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Unified algebra
 In preparation
, 1998
"... Abstract—Unified Algebra unifies booleans and numbers, values and types, functions and function spaces. It incorporates basic structures, such as sets and lists, and advanced structures, such as quantifications and limits. It does so with an economy of symbols and rules. The presentation is basic an ..."
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Cited by 2 (0 self)
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Abstract—Unified Algebra unifies booleans and numbers, values and types, functions and function spaces. It incorporates basic structures, such as sets and lists, and advanced structures, such as quantifications and limits. It does so with an economy of symbols and rules. The presentation is basic
Unified Algebras and Abstract Syntax
 IN RECENT TRENDS IN DATA TYPE SPECIFICATION
, 1994
"... We consider the algebraic specification of abstract syntax in the framework of unified algebras. We illustrate the expressiveness of unified algebraic specifications, and provide a grammarlike notation for specifying abstract syntax, particularly attractive for use in semantic descriptions of fu ..."
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Cited by 7 (0 self)
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We consider the algebraic specification of abstract syntax in the framework of unified algebras. We illustrate the expressiveness of unified algebraic specifications, and provide a grammarlike notation for specifying abstract syntax, particularly attractive for use in semantic descriptions
Abstract—Unified Algebra unifies booleans and
"... numbers, values and types, functions and function spaces. It incorporates basic structures, such as sets and lists, and advanced structures, such as quantifications and limits. It does so with an economy of symbols and rules. The presentation is basic and detailed enough to serve as a foundation of ..."
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of that part of mathematics that serves much of computer science, with comments on what constitutes good mathematical practice. Keywords—boolean algebra, foundation of computer science, foundation of mathematics, unified algebra
from Boolean Algebra to Unified Algebra
"... Boolean algebra is simpler than number algebra, with applications in programming, circuit design, law, specifications, mathematical proof, and reasoning in any domain. So why is number algebra taught in primary school and used routinely by scientists, engineers, economists, and the general public, w ..."
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Cited by 7 (1 self)
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Boolean algebra is simpler than number algebra, with applications in programming, circuit design, law, specifications, mathematical proof, and reasoning in any domain. So why is number algebra taught in primary school and used routinely by scientists, engineers, economists, and the general public
Unified Algebraic Synthesis of Generalized Fibonacci Switched Capacitor Converters
"... Abstract—A unified algebraic approach to the synthesis of ..."
USER ACCEPTANCE OF INFORMATION TECHNOLOGY: TOWARD A UNIFIED VIEW
, 2003
"... Information technology (IT) acceptance research has yielded many competing models, each with different sets of acceptance determinants. In this paper, we (1) review user acceptance literature and discuss eight prominent models, (2) empirically compare the eight models and their extensions, (3) formu ..."
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Cited by 1665 (9 self)
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) formulate a unified model that integrates elements across the eight models, and (4) empirically validate the unified model. The eight models reviewed are the theory of reasoned action, the technology acceptance model, the motivational model, the theory of planned behavior, a model combining the technology
Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2000
"... We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a marginbased binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class ..."
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Cited by 560 (20 self)
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We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a marginbased binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class
LucasKanade 20 Years On: A Unifying Framework: Part 3
 International Journal of Computer Vision
, 2002
"... Since the LucasKanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision. Applications range from optical flow, tracking, and layered motion, to mosaic construction, medical image registration, and face coding. Numerous algorithms hav ..."
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Cited by 698 (30 self)
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Since the LucasKanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision. Applications range from optical flow, tracking, and layered motion, to mosaic construction, medical image registration, and face coding. Numerous algorithms have been proposed and a variety of extensions have been made to the original formulation. We present an overview of image alignment, describing most of the algorithms in a consistent framework. We concentrate on the inverse compositional algorithm, an efficient algorithm that we recently proposed. We examine which of the extensions to the LucasKanade algorithm can be used with the inverse compositional algorithm without any significant loss of efficiency, and which cannot. In this paper, Part 3 in a series of papers, we cover the extension of image alignment to allow linear appearance variation. We first consider linear appearance variation when the error function is the Euclidean L2 norm. We describe three different algorithms, the simultaneous, project out, and normalization inverse compositional algorithms, and empirically compare them. Afterwards we consider the combination of linear appearance variation with the robust error functions described in Part 2 of this series. We first derive robust versions of the simultaneous and normalization algorithms. Since both of these algorithms are very inefficient, as in Part 2 we derive efficient approximations based on spatial coherence. We end with an empirical evaluation of the robust algorithms.
Particles as Field Singularities in the Unified Algebraic Dynamics
"... Nonlinear generalization of CauchyRiemann equations to the algebra of biquaternions is considered. In a particular case the latters reduce to the “iversal generating equations ” which deal with the 2spinor and the gauge fields and form the basis of a unified algebraic field theory. For every solut ..."
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Cited by 1 (1 self)
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Nonlinear generalization of CauchyRiemann equations to the algebra of biquaternions is considered. In a particular case the latters reduce to the “iversal generating equations ” which deal with the 2spinor and the gauge fields and form the basis of a unified algebraic field theory. For every
A unified algebraic approach to the classical YangBaxter equation
, 2007
"... In this paper, the different operator forms of classical YangBaxter equation are given in the tensor expression through a unified algebraic method. It is closely related to leftsymmetric algebras which play an important role in many fields in mathematics and mathematical physics. By studying the r ..."
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Cited by 29 (14 self)
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In this paper, the different operator forms of classical YangBaxter equation are given in the tensor expression through a unified algebraic method. It is closely related to leftsymmetric algebras which play an important role in many fields in mathematics and mathematical physics. By studying
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