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A holomorphic Casson invariant for CalabiYau 3folds, and bundles on K3 fibrations
 J. DIFFERENTIAL GEOM
, 2000
"... We briefly review the formal picture in which a CalabiYau nfold is the complex analogue of an oriented real nmanifold, and a Fano with a fixed smooth anticanonical divisor is the analogue of a manifold with boundary, motivating a holomorphic Casson invariant counting bundles on a CalabiYau 3fol ..."
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Cited by 199 (8 self)
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invariants of Fano 3folds. It also allows us to define the holomorphic Casson invariant of a CalabiYau 3fold X, prove it is deformation invariant, and compute it explicitly in some examples. Then we calculate moduli spaces of sheaves on a general K3 fibration X, enabling us to compute the invariant
An Efficient ContextFree Parsing Algorithm
, 1970
"... A parsing algorithm which seems to be the most efficient general contextfree algorithm known is described. It is similar to both Knuth's LR(k) algorithm and the familiar topdown algorithm. It has a time bound proportional to n 3 (where n is the length of the string being parsed) in general; i ..."
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Cited by 798 (0 self)
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A parsing algorithm which seems to be the most efficient general contextfree algorithm known is described. It is similar to both Knuth's LR(k) algorithm and the familiar topdown algorithm. It has a time bound proportional to n 3 (where n is the length of the string being parsed) in general
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer 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 σfinite. 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
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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tiply connected networks: When loops are present, the network is no longer singly connected and local propaga tion schemes will invariably run into trouble . We believe there are general undiscovered theorems about the performance of belief propagation on loopy DAGs. These theo rems, which may have
Reveal, A General Reverse Engineering Algorithm For Inference Of Genetic Network Architectures
, 1998
"... Given the immanent gene expression mapping covering whole genomes during development, health and disease, we seek computational methods to maximize functional inference from such large data sets. Is it possible, in principle, to completely infer a complex regulatory network architecture from input/o ..."
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Cited by 344 (5 self)
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far. For n=50 (elements) and k=3 (inputs per element), the analysis of incomplete state transition tables (100 state transition pairs out of a possible 10 15) reliably produced the original rule and wiring sets. While this study is limited to synchronous Boolean
EXERCISES IN THE BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES
, 2008
"... The book [KM98] gave an introduction to the birational geometry of algebraic varieties, as the subject stood in 1998. The developments of the last decade made the more advanced parts of Chapters 6 and 7 less important and the detailed treatment of surface singularities in Chapter 4 less necessary. H ..."
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Cited by 322 (1 self)
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literature and in “true ” applications. (CalabiYau): These are completely classified (Abelian, K3, Enriques, hyperelliptic) and their geometry is rich. They are of great interest to other mathematicians. (General type): They have a canonical model with Du Val singularities and ample canonical class
Fibrations of low genus
"... Abstract. In the present paper we consider fibrations f: S → B of an algebraic surface onto a curve B, with general fibre a curve of genus g. Our main results are: 1) A structure theorem for such fibrations in the case g = 2 2) A structure theorem for such fibrations in the case g = 3 and general fi ..."
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Cited by 22 (4 self)
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Abstract. In the present paper we consider fibrations f: S → B of an algebraic surface onto a curve B, with general fibre a curve of genus g. Our main results are: 1) A structure theorem for such fibrations in the case g = 2 2) A structure theorem for such fibrations in the case g = 3 and general
On the ubiquity of K3 fibrations in string duality
, 1996
"... We consider the general case of N = 2 dual pairs of type IIA/heterotic string theories in four dimensions. We show that if the type IIA string in this pair can be viewed as having been compactified on a CalabiYau manifold in the usual way then this manifold must be of the form of a K3 fibration. We ..."
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Cited by 13 (1 self)
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We consider the general case of N = 2 dual pairs of type IIA/heterotic string theories in four dimensions. We show that if the type IIA string in this pair can be viewed as having been compactified on a CalabiYau manifold in the usual way then this manifold must be of the form of a K3 fibration
NONRATIONAL DEL PEZZO FIBRATIONS
, 2007
"... Abstract. Let X be a general divisor in 3M + nL  on the rational scroll Proj( ⊕ 4 i=1O P 1(di)), where di and n are integers, M is the tautological line bundle, L is a fibre of the natural projection to P 1, and d1 � · · · � d4 = 0. We prove that X is rational ⇐ ⇒ d1 = 0 and n = 1. 1. Introduc ..."
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Cited by 4 (1 self)
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Abstract. Let X be a general divisor in 3M + nL  on the rational scroll Proj( ⊕ 4 i=1O P 1(di)), where di and n are integers, M is the tautological line bundle, L is a fibre of the natural projection to P 1, and d1 � · · · � d4 = 0. We prove that X is rational ⇐ ⇒ d1 = 0 and n = 1. 1
Which Problems Have Strongly Exponential Complexity?
 Journal of Computer and System Sciences
, 1998
"... For several NPcomplete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of subexponential algorithms for these problems. We introduce a generalized reduction which we call SubExponential Reduction Family (SERF) t ..."
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Cited by 242 (11 self)
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For several NPcomplete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of subexponential algorithms for these problems. We introduce a generalized reduction which we call SubExponential Reduction Family (SERF
Results 1  10
of
10,065