of the algorithm. In addition, a limitation property of FXLMS algorithm is proved, which implies that the negative effects of secondary path modeling error can be compensated by increasing the adaptive filter length. At last, some insights into the "spillover" phenomenon of FXLMS algorithm are given.
Zapatrin, R R
1998-01-01
An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. As an example, a toy model producing spacetimes of four points with different topologies is presented. The possibility of incorporating this scheme into the framework of non-commutative differential geometry is discussed.
Clifford algebra, geometric algebra, and applications
Lundholm, Douglas
2009-01-01
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (then called geometric algebra) with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra. The various applications presented include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.
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
O'Hanlon, Angela L.
2011-01-01
The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…
Central simple Poisson algebras
Institute of Scientific and Technical Information of China (English)
SU; Yucai; XU; Xiaoping
2004-01-01
Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
El-Chaar, Caroline
2012-01-01
In this thesis, four realizations of the Onsager algebra are explored. We begin with its original definition as introduced by Lars Onsager. We then examine how the Onsager algebra can be presented as a Lie algebra with two generators and two relations. The third realization of the Onsager algebra consists of viewing it as an equivariant map algebra which then gives us the tools to classify its closed ideals. Finally, we examine the Onsager algebra as a subalgebra of the tetrahedron algebra. U...
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Z2n Grading
Institute of Scientific and Technical Information of China (English)
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 Z2n 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 AdS5 × S5 string theory (when the ghost terms are omitted).%The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Z2n 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 AdS5 × S5 string theory (when the ghost terms are omitted).Bena,Polchinski and Roiban[1] found an infinite number of non-local classically conserved charges for the Grecn-Schwarz superstring in AdS5 × S5 background.[2] Similar results were obtained for some other strings[3-9] that propagate in AdS space-time,as discussed in Refs.[7 9].Vallilo[10] showed that such charges also exist in the pure-spinor formalism of the superstring in AdS5 × S5.Bianchi and Klǔson[11] gave the current algebra of the pure-spinor superstring.Berkovits[12] proved that the nonlocal charges in the string theory are BRST-invariant and physical.
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.
Falcon, Raymond
2009-01-01
Teachers use action research in order to improve their teaching and student learning. This action research will analyze students' algebraic reasoning in finding values of variables in systems of equations pictorially and algebraically. This research will look at students solving linear systems of equations without knowing the algebraic algorithms.…
Decomposition of semigroup algebras
Boehm, Janko; Nitsche, Max Joachim
2011-01-01
Let A \\subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.
Heterogenous Acceleration for Linear Algebra in Multi-coprocessor Environments
Energy Technology Data Exchange (ETDEWEB)
Luszczek, Piotr R [ORNL; Tomov, Stanimire Z [ORNL; Dongarra, Jack J [ORNL
2015-01-01
We present an efficient and scalable programming model for the development of linear algebra in heterogeneous multi-coprocessor environments. The model incorporates some of the current best design and implementation practices for the heterogeneous acceleration of dense linear algebra (DLA). Examples are given as the basis for solving linear systems' algorithms - the LU, QR, and Cholesky factorizations. To generate the extreme level of parallelism needed for the efficient use of coprocessors, algorithms of interest are redesigned and then split into well-chosen computational tasks. The tasks execution is scheduled over the computational components of a hybrid system of multi-core CPUs and coprocessors using a light-weight runtime system. The use of lightweight runtime systems keeps scheduling overhead low, while enabling the expression of parallelism through otherwise sequential code. This simplifies the development efforts and allows the exploration of the unique strengths of the various hardware components.
Constructing semisimple subalgebras of semisimple Lie algebras
de Graaf, Willem A
2010-01-01
Algorithms are described that help with obtaining a classification of the semisimple subalgebras of a given semisimple Lie algebra, up to linear equivalence. The algorithms have been used to obtain classifications of the semisimple subalgebras of the simple Lie algebras of ranks <= 8. These have been made available as a database inside the SLA package of GAP4. The subalgebras in this database are explicitly given, as well as the inclusion relations among them.
