Results 1  10
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29
Prior Probabilities
 IEEE Transactions on Systems Science and Cybernetics
, 1968
"... e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determ ..."
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Cited by 166 (3 self)
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e case of location and scale parameters, rate constants, and in Bernoulli trials with unknown probability of success. In realistic problems, both the transformation group analysis and the principle of maximum entropy are needed to determine the prior. The distributions thus found are uniquely determined by the prior information, independently of the choice of parameters. In a certain class of problems, therefore, the prior distributions may now be claimed to be fully as "objective" as the sampling distributions. I. Background of the problem Since the time of Laplace, applications of probability theory have been hampered by difficulties in the treatment of prior information. In realistic problems of decision or inference, we often have prior information which is highly relevant to the question being asked; to fail to take it into account is to commit the most obvious inconsistency of reasoning and may lead to absurd or dangerously misleading results. As an extreme examp
AF embeddability of crossed products of AF algebras by the integers
 J. Funct. Anal
, 1998
"... This paper is concerned with the question of when the crossed product of an AF algebra by an action of Z is itself AF embeddable. It is well known that quasidiagonality and stable finiteness are hereditary properties. That is, if A and B are C ∗algebras with A ⊂ B and B has either of these properti ..."
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Cited by 10 (2 self)
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This paper is concerned with the question of when the crossed product of an AF algebra by an action of Z is itself AF embeddable. It is well known that quasidiagonality and stable finiteness are hereditary properties. That is, if A and B are C ∗algebras with A ⊂ B and B has either of these properties, then so does A. Since AF algebras enjoy both of these properties we have that quasidiagonality and stable finiteness are geometric obstructions to AF embeddability. For crossed products of AF algebras by Z, these turn out to be the only obstructions. If A is an AF algebra, then we may easily describe an algebraic obstruction to the AF embeddability of A ×α Z. Definition 0.1 If A is an AF algebra and α ∈ Aut(A) then we denote by Hα the subgroup of K0(A) given by all elements of the form α∗(x) − x for x ∈ K0(A). It follows from the PimsnerVoiculescu six term exact sequence ([PV]) that if A is unital and AF then K0(A ×α Z) = K0(A)/Hα. Now, if B is unital and stably finite (in particular, if B is AF) and p ∈ Mn(B) is a projection then [p] must be a nonzero element of K0(B). Thus, if A ×α Z embeds into B (or if A ×α Z is
Moufang symmetry I. Generalized Lie and MaurerCartan equations
, 2008
"... The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the MaurerCartan equations. ..."
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Cited by 8 (8 self)
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The differential equations for a local analytic Moufang loop are established. The commutation relations for the infinitesimal translations of the analytic Moufang are found. These commutation relations can be seen as a (minimal) generalization of the MaurerCartan equations.
The dynamics of group codes: Dual abelian group codes and systems
 IEEE Trans. Inform. Theory
, 1997
"... Abstract — Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of ..."
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Cited by 5 (0 self)
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Abstract — Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti)Laurent. If C and C ⊥ are dual codes, then the state spaces of C act as the character groups of the state spaces of C ⊥. The controllability properties of C are the observability properties of C ⊥. In particular, C is (strongly) controllable if and only if C ⊥ is (strongly) observable, and the controller memory of C is the observer memory of C ⊥. The controller granules of C act as the character groups of the observer granules of C ⊥. Examples of minimal observerform encoder and syndromeformer constructions are given. Finally, every observer granule of C is an “endaround ” controller granule of C. Index Terms — Group codes, group systems, linear systems, behavioral systems, duality, controllability, observability. I.
On approximations of groups, group actions and Hopf algebras
, 1999
"... We give new examples and criteria in the theory of approximation of groups by finite groups. ..."
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Cited by 4 (2 self)
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We give new examples and criteria in the theory of approximation of groups by finite groups.
Control Theory for a Class of 2D ContinuousDiscrete Linear Systems
"... This paper considers a general class of 2D continuousdiscrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and ..."
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Cited by 3 (0 self)
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This paper considers a general class of 2D continuousdiscrete linear systems of both systems theoretic and applications interest. The focus is on the development of a comprehensive control systems theory for members of this class in a unified manner based on analysis in an appropriate algebraic and operator setting. In particular, important new results are developed on stability, controllability, stabilization, and optimal control. 1
Topological characterization of torus groups
 Topology Appl
"... To the memory of Professor Ball Abstract. Topological characterization of torus groups is given. ..."
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Cited by 2 (2 self)
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To the memory of Professor Ball Abstract. Topological characterization of torus groups is given.
Oscillator topologies on a paratopological group and related number invariants
 In: Algebraic structures and their Applications, Institute of Math., Kyiv
, 2002
"... Abstract. We introduce and study oscillator topologies on paratopological groups and define certain related number invariants. As an application we prove that a Hausdorff paratopological group G admits a weaker Hausdorff group topology provided G is 3oscillating. A paratopological group G is 3osci ..."
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Cited by 2 (1 self)
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Abstract. We introduce and study oscillator topologies on paratopological groups and define certain related number invariants. As an application we prove that a Hausdorff paratopological group G admits a weaker Hausdorff group topology provided G is 3oscillating. A paratopological group G is 3oscillating (resp. 2oscillating) provided for any neighborhood U of the unity e of G there is a neighborhood V ⊂ G of e such that V −1 V V −1 ⊂ UU −1 U (resp. V −1 V ⊂ UU −1). The class of 2oscillating paratopological groups includes all collapsing, all nilpotent paratopological groups, all paratopological groups satisfying a positive law, all paratopological SINgroup and all saturated paratopological groups (the latter means that for any nonempty open set U ⊂ G the set U −1 has nonempty interior). We prove that each totally bounded paratopological group G is countably cellular; moreover, every cardinal of uncountable cofinality is a precaliber of G. Also we give an example of a saturated paratopological group which is not isomorphic to its mirror paratopological group as well as an example of a 2oscillating paratopological group whose mirror paratopological group is not 2oscillating. This note was motivated by the following question of I. Guran [Gu]: Does every (regular)
Codes on Graphs: Generalized State Realizations
, 1999
"... A class of generalized state realizations of codes is introduced. In the graph of such a realization, leaf edges represent symbols, ordinary edges represent states, and vertices represent local constraints on incident edges. Such a graph can be decoded by any version of the sumproduct algorithm. An ..."
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Cited by 1 (0 self)
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A class of generalized state realizations of codes is introduced. In the graph of such a realization, leaf edges represent symbols, ordinary edges represent states, and vertices represent local constraints on incident edges. Such a graph can be decoded by any version of the sumproduct algorithm. Any factor graph representation of a code can be put into this form, and any generalized state realization can be converted to a "normalized" factor graph, without essential change in decoding complexity. Group codes are generated by group generalized state realizations. The dual of such a realization, appropriately defined, generates the dual group code. The dual realization uses the same symbol and state variables in the same graph topology as the primal realization, but replaces primal local constraints by their duals. A group code may be decoded using the dual graph, with appropriate Fourier transforms of the inputs and outputs; this can simplify decoding of highrate codes. Examples are g...