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23,574
SIMPLE CURVES ON SURFACES
, 1999
"... We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order L 6g+2b+2c−6. This answers a longstanding open question. ..."
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Cited by 19 (6 self)
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We study simple closed geodesics on a hyperbolic surface of genus g with b geodesic boundary components and c cusps. We show that the number of such geodesics of length at most L is of order L 6g+2b+2c−6. This answers a longstanding open question.
An inverse problem with single measurement generated
, 2011
"... Global uniqueness of inverse problem for a hyperbolic PDE with the unknown potential and a single incident plane wave is a well known long standing open question. This question is addressed for the case when derivatives with respect to variables orthogonal to this plane wave are expressed via finite ..."
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Global uniqueness of inverse problem for a hyperbolic PDE with the unknown potential and a single incident plane wave is a well known long standing open question. This question is addressed for the case when derivatives with respect to variables orthogonal to this plane wave are expressed via
Cognition and Categorization,
, 1978
"... Abstract Many concepts have stereotypes. This leaves open the question of whether concepts are stereotypes. It has been argued elsewhere that theories that identify concepts with their stereotypes or with stereotypical properties of their instances (e.g., ..."
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Cited by 1191 (0 self)
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Abstract Many concepts have stereotypes. This leaves open the question of whether concepts are stereotypes. It has been argued elsewhere that theories that identify concepts with their stereotypes or with stereotypical properties of their instances (e.g.,
Finding the Medial Axis of a Simple Polygon in Linear Time
 DISCRETE COMPUT. GEOM
, 1995
"... We give a lineartime algorithm for computing the medial axis of a simple polygon P, This answers a longstanding open question  previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudonormal histograms, then influence histograms and xy monotone histograms. ..."
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Cited by 80 (5 self)
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We give a lineartime algorithm for computing the medial axis of a simple polygon P, This answers a longstanding open question  previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudonormal histograms, then influence histograms and xy monotone histograms
New directions in cryptography.
 IEEE Trans. Inf. Theory,
, 1976
"... Abstract Two kinds of contemporary developments in crypcommunications over an insecure channel order to use cryptogtography are examined. Widening applications of teleprocessraphy to insure privacy, however, it currently necessary for the ing have given rise to a need for new types of cryptograph ..."
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Cited by 3542 (7 self)
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cryptographic unrealistic to expect initial business contacts to be postponed problems of long standing. long enough for keys to be transmitted by some physical means. The cost and delay imposed by this key distribution problem is a major barrier to the transfer of business communications
Approximation by Superpositions of a Sigmoidal Function
, 1989
"... In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set ofaffine functionals can uniformly approximate any continuous function of n real variables with support in the unit hypercube; only mild conditions are imposed on the univariate fun ..."
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Cited by 1248 (2 self)
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function. Our results settle an open question about representability in the class of single bidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any
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 572 (11 self)
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quantum gravity may provide predictions for their outcomes. Finally, we provide answers to frequently asked questions and a list of key open problems.
The Wealth of Networks: How Social Production Transforms Markets and Freedom
, 2007
"... This is a visionary book written by a man on a mission. It articulates one possible answer to the question of what might come after the proprietarybased knowledgebased economy that currently exists in advanced countries. Benkler is professor of law at Yale Law School and one of the most ardent pro ..."
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Cited by 729 (5 self)
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This is a visionary book written by a man on a mission. It articulates one possible answer to the question of what might come after the proprietarybased knowledgebased economy that currently exists in advanced countries. Benkler is professor of law at Yale Law School and one of the most ardent
Features of similarity.
 Psychological Review
, 1977
"... Similarity plays a fundamental role in theories of knowledge and behavior. It serves as an organizing principle by which individuals classify objects, form concepts, and make generalizations. Indeed, the concept of similarity is ubiquitous in psychological theory. It underlies the accounts of stimu ..."
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Cited by 1455 (2 self)
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and metric assumptions are open to question. It has been argued by many authors that dimensional representations are appropriate for certain stimuli (e.g., colors, tones) but not for others. It seems more appropriate to represent faces, countries, or personalities in terms of many qualitative features than
Neural Networks with Quadratic VC Dimension
, 1996
"... This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a longstanding open question, namely whether the wellknown O(w log w) bound, known for hardthreshold nets, also held fo ..."
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Cited by 47 (6 self)
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This paper shows that neural networks which use continuous activation functions have VC dimension at least as large as the square of the number of weights w. This result settles a longstanding open question, namely whether the wellknown O(w log w) bound, known for hardthreshold nets, also held
Results 1  10
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23,574