Isomorphisms of Algebraic Number Fields
van Hoeij, Mark
2010-01-01
Let $\\mathbb{Q}(\\alpha)$ and $\\mathbb{Q}(\\beta)$ be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, $\\mathbb{Q}(\\beta) \\rightarrow \\mathbb{Q}(\\alpha)$. The algorithm is particularly efficient if the number of isomorphisms is one.
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.
Chirvasitu, Alex; Smith, S. Paul
2015-01-01
This paper examines a general method for producing twists of a comodule algebra by tensoring it with a torsor then taking co-invariants. We examine the properties that pass from the original algebra to the twisted algebra and vice versa. We then examine the special case where the algebra is a 4-dimensional Sklyanin algebra viewed as a comodule algebra over the Hopf algebra of functions on the non-cyclic group of order 4 with the torsor being the 2x2 matrix algebra. The twisted algebra is an "...
Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids
Directory of Open Access Journals (Sweden)
Marco V. José
2014-08-01
Full Text Available Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C, and the Human tRNA code (H-tRNA-C. New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state.
Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi
2014-03-01
In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.
Nonmonotonic logics and algebras
Institute of Scientific and Technical Information of China (English)
CHAKRABORTY Mihir Kr; GHOSH Sujata
2008-01-01
Several nonmonotonie logic systems together with their algebraic semantics are discussed. NM-algebra is defined.An elegant construction of an NM-algebra starting from a Boolean algebra is described which gives rise to a few interesting algebraic issues.
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.
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
Asymptotic algebra of quantum electrodynamics
Herdegen, Andrzej
2004-01-01
The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
Directory of Open Access Journals (Sweden)
Vladimir S. Gerdjikov
2006-02-01
Full Text Available The construction of a family of real Hamiltonian forms (RHF for the special class of affine 1+1-dimensional Toda field theories (ATFT is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E_6 and E_7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.
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.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
António, N Cirilo; Salom, I
2014-01-01
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 corresponding Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the Bethe vectors through the so-called quasi-classical limit.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Belliard, Samuel; Crampé, Nicolas
2013-11-01
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.
Heisenberg XXX model with general boundaries: Eigenvectors from Algebraic Bethe ansatz
Belliard, S
2013-01-01
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.
Algebraic Bethe ansatz for the sl(2) Gaudin model with boundary
António, N Cirilo; Ragoucy, E; Salom, I
2015-01-01
Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.
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.
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
A motion retargeting algorithm based on model simplification
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A new motion retargeting algorithm is presented, which adapts the motion capture data to a new character. To make the resulting motion realistic, the physically-based optimization method is adopted. However, the optimization process is difficult to converge to the optimal value because of high complexity of the physical human model. In order to address this problem, an appropriate simplified model automatically determined by a motion analysis technique is utilized, and then motion retargeting with this simplified model as an intermediate agent is implemented. The entire motion retargeting algorithm involves three steps of nonlinearly constrained optimization: forward retargeting, motion scaling and inverse retargeting. Experimental results show the validity of this algorithm.
Quantum Monte Carlo methods algorithms for lattice models
Gubernatis, James; Werner, Philipp
2016-01-01
Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in ...
Quaternionen and Geometric Algebra (Quaternionen und Geometrische Algebra)
Horn, Martin Erik
2007-01-01
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same time, Hestenes geometric algebra provides a didactically promising instrument to model phenomena in physics mathematically and in a tangible manner. Quaternions particularly have a catchy interpretation in the context of geometric algebra which can be used didactically. The relation between quaternions and geometric algebra is presented with a view to analysing its didactical possibilities.
