Distributed synchronization algorithms for wireless sensor networks

The ability to distribute time and frequency among a large population of interacting agents is of interest for diverse disciplines, inasmuch as it enables to carry out complex cooperative tasks. In a wireless sensor network (WSN), time/frequency synchronization allows the implementation of distributed signal processing and coding techniques, and the realization of coordinated access to the shared wireless medium. Large multi-hop WSN\u27s constitute a new regime for network synchronization, as they call for the development of scalable, fully distributed synchronization algorithms. While most of previous research focused on synchronization at the application layer, this thesis considers synchronization at the lowest layers of the communication protocol stack of a WSN, namely the physical and the medium access control (MAC) layer. At the physical layer, the focus is on the compensation of carrier frequency offsets (CFO), while time synchronization is studied for application at the MAC layer. In both cases, the problem of realizing network-wide synchronization is approached by employing distributed clock control algorithms based on the classical concept of coupled phase and frequency locked loops (PLL and FLL). The analysis takes into account communication, signaling and energy consumption constraints arising in the novel context of multi-hop WSN\u27s. In particular, the robustness of the algorithms is checked against packet collision events, infrequent sync updates, and errors introduced by different noise sources, such as transmission delays and clock frequency instabilities. By observing that WSN\u27s allow for greater flexibility in the design of the synchronization network architecture, this work examines also the relative merits of both peer-to-peer (mutually coupled - MC) and hierarchical (master-slave - MS) architectures. With both MC and MS architectures, synchronization accuracy degrades smoothly with the network size, provided that loop parameters are conveniently chosen. In particular, MS topologies guarantee faster synchronization, but they are hindered by higher noise accumulation, while MC topologies allow for an almost uniform error distribution at the price of much slower convergence. For all the considered cases, synchronization algorithms based on adaptive PLL and FLL designs are shown to provide robust and scalable network-wide time and frequency distribution in a WSN

On the dichotomic collective behaviors of large populations of pulse-coupled firing oscillators

The study of populations of pulse-coupled firing oscillators is a general and simple paradigm to investigate a wealth of natural phenomena, including the collective behaviors of neurons, the synchronization of cardiac pacemaker cells, or the dynamics of earthquakes. In this framework, the oscillators of the network interact through an instantaneous impulsive coupling: whenever an oscillator fires, it sends out a pulse which instantaneously increments the state of the other oscillators by a constant value. There is an extensive literature on the subject, which investigates various model extensions, but only in the case of leaky integrate-and-fire oscillators. In contrast, the present dissertation addresses the study of other integrate-and-fire dynamics: general monotone integrate-and-fire dynamics and quadratic integrate-and-fire dynamics. The main contribution of the thesis highlights that the populations of oscillators exhibit a dichotomic collective behavior: either the oscillators achieve perfect synchrony (slow firing frequency) or the oscillators converge toward a phase-locked clustering configuration (fast firing frequency). The dichotomic behavior is established both for finite and infinite populations of oscillators, drawing a strong parallel between discrete-time systems in finite-dimensional spaces and continuous-time systems in infinite-dimensional spaces. The first part of the dissertation is dedicated to the study of monotone integrate-and-fire dynamics. We show that the dichotomic behavior of the oscillators results from the monotonicity property of the dynamics: the monotonicity property induces a global contraction property of the network, that forces the dichotomic behavior. Interestingly, the analysis emphasizes that the contraction property is captured through a 1-norm, instead of a (more common) quadratic norm. In the second part of the dissertation, we investigate the collective behavior of quadratic integrate-and-fire oscillators. Although the dynamics is not monotone, an “average” monotonicity property ensures that the collective behavior is still dichotomic. However, a global analysis of the dichotomic behavior is elusive and leads to a standing conjecture. A local stability analysis circumvents this issue and proves the dichotomic behavior in particular situations (small networks, weak coupling, etc.). Surprisingly, the local stability analysis shows that specific integrate-and-fire oscillators exhibit a non-dichotomic behavior, thereby suggesting that the dichotomic behavior is not a general feature of every network of pulse-coupled oscillators. The present thesis investigates the remarkable dichotomic behavior that emerges from networks of pulse-coupled integrate-and-fire oscillators, putting emphasis on the stability properties of these particular networks and developing theoretical results for the analysis of the corresponding dynamical systems.Les populations d’oscillateurs impulsivement couplés constituent un paradigme simple et général pour étudier une multitude de phénomènes naturels, tels que les comportements collectifs des neurones, la synchronisation des cellules pacemaker du coeur, ou encore la dynamique des tremblements de terre. Dans ce contexte, les oscillateurs interagissent au sein du réseau par le biais d’un couplage instantané: quand un oscillateur décharge, il envoie vers les autres oscillateurs une impulsion qui incrémente instantanément leur état par une valeur constante. Diverses extensions du modèle ont été intensément étudiées dans la littérature, mais seulement dans le cas d’oscillateurs leaky integrate-and-fire. Afin de pallier cette restriction, le présent manuscrit traite de l’étude d’autres dynamiques integrate-and-fire: les dynamiques générales integrate-and-fire monotones et les dynamiques integrate-and-fire quadratiques. La contribution principale de la thèse met en évidence le comportement d’ensemble dichotomique selon lequel s’organisent les populations d’oscillateurs: soit les oscillateurs atteignent un état de synchronisation parfaite (taux de décharge lent), soit ils convergent vers une configuration de clustering en blocage de phase (taux de décharge rapide). Ce comportement dichotomique est établi aussi bien pour des populations finies que pour des populations infinies, ce qui démontre un parallèle élégant entre des systèmes en temps-discret dans des espaces de dimension finie et des systèmes en temps-continu dans des espaces de dimension infinie. La première partie du manuscrit se concentre sur l’étude des dynamiques integrate-and-fire monotones. Dans ce cadre, nous montrons que le comportement dichotomique résulte de la propriété de monotonicité des oscillateurs. Cette dernière induit une propriété de contraction globale, elle-même engendrant le comportement dichotomique. En outre, l’analyse révèle que la propriété de contraction est capturée par une norme 1, au lieu d’une norme quadratique (plus usuelle). Dans la seconde partie de la thèse, nous étudions le comportement d’ensemble d’oscillateurs integrate-and-fire quadratiques. Bien que la dynamique ne soit plus monotone, une propriété de monotonicité “en moyenne” implique que le comportement collectif est encore dichotomique. Alors qu’une analyse de stabilité globale s’avère être difficile et conduit à plusieurs conjectures, une analyse locale permet de prouver le comportement dichomique dans certaines situations (réseaux de petite taille, couplage faible, etc.). De plus, l’analyse locale prouve que des oscillateurs integrate-and-fire particuliers ne s’organisent pas suivant un comportement dichotomique, ce qui suggère que ce dernier n’est pas une caractéristique générale de tous les réseaux d’oscillateurs impulsivement couplés. En résumé, la thèse étudie le remarquable comportement dichotomique qui émerge des réseaux d’oscillateurs integrate-and-fire impulsivement couplés, mettant ainsi l’emphase sur les propriétés de stabilité desdits réseaux et développant les résultats théoriques nécessaires à l’étude mathématique des systèmes dynamiques correspondants

