Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

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: 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

A new way of teaching different subjects in a foreign language in the Building Engineering Degree at the Universidad Politécnica.

The European Union has been promoting linguistic diversity for many years as one of its main educational goals. This is an element that facilitates student mobility and student exchanges between different universities and countries and enriches the education of young undergraduates. In particular, a higher degree of competence in the English language is becoming essential for engineers, architects and researchers in general, as English has become the lingua franca that opens up horizons to internationalisation and the transfer of knowledge in today’s world. Many experts point to the Integrated Approach to Contents and Foreign Languages System as being an option that has certain benefits over the traditional method of teaching a second language that is exclusively based on specific subjects. This system advocates teaching the different subjects in the syllabus in a language other than one’s mother tongue, without prioritising knowledge of the language over the subject. This was the idea that in the 2009/10 academic year gave rise to the Second Language Integration Programme (SLI Programme) at the Escuela Arquitectura Técnica in the Universidad Politécnica Madrid (EUATM-UPM), just at the beginning of the tuition of the new Building Engineering Degree, which had been adapted to the European Higher Education Area (EHEA) model. This programme is an interdisciplinary initiative for the set of subjects taught during the semester and is coordinated through the Assistant Director Office for Educational Innovation. The SLI Programme has a dual goal; to familiarise students with the specific English terminology of the subject being taught, and at the same time improve their communication skills in English. A total of thirty lecturers are taking part in the teaching of eleven first year subjects and twelve in the second year, with around 120 students who have voluntarily enrolled in a special group in each semester. During the 2010/2011 academic year the degree of acceptance and the results of the SLI Programme have been monitored. Tools have been designed to aid interdisciplinary coordination and to analyse satisfaction, such as coordination records and surveys. The results currently available refer to the first and second year and are divided into specific aspects of the different subjects involved and into general aspects of the ongoing experience.

Variación de las características mecánicas de armaduras de alta ductilidad B500SD en función de su grado de corrosión / Mechanical properties variation of B500SD high ductility reinforcement regarding its corrosion degree

Los efectos de la corrosión sobre las armaduras se manifiestan por la pérdida de sección y la variación de las propiedades mecánicas relacionadas con la ductilidad. En este trabajo se han ensayado a tracción 96 barras de acero B500SD que previamente se han sometido a niveles variables de corrosión. Los resultados muestran que los alargamientos de las barras disminuyen y el cociente entre la tensión máxima y el límite elástico aumenta conforme el nivel de corrosión avanza. A partir del estudio del efecto de entalla y de la distinta constitución metalográfica del acero a nivel de sección debido a su procedimiento de fabricación se pueden explicar los fenómenos anteriores.

A new DSATUR-based algorithm for exact vertex coloring

This paper describes a new exact algorithm PASS for the vertex coloring problem based on the well known DSATUR algorithm. At each step DSATUR maximizes saturation degree to select a new candidate vertex to color, breaking ties by maximum degree w.r.t. uncolored vertices. Later Sewell introduced a new tiebreaking strategy, which evaluated available colors for each vertex explicitly. PASS differs from Sewell in that it restricts its application to a particular set of vertices. Overall performance is improved when the new strategy is applied selectively instead of at every step. The paper also reports systematic experiments over 1500 random graphs and a subset of the DIMACS color benchmark.

Band gap control via tuning of inversion degree in CdIn2S4 spinel

Based on theoretical arguments, we propose a possible route for controlling the band-gap in the promising photovoltaic material CdIn2S4. Our ab initio calculations show that the experimental degree of inversion in this spinel (fraction of tetrahedral sites occupied by In) corresponds approximately to the equilibrium value given by the minimum of the theoretical inversion free energy at a typical synthesis temperature. Modification of this temperature, or of the cooling rate after synthesis, is then expected to change the inversion degree, which in turn sensitively tunes the electronic band-gap of the solid, as shown here by screened hybrid functional calculations.

Approximate entropy of network parameters

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural entropy obtained by computing the approximate entropy of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erdös-Rényi networks. By using classical results of Pincus, we show that our entropy measure often converges with network size to a certain binary Shannon entropy. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate entropy of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate entropy distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

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.

