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.

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two different tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally efficient and does not require any ad hoc symbolization process. We find that the method correctly distinguishes between reversible and irreversible stationary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic processes (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identify the irreversible nature of the series

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.

Dry cooling with night cool storage to enhance solar power plants performance in extreme conditions areas

Solar thermal power plants are usually installed in locations with high yearly average solar radiation, often deserts. In such conditions, cooling water required for thermodynamic cycles is rarely available. Moreover, when solar radiation is high, ambient temperature is very high as well; this leads to excessive condensation temperature, especially when air-condensers are used, and decreases the plant efficiency. However, temperature variation in deserts is often very high, which drives to relatively low temperatures during the night. This fact can be exploited with the use of a closed cooling system, so that the coolant (water) is chilled during the night and store. Chilled water is then used during peak temperature hours to cool the condenser (dry cooling), thus enhancing power output and efficiency. The present work analyzes the performance improvement achieved by night thermal cool storage, compared to its equivalent air cooled power plant. Dry cooling is proved to be energy-effective for moderately high day–night temperature differences (20 °C), often found in desert locations. The storage volume requirement for different power plant efficiencies has also been studied, resulting on an asymptotic tendency.

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.

Visibility. Sobre la arquitectura de Emilio Tuñón y Luis Moreno Mansilla. Mansilla + Tuñón. Madrid

When I lncluded the then very young Emilio Tunon ln the book Young Spanish Architecture twenty years ago, he had just built a beautlful chapel in Alcala. Some people criticized this vote of confidence, as they saw it as a bit premature.

Mapping Dynamics into Graphs. The Visibility Algorithm

Si no tenemos en cuenta posibles procesos subyacentes con significado físico, químico, económico, etc., podemos considerar una serie temporal como un mero conjunto ordenado de valores y jugar con él algún inocente juego matemático como transformar dicho conjunto en otro objeto con la ayuda de una operación matemática para ver qué sucede: qué propiedades del conjunto original se conservan, cuáles se transforman y cómo, qué podemos decir de alguna de las dos representaciones matemáticas del objeto con sólo atender a la otra... Este ejercicio sería de cierto interés matemático por sí solo. Ocurre, además, que las series temporales son un método universal de extraer información de sistemas dinámicos en cualquier campo de la ciencia. Esto hace ganar un inesperado interés práctico al juego matemático anteriormente descrito, ya que abre la posibilidad de analizar las series temporales (vistas ahora como evolución temporal de procesos dinámicos) desde una nueva perspectiva. Hemos para esto de asumir la hipótesis de que la información codificada en la serie original se conserva de algún modo en la transformación (al menos una parte de ella). El interés resulta completo cuando la nueva representación del objeto pertencece a un campo de la matemáticas relativamente maduro, en el cual la información codificada en dicha representación puede ser descodificada y procesada de manera efectiva. ABSTRACT Disregarding any underlying process (and therefore any physical, chemical, economical or whichever meaning of its mere numeric values), we can consider a time series just as an ordered set of values and play the naive mathematical game of turning this set into a different mathematical object with the aids of an abstract mapping, and see what happens: which properties of the original set are conserved, which are transformed and how, what can we say about one of the mathematical representations just by looking at the other... This exercise is of mathematical interest by itself. In addition, it turns out that time series or signals is a universal method of extracting information from dynamical systems in any field of science. Therefore, the preceding mathematical game gains some unexpected practical interest as it opens the possibility of analyzing a time series (i.e. the outcome of a dynamical process) from an alternative angle. Of course, the information stored in the original time series should be somehow conserved in the mapping. The motivation is completed when the new representation belongs to a relatively mature mathematical field, where information encoded in such a representation can be effectively disentangled and processed. This is, in a nutshell, a first motivation to map time series into networks.

Night time performance of a storage integrated solar thermophotovoltaic (SISTPV) system

Energy storage at low maintenance cost is one of the key challenges for generating electricity from the solar energy. This paper presents the theoretical analysis (verified by CFD) of the night time performance of a recently proposed conceptual system that integrates thermal storage (via phase change materials) and thermophotovoltaics for power generation. These storage integrated solar thermophotovoltaic (SISTPV) systems are attractive owing to their simple design (no moving parts) and modularity compared to conventional Concentrated Solar Power (CSP) technologies. Importantly, the ability of high temperature operation of these systems allows the use of silicon (melting point of 1680 K) as the phase change material (PCM). Silicon's very high latent heat of fusion of 1800 kJ/kg and low cost ($1.70/kg), makes it an ideal heat storage medium enabling for an extremely high storage energy density and low weight modular systems. In this paper, the night time operation of the SISTPV system optimised for steady state is analysed. The results indicate that for any given PCM length, a combination of small taper ratio and large inlet hole-to-absorber area ratio are essential to increase the operation time and the average power produced during the night time. Additionally, the overall results show that there is a trade-off between running time and the average power produced during the night time. Average night time power densities as high as 30 W/cm(2) are possible if the system is designed with a small PCM length (10 cm) to operate just a few hours after sun-set, but running times longer than 72 h (3 days) are possible for larger lengths (50 cm) at the expense of a lower average power density of about 14 W/cm(2). In both cases the steady state system efficiency has been predicted to be about 30%. This makes SISTPV systems to be a versatile solution that can be adapted for operation in a broad range of locations with different climate conditions, even being used off-grid and in space applications.

Experimentación radical italiana en torno al night-club. Warhol-MacLuhan-Price y la arquitectura eléctrica de los años 60.

La segunda mitad de los años 60, ese convulso periodo generador de experiencias largamente revisitadas, es testigo también de un curioso fenómeno en Italia que, vinculado al auge de los locales nocturnos en Estados Unidos y a un intenso clima de emancipación social, utiliza estos nuevos “palacios de la diversión” como fuente de inspiración ideológica al ser percibidos entre los jóvenes arquitectos y diseñadores radicales italianos como un laboratorio experimental estilístico y funcional capaz de generar modelos para un nuevo orden social ligado al entretenimiento. La intensidad productiva de estos años da como resultado multitud de propuestas donde la arqui­tectura actúa como catalizadora de una pulsión social que mezcla en el mismo espa­cio la vanguardia cultural y experimental más radical con el fenómeno de masas de la sociedad del espectáculo, permitiendo a la industria del placer ocupar sin complejos una posición clave en el discurso de una nueva generación que traslada intenciona­damente su interés desde la forma construida a la producción de ambientes artificia­les, electrónicamente amplificados, demostrando al mismo tiempo su compromiso con las formas y la lógica de las nuevas tecnologías.