@article{3973,
abstract = {In this paper we bound the difference between the total mean curvatures of two closed surfaces in R-3 in terms of their total absolute curvatures and the Frechet distance between the volumes they enclose. The proof relies on a combination of methods from algebraic topology and integral geometry. We also bound the difference between the lengths of two curves using the same methods.},
author = {Cohen-Steiner, David and Herbert Edelsbrunner},
journal = {Foundations of Computational Mathematics},
number = {4},
pages = {391 -- 404},
publisher = {Springer},
title = {{Inequalities for the curvature of curves and surfaces}},
doi = {10.1007/s10208-005-0200-3},
volume = {7},
year = {2007},
}
@inproceedings{3975,
abstract = {We study the reconstruction of a stratified space from a possibly noisy point sample. Specifically, we use the vineyard of the distance function restricted to a I-parameter family of neighborhoods of a point to assess the local homology of the stratified space at that point. We prove the correctness of this assessment under the assumption of a sufficiently dense sample. We also give an algorithm that constructs the vineyard and makes the local assessment in time at most cubic in the size of the Delaunay triangulation of the point sample.},
author = {Paul Bendich and Cohen-Steiner, David and Herbert Edelsbrunner and Harer, John and Morozov, Dmitriy},
pages = {536 -- 546},
publisher = {IEEE},
title = {{Inferring local homology from sampled stratified spaces}},
doi = {10.1109/FOCS.2007.33},
year = {2007},
}
@article{3976,
abstract = {Herein, we study the interfaces of a set of 146 transient protein-protein interfaces in order to better understand the principles of their interactions. We define and generate the protein interface using tools from computational geometry and topology and then apply statistical analysis to its residue composition. In addition to counting individual occurrences, we evaluate pairing preferences, both across and as neighbors on one side of an interface. Likelihood correction emphasizes novel and unexpected pairs, such as the His-Cys pair found in most complexes of serine proteases with their diverse inhibitors and the Met-Met neighbor pair found in unrelated protein interfaces. We also present a visualization of the protein interface that allows for facile identification of residue-residue contacts and other biochemical properties.},
author = {Headd, Jeffrey J and Ban, Y E Andrew and Brown, Paul and Herbert Edelsbrunner and Vaidya, Madhuwanti and Rudolph, Johannes},
journal = {Journal of Proteome Research},
number = {7},
pages = {2576 -- 2586},
publisher = {American Chemical Society},
title = {{Protein-protein interfaces: Properties, preferences, and projections}},
doi = {10.1021/pr070018+},
volume = {6},
year = {2007},
}
@article{3977,
abstract = {Using inclusion-exclusion, we can write the indicator function of a union of finitely many balls as an alternating sum of indicator functions of common intersections of balls. We exhibit abstract simplicial complexes that correspond to minimal inclusion-exclusion formulas. They include the dual complex, as defined in [3], and are characterized by the independence of their simplices and by geometric realizations with the same underlying space as the dual complex.},
author = {Attali, Dominique and Herbert Edelsbrunner},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {59 -- 77},
publisher = {Springer},
title = {{Inclusion-exclusion formulas from independent complexes}},
doi = {10.1007/s00454-006-1274-7},
volume = {37},
year = {2007},
}
@inproceedings{3981,
abstract = {Building on the work of Martinetz, Schulten and de Silva, Carlsson, we introduce a 2-parameter family of witness complexes and algorithms for constructing them. This family can be used to determine the gross topology of point cloud data in R-d or other metric spaces. The 2-parameter family is sensitive to differences in sampling density and thus amenable to detecting patterns within the data set. It also lends itself to theoretical analysis. For example, we can prove that in the limit, when the witnesses cover the entire domain, witness complexes in the family that share the first, scale parameter have the same homotopy type.},
author = {Attali, Dominique and Herbert Edelsbrunner and Harer, John and Mileyko, Yuriy},
pages = {386 -- 397},
publisher = {Springer},
title = {{Alpha-beta witness complexes}},
doi = {10.1007/978-3-540-73951-7_34},
volume = {4619},
year = {2007},
}