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The homogeneous coordinate ring of a toric variety
, 1992
"... This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of ..."
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Cited by 474 (7 self)
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sheaves on X. We also define a monomial ideal B ⊂ S that describes the combinatorial structure of the fan ∆. In the case of projective space, the ring S is just the usual homogeneous coordinate ring C[x0,..., xn], and the ideal B is the “irrelevant ” ideal 〈x0,..., xn〉. Projective space P n can
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
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Cited by 879 (14 self)
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≪ p, and the zi’s are i.i.d. N(0, σ 2). Is it possible to estimate x reliably based on the noisy data y? To estimate x, we introduce a new estimator—we call the Dantzig selector—which is solution to the ℓ1regularization problem min ˜x∈R p ‖˜x‖ℓ1 subject to ‖A T r‖ℓ ∞ ≤ (1 + t −1) √ 2 log p · σ
Developments in the Measurement of Subjective WellBeing
 Psychological Science.
, 1993
"... F or good reasons, economists have had a longstanding preference for studying peoples' revealed preferences; that is, looking at individuals' actual choices and decisions rather than their stated intentions or subjective reports of likes and dislikes. Yet people often make choices that b ..."
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Cited by 284 (7 self)
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to the stimulus in a sensible way. For example, in an experiment described in Kahneman, Fredrickson, Schreiber and Redelmeier (1993), participant ratings of pain on a 0 14 scale increased from an average of 4.0 (after the first ten seconds) to an average of 8.4 after 60 seconds of immersing their hand in water
MultiService Search and Comparison Using the MetaCrawler
 In Proceedings of the 4th International World Wide Web Conference
, 1995
"... Standard Web search services, though useful, are far from ideal. There are over a dozen different search services currently in existence, each with a unique interface and a database covering a different portion of the Web. As a result, users are forced to repeatedly try and retry their queries acros ..."
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Cited by 214 (8 self)
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Standard Web search services, though useful, are far from ideal. There are over a dozen different search services currently in existence, each with a unique interface and a database covering a different portion of the Web. As a result, users are forced to repeatedly try and retry their queries
Coil sensitivity encoding for fast MRI. In:
 Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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matrix X is minimized under condition . [16] 954 Pruessmann et al. In this case the image noise matrix reads The reconstruction formulae The limitations of weak reconstruction may be understood by considering Dirac distributions as ideal voxel functions: where r denotes the center of the th voxel
Behavioral theories and the neurophysiology of reward,
 Annu. Rev. Psychol.
, 2006
"... ■ Abstract The functions of rewards are based primarily on their effects on behavior and are less directly governed by the physics and chemistry of input events as in sensory systems. Therefore, the investigation of neural mechanisms underlying reward functions requires behavioral theories that can ..."
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Cited by 187 (0 self)
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(Amador et al. 2000, Apicella et al. 1991 Contiguity Procedures involving Pavlovian conditioning provide simple paradigms for learning and allow the experimenter to test the basic requirements of contiguity, contingency, and prediction error. Contiguity can be tested by presenting a reward 1.52.0 seconds
The Ideal Structure of CuntzKrieger Algebras
 Ergod. Th. and Dyn. Sys
, 1996
"... We construct a universal CuntzKrieger algebra AO A , which is isomorphic to the usual CuntzKrieger algebra O A when A satises the condition (I) of Cuntz and Krieger. Cuntz's classication of ideals in O A when A satises condition (II) extends to a classication of the gauge invariant ideals ..."
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Cited by 65 (15 self)
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ideals in AO A . We use this to describe the topology on the primitive ideal space of AO A . 1 Introduction In [4] Cuntz and Krieger studied C algebras generated by families of n nonzero partial isometries S i satisfying S i S i = n X i=1 A(i; j)S j S j and n X i=1 S i S i = 1
On Feature Selection: Learning with Exponentially many Irrelevant Features as Training Examples
 Proceedings of the Fifteenth International Conference on Machine Learning
, 1998
"... We consider feature selection in the "wrapper " model of feature selection. This typically involves an NPhard optimization problem that is approximated by heuristic search for a "good" feature subset. First considering the idealization where this optimization is performed exactl ..."
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Cited by 47 (4 self)
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, in the presence of many "irrelevant" features, the main source of error in wrapper model feature selection is from "overfitting " holdout or crossvalidation data. This motivates a new algorithm that, again under the idealization of performing search exactly, has sample complexity (and error
Monomial ideals
 Mathematical Computations with Macaulay 2
, 2002
"... Monomial ideals form an important link between commutative algebra and combinatorics. In this chapter, we demonstrate how to implement algorithms in Macaulay 2 for studying and using monomial ideals. We illustrate these methods with examples from combinatorics, integer programming, and algebraic geo ..."
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Cited by 16 (2 self)
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geometry. An ideal I in S = Q[x1,..., xn] is called a monomial ideal if it satisfies any of the following equivalent conditions: (a) I is generated by monomials, (b) if f = ∑ α∈Nn kαxα belongs to I then xα ∈ I whenever kα ̸ = 0, (c) I is torusfixed; in other words, if (c1,...,cn) ∈ (Q∗) n, then I
Results 1  10
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