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ON THE TRANSLATION OF AN ALMOST LINEAR TOPOLOGY
"... Abstract: We present some characterizations of T1, T2 separation and metrizability for the translation of an almost linear topology. Key–words: almost linear space, almost linear topological space, translation of a topology. 1 ..."
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Abstract: We present some characterizations of T1, T2 separation and metrizability for the translation of an almost linear topology. Key–words: almost linear space, almost linear topological space, translation of a topology. 1
Measuring ISP Topologies with Rocketfuel
 In Proc. ACM SIGCOMM
, 2002
"... To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure routerlevel ISP topologies. Our techniques reduce t ..."
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Cited by 838 (30 self)
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To date, realistic ISP topologies have not been accessible to the research community, leaving work that depends on topology on an uncertain footing. In this paper, we present new Internet mapping techniques that have enabled us to directly measure routerlevel ISP topologies. Our techniques reduce
On Duality in Linearly Topologized Spaces
"... open access article distributed under the Creative Commons Attribution Licence, with permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For a weakly continuous linear mapping u, a necessary and sufficient condition for the solubilit ..."
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open access article distributed under the Creative Commons Attribution Licence, with permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For a weakly continuous linear mapping u, a necessary and sufficient condition
Evolving Neural Networks through Augmenting Topologies
 Evolutionary Computation
"... An important question in neuroevolution is how to gain an advantage from evolving neural network topologies along with weights. We present a method, NeuroEvolution of Augmenting Topologies (NEAT), which outperforms the best fixedtopology method on a challenging benchmark reinforcement learning task ..."
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Cited by 524 (113 self)
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An important question in neuroevolution is how to gain an advantage from evolving neural network topologies along with weights. We present a method, NeuroEvolution of Augmenting Topologies (NEAT), which outperforms the best fixedtopology method on a challenging benchmark reinforcement learning
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 1052 (17 self)
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In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or
Separation of Convex Sets in Linear Topological Spaces
, 1988
"... This paper discusses under what conditions two disjoint convex subsets of a linear topological space can be separated by a continuous linear functional. The equivalence of several forms of the HahnBanach theorem is proven. The separation problem is considered in linear topological spaces, locally c ..."
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This paper discusses under what conditions two disjoint convex subsets of a linear topological space can be separated by a continuous linear functional. The equivalence of several forms of the HahnBanach theorem is proven. The separation problem is considered in linear topological spaces, locally
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented by 200300 of the largest singular vectors are then matched against user queries. We call this retrieval method Latent Semantic Indexing (LSI) because the subspace represents important associative relationships between terms and documents that are not evident in individual documents. LSI is a completely automatic yet intelligent indexing method, widely applicable, and a promising way to improve users...
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
, 2008
"... ..."
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
ASCENT: Adaptive selfconfiguring sensor networks topologies
, 2004
"... Advances in microsensor and radio technology will enable small but smart sensors to be deployed for a wide range of environmental monitoring applications. The low pernode cost will allow these wireless networks of sensors and actuators to be densely distributed. The nodes in these dense networks w ..."
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Cited by 447 (15 self)
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configuration, and the environmental dynamics will preclude designtime preconfiguration. Therefore, nodes will have to selfconfigure to establish a topology that provides communication under stringent energy constraints. ASCENT builds on the notion that, as density increases, only a subset of the nodes
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