Optically Induced Nanostructures

Nanostructuring of materials is a task at the heart of many modern disciplines in mechanical engineering, as well as optics, electronics, and the life sciences. This book includes an introduction to the relevant nonlinear optical processes associated with very short laser pulses for the generation of structures far below the classical optical diffraction limit of about 200 nanometers as well as coverage of state-of-the-art technical and biomedical applications. These applications include silicon and glass wafer processing, production of nanowires, laser transfection and cell reprogramming, optical cleaning, surface treatments of implants, nanowires, 3D nanoprinting, STED lithography, friction modification, and integrated optics. The book highlights also the use of modern femtosecond laser microscopes and nanoscopes as novel nanoprocessing tools

Understanding spiking and bursting electrical activity through piece-wise linear systems

In recent years there has been an increased interest in working with piece-wise linear caricatures of nonlinear models. Such models are often preferred over more detailed conductance based models for their small number of parameters and low computational overhead. Moreover, their piece-wise linear (PWL) form, allow the construction of action potential shapes in closed form as well as the calculation of phase response curves (PRC). With the inclusion of PWL adaptive currents they can also support bursting behaviour, though remain amenable to mathematical analysis at both the single neuron and network level. In fact, PWL models caricaturing conductance based models such as that of Morris-Lecar or McKean have also been studied for some time now and are known to be mathematically tractable at the network level. In this work we proceed to analyse PWL neuron models of conductance type. In particular we focus on PWL models of the FitzHugh-Nagumo type and describe in detail the mechanism for a canard explosion. This model is further explored at the network level in the presence of gap junction coupling. The study moves to a different area where excitable cells (pancreatic beta-cells) are used to explain insulin secretion phenomena. Here, Ca2+ signals obtained from pancreatic beta-cells of mice are extracted from image data and analysed using signal processing techniques. Both synchrony and functional connectivity analyses are performed. As regards to PWL bursting models we focus on a variant of the adaptive absolute IF model that can support bursting. We investigate the bursting electrical activity of such models with an emphasis on pancreatic beta-cells