Feigenbaum graphs at the onset of chaos

We analyze the properties of networks obtained from the trajectories of unimodal maps at the transi- tion to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such en- tropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network.

Detecting periodicity with horizontal visibility graphs

The horizontal visibility algorithm was recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are in its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.

Proyecto de camino forestal de saca y acceso del monte comuna de buñola. Numero 5 del catalogo (provincia de Baleares)

Tratase de construir la vía principal de saca y acceso al monte citado. Hoy en día solo detestables caminos de carro ponen en comunicación este monte de 723,77 Has. y 500 m3 de posibilidad con el mundo exterior y las consecuencias son funestas tanto con respecto a la economía maderera como para la conservación y mejora de la masa forestal.

Coleccion de cartas eruditas

Índice de los textos que se ilustran en este tomo

[Cartas a Gregorio Mayans y Siscar]

Contiene : material de estudio sobre R. Llull, incluido el indice de autores que han tratado su obra, enviado a G. Mayans en carta fechada en Mallorca, 1762 oct. 27 : h. 6-20

Cartas de Santa Teresa de Jesus ... fundadora ... de la Orden... del Carmen ...

Indice de las cartas, p. [19] ; Indice de las cosas notables, p. I-XXVIII

Cartas de Santa Teresa de Jesus, madre y fundadora de la reforma de la Orden de Nuestra Señora del Carmen ...

Tít. en antep.:" Cartas de Sta. Teresa de Jesus. Tomo II"

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Cartas de Santa Teresa de Jesus, madre y fundadora ... de la Orden de nuestra señora del Carmen ...

Indice de las cartas que se contienen en este tomo, p.[19]-[21] ; Indice de las cosas notables, p. I-XLI ; Indice de los lugares de la Sagrada Escritura, p. XLII

Cartas de Santa Teresa de Jesus ... fundadora ... de la Orden ... del Carmen ...

Indice de las cartas que se contienen en este tomo, [calderón]1-[calderón]4 ; Indice de las cosas notables, p. 502-448 [i.e. 548] ; Indice de los lugares de la Sagrada Escritura, p. 549-550

Glorias de el Señor D. Felipe Quinto, rey de las Españas y emperador del nuevo mundo ... y fatales consequencias ...

Indice

Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are const ructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Far ey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy