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CuntzKrieger algebras of directed graphs
, 1996
"... We associate to each rowfinite directed graph E a universal CuntzKrieger C  algebra C (E), and study how the distribution of loops in E affects the structure of C (E). We prove that C (E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which allow ..."
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Cited by 213 (45 self)
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We associate to each rowfinite directed graph E a universal CuntzKrieger C  algebra C (E), and study how the distribution of loops in E affects the structure of C (E). We prove that C (E) is AF if and only if E has no loops. We describe an exit condition (L) on loops in E which
Reevaluating Amdahl’s law
 Commun. ACM
, 1988
"... At Sandia National Laboratories, we are currently engaged in research involving massively parallel processing. There is considerable skepticism regarding the viability of massive parallelism; the skepticism centers around Amdahl’s law, an argument put forth by Gene Amda.hl in 1967 [l] that even w ..."
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Cited by 316 (4 self)
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, then Amdahl’s law says that speedup is given by Speedup = (s + p)/(s + p/N) = l/b + p/N), where we have set total time s + p = 1 for algebraic simphcity. For N = 1024 this is an unforgivingly steep function of s near s = 0 (see Figure 1). The steepness of the graph near s = 0 (approximatelyN’) implies
Algebras and Modules in Monoidal Model Categories
 Proc. London Math. Soc
, 1998
"... In recent years the theory of structured ring spectra (formerly known as A #  and E # ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect t ..."
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Cited by 231 (30 self)
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In recent years the theory of structured ring spectra (formerly known as A #  and E # ring spectra) has been signicantly simplified by the discovery of categories of spectra with strictly associative and commutative smash products. Now a ring spectrum can simply be dened as a monoid with respect
www.ijacsa.thesai.org On Algebraic Spectrum of Ontology Evaluation
"... Abstract — Ontology evaluation remains an important open problem in the area of its application. The ontology structure evaluation framework for benchmarking the internal graph structures was proposed. The framework was used in transport and biochemical ontology. The corresponding adjacency, inciden ..."
The Contour Spectrum
, 1997
"... We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides realtime exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over t ..."
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Cited by 187 (33 self)
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We introduce the contour spectrum, a user interface component that improves qualitative user interaction and provides realtime exact quantification in the visualization of isocontours. The contour spectrum is a signature consisting of a variety of scalar data and contour attributes, computed over
PolySet Theory
 http://www.rbjones.com/rbjpub/pp/doc/t020.pdf. p011.tex; 25/01/2010; 13:13; p.12 13
"... This document is concerned with the specification of an interpretation of the first order language of set theory. The purpose of this is to provide an ontological basis for foundation systems suitable for the formal derivation of mathematics. The ontology is to include the pure wellfounded sets of ..."
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Cited by 259 (2 self)
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of rank up to some arbitrary large cardinal together with the graphs of the polymorphic functions definable mathematical concepts. The interpretation is constructed by defining “names ” or “representatives ” for the sets in the domain of discourse by transfinite inductive definition in the context of a
The factorized Smatrix of CFT/AdS
, 2004
"... We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s dilatati ..."
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Cited by 240 (7 self)
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We argue that the recently discovered integrability in the largeN CFT/AdS system is equivalent to diffractionless scattering of the corresponding hidden elementary excitations. This suggests that, perhaps, the key tool for finding the spectrum of this system is neither the gauge theory’s
Which graphs are determined by their spectrum?
 LINEAR ALGEBRA AND ITS APPLICATIONS 373 (2003) 241–272
, 2003
"... For almost all graphs the answer to the question in the title is still unknown. Here we survey the cases for which the answer is known. Not only the adjacency matrix, but also other types of matrices, such as the Laplacian matrix, are considered. ..."
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Cited by 100 (11 self)
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For almost all graphs the answer to the question in the title is still unknown. Here we survey the cases for which the answer is known. Not only the adjacency matrix, but also other types of matrices, such as the Laplacian matrix, are considered.
From triangulated categories to cluster algebras
"... Abstract. In the acyclic case, we establish a onetoone correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator ..."
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Cited by 173 (20 self)
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Abstract. In the acyclic case, we establish a onetoone correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator
Spectra of random graphs with given expected degrees
, 2003
"... In the study of the spectra of power law graphs, there are basically two competing approaches. One is to prove analogues of Wigner’s semicircle law while the other predicts that the eigenvalues follow a power law distributions. Although the semicircle law and the power law have nothing in common, ..."
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Cited by 180 (19 self)
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, we will show that both approaches are essentially correct if one considers the appropriate matrices. We will prove that (under certain mild conditions) the eigenvalues of the (normalized) Laplacian of a random power law graph follow the semicircle law while the spectrum of the adjacency matrix of a
Results 11  20
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