Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Topological Summaries for Analyzing the Organization of Cells in
  a Packed Tissue   We use Topological Data Analysis tools for studying the inner organization of
cells in segmented images of epithelial tissues. More specifically, for each
segmented image, we compute different persistence barcodes, which codify
lifetime of homology classes (persistent homology) along different filtrations
(increasing nested sequences of simplicial complexes) that are built from the
regions representing the cells in the tissue. We use a complete and
well-grounded set of numerical variables over those persistence barcodes, also
known as topological summaries. A novel combination of normalization methods
for both, the set of input segmented images and the produced barcodes, allows
to prove stability results for those variables with respect to small changes in
the input, as well as invariance to image scale. Our study provides new
insights to this problem, such as a possible novel indicator for the
development of the drosophila wing disc tissue or the importance of centroids
distribution to differentiate some tissues from their CVT-path counterpart (a
mathematical model of epithelia based on Voronoi diagrams). We also show how
the use of topological summaries may improve the classification accuracy of
epithelial images using Random Forests algorithm.

14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg