13,773 research outputs found
Teichmüller spaces and HR structures for hyperbolic surface dynamics
We construct a Teichmüller space for the C^{1+}-conjugacy classes of hyperbolic dynamical systems on surfaces. After introducing the notion of an HR structure which associates an affine structure with each of the stable and unstable laminations, we show that there is a one-to-one correspondence between these HR structures and the C^{1+}-conjugacy classes. As part of the proof we construct a canonical representative dynamical system for each HR structure. This has the smoothest holonomies of any representative of the corresponding C^{1+}-conjugacy class. Finally, we introduce solenoid functions and show that they provide a good Teichmüller space
Beyond topological persistence: Starting from networks
Persistent homology enables fast and computable comparison of topological
objects. However, it is naturally limited to the analysis of topological
spaces. We extend the theory of persistence, by guaranteeing robustness and
computability to significant data types as simple graphs and quivers. We focus
on categorical persistence functions that allow us to study in full generality
strong kinds of connectedness such as clique communities, -vertex and
-edge connectedness directly on simple graphs and monic coherent categories.Comment: arXiv admin note: text overlap with arXiv:1707.0967
The mixing time of the switch Markov chains: a unified approach
Since 1997 a considerable effort has been spent to study the mixing time of
switch Markov chains on the realizations of graphic degree sequences of simple
graphs. Several results were proved on rapidly mixing Markov chains on
unconstrained, bipartite, and directed sequences, using different mechanisms.
The aim of this paper is to unify these approaches. We will illustrate the
strength of the unified method by showing that on any -stable family of
unconstrained/bipartite/directed degree sequences the switch Markov chain is
rapidly mixing. This is a common generalization of every known result that
shows the rapid mixing nature of the switch Markov chain on a region of degree
sequences. Two applications of this general result will be presented. One is an
almost uniform sampler for power-law degree sequences with exponent
. The other one shows that the switch Markov chain on the
degree sequence of an Erd\H{o}s-R\'enyi random graph is asymptotically
almost surely rapidly mixing if is bounded away from 0 and 1 by at least
.Comment: Clarification
Part-to-whole Registration of Histology and MRI using Shape Elements
Image registration between histology and magnetic resonance imaging (MRI) is
a challenging task due to differences in structural content and contrast. Too
thick and wide specimens cannot be processed all at once and must be cut into
smaller pieces. This dramatically increases the complexity of the problem,
since each piece should be individually and manually pre-aligned. To the best
of our knowledge, no automatic method can reliably locate such piece of tissue
within its respective whole in the MRI slice, and align it without any prior
information. We propose here a novel automatic approach to the joint problem of
multimodal registration between histology and MRI, when only a fraction of
tissue is available from histology. The approach relies on the representation
of images using their level lines so as to reach contrast invariance. Shape
elements obtained via the extraction of bitangents are encoded in a
projective-invariant manner, which permits the identification of common pieces
of curves between two images. We evaluated the approach on human brain
histology and compared resulting alignments against manually annotated ground
truths. Considering the complexity of the brain folding patterns, preliminary
results are promising and suggest the use of characteristic and meaningful
shape elements for improved robustness and efficiency.Comment: Paper accepted at ICCV Workshop (Bio-Image Computing
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