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The Chromatic Numbers of Random Hypergraphs
 Random Struct. Alg
, 1998
"... : For a pair of integers 1### r, the #chromatic number of an runiform Z. hypergraph H# V, E is the minimal k, for which there exists a partition of V into subsets ## T,...,T such that e#T ## for every e#E. In this paper we determine the asymptotic 1 ki Z. behavior of the #chromatic number of t ..."
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Cited by 2 (1 self)
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of the random runiform hypergraph Hn,pfor all r Z #r#1 . possible values of # and for all values of p down to p## n . # 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 381#403, 1998 Key Words: random hypergraphs; chromatic number 1. INTRODUCTION Z. Z Ahypergraph H is an ordered pair H# V, E
The weak choice number of random hypergraphs
"... Abstract. We generalize the notion of choice number from graphs to hypergraphs and estimate the sharp order of magnitude of the choice number of random hypergraphs. It turns out that the choice number and the chromatic number of a random hypergraph have the same order of magnitude, almost surely. Ou ..."
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Cited by 4 (4 self)
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Abstract. We generalize the notion of choice number from graphs to hypergraphs and estimate the sharp order of magnitude of the choice number of random hypergraphs. It turns out that the choice number and the chromatic number of a random hypergraph have the same order of magnitude, almost surely
PROBLEMS AND RESULTS ON 3CHROMATIC HYPERGRAPHS AND SOME RELATED QUESTIONS
 COLLOQUIA MATHEMATICA SOCIETATIS JANOS BOLYAI 10. INFINITE AND FINITE SETS, KESZTHELY (HUNGARY)
, 1973
"... A hypergraph is a collection of sets. This paper deals with finite hypergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is the number of edges containing it. The hypergraph is runiform if every edge has r points. A hypergraph i ..."
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Cited by 317 (0 self)
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is simple if any two edges have at most one common point, and it is called a clique if any two edges have at least one common point. The chromatic number of a hypergraph is the least number k such that the points can be kcolored so that no edge is monochromatic. As far as we know families of sets
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 511 (8 self)
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then almost surely all components in such graphs are small. We can apply these results to G n;p ; G n;M , and other wellknown models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
On the chromatic number of a random hypergraph
, 2012
"... We consider the problem of kcolouring a random runiform hypergraph with n vertices and cn edges, where k, r, c remain constant as n → ∞. Achlioptas and Naor showed that the chromatic number of a random graph in this setting, the case r = 2, must have one of two easily computable values as n → ∞. W ..."
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Cited by 2 (0 self)
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We consider the problem of kcolouring a random runiform hypergraph with n vertices and cn edges, where k, r, c remain constant as n → ∞. Achlioptas and Naor showed that the chromatic number of a random graph in this setting, the case r = 2, must have one of two easily computable values as n
ON THE CHROMATIC NUMBER OF GEOMETRIC HYPERGRAPHS
 VOL. 21, NO. 3, PP. 676–687
, 2007
"... A finite family R of simple Jordan regions in the plane defines a hypergraph H = H(R) where the vertex set of H is R and the hyperedges are all subsets S ⊂Rfor which there is a point p such that S = {r ∈Rp ∈ r}. The chromatic number of H(R) is the minimum number of colors needed to color the membe ..."
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Cited by 3 (0 self)
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A finite family R of simple Jordan regions in the plane defines a hypergraph H = H(R) where the vertex set of H is R and the hyperedges are all subsets S ⊂Rfor which there is a point p such that S = {r ∈Rp ∈ r}. The chromatic number of H(R) is the minimum number of colors needed to color
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for Kcolorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability
The Plenoptic Function and the Elements of Early Vision
 Computational Models of Visual Processing
, 1991
"... experiment. Electrophysiologists have described neurons in striate cortex that are selectively sensitive to certain visual properties; for reviews, see Hubel (1988) and DeValois and DeValois (1988). Psychophysicists have inferred the existence of channels that are tuned for certain visual properties ..."
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Cited by 573 (4 self)
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experiment. Electrophysiologists have described neurons in striate cortex that are selectively sensitive to certain visual properties; for reviews, see Hubel (1988) and DeValois and DeValois (1988). Psychophysicists have inferred the existence of channels that are tuned for certain visual properties; for reviews, see Graham (1989), Olzak and Thomas (1986), Pokorny and Smith (1986), and Watson (1986). Researchers in perception have found aspects of visual stimuli that are processed preattentively (Beck, 1966; Bergen & Julesz, 1983; Julesz & Bergen, Motion Color Binocular disparity Retinal processing Early vision Memory Higherlevel vision Etc... Retina More processing Still more processing Orientation Fig.1.1 A generic diagram for visual processing. In this approach, early vision consists of a set of parallel pathways, each analyzing some particular aspect of the visual stimulus. 1983; Treisman, 1986; Treisman & Gelade, 1980). And in computational
Nonparametric model for background subtraction
 in ECCV ’00
, 2000
"... Abstract. Background subtraction is a method typically used to segment moving regions in image sequences taken from a static camera by comparing each new frame to a model of the scene background. We present a novel nonparametric background model and a background subtraction approach. The model can ..."
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Cited by 538 (17 self)
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Abstract. Background subtraction is a method typically used to segment moving regions in image sequences taken from a static camera by comparing each new frame to a model of the scene background. We present a novel nonparametric background model and a background subtraction approach. The model can handle situations where the background of the scene is cluttered and not completely static but contains small motions such as tree branches and bushes. The model estimates the probability of observing pixel intensity values based on a sample of intensity values for each pixel. The model adapts quickly to changes in the scene which enables very sensitive detection of moving targets. We also show how the model can use color information to suppress detection of shadows. The implementation of the model runs in realtime for both gray level and color imagery. Evaluation shows that this approach achieves very sensitive detection with very low false alarm rates. Key words: visual motion, active and real time vision, motion detection, nonparametric estimation, visual surveillance, shadow detection 1
Results 1  10
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