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Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves
Powerlaw distributions in empirical data
 ISSN 00361445. doi: 10.1137/ 070710111. URL http://dx.doi.org/10.1137/070710111
, 2009
"... Powerlaw distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and manmade phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the t ..."
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Cited by 589 (7 self)
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demonstrate these methods by applying them to twentyfour realworld data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a powerlaw distribution. In some cases we find these conjectures to be consistent with the data while in others the power law
Entrepreneurship: Productive, Unproductive, and Destructive
 Journal of Political Economy
, 1990
"... The basic hypothesis is that, while the total supply of entrepreneurs varies anlong societies, the productive contribution of the society's entrepreneurial activities varies much more because of their allocation between productive activities such as innovation and largely unproductive activitie ..."
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Cited by 599 (2 self)
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Rome. early China, and the Middle Ages and Renaissance in Europe is used to investigate the hypotheses. It is often assumed that an economy of private enterprise has an automatic bias towards innovation, but this is not so. It has a bias only towards profit. [HOBSBAWM 1969, p. 401 When conjectures
The large N limit of superconformal field theories and supergravity
, 1998
"... We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of AntideSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and ..."
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Cited by 5673 (21 self)
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in the superconformal group (as opposed to just the superPoincare group). The ’t Hooft limit of 3+1 N = 4 superYangMills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various AntideSitter spacetimes is dual to various conformal
StrategyProofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions
 J. Econ. Theory
, 1975
"... Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategyproof if it always induces every committee member to cast a ballot revealing his preference. I pro ..."
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Cited by 542 (0 self)
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welfare functions. Third, Arrow’s general possibility theorem is proven in a new manner. 1. INTR~OUOTI~N Almost every participant in the formal deliberations of a committee realizes that situations may occur where he can manipulate the outcome of the committee’s vote by misrepresenting his preferences
The lexical nature of syntactic ambiguity resolution
 Psychological Review
, 1994
"... Ambiguity resolution is a central problem in language comprehension. Lexical and syntactic ambiguities are standardly assumed to involve different types of knowledge representations and be resolved by different mechanisms. An alternative account is provided in which both types of ambiguity derive fr ..."
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Cited by 556 (23 self)
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for a theory of language compre third section we consider processing issues: how information is hension is to explain how the reader or listener copes with a processed within the mental lexicon and how contextual inforpervasive ambiguity problem. Languages are structured at mation can influence
A MaximumEntropyInspired Parser
, 1999
"... We present a new parser for parsing down to Penn treebank style parse trees that achieves 90.1% average precision/recall for sentences of length 40 and less, and 89.5% for sentences of length 100 and less when trained and tested on the previously established [5,9,10,15,17] "stan dard" se ..."
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Cited by 963 (19 self)
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We present a new parser for parsing down to Penn treebank style parse trees that achieves 90.1% average precision/recall for sentences of length 40 and less, and 89.5% for sentences of length 100 and less when trained and tested on the previously established [5,9,10,15,17] "stan dard" sections of the Wall Street Journal tree bank. This represents a 13% decrease in error rate over the best singleparser results on this corpus [9]. The major technical innova tion is the use of a "maximumentropyinspired" model for conditioning and smoothing that let us successfully to test and combine many different conditioning events. We also present some partial results showing the effects of different conditioning information, including a surprising 2% improvement due to guessing the lexical head's preterminal before guessing the lexical head.
Quantum Gravity
, 2004
"... We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theor ..."
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Cited by 566 (11 self)
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We describe the basic assumptions and key results of loop quantum gravity, which is a background independent approach to quantum gravity. The emphasis is on the basic physical principles and how one deduces predictions from them, at a level suitable for physicists in other areas such as string theory, cosmology, particle physics, astrophysics and condensed matter physics. No details are given, but references are provided to guide the interested reader to the literature. The present state of knowledge is summarized in a list of 35 key results on topics including the hamiltonian and path integral quantizations, coupling to matter, extensions to supergravity and higher dimensional theories, as well as applications to black holes, cosmology and Plank scale phenomenology. We describe the near term prospects for observational tests of quantum theories of gravity and the expectations that loop quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.
Network information flow
 IEEE TRANS. INFORM. THEORY
, 2000
"... We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a pointtopoint communication network on which a number of information sources are to be mulitcast to certain sets of destinations. We assume that the information source ..."
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Cited by 1961 (24 self)
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We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a pointtopoint communication network on which a number of information sources are to be mulitcast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. In this paper, we study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the Maxflow Mincut Theorem for network information flow. Contrary to one’s intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a “fluid” which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.
Good News and Bad News: Representation Theorems and Applications
 Bell Journal of Economics
"... prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtai ..."
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Cited by 684 (3 self)
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prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
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