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On the Expected Surface Area of the Wiener Sausage
, 2006
"... For parallel neighborhoods of the paths of the d–dimensional Brownian motion, so–called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by means of geometric arguments that the expected surface area is equal to the first derivative of the mean v ..."
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Cited by 7 (4 self)
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For parallel neighborhoods of the paths of the d–dimensional Brownian motion, so–called Wiener sausages, formulae for the expected surface area are given for any dimension d ≥ 2. It is shown by means of geometric arguments that the expected surface area is equal to the first derivative of the mean
On the Steiner ratio in 3space
 J. of Combinatorial Theory, A
, 1992
"... The "Steiner minimal tree" (SMT) of a point set P is the shortest network of "wires" which will suffice to "electrically" interconnect P . The "minimum spanning tree" (MST) is the shortest such network when only intersite line segments are permitted. The " ..."
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Cited by 8 (1 self)
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. The "Steiner ratio" ae(P ) of a point set P is the length of its SMT divided by the length of its MST. It is of interest to understand which point set (or point sets) in R d have minimal Steiner ratio. In this paper, we introduce a point set in R d which we call the "ddimensional sausage
DISPATCHES Hepatitis E Virus in Pork Liver Sausage, France
"... We investigated viability of hepatitis E virus (HEV) identified in contaminated pork liver sausages obtained from France. HEV replication was demonstrated in 1 of 4 samples by using a 3dimensional cell culture system. The risk for human infection with HEV by consumption of these sausages should be ..."
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We investigated viability of hepatitis E virus (HEV) identified in contaminated pork liver sausages obtained from France. HEV replication was demonstrated in 1 of 4 samples by using a 3dimensional cell culture system. The risk for human infection with HEV by consumption of these sausages should
THE ANNALS OF APPLIED PROBABILITY 8(3), 708–748 (1998) BROWNIAN MOTION IN A BROWNIAN CRACK
"... Abstract. LetD be the Wiener sausage of width ε around twosided Brownian motion. The components of 2dimensional reflected Brownian motion in D converge to 1dimensional Brownian motion and iterated Brownian motion, resp., as ε goes to 0. ..."
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Abstract. LetD be the Wiener sausage of width ε around twosided Brownian motion. The components of 2dimensional reflected Brownian motion in D converge to 1dimensional Brownian motion and iterated Brownian motion, resp., as ε goes to 0.
Densest Packings Of More Than Three dSpheres Are Nonplanar
, 1998
"... We prove that for a densest packing of more than three d–balls, d ≥ 3, where the density is measured by parametric density, the convex hull of their centers is either linear (a sausage) or at least 3–dimensional. This is also true for restrictions to lattice packings. The proofs require a Lagrange–t ..."
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We prove that for a densest packing of more than three d–balls, d ≥ 3, where the density is measured by parametric density, the convex hull of their centers is either linear (a sausage) or at least 3–dimensional. This is also true for restrictions to lattice packings. The proofs require a Lagrange
Renormalization group flows and continual Lie algebras”, JHEP 0308
, 2003
"... We study the renormalization group flows of twodimensional metrics in sigma models using the oneloop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the worldsheet lengt ..."
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Cited by 15 (6 self)
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We study the renormalization group flows of twodimensional metrics in sigma models using the oneloop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world
Extremal geometry of a Brownian porous medium
 PROBABILITY THEORY AND RELATED FIELDS MANUSCRIPT NO. (WILL BE INSERTED BY THE EDITOR) PROBABILITY THEORY AND RELATED FIELDS
, 2013
"... The path W [0, t] of a Brownian motion on a ddimensional torusTd run for time t is a random compact subset of Td. We study the geometric properties of the complement Td \W [0, t] as t→ ∞ for d ≥ 3. In particular, we show that the largest regions in Td \W [0, t] have a linear scale ϕd(t) = [(d log ..."
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Cited by 3 (1 self)
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The path W [0, t] of a Brownian motion on a ddimensional torusTd run for time t is a random compact subset of Td. We study the geometric properties of the complement Td \W [0, t] as t→ ∞ for d ≥ 3. In particular, we show that the largest regions in Td \W [0, t] have a linear scale ϕd(t) = [(d
Finding groups in gene expression data
 J Biomed Biotechnol
"... The vast potential of the genomic insight offered by microarray technologies has led to their widespread use since they were introduced a decade ago. Application areas include gene function discovery, disease diagnosis, and inferring regulatory networks. Microarray experiments enable largescale, h ..."
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Cited by 10 (0 self)
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scale, highthroughput investigations of gene activity and have thus provided the data analyst with a distinctive, highdimensional field of study. Many questions in this field relate to finding subgroups of data profiles which are very similar. A popular type of exploratory tool for finding subgroups