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21,727
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 507 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
An Optimal Algorithm for Approximate Nearest Neighbor Searching in Fixed Dimensions
 ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1994
"... Consider a set S of n data points in real ddimensional space, R d , where distances are measured using any Minkowski metric. In nearest neighbor searching we preprocess S into a data structure, so that given any query point q 2 R d , the closest point of S to q can be reported quickly. Given any po ..."
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Cited by 984 (32 self)
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positive real ffl, a data point p is a (1 + ffl)approximate nearest neighbor of q if its distance from q is within a factor of (1 + ffl) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in R d in O(dn log n) time and O(dn) space, so that given a
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 893 (0 self)
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amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]
Sequence Logos: A New Way to Display Consensus Sequences
 Nucleic Acids Res
, 1990
"... INTRODUCTION A logo is "a single piece of type bearing two or more usually separate elements" [1]. In this paper, we use logos to display aligned sets of sequences. Sequence logos concentrate the following information into a single graphic [2]: 1. The general consensus of the sequences. ..."
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Cited by 650 (28 self)
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. National Cancer Institute, Frederick Cancer Research and Development Center, Laboratory of Mathematical Biology, P. O. Box B, Frederick, MD 21701. Internet addresses: toms@ncifcrf.gov and stephens@ncifcrf.gov. y corresponding author 1 2. The order of predominance of the residues at every position. 3
Wireless mesh networks: a survey
 COMPUTER NETWORKS
, 2005
"... Wireless meshnet8Ex8 (WMNs)consist of meshrout6L and meshclient8 where meshroutfix have minimal mobilit and formtr backbone of WMNs. They provide netide access for bot mesh andconvent1)fi8 clientt TheintL gratLfl of WMNs wit ot8 net8866 such as t1Int6fiPx1 cellular, IEEE 802.11, IEEE 802.15, IEEE 8 ..."
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Cited by 687 (12 self)
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, local, campus, andmet8Lfix1)6fi areas. Despit recent advances in wireless mesh netjLfiP1)6 many research challenges remain in allprotjfiS layers. This paperpresent adetEfl81 stEonrecent advances and open research issues in WMNs. Syst1 architL881)6 andapplicat)68 of WMNs are described, followed
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 783 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations
Ricci Flow with Surgery on ThreeManifolds
"... This is a technical paper, which is a continuation of [I]. Here we verify most of the assertions, made in [I, §13]; the exceptions are (1) the statement that a 3manifold which collapses with local lower bound for sectional curvature is a graph manifold this is deferred to a separate paper, as the ..."
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Cited by 448 (2 self)
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has standard geometry. The point is to make h arbitrarily small while keeping r bounded away from zero. Notation and terminology B(x, t, r) denotes the open metric ball of radius r, with respect to the metric at time t, centered at x. P(x, t, r, △t) denotes a parabolic neighborhood, that is the set
Similarity estimation techniques from rounding algorithms
 In Proc. of 34th STOC
, 2002
"... A locality sensitive hashing scheme is a distribution on a family F of hash functions operating on a collection of objects, such that for two objects x, y, Prh∈F[h(x) = h(y)] = sim(x,y), where sim(x,y) ∈ [0, 1] is some similarity function defined on the collection of objects. Such a scheme leads ..."
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Cited by 449 (6 self)
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). Our hash functions map distributions to points in the metric space such that, for distributions P and Q,
The Retinoblastoma Protein and CellCycle Control
 Cell
, 1995
"... pRB, the product of the retinoblastoma tumor suppressor gene, operates in the midst of the cell cycle clock apparatus. Its main role is to act as a signal transducer connecting the cell cycle clock with the transcriptional machinery. In this role, pRB allows the clock to control the expression of b ..."
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Cited by 429 (5 self)
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of banks of genes that mediate advance of the cell through a critical phase of its growth cycle. Loss of pRB function deprives the clock and thus the cell of an important mechanism for braking cell proliferation through modulation of gene expression. pRB and the G1 Restriction Point pRB exerts most
Results 1  10
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21,727