Una Técnica para diagnóstico de la sanidad de suelos y sustratos agrícolas; Fitopatometría

En un artículo anterior, publicado por Terralia, se puso de manifiesto la complejidad y dificultades de las técnicas clásicas de análisis de suelos para conocer su estado sanitario. En dicho trabajo se presentaba la complejidad que entraña analizar todos los posibles microorganismos fitopatógenos que viven en el suelo: hongos, bacterias, virus, etc. Este trabajo pretende dar a conocer una técnica que simplifica, considerablemente, los trabajos de diagnóstico, integrando, dentro de lo posible, todos los factores que intervienen en la expresión de una enfermedad de origen edáfico (figura 1). Por ejemplo en el potencial infeccioso de un suelo aparecen como factores determinantes los siguientes: densidad de inóculo patógeno en el suelo, capacidad infecciosa del inóculo patógeno y ambiente suelo.

Comment on the existence of a long range correlation in the geomagnetic disturbance storm time (Dst) index

Very recently (Banerjee et al. in Astrophys. Space, doi:1007/s10509-011-0836-1, 2011) the statistics of geomagnetic Disturbance storm (Dst) index have been addressed, and the conclusion from this analysis suggests that the underlying dynamical process can be modeled as a fractional Brownian motion with persistent long-range correlations. In this comment we expose several misconceptions and flaws in the statistical analysis of that work. On the basis of these arguments, the former conclusion should be revisited.

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.

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.

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

Phase transition in the countdown problem

We present a combinatorial decision problem, inspired by the celebrated quiz show called Countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.

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.

Correlation Dimension of Complex Networks

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.

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.

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

La construcción de la arquitectura racionalista de Gutiérrez Soto y Fernández Shaw, frente al "estilo Salmón" de Laciana y Arrillaga de la Vega, en Madrid

El racionalismo arquitectónico transforma la arquitectura del primer tercio del siglo XX impulsado, según palabras de Luis Lacasa, por los cambios en las necesidades de la sociedad y las posibilidades de las nuevas técnicas y materiales. En España buscó sacar a su arquitectura del letargo historicista para llevarla a la modernidad, pero también fue una moda que llego de la mano de las vanguardias europeas, que se simplificó a unos pocos criterios, fundamentalmente estéticos, que nutrieron de recursos compositivos a numerosos arquitectos que hicieron sus obras bajo la Ley Salmón. Esta comunicación compara constructivamente estos dos fenómenos que se dieron en Madrid entre 1920 y 1936, y describe hasta donde llegó la implicación constructiva y compositiva de ambos. Se comparan así algunas de las obras realizadas por los arquitectos más vinculados históricamente por los estudiosos al racionalismo funcionalista, con las realizadas por otros que la critica a vinculado a la moda racionalista, y se analiza si sus diferencias conceptuales se reflejan en la técnica constructiva residencial, y cuáles son las principales diferencias y semejanzas que existan entre estos dos caminos.

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.

