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Algebraic View Specification?
, 1996
"... The application of algebraic specification techniques in the early phases of software development requires a means for specifying views. In this paper we argue for algebraic view specification based on an algebraic concept model. The concept model consists of two parts: a meta model defining the con ..."
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Cited by 3 (1 self)
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The application of algebraic specification techniques in the early phases of software development requires a means for specifying views. In this paper we argue for algebraic view specification based on an algebraic concept model. The concept model consists of two parts: a meta model defining
An Algebraic View of Structural Induction
 Computer Science Logic 1994, number 933 in Lect. Notes Comp. Sci
, 1994
"... We propose a uniform, categorytheoretic account of structural induction for inductively defined data types. The account is based on the understanding of inductively defined data types as initial algebras for certain kind of endofunctors T : B !B on a bicartesian/distributive category B . Regarding ..."
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Cited by 10 (5 self)
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We propose a uniform, categorytheoretic account of structural induction for inductively defined data types. The account is based on the understanding of inductively defined data types as initial algebras for certain kind of endofunctors T : B !B on a bicartesian/distributive category B . Regarding
An Algebraic View of Combination Rules
, 1994
"... . Combining information from multiple sources is a topic of central importance for Uncertain Reasoning. In this paper we approach the problem of formulating appropriate Combination Rules for Uncertain Reasoning from an algebraic, latticetheoretical perspective. Our purpose is to state the problem o ..."
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Cited by 1 (1 self)
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. Combining information from multiple sources is a topic of central importance for Uncertain Reasoning. In this paper we approach the problem of formulating appropriate Combination Rules for Uncertain Reasoning from an algebraic, latticetheoretical perspective. Our purpose is to state the problem
DFT and FFT: An algebraic view
, 2009
"... In infinite, or nonperiodic, discretetime signal processing, there is a strong connection between the ztransform, Laurent series, convolution, and the discretetime Fourier transform (DTFT) [10]. As one may expect, a similar connection exists for the DFT but bears surprises. Namely, it turns out ..."
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that the proper framework for the DFT requires modulo operations of polynomials, which means working with socalled polynomial algebras [6]. Associated with polynomial algebras is the Chinese remainder theorem, which describes the DFT algebraically and can be used as a tool to concisely derive various FFTs
An Algebraic View on Recursive Types
 Applied Categorical Structures
, 1996
"... This paper is a translated extract of my diploma thesis, see [Mar95]. I would like to thank Pawe/l Urzyczyn for some useful hints, Martin Hofmann, Mathias Kegelmann and Hermann Puhlmann for their careful proof reading, and especially Achim Jung for his stimulating supervision ..."
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Cited by 2 (0 self)
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This paper is a translated extract of my diploma thesis, see [Mar95]. I would like to thank Pawe/l Urzyczyn for some useful hints, Martin Hofmann, Mathias Kegelmann and Hermann Puhlmann for their careful proof reading, and especially Achim Jung for his stimulating supervision
An algebraic view of program composition
 Algebraic Methodology and Software Technology, number 1548 in Lect. Notes Comp. Sci
, 1998
"... Abstract. We propose a general categorical setting for modeling program composition in which the callbyvalue and callbyname disciplines fit as special cases. Other notions of composition arising in denotational semantics are captured in the same framework: our leading examples are nondeterminist ..."
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Cited by 1 (0 self)
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Abstract. We propose a general categorical setting for modeling program composition in which the callbyvalue and callbyname disciplines fit as special cases. Other notions of composition arising in denotational semantics are captured in the same framework: our leading examples are nondeterministic callbyneed programs and nonstrict functions with side effects. Composition of such functions is treated in our framework with the same degree of abstraction that Moggi’s categorical approach based on monads allows in the treatment of callbyvalue programs. By virtue of such abstraction, interesting program equivalences can be validated axiomatically in mathematical models obtained by means of modular constructions. 1
An algebraic view of multidimensional . . .
, 2003
"... The problem of computing equalizers for multidimensional multipleinput multipleoutput (MIMO) finite impulse response (FIR) filters using MIMO FIR filters is considered. Prior results are reviewed establishing conditions for the equalizability of a given MIMO FIR filter and of a generic MIMO FIR f ..."
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The problem of computing equalizers for multidimensional multipleinput multipleoutput (MIMO) finite impulse response (FIR) filters using MIMO FIR filters is considered. Prior results are reviewed establishing conditions for the equalizability of a given MIMO FIR filter and of a generic MIMO FIR filter. Algorithms for the computation of MIMO FIR equalizers are derived and their relative strengths and weaknesses are discussed. A parametrization of the set of all equalizers for a given MIMO FIR filter is derived. Known bounds on the orders of the equalizer are doubly exponential in the order of the given MIMO FIR filter; alternative generic bounds are derived which are linear in the order of the given MIMO FIR filter, and the behavior of the bound for large number of outputs is characterized. A fast algorithm (generalizing the Levinson algorithm to the multidimensional case) is proposed for multidimensional Wiener filtering and for computing equalizers for singleinput multipleoutput (SIMO) systems. A minimal set of test targets is established for polarimetric calibration of ultrawide band synthetic aperture radar systems, and equalizer orders for
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
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Cited by 852 (10 self)
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in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A 5dimensional depiction is developed, which completely describes the system. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system
An Algebraic View on the Semantics of Model Composition
 Model Driven Architecture  Foundations and Applications (ECMDAFA), volume 4530 of LNCS
, 2007
"... Abstract. Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide several complementary views on the system to be de ..."
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Cited by 21 (9 self)
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Abstract. Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide several complementary views on the system
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 640 (1 self)
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processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view
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