414 research outputs found
On three quantization methods for particle on hyperboloid
We compare the respective efficiencies of three quantization methods (group
theoretical, coherent state and geometric) by quantizing the dynamics of a free
massive particle in two-dimensional de Sitter space. For each case we consider
the realization of the principal series representation of group
and its two-fold covering SU(1,1). We demonstrate that standard technique for
finding an irreducible representation within the geometric quantization scheme
fails. For consistency we recall our earlier results concerning the other two
methods, make some improvements and generalizations.Comment: 22 pages, no figures, revte
Statistical Study of the Galaxy Distribution
Large-scale structures in the Universe provide crucial information about formation of structures and can be used to test cosmological models. The good agreement between large-scale observations and the now-standard Lambda-Cold Dark Matter (ÎCDM) model gives hope for this model to be a lasting foundation. Going a step further, these observation
Topological data analysis of human vowels: Persistent homologies across representation spaces
Topological Data Analysis (TDA) has been successfully used for various tasks
in signal/image processing, from visualization to supervised/unsupervised
classification. Often, topological characteristics are obtained from persistent
homology theory. The standard TDA pipeline starts from the raw signal data or a
representation of it. Then, it consists in building a multiscale topological
structure on the top of the data using a pre-specified filtration, and finally
to compute the topological signature to be further exploited. The commonly used
topological signature is a persistent diagram (or transformations of it).
Current research discusses the consequences of the many ways to exploit
topological signatures, much less often the choice of the filtration, but to
the best of our knowledge, the choice of the representation of a signal has not
been the subject of any study yet. This paper attempts to provide some answers
on the latter problem. To this end, we collected real audio data and built a
comparative study to assess the quality of the discriminant information of the
topological signatures extracted from three different representation spaces.
Each audio signal is represented as i) an embedding of observed data in a
higher dimensional space using Taken's representation, ii) a spectrogram viewed
as a surface in a 3D ambient space, iii) the set of spectrogram's zeroes. From
vowel audio recordings, we use topological signature for three prediction
problems: speaker gender, vowel type, and individual. We show that
topologically-augmented random forest improves the Out-of-Bag Error (OOB) over
solely based Mel-Frequency Cepstral Coefficients (MFCC) for the last two
problems. Our results also suggest that the topological information extracted
from different signal representations is complementary, and that spectrogram's
zeros offers the best improvement for gender prediction
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