Idas y venidas. Los viajes de arquitectura en España entre 1920 y 1960

Esta tesis se propone indagar en las vias por las que la arquitectura española cambió en el periodo comprendido entre 1920 y 1960 y el papel que los viajes tuvieron en dicho cambio. La investigación busca demostrar que, junto a otros factores como la llegada de revistas y libros y las conferencias de arquitectos de la talla de Le Corbusier, Gropius, Mendelsohn, Neutra o Aalto, los viajes tuvieron un papel clave en el proceso de apertura de miras y que provocó que, bien a traves de lo publicado en las revistas por los “arquitectos viajeros” o por el reflejo que tuvo lo conocido fuera de nuestras fronteras en proyectos y obras concretas, un buen numero de arquitectos, que no tuvieron la posibilidad de viajar, pudieron conocer que existía una realidad muy distinta a la que los profesores en la Escuela les habían enseñado o a la que estaban acostumbrados a ver en otros arquitectos de generaciones anteriores basada, en buena medida, en la recuperación de un estilo propio nacional centrandose en los historicismos. A lo largo de la investigación trataremos de ver que efecto produjo la apertura de fronteras y que papel tuvieron los viajes en dicho proceso. También nos centraremos en comprobar hasta qué punto cambió la manera de ver la arquitectura de los protagonistas del viaje y de aquellos que recibieron la información por ellos encontrada. Veremos cómo dicha información es cuantificable, clasificable y demostrable en propuestas concretas. Será importante ver que motivó su salida, que buscaban y que encontraron así como, entre las influencias recibidas, cuales tuvieron un mayor calado: las propuestas europeas o las americanas, y dentro de las primeras, las holandesas, las alemanas o las francesas. Los objetivos que se persigue conseguir son: contribuir a un mayor conocimiento de la arquitectura entre 1920 y 1960 a través de las conexiones internacionales y el ensanchamiento de horizontes, recopilar, clasificar y analizar todo el material obtenido relacionando los viajes con las biografías de los arquitectos protagonistas, estudiar qué interesa a los arquitectos españoles cuando van fuera y porqué (será importante ver quiénes de entre los arquitectos son más abiertos a las corrientes europeas y que motivó su salida en busca de nuevos lenguajes), ordenar las reflexiones que exponen los arquitectos a la vuelta de sus viajes y ver en que propuestas y de qué forma los arquitectos plasman lo encontrado en su búsqueda en el extranjero. Para conseguir estos objetivos estructuraremos la investigación en tres bloques: En el primero de ellos nos centraremos en profundizar como era la arquitectura española a principios del siglo XX. Para poder entender mejor las transformaciones que los viajes provocaron será necesario conocer cuál era la arquitectura predominante en estos años que, como veremos, consistía en la búsqueda de un estilo nacional propio dirigiendo su mirada al pasado. También veremos cómo un grupo de arquitectos (Palacios, Flórez, Torres Balbás o Anasagasti) fueron pioneros en el deseo de mirar fuera de nuestras fronteras así como dedicaremos especial atención a cómo era la formación en la Escuela. El segundo capítulo, que abarca desde principios de los años 20 hasta la Guerra Civil, tratará de demostrar la importancia que tuvo en el proceso de permeabilidad frente a las corrientes extranjeras los viajes que los arquitectos realizaron y que, sumados a la llegada de revistas y las visitas de los principales arquitectos modernos, provocaron una primera apertura como respuesta a los historicismos predominantes. Entre los arquitectos viajeros destacaremos las figuras de Fernando García Mercadal (incidiendo en su importancia como difusor de la arquitectura moderna), Rafael Bergamín, Ramón Sánchez Arcas y Luis Lacasa. También nos detendremos en ver la importancia que tuvieron las exposiciones (con especial atención a la de Artes Decorativas de París de 1925 y la de la Deutscher Werkbund en Stuttgart en 1927) que se realizaron estos años y como llegó la información a nuestro país. El tercer y último capítulo arranca con el periodo de posguerra, una época de transición pues los viajes que se realizaron fueron escasos y en la mayoría de las ocasiones no se llevaron a cabo en busca de nuevos caminos. Veremos cómo tras la Guerra y de la mano de la dictadura se produce, de la misma forma que en la Alemania nazi, una vuelta al interés por los historicismos de principios de siglo. Para entender mejor este periodo haremos un repaso a la obra de Luis Gutiérrez Soto por ser explicativa de lo cambiante de las corrientes arquitectónicas de estos años. Tras el análisis de los sucedido en posguerra nos dedicaremos a analizar, de la misma forma que en el primer periodo, la manera en que se produjo el rechazo al estilo nacional de nuevo gracias a la llegada de libros y revistas, lo publicado por las revistas españolas, las visitas de arquitectos de prestigio así como los viajes de un grupo de arquitectos que, de manera individual, salieron al extranjero en busca de apoyo, de referencias en los que cimentar su arquitectura. De este grupo, por la importancia que los propios protagonistas dieron al hecho de viajar como complemento a su formación y por la manera en la que reflejaron lo aprendido en proyectos concretos destacamos a Francisco de Asís Cabrero, Miguel Fisac, Ramón Vázquez Molezún y Francisco Javier Sáenz de Oiza. De nuevo, igual que en el primer capítulo finalizaremos la investigación dedicando un apartado a las exposiciones (fundamentalmente la Interbau de Berlín de 1957) celebradas en estos años. Para finalizar estableceremos las conclusiones que nos llevarán a comprobar hasta qué punto la arquitectura española en los periodos previo y posterior a la guerra cambió y en qué medida tuvieron importancia los viajes que los arquitectos españoles realizaron al extranjero en dicho cambio… ABSTRACT This thesis aims to look at the ways which Spanish architecture changed in the period between 1920 and 1960, and the way it was effected by travelling . The research will demonstrate that, together with other factors, such as the arrival of magazines, books, conferences and architects like Le Corbusier, Gropius, Mendelsohn, Neutra or Aalto, travelling played a key role in architecture. Also, it changed the way we look at architecture. Travelling, thanks to the published journals by "travelling architects” and the influence that they had - known beyond our borders in projects and concrete works, caused the arrival of a new type of architects. Even those who were not able to travel, knew that there was a very different reality than the reality the teachers at the school had taught them. Also, the “new reality” was different from the one that they were used to seeing in other architects of earlier generations, based mainly on the recovery of a national style focused on historicism. Throughout the investigation I will try to show the effect that the opening of borders and travelling had on this process. We will also focus on checking how it changed the way we see the architecture, from the point of view of the protagonists of the travels and those who received the information . We will see how that information is quantifiable and demonstrably classifiable into concrete proposals. It will be important to see which led to their departure. They sought and found among the influences, which had a major impact: the proposed European or American, and within the first, Dutch, German or French. The objectives to be achieved are: To contribute to a better understanding of architecture between 1920 to 1960 by the international connections, and widening the horizon. To collect, classify and analyze all obtained materials related to travelling with biographies of architects protagonists. To study what the interests of the Spanish architects were when they went abroad and why ( it will be important to see who among those architects were more open to European trends and prompted their departures for new languages). To order reflections exhibited by architects around his travels and to see what proposals and how architects reflected what they found in their search abroad. To achieve these objectives we will structure this research in three areas: In the first one, we will focus on how the Spanish architecture in the early twentieth century was. To better understand the changes that travelling caused it is necessary to understand that the predominant architecture in these years was in pursuit of its own national style, directing its gaze to the past, like we shall see. We will also see how a group of architects (Palacios, Flórez, Torres Balbás or Anasagasti) pioneered by looking beyond our borders and devote special attention to how the training was in the School. The second chapter, ranging from early 20s to the Civil War, will try to demonstrate the importance that travelling had in the process of diffusion currents. That, together with the arrival of magazines and visits by leading modern architects, led to a first opening in architecture, in response to the prevailing historicism. Among the travelers we highlight architects like Fernando García Mercadal (stressing his importance as a disseminator of modern architecture), Rafael Bergamín, Ramón Sánchez Arcas and Luis Lacasa. We will also stop to see the importance of exhibitions (with special attention to the Decorative Arts in Paris in 1925 and the Deutscher Werkbund in Stuttgart in 1927) that were held over the years and how the information came to our country . The third and final chapter starts with the post war period, a time of transition for the travels, which were scarce and in most cases were not conducted on new roads. We will see that after the war and with the dictatorship, a return to interest in historicism of the century occurred, just as in Nazi Germany. For better understanding of this period we will review the work of Luis Gutiérrez Soto. His work is explanatory of the changing of architectural trends over these years. After analyzing the case in post war, we turn to analyze, in the same way as in the first period, the manner in which rejection occurred in national style again with the arrival of books and magazines. Visits by prestigious architects and group travels of architects who, individually, went abroad in search of support, references on which to base their architecture. In this group of architects, due to the importance that the protagonists gave to the act of traveling to improve their training and the way in which they reflected what they learned in practical projects, I include Francisco de Asís Cabrero, Miguel Fisac, Ramon Vazquez Molezún and Francisco Javier Saenz de Oiza. Again, as in the first chapter, we will conclude the investigation dedicating a section to the exhibitions held in these years (mainly Interbau Berlin, 1957). Finally establishing conclusions lead us to see how far the Spanish architecture in the pre- and post -war periods changed and how much the trips were important to Spanish architects who performed abroad on the change...