Quasiperiodic graphs at the onset of chaos

Luque, Bartolo; Cordero-Gracia, M.; Gómez, Miguel–Ángel; Robledo, Á.

doi:10.1103/physreve.88.062918

Cited by 4 publications

(4 citation statements)

References 32 publications

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“…Finally, we also measure the luminosity of the two newly discovered satellites. The number of stars with g, r < 23 CarinaII CarinaIII MW galaxies M31 galaxies Globular Clusters Extended objects Local Group/Nearby galaxies Belokurov et al 2010;Muñoz et al 2012;Balbinot et al 2013;Kim & Jerjen 2015a;Kim et al 2015Kim et al , 2016Laevens et al 2015;Weisz et al 2016;Luque et al 2015Luque et al , 2016Martin et al 2016;Koposov, Belokurov & Torrealba 2017) and gray dots are the extended objects smaller than 100 pc from Brodie et al (2011). The black solid (dashed) line corresponds to the constant (effective) surface brightness (i.e that within half-light radius) of µ = 31 (30) mag arcsec −2 .…”

Section: Structural Parametersmentioning

confidence: 99%

Discovery of two neighbouring satellites in the Carina constellation with MagLiteS

Torrealba

Belokurov

Koposov

et al. 2018

Monthly Notices of the Royal Astronomical Society

140

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We report the discovery of two ultra-faint satellites in the vicinity of the Large Magellanic Cloud (LMC) in data from the Magellanic Satellites Survey (MagLiteS). Situated 18 • (∼ 20 kpc) from the LMC and separated from each other by only 18 ′ , Carina II and III form an intriguing pair. By simultaneously modeling the spatial and the color-magnitude stellar distributions, we find that both Carina II and Carina III are likely dwarf galaxies, although this is less clear for Carina III. There are in fact several obvious differences between the two satellites. While both are well described by an old and metal poor population, Carina II is located at ∼ 36 kpc from the Sun, with M V ∼ −4.5 and r h ∼ 90 pc, and it is further confirmed by the discovery of 3 RR Lyrae at the right distance. In contrast, Carina III is much more elongated, measured to be fainter (M V ∼ −2.4), significantly more compact (r h ∼ 30 pc), and closer to the Sun, at ∼ 28 kpc, placing it only 8 kpc away from Car II. Together with several other systems detected by the Dark Energy Camera, Carina II and III form a strongly anisotropic cloud of satellites in the vicinity of the Magellanic Clouds.

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Section: Structural Parametersmentioning

confidence: 99%

Discovery of two neighbouring satellites in the Carina constellation with MagLiteS

Torrealba

Belokurov

Koposov

et al. 2018

Monthly Notices of the Royal Astronomical Society

140

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“…10), as the size of the motif has grown to infinity. The examination of their network structure, their degree distribution and their entropy expressions produced another significant result: the occurrence of an HV network version of the q-generalized Pesin identity at the period-doubling [38] and the quasi-periodic [41] transitions to chaos, described earlier in Subsection IIA, Sensitivities. In both cases, the 'distilla-tory' quality of the HV algorithm, many time series into one graph, simplifies the multifractal set at the transition to chaos attractor into a fractal set.…”

Section: Networkmentioning

confidence: 92%

“…Networks. The transformation of iterated map trajectories into (Horizontal Visibility) graphs opened the possibility of reevaluating the link of the renormalization group technique with entropy optimization, and likewise the generalization of the Pesin theorem at the transitions to chaos [36][37][38][39][40][41][42]. Measures.…”

Section: Introductionmentioning

confidence: 99%

A zodiac of studies on complex systems

Robledo¹,

Camacho-Vidales

2020

Supl. Rev. Mex. Fis.

Self Cite

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We offer a brief description of a set of interrelated research lines on the physics of complex systems developed under a unifying methodology grown out from nonlinear dynamics of low dimensionality. The research lines were, and are, developed over a two-decade period (tacitly or not) under a simplifying assumption (and a posteriori corroboration) of a drastic reduction of degrees of freedom. The studies are conveniently grouped into twelve units, and these in turn into four groups, as in a zodiac. The studies in the first group, named Sensitivities, Glasses and Localizations, have in common a clear-cut original opening in the sense that, to our knowledge, the main tenet or result is not found elsewhere. Those in the second group, named Sums, Rankings and Fluctuations, have as a starting point previous stimulating studies or ideas that we followed up but then we converted into separate approaches. The subjects in the third group, named Networks, Measures and Games, involve preset work programs to be followed but ended up within unanticipated, perhaps deeper, grounds. The topics in the final fourth group, named Partitions, Diagonals and Windows, occurred, or are taking place, as specific technical goals that have become after belated realizations to be possible contributions towards the answer of fundamental quests. We discuss connections underlying different aspects of these investigations. Nonlinear dynamics

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“…HVGs are planar graphs built from real-valued time series, whose elements have one-to-one correspondence with the vertices. Important properties, linking the structure of HVGs with features (e.g., onset of chaotic behavior) of the dynamic system underlying the analyzed time series, have been recently studied 42 43 44 45 46 . This last aspect provides an important justification for using HVGs to model neuron activations for the purpose of hyperparameter tuning.…”

mentioning

confidence: 99%

Multiplex visibility graphs to investigate recurrent neural network dynamics

Bianchi

Livi

Alippi

et al. 2017

Sci Rep

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A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning them properly may be difficult and, typically, based on a trial-and-error approach. In this work, we adopt a graph-based framework to interpret and characterize internal dynamics of a class of RNNs called echo state networks (ESNs). We design principled unsupervised methods to derive hyperparameters configurations yielding maximal ESN performance, expressed in terms of prediction error and memory capacity. In particular, we propose to model time series generated by each neuron activations with a horizontal visibility graph, whose topological properties have been shown to be related to the underlying system dynamics. Successively, horizontal visibility graphs associated with all neurons become layers of a larger structure called a multiplex. We show that topological properties of such a multiplex reflect important features of ESN dynamics that can be used to guide the tuning of its hyperparamers. Results obtained on several benchmarks and a real-world dataset of telephone call data records show the effectiveness of the proposed methods.

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Quasiperiodic graphs at the onset of chaos

Cited by 4 publications

References 32 publications

Discovery of two neighbouring satellites in the Carina constellation with MagLiteS

Discovery of two neighbouring satellites in the Carina constellation with MagLiteS

A zodiac of studies on complex systems

Multiplex visibility graphs to investigate recurrent neural network dynamics

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