Synchronization, diversity, and topology of networks of integrate and fire oscillators

We study synchronization dynamics of a population of pulse-coupled oscillators. In particular, we focus our attention on the interplay between topological disorder and synchronization features of networks. First, we analyze synchronization time T in random networks, and find a scaling law which relates T to network connectivity. Then, we compare synchronization time for several other topological configurations, characterized by a different degree of randomness. The analysis shows that regular lattices perform better than a disordered network. This fact can be understood by considering the variability in the number of links between two adjacent neighbors. This phenomenon is equivalent to having a nonrandom topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings.

Tuning synchronization of integrate-and-fire oscillators through mobility

We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a nonmonotonic dependence of the synchronization time on the velocity of the agents. Moreover, we find that mechanisms that drive synchronization are different for different dynamical regimes. We report the extreme situation where an interplay between the time scales involved in the dynamical processes completely inhibits the achievement of a coherent state. We also provide estimators for the transitions between the different regimes.

Remote Synchronization Reveals Network Symmetries and Functional Modules

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result, and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

Synchronization of symmetric chaotic systems

This paper contains a study of the synchronization by homogeneous nonlinear driving of systems that are symmetric in phase space. The main consequence of this symmetry is the ability of the response to synchronize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchronization states in which the motions of drive and response are in complete correlation, but the phase space distance between them does not converge to zero. In this case the synchronization phenomenon becomes enriched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear systems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually complicated, frequently fractal, and robust under the changes in the parameters, and (iii) the effect of external noise is to weaken the synchronization, and in some cases to produce jumps between the various synchronization states available

Amplitude envelope synchronization in coupled chaotic oscillators.

A peculiar type of synchronization has been found when two Van der PolDuffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.

Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of this results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties.

Homotopy limits for 2-categories

We study homotopy limits for 2-categories using the theory of Quillen model categories. In order to do so, we establish the existence of projective and injective model structures on diagram 2-categories. Using these results, we describe the homotopical behaviour not only of conical limits but also of weighted limits. Finally, pseudo-limits are related to homotopy limits.

Estudio de sincronización cooperativa en redes de sensores

En este informe se estudia cómo es posible utilizar redes de sensores inalámbricos (WSN), para la localización de determinados eventos. Se hace un estudio previo de cómo una red de sensores puede llegar a estar sincronizada de una manera cooperativa, interactuando todos los sensores de la red entre sí. Primero se realiza el estudio para la sincronización de dos sensores con frecuencias diferentes, viéndose los parámetros que intervienen para que esta sincronización se realice con éxito, y también los efectos que en ella se produce al añadirle ruido. Seguidamente, se realiza el estudio para la sincronización de redes de N sensores, de manera que interactúen entre ellos de forma cooperativa. Se observan las características de la sincronización cuando todos los sensores llegan a consenso y, después, se busca la forma para que el consenso tienda hacia un valor determinado por mutuo acuerdo de los sensores. Finalmente, a partir de las características obtenidas en el consenso de N sensores, se realiza una aplicación práctica para la localización de eventos por medio del consenso de estas redes de sensores inalámbricos.

Implementación de técnicas de estimación y sincronización para sistemas OFDM: aplicación directa sobre la implementación de la capa física del estándar DVB-T

El sistema de modulación ODFM es utilizado en diversas aplicaciones de banda ancha, tanto en comunicaciones por cable como en aplicaciones inalámbricas. Presenta numerosas ventajas frente a sistemas de banda ancha de portadora única ya que permite una alta eficiencia espectral, una fácil ecualización y una reducción del ISI. Por el contrario, presenta dificultades inherentes a su estructura, que son de vital importancia solventar, entre las cuales se encuentran los altos requisitos de sincronización. Este proyecto presenta métodos de sincronización de tiempo y frecuencia implementados y evaluados sobre una plataforma software basada en Matlab®, que recoge el sistema completo de transmisión basado fielmente en el estándar DVB-T. Tras una presentación de los principios de la modulación OFDM, en este documento se presenta un estudio detallado de este sistema de transmisión y su implementación, formando conjuntamente una plataforma de simulación para la evaluación de los estimadores implementados.

Geometria integral i convexitat en espais de curvatura holomorfa constant

En aquest treball es tracten qüestions de la geometria integral clàssica a l'espai hiperbòlic i projectiu complex i a l'espai hermític estàndard, els anomenats espais de curvatura holomorfa constant. La geometria integral clàssica estudia, entre d'altres, l'expressió en termes geomètrics de la mesura de plans que tallen un domini convex fixat de l'espai euclidià. Aquesta expressió es dóna en termes de les integrals de curvatura mitja. Un dels resultats principals d'aquest treball expressa la mesura de plans complexos que tallen un domini fixat a l'espai hiperbòlic complex, en termes del que definim com volums intrínsecs hermítics, que generalitzen les integrals de curvatura mitja. Una altra de les preguntes que tracta la geometria integral clàssica és: donat un domini convex i l'espai de plans, com s'expressa la integral de la s-èssima integral de curvatura mitja del convex intersecció entre un pla i el convex fixat? A l'espai euclidià, a l'espai projectiu i hiperbòlic reals, aquesta integral correspon amb la s-èssima integral de curvatura mitja del convex inicial: se satisfà una propietat de reproductibitat, que no es té en els espais de curvatura holomorfa constant. En el treball donem l'expressió explícita de la integral de la curvatura mitja quan integrem sobre l'espai de plans complexos. L'expressem en termes de la integral de curvatura mitja del domini inicial i de la integral de la curvatura normal en una direcció especial: l'obtinguda en aplicar l'estructura complexa al vector normal. La motivació per estudiar els espais de curvatura holomorfa constant i, en particular, l'espai hiperbòlic complex, es troba en l'estudi del següent problema clàssic en geometria. Quin valor pren el quocient entre l'àrea i el perímetre per a successions de figures convexes del pla que creixen tendint a omplir-lo? Fins ara es coneixia el comportament d'aquest quocient en els espais de curvatura seccional negativa i que a l'espai hiperbòlic real les fites obtingudes són òptimes. Aquí provem que a l'espai hiperbòlic complex, les cotes generals no són òptimes i optimitzem la superior.

Testing low-altitude infrared digital photography from a mini-UAV to retrieve information for biological conservation

Satellite remote sensing imagery is used for forestry, conservation and environmental applications, but insufficient spatial resolution, and, in particular, unavailability of images at the precise timing required for a given application, often prevent achieving a fully operational stage. Airborne remote sensing has the advantage of custom-tuned sensors, resolution and timing, but its price prevents using it as a routine technique for the mentioned fields. Some Unmanned Aerial Vehicles might provide a “third way” solution as low-cost techniques for acquiring remotely sensed information, under close control of the end-user, albeit at the expense of lower quality instrumentation and instability. This report evaluates a light remote sensing system based on a remotely-controlled mini-UAV (ATMOS-3) equipped with a color infra-red camera (VEGCAM-1) designed and operated by CATUAV. We conducted a testing mission over a Mediterranean landscape dominated by an evergreen woodland of Aleppo pine (Pinus halepensis) and (Holm) oak (Quercus ilex) in the Montseny National Park (Catalonia, NE Spain). We took advantage of state-of-the-art ortho-rectified digital aerial imagery (acquired by the Institut Cartogràfic de Catalunya over the area during the previous year) and used it as quality reference. In particular, we paid attention to: 1) Operationality of flight and image acquisition according to a previously defined plan; 2) Radiometric and geometric quality of the images; and 3) Operational use of the images in the context of applications. We conclude that the system has achieved an operational stage regarding flight activities, although with meteorological limits set by wind speed and turbulence. Appropriate landing areas can be sometimes limiting also, but the system is able to land on small and relatively rough terrains such as patches of grassland or short matorral, and we have operated the UAV as far as 7 km from the control unit. Radiometric quality is sufficient for interactive analysis, but probably insufficient for automated processing. A forthcoming camera is supposed to greatly improve radiometric quality and consistency. Conventional GPS positioning through time synchronization provides coarse orientation of the images, with no roll information.

On the existence of hysteresis in the Kuramoto model with bimodal frequency distributions

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.

Higher arithmetic Chow groups

We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.

Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.