130 research outputs found
Characterising epithelial tissues using persistent entropy
In this paper, we apply persistent entropy, a novel topological statis-
tic, for characterization of images of epithelial tissues. We have found
out that persistent entropy is able to summarize topological and geomet-
ric information encoded by -complexes and persistent homology. After
using some statistical tests, we can guarantee the existence of signi cant
di erences in the studied tissues.Ministerio de Economía y Competitividad MTM2015-67072-
Characterising epithelial tissues using persistent entropy
In this paper, we apply persistent entropy, a novel topological statistic,
for characterization of images of epithelial tissues. We have found out that
persistent entropy is able to summarize topological and geometric information
encoded by \alpha-complexes and persistent homology. After using some
statistical tests, we can guarantee the existence of significant differences in
the studied tissues.Comment: 12 pages, 7 figures, 4 table
On the stability of persistent entropy and new summary functions for Topological Data Analysis
Persistent entropy of persistence barcodes, which is based on the Shannon entropy, has
been recently defined and successfully applied to different scenarios: characterization of the
idiotypic immune network, detection of the transition between the preictal and ictal states in
EEG signals, or the classification problem of real long-length noisy signals of DC electrical
motors, to name a few. In this paper, we study properties of persistent entropy and prove its
stability under small perturbations in the given input data. From this concept, we define three
summary functions and show how to use them to detect patterns and topological features
Towards Emotion Recognition: A Persistent Entropy Application
Emotion recognition and classification is a very active area of research. In this paper, we present
a first approach to emotion classification using persistent entropy and support vector machines. A
topology-based model is applied to obtain a single real number from each raw signal. These data are
used as input of a support vector machine to classify signals into 8 different emotions (calm, happy,
sad, angry, fearful, disgust and surprised)
Towards Emotion Recognition: A Persistent Entropy Application
Emotion recognition and classification is a very active area of research. In
this paper, we present a first approach to emotion classification using
persistent entropy and support vector machines. A topology-based model is
applied to obtain a single real number from each raw signal. These data are
used as input of a support vector machine to classify signals into 8 different
emotions (calm, happy, sad, angry, fearful, disgust and surprised)
Separating Topological Noise from Features Using Persistent Entropy
Topology is the branch of mathematics that studies shapes
and maps among them. From the algebraic definition of topology a new
set of algorithms have been derived. These algorithms are identified
with “computational topology” or often pointed out as Topological Data
Analysis (TDA) and are used for investigating high-dimensional data in a
quantitative manner. Persistent homology appears as a fundamental tool
in Topological Data Analysis. It studies the evolution of k−dimensional
holes along a sequence of simplicial complexes (i.e. a filtration). The set
of intervals representing birth and death times of k−dimensional holes
along such sequence is called the persistence barcode. k−dimensional
holes with short lifetimes are informally considered to be topological
noise, and those with a long lifetime are considered to be topological
feature associated to the given data (i.e. the filtration). In this paper, we
derive a simple method for separating topological noise from topological
features using a novel measure for comparing persistence barcodes called
persistent entropy.Ministerio de Economía y Competitividad MTM2015-67072-
Persistent entropy: a scale-invariant topological statistic for analyzing cell arrangements
In this work, we develop a method for detecting differences in the topological distribution of cells forming epithelial tissues. In particular, we extract topological information from their images using persistent homology and a summary statistic called persistent entropy. This method is scale invariant, robust to noise and sensitive to global topological features of the tissue. We have found significant differences between chick neuroepithelium and epithelium of Drosophila wing discs in both, larva and prepupal stages. Besides, we have tested our method, with good results, with images of mathematical tesselations that model biological tissues
Persistent homology analysis of a generalized Aubry-Andr\'{e}-Harper model
Observing critical phases in lattice models is challenging due to the need to
analyze the finite time or size scaling of observables. We study how the
computational topology technique of persistent homology can be used to
characterize phases of a generalized Aubry-Andr\'{e}-Harper model. The
persistent entropy and mean squared lifetime of features obtained using
persistent homology behave similarly to conventional measures (Shannon entropy
and inverse participation ratio) and can distinguish localized, extended, and
crticial phases. However, we find that the persistent entropy also clearly
distinguishes ordered from disordered regimes of the model. The persistent
homology approach can be applied to both the energy eigenstates and the
wavepacket propagation dynamics.Comment: Published version. 8 pages, 9 figure
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