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SparseSets for Domain Implementation
, 2013
"... This paper discusses the usage of sparse sets for integer domain implementation over traditional representations. A first benefit of sparse sets is that they are very cheap to trail and restore. A second key advantage introduced in this work is that sparse sets permit to get delta changes with a ver ..."
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Cited by 1 (0 self)
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This paper discusses the usage of sparse sets for integer domain implementation over traditional representations. A first benefit of sparse sets is that they are very cheap to trail and restore. A second key advantage introduced in this work is that sparse sets permit to get delta changes with a
On reducibility to complex or sparse sets
 Journal of the ACM
, 1975
"... ABSTRACT. Sets which are efficiently reducible (in Karp's sense) to arbitrarily complex sets are shown to be polynomial computable. Analogously, sets efficiently reducible to arbitrarily sparse sets are polynomial computable. A key lemma for both proofs shows that any set which is not polynomia ..."
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Cited by 27 (1 self)
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ABSTRACT. Sets which are efficiently reducible (in Karp's sense) to arbitrarily complex sets are shown to be polynomial computable. Analogously, sets efficiently reducible to arbitrarily sparse sets are polynomial computable. A key lemma for both proofs shows that any set which
An Efficient Representation for Sparse Sets
 ACM LETTERS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1993
"... ..."
Learning Reductions to Sparse Sets
"... Abstract. We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold ..."
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majority truthtable) reduces to a sparse set then Sat ≤ p m LT1 and hence a collapse of PH to P NP also follows. Lastly we show several interesting consequences of Sat ≤ p dtt SPARSE.
Finite configurations in sparse sets
, 2013
"... Let E ⊆ Rn be a closed set of Hausdorff dimension α. For m ≥ n, let {B1,..., Bk} be n × (m − n) matrices. We prove that if the system of matrices Bj is nondegenerate in a suitable sense, α is sufficiently close to n, and if E supports a probability measure obeying appropriate dimensionality and Fou ..."
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Cited by 2 (1 self)
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Let E ⊆ Rn be a closed set of Hausdorff dimension α. For m ≥ n, let {B1,..., Bk} be n × (m − n) matrices. We prove that if the system of matrices Bj is nondegenerate in a suitable sense, α is sufficiently close to n, and if E supports a probability measure obeying appropriate dimensionality
Monotonous and Randomized Reductions to Sparse Sets
, 1994
"... An oracle machine is called monotonous, if after a negative answer the machine does not ask further queries to the oracle. For example, one truthtable, conjunctive, and Hausdorff reducibilities are monotonous. We study the consequences of the existence of sparse hard sets for different complexity cl ..."
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Cited by 4 (2 self)
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An oracle machine is called monotonous, if after a negative answer the machine does not ask further queries to the oracle. For example, one truthtable, conjunctive, and Hausdorff reducibilities are monotonous. We study the consequences of the existence of sparse hard sets for different complexity
Learning Weak Reductions to Sparse Sets
"... We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold gate. (Sa ..."
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truthtable) reduces to a sparse set then Sat ≤pm LT1 and hence a collapse of PH to PNP also follows. Lastly we show several interesting consequences of Sat ≤pdtt SPARSE. 1
On Reductions of P Sets to Sparse Sets
, 1995
"... We prove unlikely consequences of the existence of sparse hard sets for P under deterministic as well as onesided error randomized truthtable reductions. Our main results are as follows. We establish that the existence of a polynomially dense hard set for P under (randomized) logspace bounded trut ..."
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Cited by 4 (0 self)
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We prove unlikely consequences of the existence of sparse hard sets for P under deterministic as well as onesided error randomized truthtable reductions. Our main results are as follows. We establish that the existence of a polynomially dense hard set for P under (randomized) logspace bounded
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 954 (12 self)
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field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest
Results 1  10
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394,915