Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation.

This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation. In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The main contribution is threefold. First of all, a convergence analysis of the iterative behavior of two novel classes of order-preserving nonlinear maps is carried out, thus establishing sufficient conditions which guarantee convergence toward a fixed point of the map: nonnegative row-stochastic matrices turns out to be a special case. Secondly, these results are applied to MASs, both in discrete and continuous-time: local properties of the agents' dynamics have been identified so that the global interconnected system falls into one of the above mentioned classes, thus guaranteeing its global stability. Lastly, a sufficient condition on the connectivity of the communication network is provided to restrict the set of equilibrium points of the system to the consensus points, thus ensuring the agents to achieve consensus. These results do not rely on standard tools (e.g., Lyapunov theory) and thus they constitute a novel approach to the analysis and control of multi-agent dynamical systems. In the second part the focus is on the design of dynamic estimation algorithms in large networks which enable to solve specific problems. The first problem consists in breaking synchronization in networks of diffusively coupled harmonic oscillators. The design of a local state feedback that achieves desynchronization in connected networks with arbitrary undirected interactions is provided. The proposed control law is obtained via a novel protocol for the distributed estimation of the Fiedler vector of the Laplacian matrix. The second problem consists in the estimation of the number of active agents in networks wherein agents are allowed to join or leave. The adopted strategy consists in the distributed and dynamic estimation of the maximum among numbers locally generated by the active agents and the subsequent inference of the number of the agents that took part in the experiment. Two protocols are proposed and characterized to solve the consensus problem on the time-varying max value. The third problem consists in the average state estimation of a large network of agents where only a few agents' states are accessible to a centralized observer. The proposed strategy projects the dynamics of the original system into a lower dimensional state space, which is useful when dealing with large-scale systems. Necessary and sufficient conditions for the existence of a linear and a sliding mode observers are derived, along with a characterization of their design and convergence properties

The Physics of Open Ended Evolution

abstract: What makes living systems different than non-living ones? Unfortunately this question is impossible to answer, at least currently. Instead, we must face computationally tangible questions based on our current understanding of physics, computation, information, and biology. Yet we have few insights into how living systems might quantifiably differ from their non-living counterparts, as in a mathematical foundation to explain away our observations of biological evolution, emergence, innovation, and organization. The development of a theory of living systems, if at all possible, demands a mathematical understanding of how data generated by complex biological systems changes over time. In addition, this theory ought to be broad enough as to not be constrained to an Earth-based biochemistry. In this dissertation, the philosophy of studying living systems from the perspective of traditional physics is first explored as a motivating discussion for subsequent research. Traditionally, we have often thought of the physical world from a bottom-up approach: things happening on a smaller scale aggregate into things happening on a larger scale. In addition, the laws of physics are generally considered static over time. Research suggests that biological evolution may follow dynamic laws that (at least in part) change as a function of the state of the system. Of the three featured research projects, cellular automata (CA) are used as a model to study certain aspects of living systems in two of them. These aspects include self-reference, open-ended evolution, local physical universality, subjectivity, and information processing. Open-ended evolution and local physical universality are attributed to the vast amount of innovation observed throughout biological evolution. Biological systems may distinguish themselves in terms of information processing and storage, not outside the theory of computation. The final research project concretely explores real-world phenomenon by means of mapping dominance hierarchies in the evolution of video game strategies. Though the main question of how life differs from non-life remains unanswered, the mechanisms behind open-ended evolution and physical universality are revealed.Dissertation/ThesisDoctoral Dissertation Physics 201