An Automatic Registration Algorithm for 3D Maxillofacial Model
Qiu, Luwen; Zhou, Zhongwei; Guo, Jixiang; Lv, Jiancheng
2016-09-01
3D image registration aims at aligning two 3D data sets in a common coordinate system, which has been widely used in computer vision, pattern recognition and computer assisted surgery. One challenging problem in 3D registration is that point-wise correspondences between two point sets are often unknown apriori. In this work, we develop an automatic algorithm for 3D maxillofacial models registration including facial surface model and skull model. Our proposed registration algorithm can achieve a good alignment result between partial and whole maxillofacial model in spite of ambiguous matching, which has a potential application in the oral and maxillofacial reparative and reconstructive surgery. The proposed algorithm includes three steps: (1) 3D-SIFT features extraction and FPFH descriptors construction; (2) feature matching using SAC-IA; (3) coarse rigid alignment and refinement by ICP. Experiments on facial surfaces and mandible skull models demonstrate the efficiency and robustness of our algorithm.
Surzhykov, Andrey; Koval, Peter; Fritzsche, Stephan
2005-01-01
Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the DIRAC program which has been developed originally for studying the properties and dynamical behavior of the (hydrogen-like) ions. In the present version, a set of MAPLE procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the DIRAC program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. Program summaryTitle of program:DIRAC Catalogue number: ADUQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed and has been tested: All computers with a license of the computer algebra package MAPLE [1] Program language used: Maple 8 and 9 No. of lines in distributed program, including test data, etc.:2186 No. of bytes in distributed program, including test data, etc.: 162 591 Distribution format: tar gzip file CPC Program Library subprograms required: None Nature of the physical problem: Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure
Twisted C⋆-algebra formulation of quantum cosmology with application to the Bianchi I model
Rosenbaum, Marcos; Vergara, J. David; Juárez, Román; Minzoni, A. A.
2014-04-01
A twisted C⋆-algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the uncertainty principle for coordinates in the Planck-length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I cosmology, leads to a new set of equations that describe the quantum evolution of the Universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding regions of a collapsing Bianchi universe. There is, however, an additional effect introduced by the dynamics generated by the noncommutativity. This is an oscillation in the spectrum of the volume operator of the Universe, within the bouncing region of the commutative theories. We show that this effect is generic and produced by the noncommutative momentum exchange between the degrees of freedom in the cosmology. We give asymptotic and numerical solutions which show the above mentioned effects of the noncommutativity.
Energy Technology Data Exchange (ETDEWEB)
Fakhri, H [Department of Theoretical Physics and Astrophysics, Physics Faculty, University of Tabriz, PO Box 51666-16471, Tabriz (Iran, Islamic Republic of); Chenaghlou, A [Research Institute for Fundamental Sciences, Tabriz (Iran, Islamic Republic of)
2007-05-25
Introducing p - 1 new parameters into the multilinear relations, we extend the standard unitary parasupersymmetry algebra of order p so that by embedding the quantum solvable models possessing gl(2, c) Lie algebra symmetry into it, the partitions of integer numbers p - 1 and 1/2 p(p-1) are established. These two partitions are performed by the new parameters and the product of new parameters with their labels, respectively. The former partition is just necessary for the real form h{sub 4}; however, both of them are essential for the real forms u(2) and u(1, 1). By occupying these parameters with arbitrary values, the energy spectra are determined by the mean value of proposed parameters for the real form h{sub 4} with their label weight function as well as for the real forms u(2) and u(1, 1) with the weight function of their squared label. So for the given energies, the multilinear behaviour of parasupercharges is not specified uniquely by varying the new parameters continuously.
Fakhri, H.; Chenaghlou, A.
