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Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 639 (15 self)
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The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic
Bounded geometries, fractals, and lowdistortion embeddings
"... The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension is ..."
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Cited by 198 (40 self)
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The doubling constant of a metric space (X; d) is thesmallest value * such that every ball in X can be covered by * balls of half the radius. The doubling dimension of X isthen defined as dim(X) = log2 *. A metric (or sequence ofmetrics) is called doubling precisely when its doubling dimension
Distortion of the hyperbolicity constant of a graph
"... If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δhyperbolic (in the Gromov sense) if any side of T is contained in a δneighborhood of the union of the other two sides, for ev ..."
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of the main aims of this paper is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph G \ e obtained from the graph G by deleting an arbitrary edge e from it. These inequalities allow to obtain the other main result of this paper, which characterizes in a
Are constants constant
"... The prospect of a timedependent Higgs vacuum expectation value is examined within the standard model of electroweak interactions. It is shown that the classical equation of motion for the Higgs field admits a solution that is a doublyperiodic function of time. The corresponding Dirac equation for ..."
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Cited by 1 (0 self)
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for the electron field is equivalent to a second order differential equation with doublyperiodic coefficients. In the limit of very large primitive period of the Higgs background this equation can be solved in WKBJ approximation, showing planewave solutions with a timedependent distortion factor which can
The Unique Games Conjecture, integrality gap for cut problems and embeddability of negative type metrics into `1
 In Proc. 46th IEEE Symp. on Foundations of Comp. Sci
, 2005
"... In this paper we disprove the following conjecture due to Goemans [17] and Linial [25] (also see [5, 27]): “Every negative type metric embeds into `1 with constant distortion. ” We show that for every δ> 0, and for large enough n, there is an npoint negative type metric which requires distortion ..."
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Cited by 170 (11 self)
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In this paper we disprove the following conjecture due to Goemans [17] and Linial [25] (also see [5, 27]): “Every negative type metric embeds into `1 with constant distortion. ” We show that for every δ> 0, and for large enough n, there is an npoint negative type metric which requires
Asset pricing with distorted beliefs: Are equity returns too good to be true?, Working paper
, 1997
"... We study a Lucas asset pricing model that is standard in all respects, except that the representative agent’s subjective beliefs about endowment growth are distorted. Using constantrelativeriskaversion utility, with relative risk aversion coefficient below ten, and fluctuating beliefs that exhibi ..."
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Cited by 143 (1 self)
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We study a Lucas asset pricing model that is standard in all respects, except that the representative agent’s subjective beliefs about endowment growth are distorted. Using constantrelativeriskaversion utility, with relative risk aversion coefficient below ten, and fluctuating beliefs
Distortion and topology
"... For a self mapping f: D → D of the unit disk in C which has finite distortion, we give a separation condition on the components of the set where the distortion is large say greater than a given constant which implies that f extends homeomorphically and quasisymetrically to the boundary S and thus ..."
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For a self mapping f: D → D of the unit disk in C which has finite distortion, we give a separation condition on the components of the set where the distortion is large say greater than a given constant which implies that f extends homeomorphically and quasisymetrically to the boundary S and thus
Dollarization, Distortion, and
"... of change.1 For ordinary Cuban workers, one consequence is a constantly shifting constellation of incomeearning options, including work in the formal state sector, a newly established “private ” sector,2 and/or growing informal and black markets. This paper assesses the choices facing Cuban workers ..."
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of change.1 For ordinary Cuban workers, one consequence is a constantly shifting constellation of incomeearning options, including work in the formal state sector, a newly established “private ” sector,2 and/or growing informal and black markets. This paper assesses the choices facing Cuban
Low Distortion Spanners
"... A spanner of an undirected unweighted graph is a subgraph that approximates the distance metric of the original graph with some specified accuracy. Specifically, we say H ⊆ G is an fspanner of G if any two vertices u, v at distance d in G are at distance at most f(d) in H. There is clearly some tr ..."
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Cited by 26 (3 self)
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tradeoff between the sparsity of H and the distortion function f, though the nature of this tradeoff is still poorly understood. In this paper we present a simple, modular framework for constructing sparse spanners that is based on interchangable components called connection schemes. By assembling
Distorting mixed Tsirelson spaces
 Israel J. Math
, 1999
"... Abstract: Any regular mixed Tsirelson space T(θn, Sn)IN for which θn θn → 0, where θ = limn θ1/n n, is shown to be arbitrarily distortable. Certain asymptotic ℓ1 constants for those and other mixed Tsirelson spaces are calculated. Also a combinatorial result on the Schreier families (Sα)α<ω1 is p ..."
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Cited by 13 (3 self)
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Abstract: Any regular mixed Tsirelson space T(θn, Sn)IN for which θn θn → 0, where θ = limn θ1/n n, is shown to be arbitrarily distortable. Certain asymptotic ℓ1 constants for those and other mixed Tsirelson spaces are calculated. Also a combinatorial result on the Schreier families (Sα)α<ω1
Results 1  10
of
1,440