Analysis of Embedded Controllers Subject to Computational Overruns

Microcontrollers have become an integral part of modern everyday embedded systems, such as smart bikes, cars, and drones. Typically, microcontrollers operate under real-time constraints, which require the timely execution of programs on the resource-constrained hardware. As embedded systems are becoming increasingly more complex, microcontrollers run the risk of violating their timing constraints, i.e., overrunning the program deadlines. Breaking these constraints can cause severe damage to both the embedded system and the humans interacting with the device. Therefore, it is crucial to analyse embedded systems properly to ensure that they do not pose any significant danger if the microcontroller overruns a few deadlines.However, there are very few tools available for assessing the safety and performance of embedded control systems when considering the implementation of the microcontroller. This thesis aims to fill this gap in the literature by presenting five papers on the analysis of embedded controllers subject to computational overruns. Details about the real-time operating system's implementation are included into the analysis, such as what happens to the controller's internal state representation when the timing constraints are violated. The contribution includes theoretical and computational tools for analysing the embedded system's stability, performance, and real-time properties.The embedded controller is analysed under three different types of timing violations: blackout events (when no control computation is completed during long periods), weakly-hard constraints (when the number of deadline overruns is constrained over a window), and stochastic overruns (when violations of timing constraints are governed by a probabilistic process). These scenarios are combined with different implementation policies to reduce the gap between the analysis and its practical applicability. The analyses are further validated with a comprehensive experimental campaign performed on both a set of physical processes and multiple simulations.In conclusion, the findings of this thesis reveal that the effect deadline overruns have on the embedded system heavily depends the implementation details and the system's dynamics. Additionally, the stability analysis of embedded controllers subject to deadline overruns is typically conservative, implying that additional insights can be gained by also analysing the system's performance

ANOMALOUS TRANSPORT, QUASIPERIODICITY, AND MEASUREMENT INDUCED PHASE TRANSITIONS

With the advent of the noisy-intermediate scale quantum (NISQ) era quantum computers are increasingly becoming a reality of the near future. Though universal computation still seems daunting, a great part of the excitement is about using quantum simulators to solve fundamental problems in fields ranging from quantum gravity to quantum many-body systems. This so-called second quantum revolution rests on two pillars. First, the ability to have precise control over experimental degrees of freedom is crucial for the realization of NISQ devices. Significant progress in the control and manipulation of qubits, atoms, and ions, as well as their interactions, has not only allowed for emulation of diverse range of physical systems but has also led to realization of quantum systems in non-conventional settings such as systems out-of-equilibrium, driven by oscillating fields, and with quasiperiodic (QP) modulation. These systems often show novel properties which not only provide an interesting testbed for NISQ devices but also an opportunity to exploit them for further development of quantum computing devices. Second, the study of dynamics of quantum information in quantum systems is essential for understanding and designing better quantum computers. In addition to their practical application as resource for quantum computation, quantum information has also become an essential element for our understanding of various physical problems, such as thermalization of isolated quantum many-body systems. This interplay between quantum information and computation, and quantum many-body systems is only expected to increase with time. In this thesis, we explore these topics in two parts, corresponding respectively to the two pillars mentioned above. In the first part, we study effects of quasiperiodicity on many-body quantum systems in low dimensions. QP systems are aperiodic but deterministic, so their behavior differs from that of clean systems and disordered ones as well. Moreover, these systems can be conveniently realized in an experimental setting where it is easier to isolate them from external decoherence. %Recent advancement in experimental techniques has made it easier to design and probe quantum systems with quasi-periodic modulations. We start with the easy-plane regime of the XXZ spin chain and show that the well-known fractal behavior of the spin Drude weight implies the divergence of the low-frequency conductivity for generic values of anisotropy. We tie this to the quasi-periodic structure in the Bethe ansatz solution resulting in different species of quasiparticles getting activated along the time evolution in a quasi-periodic pattern. We then study quantum critical systems under generic quasi-periodic modulations using real-space renormalization group (RSRG) procedure. In 1d, we show that the system flows to a new fixed point with the couplings following a discrete aperiodic sequence which allows us to analytically calculate the critical properties. We dub these new classes of quasi-periodic fixed points infinite-quasiperiodicity fixed points in line with the infinite-randomness fixed point observed in random quantum systems. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains. The RSRG is not analytically tractable in 2d, but numerically implementing it for the 2d quasi-periodic $q$-state quantum Potts model, we find that it is well controlled and becomes exact in the asymptotic limit. The critical behavior is shown to be largely independent of $q$ and is controlled by an infinite-quasiperiodicity fixed point. We also provide a heuristic argument for the correlation length exponent and the scaling of the energy gap. Moving on to the second part, we study monitored quantum circuits which have recently emerged as a powerful platform for exploring the dynamics of quantum information and errors in quantum systems. Unitary evolution generates entanglement between distant particles of the system. The dynamics of entanglement has been successfully studied by replacing the Hamiltonian evolution with random quantum circuits. Recently, the robustness of unitary evolution\u27s ability to protect the entanglement against external projective measurements has received much attention. Entanglement is also a resource for quantum information, so its stability is directly related to the stability of a quantum computer against external noises. It has been observed that, in absence of any symmetry, there is a measurement induced phase transition (MIPT) in the behavior of bipartite entanglement that goes from volume law to area law as we tune the rate of measurements. Here we focus on monitored quantum circuits with U(1) symmetry which leads to the presence of a conserved charge density. These diffusive hydrodynamic modes scramble very differently than non-symmetric modes and we find that in addition to the entanglement transition, there is another transition \textit{inside} the volume phase which we call a ``charge sharpening\u27\u27 transition. The sharpening transition is a transition in the ability/inability of the measurements to detect the global charge of the system. We study this sharpening transition in a variety of settings, including an effective field theory that predicts the transition to be in a modified Kosterlitz-Thouless universality class. We provide various numerical evidence to back our predictions