2007-05-01
Introducing p - 1 new parameters into the multilinear relations, we extend the standard unitary parasupersymmetry algebra of order p so that by embedding the quantum solvable models possessing gl(2, c) Lie algebra symmetry into it, the partitions of integer numbers p - 1 and \\frac{1}{2}p(p-1) are established. These two partitions are performed by the new parameters and the product of new parameters with their labels, respectively. The former partition is just necessary for the real form h4; however, both of them are essential for the real forms u(2) and u(1, 1). By occupying these parameters with arbitrary values, the energy spectra are determined by the mean value of proposed parameters for the real form h4 with their label weight function as well as for the real forms u(2) and u(1, 1) with the weight function of their squared label. So for the given energies, the multilinear behaviour of parasupercharges is not specified uniquely by varying the new parameters continuously.
International Nuclear Information System (INIS)
Introducing p - 1 new parameters into the multilinear relations, we extend the standard unitary parasupersymmetry algebra of order p so that by embedding the quantum solvable models possessing gl(2, c) Lie algebra symmetry into it, the partitions of integer numbers p - 1 and 1/2 p(p-1) are established. These two partitions are performed by the new parameters and the product of new parameters with their labels, respectively. The former partition is just necessary for the real form h4; however, both of them are essential for the real forms u(2) and u(1, 1). By occupying these parameters with arbitrary values, the energy spectra are determined by the mean value of proposed parameters for the real form h4 with their label weight function as well as for the real forms u(2) and u(1, 1) with the weight function of their squared label. So for the given energies, the multilinear behaviour of parasupercharges is not specified uniquely by varying the new parameters continuously
Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.
2016-02-01
A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper
New Model and Algorithm for Hardware/Software Partitioning
Institute of Scientific and Technical Information of China (English)
Ji-Gang Wu; Thambipillai Srikanthan; Guang-Wei Zou
2008-01-01
This paper focuses on the algorithmic aspects for the hardware/software (HW/SW) partitioning which searches a reasonable composition of hardware and software components which not only satisfies the constraint of hardware area but also optimizes the execution time. The computational model is extended so that all possible types of communications can be taken into account for the HW/SW partitioning. Also, a new dynamic programming algorithm is proposed on the basis of the computational model, in which source data, rather than speedup in previous work, of basic scheduling blocks are directly utilized to calculate the optimal solution. The proposed algorithm runs in O(n. A) for n code fragments and the available hardware area A. Simulation results show that the proposed algorithm solves the HW/SW partitioning without increase in running time, compared with the algorithm cited in the literature.
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...... for these types of models, although at a more expensive computational cost. The main purpose of this study is to investigate the performance of a global and a local parameter optimization algorithm, respectively, the Shuffled Complex Evolution (SCE) algorithm and the gradient-based Gauss......-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...
Improved Based on "Self-Adaptive Turning Rate" Model Algorithm
Directory of Open Access Journals (Sweden)
Xiuling He
2013-06-01
Full Text Available For tracking the object with tracking nonlinear, high maneuvering target，traditional interactive multiple model self-adaptive filter algorithm was usually adopted．The turning rate estimate was very important. However，the performance of turning rate algorithm was not so satisfactory in the model．Thus，a new the average value turning rate algorithm based on self-adaptive turning model was proposed．Aiming at additional device for turning rate estimation turning model, the parameters α and β were introduced to adjust the roughness of turning rate．Aiming at target constant turning movement and orthogonal turning rate unequal, estimates, turning rate was used the average value model to reduce the noise and error influence. Simulation results showed that the proposed algorithm was more suitable for the objects with Nonlinear, high maneuvering target tracking and could remarkably reduce the sample，and thus achieve much better tracking performance.
Solvable quadratic Lie algebras
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
Grabowski, Jan
2015-01-01
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We transfer a definition of Gekhtman, Shapiro and Vainshtein to the algebraic setting, yielding the notion of a multi-graded cluster algebra. We then study gradings for finite type cluster algebras without coefficients, giving a full classification. Translating ...
Coverings of topological semi-abelian algebras
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Scalable Parallel Algebraic Multigrid Solvers
Energy Technology Data Exchange (ETDEWEB)
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
Malware propagation modeling by the means of genetic algorithms
Goranin, N.; Čenys, A.
