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The canonical representation
"... f = h + g, g(0) = 0, of a harmonic function f in the unit disk D as the sum of an analytic function h and the conjugate of an analytic function g. With the convention that g(0) = 0, the representation is unique. The power series expansions of h and g are denoted by h(z) = n=0 anz n and g(z) = n=0 ..."
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f = h + g, g(0) = 0, of a harmonic function f in the unit disk D as the sum of an analytic function h and the conjugate of an analytic function g. With the convention that g(0) = 0, the representation is unique. The power series expansions of h and g are denoted by h(z) = n=0 anz n and g(z) = n=0
Canonical Representation Genetic Programming
"... Search spaces sampled by the process of Genetic Programming often consist of programs which can represent a function in many different ways. Thus, when the space is examined it is highly likely that different programs may be tested which represent the same function, which is an undesirable waste of ..."
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Cited by 1 (0 self)
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of resources. It is argued that, if a search space can be constructed where only unique representations of a function are permitted, then this will be more successful than employing multiple representations. When the search space consists of canonical representations it is called a canonical search space
UNIQUENESS OF POLYNOMIAL CANONICAL REPRESENTATIONS
, 705
"... Abstract. Let P(z) and Q(y) be polynomials of the same degree k≥1 in the complex variables z and y, respectively. In this extended abstract we study the nonlinear functional equation P(z) = Q(y(z)), where y(z) is restricted to be analytic in a neighborhood of z = 0. We provide sufficient condition ..."
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conditions to ensure that all the roots of Q(y) are contained within the range of y(z) as well as to have y(z) = z as the unique analytic solution of the nonlinear equation. Our results are motivated from uniqueness considerations of polynomial canonical representations of the phase or amplitude terms
On the Canonical Representation of Phase Type Distributions
"... The characterization and the canonical representation of ordern phase type distributions (PH(n)) is an open research problem. This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representatio ..."
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The characterization and the canonical representation of ordern phase type distributions (PH(n)) is an open research problem. This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical
INTERVAL GRAPHS: CANONICAL REPRESENTATIONS IN LOGSPACE
, 2011
"... We present a logspace algorithm for computing a canonical labeling, in fact, a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a consequ ..."
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Cited by 7 (4 self)
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We present a logspace algorithm for computing a canonical labeling, in fact, a canonical interval representation, for interval graphs. To achieve this, we compute canonical interval representations of interval hypergraphs. This approach also yields a canonical labeling of convex graphs. As a
A Canonical Representation for the Assignment Game: the Kernel and the Nucleolus
"... A canonical representation for the assignment game: the kernel and the nucleolus Marina Núñez and Carles Rafels ∗† ..."
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A canonical representation for the assignment game: the kernel and the nucleolus Marina Núñez and Carles Rafels ∗†
Canonical Representations of Partial 2 and 3Trees
 In: Proc. of the 2nd Scandinavian Workshop on Algorithm Theory, SpringerVerlag, Lecture Notes in Computer Science 477
, 1998
"... We give linear time algorithms constructing canonical representations of partial 2trees (seriesparallel graphs) and partial 3trees. 1 Introduction A canonical representation of a family of graphs assigns to each member of the family a label that is independent of any arbitrary vertex numbering: ..."
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Cited by 5 (0 self)
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We give linear time algorithms constructing canonical representations of partial 2trees (seriesparallel graphs) and partial 3trees. 1 Introduction A canonical representation of a family of graphs assigns to each member of the family a label that is independent of any arbitrary vertex numbering
Canonical representation and three view geometry of cylinders, Intl
 Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Commission III, Vol. XXXIV, Part 3A
, 2002
"... This paper first introduces a canonical representation for cylinders. The canonical representation introduced here is closely related to the Plücker line respresentation. It then drives the general equation of a cylinder using this representation. In this paper, we also show that this representation ..."
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This paper first introduces a canonical representation for cylinders. The canonical representation introduced here is closely related to the Plücker line respresentation. It then drives the general equation of a cylinder using this representation. In this paper, we also show
A Canonical Representation for Aggregated Markov Processes
 J. Appl. Probab
, 1998
"... A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuoustime aggregated Markov processes. For both discrete and continuoustime, we show that any aggregated Markov process which satisfies mild ..."
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mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization of all that can be identified about the underlying Markov process. Hidden Markov models on finite state spaces may
Results 1  10
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