Full stack development toward a trapped ion logical qubit

Quantum error correction is a key step toward the construction of a large-scale quantum computer, by preventing small infidelities in quantum gates from accumulating over the course of an algorithm. Detecting and correcting errors is achieved by using multiple physical qubits to form a smaller number of robust logical qubits. The physical implementation of a logical qubit requires multiple qubits, on which high fidelity gates can be performed. The project aims to realize a logical qubit based on ions confined on a microfabricated surface trap. Each physical qubit will be a microwave dressed state qubit based on 171Yb+ ions. Gates are intended to be realized through RF and microwave radiation in combination with magnetic field gradients. The project vertically integrates software down to hardware compilation layers in order to deliver, in the near future, a fully functional small device demonstrator. This thesis presents novel results on multiple layers of a full stack quantum computer model. On the hardware level a robust quantum gate is studied and ion displacement over the X-junction geometry is demonstrated. The experimental organization is optimized through automation and compressed waveform data transmission. A new quantum assembly language purely dedicated to trapped ion quantum computers is introduced. The demonstrator is aimed at testing implementation of quantum error correction codes while preparing for larger scale iterations.Open Acces

Avalanches and the edge-of-chaos in neuromorphic nanowire networks

The brain's efficient information processing is enabled by the interplay between its neuro-synaptic elements and complex network structure. This work reports on the neuromorphic dynamics of nanowire networks (NWNs), a brain-inspired system with synapse-like memristive junctions embedded within a recurrent neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, thus satisfying criteria for criticality. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos. Dynamical states at the edge-of-chaos are found to optimise information processing for increasingly complex learning tasks. Overall, these results reveal a rich repertoire of emergent, collective dynamics in NWNs which may be harnessed in novel, brain-inspired computing approaches

Low-dimensional representations of neural time-series data with applications to peripheral nerve decoding

Bioelectronic medicines, implanted devices that influence physiological states by peripheral neuromodulation, have promise as a new way of treating diverse conditions from rheumatism to diabetes. We here explore ways of creating nerve-based feedback for the implanted systems to act in a dynamically adapting closed loop. In a first empirical component, we carried out decoding studies on in vivo recordings of cat and rat bladder afferents. In a low-resolution data-set, we selected informative frequency bands of the neural activity using information theory to then relate to bladder pressure. In a second high-resolution dataset, we analysed the population code for bladder pressure, again using information theory, and proposed an informed decoding approach that promises enhanced robustness and automatic re-calibration by creating a low-dimensional population vector. Coming from a different direction of more general time-series analysis, we embedded a set of peripheral nerve recordings in a space of main firing characteristics by dimensionality reduction in a high-dimensional feature-space and automatically proposed single efficiently implementable estimators for each identified characteristic. For bioelectronic medicines, this feature-based pre-processing method enables an online signal characterisation of low-resolution data where spike sorting is impossible but simple power-measures discard informative structure. Analyses were based on surrogate data from a self-developed and flexibly adaptable computer model that we made publicly available. The wider utility of two feature-based analysis methods developed in this work was demonstrated on a variety of datasets from across science and industry. (1) Our feature-based generation of interpretable low-dimensional embeddings for unknown time-series datasets answers a need for simplifying and harvesting the growing body of sequential data that characterises modern science. (2) We propose an additional, supervised pipeline to tailor feature subsets to collections of classification problems. On a literature standard library of time-series classification tasks, we distilled 22 generically useful estimators and made them easily accessible.Open Acces

