TY - JOUR
AU - Edelsbrunner, Herbert
AU - Strelkova, Nataliya
ID - 2849
IS - 6
JF - Russian Mathematical Surveys
TI - On the configuration space of Steiner minimal trees
VL - 67
ER -
TY - CONF
AB - In order to enjoy a digital version of the Jordan Curve Theorem, it is common to use the closed topology for the foreground and the open topology for the background of a 2-dimensional binary image. In this paper, we introduce a single topology that enjoys this theorem for all thresholds decomposing a real-valued image into foreground and background. This topology is easy to construct and it generalizes to n-dimensional images.
AU - Edelsbrunner, Herbert
AU - Symonova, Olga
ID - 2903
TI - The adaptive topology of a digital image
ER -
TY - JOUR
AB - Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base b and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form P(i) = ai (mod b) for coprime integers a and b. We show that multipliers a that either divide b - 1 or b + 1 generate van der Corput sequences with weak distribution properties. We give explicit lower bounds for the asymptotic distribution behavior of these sequences and relate them to sequences generated from the identity permutation in smaller bases, which are, due to Faure, the weakest distributed generalized van der Corput sequences.
AU - Pausinger, Florian
ID - 2904
IS - 3
JF - Journal de Theorie des Nombres des Bordeaux
SN - 2118-8572
TI - Weak multipliers for generalized van der Corput sequences
VL - 24
ER -
TY - JOUR
AB - We introduce a strategy based on Kustin-Miller unprojection that allows us to construct many hundreds of Gorenstein codimension 4 ideals with 9 × 16 resolutions (that is, nine equations and sixteen first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology. © 2012 Copyright Foundation Compositio Mathematica.
AU - Brown, Gavin
AU - Kerber, Michael
AU - Reid, Miles
ID - 3120
IS - 4
JF - Compositio Mathematica
TI - Fano 3 folds in codimension 4 Tom and Jerry Part I
VL - 148
ER -
TY - CONF
AB - When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when different graph instances have different edge sets pose a serious challenge. In this work we address this challenge for the problem of finding maximum weighted cliques.
We introduce the concept of most persistent soft-clique. This is subset of vertices, that 1) is almost fully or at least densely connected, 2) occurs in all or almost all graph instances, and 3) has the maximum weight. We present a measure of clique-ness, that essentially counts the number of edge missing to make a subset of vertices into a clique. With this measure, we show that the problem of finding the most persistent soft-clique problem can be cast either as: a) a max-min two person game optimization problem, or b) a min-min soft margin optimization problem. Both formulations lead to the same solution when using a partial Lagrangian method to solve the optimization problems. By experiments on synthetic data and on real social network data, we show that the proposed method is able to reliably find soft cliques in graph data, even if that is distorted by random noise or unreliable observations.
AU - Quadrianto, Novi
AU - Lampert, Christoph
AU - Chen, Chao
ID - 3127
T2 - Proceedings of the 29th International Conference on Machine Learning
TI - The most persistent soft-clique in a set of sampled graphs
ER -