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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
Strong approximations of threedimensional Wiener sausages
, 2004
"... Abstract. In this paper we prove that the centered threedimensional Wiener sausage can be strongly approximated by a onedimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of ..."
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Cited by 2 (0 self)
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Abstract. In this paper we prove that the centered threedimensional Wiener sausage can be strongly approximated by a onedimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms
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 1 and 2dimensional sausages have minimal Steiner ratios 1 and p 3=2 respectively. (The 2sausage is the vertex set of an infinite strip of abutting equilateral triangles. The 3sausage is an infinite number of points evenly spaced along a certain helix.) We present extensive heuristic evidence
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.
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
THE ORIGIN OF TYPE I SPICULE OSCILLATIONS
"... We use images of high spatial and temporal resolution, obtained with the Rapid Oscillations in the Solar Atmosphere instrument at the Dunn Solar Telescope, to reveal how the generation of transverse waves in Type I spicules is a direct result of longitudinal oscillations occurring in the photosphere ..."
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observations with advanced twodimensional magnetohydrodynamic simulations, we provide evidence for how magnetoacoustic oscillations, generated at the solar surface, funnel upward along Type I spicule structures, before undergoing longitudinaltotransverse mode conversion into waves at twice the initial
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