Simulation of academic performance rates, estimation of indicators of subjects and of a complete degree

The purpose of this paper is to present a program written in Matlab-Octave for the simulation of the time evolution of student curricula, i.e, how students pass their subjects along time until graduation. The program computes, from the simulations, the academic performance rates for the subjects of the study plan for each semester as well as the overall rates, which are a) the efficiency rate defined as the ratio of the number of students passing the exam to the number of students who registered for it and b) the success rate, defined as the ratio of the number of students passing the exam to the number of students who not only registered for it but also actually took it. Additionally, we compute the rates for the bachelor academic degree which are established for Spain by the National Quality Evaluation and Accreditation Agency (ANECA) and which are the graduation rate (measured as the percentage of students who finish as scheduled in the plan or taking an extra year) and the efficiency rate (measured as the percentage of credits which a student who graduated has really taken). The simulation is done in terms of the probabilities of passing all the subjects in their study plan. The application of the simulator to Polytech students in Madrid, where requirements for passing are specially stiff in first and second year subjects, is particularly relevant to analyze student cohorts and the probabilities of students finishing in the minimum of four years, or taking and extra year or two extra years, and so forth. It is a very useful tool when designing new study plans. The calculation of the probability distribution of the random variable "number of semesters a student has taken to complete the curricula and graduate" is difficult or even unfeasible to obtain analytically, and this is even truer when we incorporate uncertainty in parameter estimation. This is why we apply Monte Carlo simulation which not only provides illustration of the stochastic process but also a method for computation. The stochastic simulator is proving to be a useful tool for identification of the subjects most critical in the distribution of the number of semesters for curriculum vitae (CV) completion and subsequently for a decision making process in terms of CV planning and passing standards in the University. Simulations are performed through a graphical interface where also the results are presented in appropriate figures. The Project has been funded by the Call for Innovation in Education Projects of Universidad Politécnica de Madrid (UPM) through a Project of its school Escuela Técnica Superior de Ingenieros Industriales ETSII during the period September 2010-September 2011.

Quantity and degree assessment in an RDF.based semantic language

This paper introduces a semantic language developed with the objective to be used in a semantic analyzer based on linguistic and world knowledge. Linguistic knowledge is provided by a Combinatorial Dictionary and several sets of rules. Extra-linguistic information is stored in an Ontology. The meaning of the text is represented by means of a series of RDF-type triples of the form predicate (subject, object). Semantic analyzer is one of the options of the multifunctional ETAP-3 linguistic processor. The analyzer can be used for Information Extraction and Question Answering. We describe semantic representation of expressions that provide an assessment of the number of objects involved and/or give a quantitative evaluation of different types of attributes. We focus on the following aspects: 1) parametric and non-parametric attributes; 2) gradable and non-gradable attributes; 3) ontological representation of different classes of attributes; 4) absolute and relative quantitative assessment; 5) punctual and interval quantitative assessment; 6) intervals with precise and fuzzy boundaries

On the Degree of Team Cooperation in CD Grammar Systems.

In this paper, we introduce a dynamical complexity measure, namely the degree of team cooperation, in the aim of investigating "how much" the components of a grammar system cooperate when forming a team in the process of generating terminal words. We present several results which strongly suggest that this measure is trivial in the sense that the degree of team cooperation of any language is bounded by a constant. Finally, we prove that the degree of team cooperation of a given cooperating/distributed grammar system cannot be algorithmically computed and discuss a decision problem.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

A study the degree of concentration of the Spanish bunkering

This paper shows the Gini Coefficient of the Spanish bunkering, for the Spanish Port System 1960 to the year 2010 with the aim to describe the Spanish bunkering in these periods and propose future strategies. The stage of bunkering must change due to new regulations of marine fuels but to predict the future you must know the past On December 17 came into force on community standard marine fuels. After a complicated negotiation with the industry moves forward a project that is fully compliant with the guidelines of the International Maritime Organization (IMO) and limiting the sulphur and particulate matter of marine fuels used by ships calling or transit through maritime space of the European Union. The impact of a possible extension at European level of the Sulphur Emission Control Areas (SECA) as they are introduced in the Annex VI of the International Convention for the Prevention of Pollution From Ships, 1973 as modified by the Protocol of 1978 (MARPOL) adopted by the International Maritime Organisation (IMO).