2008-01-01
Existing malware propagation models mainly concentrate to forecasting the number of infected computers in the initial propagation phase. In this article we propose a genetic algorithm based model for estimating the propagation rates of known and perspective Internet worms after their propagation reaches the satiation phase. Estimation algorithm is based on the known worms’ propagation strategies with correlated propagation rates analysis and is presented as a decision tree, generated by GAtre...
An algorithm for model reduction in large electric power systems
Directory of Open Access Journals (Sweden)
Ze?evi? A. I.
1998-01-01
Full Text Available Model reduction has become an important issue in the analysis of electric power systems, due to their constantly increasing size and complexity. In this paper we present a decomposition algorithm which is capable of reducing the number of equations in the model, while preserving the potential for parallel computation. A variety of experimental results are provided to illustrate the performance of the algorithm.
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.
Filiform Lie algebras of order 3
Energy Technology Data Exchange (ETDEWEB)
Navarro, R. M., E-mail: rnavarro@unex.es [Rosa María Navarro. Dpto. de Matemáticas, Universidad de Extremadura, Cáceres (Spain)
2014-04-15
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.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are,in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A), and show an A∞-structure on E(A). Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos.
Li, Haisheng; Tan, Shaobin; Wang, Qing
2012-01-01
In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without vacuum can be naturally extended to a vertex algebra. On the other hand, we show that a vertex Leibniz algebra can be embedded into a vertex algebra if and only if it admits a faithful module. To each vertex Leibniz algebra we associate a vertex algebra with...
Computing Gröbner Bases within Linear Algebra
Suzuki, Akira
In this paper, we present an alternative algorithm to compute Gröbner bases, which is based on computations on sparse linear algebra. Both of S-polynomial computations and monomial reductions are computed in linear algebra simultaneously in this algorithm. So it can be implemented to any computational system which can handle linear algebra. For a given ideal in a polynomial ring, it calculates a Gröbner basis along with the corresponding term order appropriately.
Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
Zhang, Tianjie; Gao, Xing; Guo, Li
2016-10-01
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.
Petersen, Jens Lyng; Taormina, Anne
1991-05-01
The doubly extended N = 4 superconformal algebra, which contains all conventional extended superconformal algebras, is analyzed when one of the central extensions is set to 1. The modular transformations of the characters are derived, the relation between the characters and those of the N = 2 minimal is clarified, and in the process it is shown how rather simple extensions of the algebra based on rational torus theories, give rise to finite dimensional representations of the modular group.
Energy Technology Data Exchange (ETDEWEB)
Petersen, J.L. (Niels Bohr Inst., Copenhagen (Denmark)); Taormina, A. (Chicago Univ., IL (USA). Enrico Fermi Inst.)
1991-05-06
The doubly extended N = 4 superconformal algebra, which contains all conventinal extended superconformal algebras, is analyzed when one of the central extensions is set to 1. The modular transformations of the characters are derived, the relation between the characters and those of the N = 2 minimal series is clarified, and in the process it is shown how rather simple extensions of the algebra based on rational torus theories, give rise to finite dimensional representations of the modular group. (orig.).
Arrangement Computation for Planar Algebraic Curves
Berberich, Eric; Kobel, Alexander; Sagraloff, Michael
2011-01-01
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition of the plane. Compared to previous approaches, we improve in two main aspects: Firstly, we significantly reduce the amount of exact operations, that is, our algorithms only uses resultant and gcd as purely symbolic operations. Secondly, we introduce a new hybrid method in the lifting step of our algorithm which combines the usage of a certified numerical complex root solver and information derived from the resultant computation. Additionally, we never consider any coordinate transformation and the output is also given with respect to the initial coordinate system. We implemented our algorithm as a prototypical package of the C++-library CGAL. Our implementation exploits graphics hardware to expedite the resultant and gcd...
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...
An efficient Cellular Potts Model algorithm that forbids cell fragmentation
Durand, Marc; Guesnet, Etienne
2016-11-01
The Cellular Potts Model (CPM) is a lattice based modeling technique which is widely used for simulating cellular patterns such as foams or biological tissues. Despite its realism and generality, the standard Monte Carlo algorithm used in the scientific literature to evolve this model preserves connectivity of cells on a limited range of simulation temperature only. We present a new algorithm in which cell fragmentation is forbidden for all simulation temperatures. This allows to significantly enhance realism of the simulated patterns. It also increases the computational efficiency compared with the standard CPM algorithm even at same simulation temperature, thanks to the time spared in not doing unrealistic moves. Moreover, our algorithm restores the detailed balance equation, ensuring that the long-term stage is independent of the chosen acceptance rate and chosen path in the temperature space.
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...
An Algorithm of Speaker Clustering Based on Model Distance
Directory of Open Access Journals (Sweden)
Wei Li
2014-03-01
Full Text Available An algorithm based on Model Distance (MD for spectral speaker clustering is proposed to deal with the shortcoming of general spectral clustering algorithm in describing the distribution of signal source. First, an Universal Background Model (UBM is created with a large quantity of independent speakers; Then, Gaussian Mixture Model (GMM is trained from the UBM for every speech segment; At last, the probability distance between the GMM of every speech segment is used to build affinity matrix, and speaker spectral clustering is done on the affinity matrix. Experimental results based on news and conference data sets show that an average of 6.38% improvements in F measure is obtained in comparison with algorithm based on the feature vector distance. In addition, the proposed algorithm is 11.72 times faster
Application of Search Algorithms for Model Based Regression Testing
Directory of Open Access Journals (Sweden)
Sidra Noureen
2014-04-01
Full Text Available UML models have gained their significance as reported in the literature. The use of a model to describe the behavior of a system is a proven and major advantage to test. With the help of Model Based Testing (MBT, it is possible to automatically generate test cases. When MBT is applied on large industrial systems, there is problem to sampling the test cases from the suit of entire test because it is difficult to execute the huge number of test cases being generated. The motivation of this study is to design a multi objective genetic algorithm based test case selection technique which can select the most appropriate subset of test cases. NSGA (Non-dominated Sorting Genetic Algorithm is used as an optimization algorithm and its fitness function is improved for selecting test cases from the dataset. It is concluded that there is a room to improve the performance of NSGA algorithm by means of tailoring its respective fitness function.
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
Zheng Lijing
2015-11-01
Let be an algebraically closed field, a finite dimensional connected (, )-Koszul self-injective algebra with , ≥ 2. In this paper, we prove that the Yoneda algebra of is isomorphic to a twisted polynomial algebra $A^!$ [ ; ] in one indeterminate of degree +1 in which $A^!$ is the quadratic dual of , is an automorphism of $A^!$, and = () for each $t \\in A^!$. As a corollary, we recover Theorem 5.3 of [2].
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...... grown exponentially because of drastic improvements in the technology behind DNA and RNA sequencing, and focus on the research field has increased due to its potential to expand our knowledge about biological mechanisms and to improve public health. There has therefore been a continuously growing demand...... of the algorithms to exploit the parallel architecture of modern computers. In this PhD dissertation, I present my work with algorithmic optimizations and parallelizations in primarily two areas in algorithmic bioinformatics: algorithms for analyzing hidden Markov models and algorithms for computing distance...
A Deductive Approach towards Reasoning about Algebraic Transition Systems
Directory of Open Access Journals (Sweden)
Jun Fu
2015-01-01
Full Text Available Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible.
WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY
Institute of Scientific and Technical Information of China (English)
TaoChangli; LuShijie; ChenPeixin
2002-01-01
Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.
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.
Models and algorithms for stochastic online scheduling
Megow, N.; Uetz, M.J.; Vredeveld, T.
2006-01-01
We consider a model for scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to traditional stochastic scheduling models, we assume that job
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.
