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Full-Text Articles in Physical Sciences and Mathematics
On Isoconcentration Surfaces Of Three Dimensional Turing Patterns, Tilmann Glimm, H. George E. Hentschel
On Isoconcentration Surfaces Of Three Dimensional Turing Patterns, Tilmann Glimm, H. George E. Hentschel
Mathematics Faculty Publications
We consider three-dimensional Turing patterns and their isoconcentration surfaces corresponding to the equilibrium concentration of the reaction kinetics. We call these surfaces equilibrium concentration surfaces (EC surfaces). They are the interfaces between the regions of "high" and "low" concentrations in Turing patterns. We give alternate characterizations of EC surfaces by means of two variational principles, one of them being that they are optimal for diffusive transport. Several examples of EC surfaces are considered. Remarkably, they are often very well approximated by certain minimal surfaces. We give a dynamical explanation for the emergence of Scherk's surface in certain cases, a structure …
The Morphostatic Limit For A Model Of Skeletal Pattern Formation In The Vertebrate Limb, Mark Alber, Tilmann Glimm, H. George E. Hentschel, Bogdan Kazmierczak, Yong-Tao Zhang, Jianfeng Zhu, Stuart (Stuart A.) Newman
The Morphostatic Limit For A Model Of Skeletal Pattern Formation In The Vertebrate Limb, Mark Alber, Tilmann Glimm, H. George E. Hentschel, Bogdan Kazmierczak, Yong-Tao Zhang, Jianfeng Zhu, Stuart (Stuart A.) Newman
Mathematics Faculty Publications
A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions, suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722,2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as “reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to them. The full system, which has smooth solutions that exist globally …
Connectivity Of A Gaussian Network, Paul Balister, BéLa Bollobás, Amites Sarkar, Mark Walters
Connectivity Of A Gaussian Network, Paul Balister, BéLa Bollobás, Amites Sarkar, Mark Walters
Mathematics Faculty Publications
Following Etherington, Hoge and Parkes, we consider a network consisting of (approximately) N transceivers in the plane R² distributed randomly with density given by a Gaussian distribution about the origin, and assume each transceiver can communicate with all other transceivers within distance s. We give bounds for the distance from the origin to the furthest transceiver connected to the origin, and that of the closest transceiver that is not connected to the origin.
Comparison Of Marker-Based Pairwise Relatedness Estimators On A Pedigreed Plant Population, Amy D. Anderson, Marco C.A.M. Bink, W. Eric Van De Weg, Elizabeth A. Thompson
Comparison Of Marker-Based Pairwise Relatedness Estimators On A Pedigreed Plant Population, Amy D. Anderson, Marco C.A.M. Bink, W. Eric Van De Weg, Elizabeth A. Thompson
Mathematics Faculty Publications
Several estimators have been proposed that use molecular marker data to infer the degree of relatedness for pairs of individuals. The objective of this study was to evaluate the performance of seven estimators when applied to marker data of a set of 33 key individuals from a large complex apple pedigree. The evaluation considered different scenarios of allele frequencies and different numbers of marker loci. The method of moments estimators were Similarity, Queller-Goodknight, Lynch-Ritland and Wang. The maximum likelihood estimators were Thompson, Anderson-Weir and Jacquard. The pedigree-based coancestry coefficients were taken as the point of reference in calculating correlations and …
Rank Generating Functions As Weakly Holomorphic Modular Forms, Scott Ahlgren, Stephanie Treneer
Rank Generating Functions As Weakly Holomorphic Modular Forms, Scott Ahlgren, Stephanie Treneer
Mathematics Faculty Publications
Introduction and statement of results. Recent works have illustrated that the Fourier coefficients of harmonic weak Maass forms of weight 1/2 contain a wealth of number-theoretic and combinatorial information. After these works, it is known that many enigmatic q-series (the “mock theta functions” of Ramanujan, and certain rank-generating functions from the theory of partitions, for example) arise naturally as the “holomorphic parts” of such forms. See, for example, Bringmann and Ono [5, 6], Bringmann, Ono, and Rhoades [7], Zwegers [19], Bringmann and Lovejoy [4], Lovejoy and Osburn [12], or see the survey paper [13] for an overview. As another …