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Results 1 - 10
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2,553
Torsion points on an algebraic subset of an affine torus
- Internat. Math. Res. Notices
, 1996
"... Work of Laurent and Sarnak, following a conjecture of Lang, shows that the number of torsion points of order n on an algebraic subset of an affine complex torus is polynomial periodic. In this paper, we find bounds on the degree and period of this number as a function of n. Some examples, including ..."
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Cited by 6 (0 self)
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Work of Laurent and Sarnak, following a conjecture of Lang, shows that the number of torsion points of order n on an algebraic subset of an affine complex torus is polynomial periodic. In this paper, we find bounds on the degree and period of this number as a function of n. Some examples, including
K-theory for operator algebras
- Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line-5: since p. 1-2: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The Riesz-Fischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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space is not σ-finite. p. 13: add after I.2.6.16: I.2.6.17. If X is a compact subset of C not containing 0, and k ∈ N, there is in general no bound on the norm of T −1 as T ranges over all operators with ‖T ‖ ≤ k and σ(T) ⊆ X. For example, let Sn ∈ L(l 2) be the truncated shift: Sn(α1, α2,...) = (0
Finding a Nonempty Algebraic Subset of an Edge Set in Linear Time
, 2005
"... A set of edges of a hypergraph H is an algebraic set if its characteristic vector can be expressed as a linear combination of rows of the (node-edge) incidence matrix of H. Recently it was proven that deciding whether or not a given edge-set of H contains a non-empty algebraic set is an NPcomplete p ..."
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A set of edges of a hypergraph H is an algebraic set if its characteristic vector can be expressed as a linear combination of rows of the (node-edge) incidence matrix of H. Recently it was proven that deciding whether or not a given edge-set of H contains a non-empty algebraic set is an NPcomplete
Accelerated Image Reconstruction using Ordered Subsets of Projection Data
- IEEE TRANS. MED. IMAG
, 1994
"... We define ordered subset processing for standard algorithms (such as Expectation Maximization, EM) for image restoration from projections. Ordered subsets methods group projection data into an ordered sequence of subsets (or blocks). An iteration of ordered subsets EM is defined as a single pass thr ..."
Abstract
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Cited by 301 (2 self)
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) and multiplicative algebraic reconstruction (MART) techniques are well known special cases. Ordered subsets EM (OS-EM) provides a restoration imposing a natural positivity condition and with close links to the EM algorithm. OS-EM is applicable in both single photon (SPECT) and positron emission tomography (PET
Submodular functions, matroids and certain polyhedra
, 2003
"... The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts is that all ..."
Abstract
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Cited by 355 (0 self)
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The viewpoint of the subject of matroids, and related areas of lattice theory, has always been, in one way or another, abstraction of algebraic dependence or, equivalently, abstraction of the incidence relations in geometric representations of algebra. Often one of the main derived facts
Temporal Reasoning Based on Semi-Intervals
, 1992
"... A generalization of Allen's interval-based approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semi-intervals rather than intervals are used as the basic units o ..."
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Cited by 286 (15 self)
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and efficiency; 6) for a natural subset of Allen's algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.
A powerdomain construction
- SIAM J. OF COMPUTING
, 1976
"... We develop a powerdomain construction, [.], which is analogous to the powerset construction and also fits in with the usual sum, product and exponentiation constructions on domains. The desire for such a construction arises when considering programming languages with nondeterministic features or p ..."
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Cited by 234 (15 self)
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or parallel features treated in a nondeterministic way. We hope to achieve a natural, fully abstract semantics in which such equivalences as (pparq)=(qparp) hold. The domain (D Truthvalues) is not the right one, and instead we take the (finitely) generable subsets of D. When D is discrete they are ordered
An Algebraic Approach to the Subset Selection Problem
"... The need for decomposing a signal into its optimal representation arises in many applications. In such applications, one can usually represent the signal as a combination of an overcomplete dictionary elements. The non-uniqueness of signal representation, in such dictionaries, provides us with the o ..."
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with the opportunity to adapt the signal representation to the signal. The adaptation is based on sparsity, resolution and stability of the signal representation. In this paper, we propose an algebraic approach for identifying the sparsest representation of a given signal in terms of a given over-complete dictionary
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