Directory of Open Access Journals (Sweden)
Henrik Aratyn
2007-02-01
Full Text Available We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the $2n$-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for $nimes n$ matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato-Wilson relations. A reduction process leads to the AKNS, two-component Camassa-Holm and Cecotti-Vafa models and the formalism provides simple formulas for their solutions.
Po, Hoi Chun; Zhou, Qi
2015-08-01
Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.
International Nuclear Information System (INIS)
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 cq[sl(2)] quantum algebra transformations. (author)
A NEW GENETIC SIMULATED ANNEALING ALGORITHM FOR FLOOD ROUTING MODEL
Institute of Scientific and Technical Information of China (English)
KANG Ling; WANG Cheng; JIANG Tie-bing
2004-01-01
In this paper, a new approach, the Genetic Simulated Annealing (GSA), was proposed for optimizing the parameters in the Muskingum routing model. By integrating the simulated annealing method into the genetic algorithm, the hybrid method could avoid some troubles of traditional methods, such as arduous trial-and-error procedure, premature convergence in genetic algorithm and search blindness in simulated annealing. The principle and implementing procedure of this algorithm were described. Numerical experiments show that the GSA can adjust the optimization population, prevent premature convergence and seek the global optimal result.Applications to the Nanyunhe River and Qingjiang River show that the proposed approach is of higher forecast accuracy and practicability.
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.
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.
Danker, Jared F; Anderson, John R
2007-04-15
In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments.
The Cosparse Analysis Model and Algorithms
Nam, Sangnam; Elad, Michael; Gribonval, Rémi
2011-01-01
After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.
Enveloping algebras of some quantum Lie algebras
Pourkia, Arash
2014-01-01
We define a family of Hopf algebra objects, $H$, in the braided category of $\\mathbb{Z}_n$-modules (known as anyonic vector spaces), for which the property $\\psi^2_{H\\otimes H}=id_{H\\otimes H}$ holds. We will show that these anyonic Hopf algebras are, in fact, the enveloping (Hopf) algebras of particular quantum Lie algebras, also with the property $\\psi^2=id$. Then we compute the braided periodic Hopf cyclic cohomology of these Hopf algebras. For that, we will show the following fact: analog...
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.)
Quantum complexity of graph and algebraic problems
International Nuclear Information System (INIS)
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.)
Multiple QoS modeling and algorithm in computational grid
Institute of Scientific and Technical Information of China (English)
Li Chunlin; Feng Meilai; Li Layuan
2007-01-01
Multiple QoS modeling and algorithm in grid system is considered.Grid QoS requirements can be formulated as a utility function for each task as a weighted sum of its each dimensional QoS utility functions.Multiple QoS constraint resource scheduling optimization in computational grid is distributed to two subproblems: optimization of grid user and grid resource provider.Grid QoS scheduling can be achieved by solving sub problems via an iterative algorithm.
Institute of Scientific and Technical Information of China (English)
陶袁; 祝明发
2015-01-01
Linear Alebra Algorithms are the key of science and engineer computing .How to get higher performance for the existing Linear Algebra Algorithms on the platform is the problem to be solved ,because the scale of the hardware is much larger and the architecture is much more complexity .In the paper , the current situation ,the problem and challenge of the Linear Algebra Algorithm on the heterogeneous architecture platform between multi-core CPU and many-core GPU were reviewed .The problem was systematically analysed and the direction in future work was given .%线性代数算法是科学和工程计算的核心算法，高性能计算机的硬件规模越来越大，体系结构越来越复杂，已有的包含这些算法的应用程序如何在当前体系结构的高性能计算机平台上获得较高的性能是当前研究必须解决的问题。本文综述在当前多核和众核的异构平台上线性数值计算方面的现状、存在的问题和面临挑战；对这些问题可能存在的问题进行系统的分析，并给出可能发展方向。
West, Jerry G.
2013-01-01
Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…
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.
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…