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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 472 (7 self)
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be constructed as the quotient (C n+1 −{0})/C ∗. In §2, we will see that there is a similar construction for any toric variety X. In this case, the algebraic group G = HomZ(An−1(X), C ∗ ) acts on an affine space C ∆(1) such that the categorical quotient (C ∆(1) − Z)/G exists and is isomorphic to X
Insertion sequences
 Microbiol Mol. Biol. Rev
, 1998
"... These include: Receive: RSS Feeds, eTOCs, free email alerts (when new articles cite this article), more» Downloaded from ..."
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Cited by 426 (3 self)
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These include: Receive: RSS Feeds, eTOCs, free email alerts (when new articles cite this article), more» Downloaded from
VOLUME MINIMIZATION AND ESTIMATES FOR CERTAIN ISOTROPIC SUBMANIFOLDS IN COMPLEX PROJECTIVE SPACES
, 2004
"... Abstract. In this note we show the following result using the integralgeometric formula of R. Howard: Consider the totally geodesic RP 2m in CP n. Then it minimizes volume among the isotropic submanifolds in the same Z/2 homology class in CP n (but not among all submanifolds in this Z/2 homology cl ..."
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Cited by 5 (1 self)
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Abstract. In this note we show the following result using the integralgeometric formula of R. Howard: Consider the totally geodesic RP 2m in CP n. Then it minimizes volume among the isotropic submanifolds in the same Z/2 homology class in CP n (but not among all submanifolds in this Z/2 homology
Quantitative universality for a class of nonlinear Transformations
 J. Statistical Physics
, 1978
"... A large class of recursion relations xn+l = Af(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function. The functions considered all have a unique differentiable maximum 2. With f(2) f(x) ~ Ix 21 " (for Ix 21 su ..."
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Cited by 244 (0 self)
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universal function g*(x), where the 2"th iterate off, f("~, converges locally to ~"g*(~nx) for large n. For ithe class of f's considered, there exists a A ~ such that a 2"point stable limit cycle including:7 exists; A ~ ~ ~ ~ " ( ~ = 4.669201609103... for z = 2
A steepest descent method for oscillatory Riemann–Hilbert problems: asymptotics for the MKdV equation
 Ann. of Math
, 1993
"... In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory RiemannHilbert problems. Such problems arise, in particular, in evaluating the longtime behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves ..."
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Cited by 300 (27 self)
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here exclusively to the modified Korteweg de Vries (MKdV) equation, yt − 6y 2 yx + yxxx = 0, − ∞ < x < ∞, t ≥ 0, y(x, t = 0) = y0(x), but it will be clear immediately to the reader with some experience in the field, that the method extends naturally and easily to the general class of wave
FlowMap: An Optimal Technology Mapping Algorithm for Delay Optimization in LookupTable Based FPGA Designs
 IEEE TRANS. CAD
, 1994
"... The field programmable gatearray (FPGA) has become an important technology in VLSI ASIC designs. In the past a few years, a number of heuristic algorithms have been proposed for technology mapping in lookuptable (LUT) based FPGA designs, but none of them guarantees optimal solutions for general Bo ..."
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Cited by 317 (41 self)
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The field programmable gatearray (FPGA) has become an important technology in VLSI ASIC designs. In the past a few years, a number of heuristic algorithms have been proposed for technology mapping in lookuptable (LUT) based FPGA designs, but none of them guarantees optimal solutions for general Boolean networks and little is known about how far their solutions are away from the optimal ones. This paper presents a theoretical breakthrough which shows that the LUTbased FPGA technology mapping problem for depth minimization can be solved optimally in polynomial time. A key step in our algorithm is to compute a minimum height Kfeasible cut in a network, which is solved optimally in polynomial time based on network flow computation. Our algorithm also effectively minimizes the number of LUTs by maximizing the volume of each cut and by several postprocessing operations. Based on these results, we have implemented an LUTbased FPGA mapping package called FlowMap. We have tested FlowMap on a large set of benchmark examples and compared it with other LUTbased FPGA mapping algorithms for delay optimization, including Chortled, MISpgadelay, and DAGMap. FlowMap reduces the LUT network depth by up to 7% and reduces the number of LUTs by up to 50% compared to the three previous methods.
Discovery of Inference Rules for Question Answering
 Natural Language Engineering
, 2001
"... One of the main challenges in questionanswering is the potential mismatch between the expressions in questions and the expressions in texts. While humans appear to use inference rules such as “X writes Y ” implies “X is the author of Y ” in answering questions, such rules are generally unavailable ..."
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Cited by 307 (7 self)
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One of the main challenges in questionanswering is the potential mismatch between the expressions in questions and the expressions in texts. While humans appear to use inference rules such as “X writes Y ” implies “X is the author of Y ” in answering questions, such rules are generally unavailable to questionanswering systems due to the inherent difficulty in constructing them. In this paper, we present an unsupervised algorithm for discovering inference rules from text. Our algorithm is based on an extended version of Harris ’ Distributional Hypothesis, which states that words that occurred in the same contexts tend to be similar. Instead of using this hypothesis on words, we apply it to paths in the dependency trees of a parsed corpus. Essentially, if two paths tend to link the same set of words, we hypothesize that their meanings are similar. We use examples to show that our system discovers many inference rules easily missed by humans. 1
Objects and Views
 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 1991
"... Objectoriented databases have been introduced primarily to ease the development of database applications. However, the difficulties encountered when, for instance, trying to restructure data or integrate databases demonstrate that the models being used still lack flexibility. We claim that the natu ..."
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Cited by 258 (9 self)
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that the natural way to overcome these shortcomings is to introduce a sophisticated view mechanism. This paper presents such a mechanism, one which allows a programmer to restructure the class hierarchy and modify the behavior and structure of objects. The mechanism allows a programmer to specify attribute values
Automated Consistency Checking of Requirements Specifications
, 1996
"... This paper describes a formal analysis technique, called consistency checking, for automatic detection of errors, such as type errors, nondeterminism, missing cases, and circular definitions, in requirements specifications. The technique is designed to analyze requirements specifications expressed i ..."
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Cited by 268 (33 self)
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This paper describes a formal analysis technique, called consistency checking, for automatic detection of errors, such as type errors, nondeterminism, missing cases, and circular definitions, in requirements specifications. The technique is designed to analyze requirements specifications expressed in the SCR (Software Cost Reduction) tabular notation. As background, the SCR approach to specifying requirements is reviewed. To provide a formal semantics for the SCR notation and a foundation for consistency checking, a formal requirements model is introduced; the model represents a software system as a finite state automaton, which produces externally visible outputs in response to changes in monitored environmental quantities. Results are presented of two experiments which evaluated the utility and sealability of our technique for consistency checking in a realworld avionics application. The role of consistency checking during the requirements phase of software development is discussed.
Complete genome sequence of enterohemorrhagic Escherichia coli O157:H7 and genomic comparison with a laboratory strain K12. DNA Res
, 2001
"... Escherichia coli O157:H7 is a major foodborne infectious pathogen that causes diarrhea, hemorrhagic colitis, and hemolytic uremic syndrome. Here we report the complete chromosome sequence of an O157:H7 strain isolated from the Sakai outbreak, and the results of genomic comparison with a benign labo ..."
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Cited by 248 (11 self)
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Escherichia coli O157:H7 is a major foodborne infectious pathogen that causes diarrhea, hemorrhagic colitis, and hemolytic uremic syndrome. Here we report the complete chromosome sequence of an O157:H7 strain isolated from the Sakai outbreak, and the results of genomic comparison with a benign laboratory
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