368,304 research outputs found
Actions of Polish Groups and Classification Problems
We will discuss in this paper some aspects of a general program whose goal is the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This work is motivated by basic foundational questions, like understanding the nature of complete classification of mathematical objects up to some notion of equivalence by invariants, and creating a mathematical framework for
measuring the complexity of such classification problems. This theory, which has been growing rapidly over the last few years, is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of the broad scope of this theory, there are natural interactions of it with other areas of mathematics, such as the theory of topological groups, topological dynamics, ergodic theory and its relationships with the theory of operator algebras, model theory, and recursion theory
Explainable Equivariant Neural Networks for Particle Physics: PELICAN
PELICAN is a novel permutation equivariant and Lorentz invariant or covariant
aggregator network designed to overcome common limitations found in
architectures applied to particle physics problems. Compared to many approaches
that use non-specialized architectures that neglect underlying physics
principles and require very large numbers of parameters, PELICAN employs a
fundamentally symmetry group-based architecture that demonstrates benefits in
terms of reduced complexity, increased interpretability, and raw performance.
We present a comprehensive study of the PELICAN algorithm architecture in the
context of both tagging (classification) and reconstructing (regression)
Lorentz-boosted top quarks, including the difficult task of specifically
identifying and measuring the -boson inside the dense environment of the
Lorentz-boosted top-quark hadronic final state. We also extend the application
of PELICAN to the tasks of identifying quark-initiated vs.~gluon-initiated
jets, and a multi-class identification across five separate target categories
of jets. When tested on the standard task of Lorentz-boosted top-quark tagging,
PELICAN outperforms existing competitors with much lower model complexity and
high sample efficiency. On the less common and more complex task of 4-momentum
regression, PELICAN also outperforms hand-crafted, non-machine learning
algorithms. We discuss the implications of symmetry-restricted architectures
for the wider field of machine learning for physics.Comment: 52 pages, 34 figures, 12 table
On Measuring Non-Recursive Trade-Offs
We investigate the phenomenon of non-recursive trade-offs between
descriptional systems in an abstract fashion. We aim at categorizing
non-recursive trade-offs by bounds on their growth rate, and show how to deduce
such bounds in general. We also identify criteria which, in the spirit of
abstract language theory, allow us to deduce non-recursive tradeoffs from
effective closure properties of language families on the one hand, and
differences in the decidability status of basic decision problems on the other.
We develop a qualitative classification of non-recursive trade-offs in order to
obtain a better understanding of this very fundamental behaviour of
descriptional systems
Permutation entropy and irreversibility in gait kinematic time series from patients with mild cognitive decline and early alzheimer’s dementia
Gait is a basic cognitive purposeful action that has been shown to be altered in late stages
of neurodegenerative dementias. Nevertheless, alterations are less clear in mild forms of dementia,
and the potential use of gait analysis as a biomarker of initial cognitive decline has hitherto mostly
been neglected. Herein, we report the results of a study of gait kinematic time series for two groups of
patients (mild cognitive impairment and mild Alzheimer’s disease) and a group of matched control
subjects. Two metrics based on permutation patterns are considered, respectively measuring the
complexity and irreversibility of the time series. Results indicate that kinematic disorganisation is
present in early phases of cognitive impairment; in addition, they depict a rich scenario, in which
some joint movements display an increased complexity and irreversibility, while others a marked
decrease. Beyond their potential use as biomarkers, complexity and irreversibility metrics can open a
new door to the understanding of the role of the nervous system in gait, as well as its adaptation and
compensatory mechanismsThis research was funded through the Premio del Ilustre Colegio Profesional de Fisioterapeutas de la
Comunidad De Madrid, prize number ICPFM-IX-201
Examining Scientific Writing Styles from the Perspective of Linguistic Complexity
Publishing articles in high-impact English journals is difficult for scholars
around the world, especially for non-native English-speaking scholars (NNESs),
most of whom struggle with proficiency in English. In order to uncover the
differences in English scientific writing between native English-speaking
scholars (NESs) and NNESs, we collected a large-scale data set containing more
than 150,000 full-text articles published in PLoS between 2006 and 2015. We
divided these articles into three groups according to the ethnic backgrounds of
the first and corresponding authors, obtained by Ethnea, and examined the
scientific writing styles in English from a two-fold perspective of linguistic
complexity: (1) syntactic complexity, including measurements of sentence length
and sentence complexity; and (2) lexical complexity, including measurements of
lexical diversity, lexical density, and lexical sophistication. The
observations suggest marginal differences between groups in syntactical and
lexical complexity.Comment: 6 figure
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