Understanding the Interaction of CO and O2 with MgO(001) and Supported Metal Atoms: Towards Single-Atom Catalysis

This thesis contributes to the fundamental understanding of the interactions of a single gold atom supported by a defective and defect-free MgO(001) surface in a mixed CO/O2 atmosphere. Using cluster models and point charge embedding within a density functional theory framework, the CO oxidation reaction for a single gold atom is simulated on differently charged oxygen vacancies of MgO(001) to rationalise its experimentally observed lack of catalytic activity. The results show, that only the F0 colour centre promotes the electron redistribution towards an adsorbed oxygen molecule and sufficiently weakens the oxygen bond, as required for a sustainable catalytic cycle. The moderate adsorption energy of the gold atom, however, cannot prevent the insertion of oxygen atoms into the vacancy, which remains after the formation of the first CO2 molecule. The surface becomes invariably repaired, which set the focus on the chemistry on a defect-free MgO(001) surface. To contribute towards the field of heterogeneous single-atom catalysis, various analysis tools are used to shed light on the binding situation of supported group 11 metal atoms to the defect-free substrate and both CO and O2 molecules. Cooperative effects are found to enhance the stability of CO upon co-adsorption with O2 for all three metal centres. The results gives further insights to the lack of catalytic activity with respect to the CO oxidation under thermal conditions as a competition between OC-O2 bond activation and surface diffusion leading to metal atom agglomeration. For the simulation of surface dynamics, an accurate description of the potential energy surface is achieved for CO on a defect-free MgO(001) surface by parametrizing a reactive bond order force field to a new set of ab initio data. Theoretical investigation of the non-reactive scattering of CO from the surface are done by performing quasi-classical scattering dynamic simulations. The scattering behaviour for several incidence energies and different initial ro-vibrational states of impinging CO is evaluated, which illustrates the role of surface atom motion on energy transfer processes. The analysis of time of flight spectra and scattering angle distributions reveals two different scattering channels, which become particularly noticeable at low incidence energies due to the weak interaction potential of CO with MgO(001). The scattering process is strongly influenced by the anisotropy of the potential energy surface for CO impinging in upwards and downwards alignment. Eventually, the observations are in agreement with the established Baule model especially for the distinct scattering features at low incident energies.Die Arbeit vertieft das Wissen über die Wechselwirkungen zwischen einzelnen Goldatomen auf defekthaltigen und defektfreien MgO(001)-Oberflächen in einer gemischten CO/O2 Atmosphäre. Mit Hilfe der Cluster-Einbettungs-Methode und der Dichtefunktionaltheorie wird die Oxidationsreaktion von CO auf einen einzelnen Goldatom simuliert, welches verschieden geladenen Sauerstoff-Fehlstellen der Oberfläche besetzt, um experimentelle Ergebnisse nachzuvollziehen. Es zeigt sich, dass nur die neutral geladenen F0-Fehlstellen durch Elektronenumlagerung in Richtung adsorbierten Sauerstoff-Molekülen in der Lage sind, die Sauerstoffbindung soweit zu schwächen, um eine katalytische Reaktion zu ermöglichen. Dennoch ist die moderate Bindungsenergie eines Goldatoms auf der Fehlstelle nicht ausreichend um die Einlagerung eines einzelnen Sauerstoffatoms zu verhindern, das nach der Bildung des ersten CO2 Moleküls auf der Oberfläche zurückbleibt. Dies führt zur unwiderruflichen Reparatur der Oberflächendefekte. Deswegen verschiebt sich der Fokus auf die Chemie der defektfreien MgO(001)-Oberfläche. Es werden verschiedene Analysemethoden verwendet, um die Bindungsverhältnisse der Metalle der 11. Gruppe mit CO als auch O2 zu verstehen und weitere Einblicke aud den Gebiet der heterogenen Einzelatom-Katalyse zu bekommen. Die gemeinsame Anlagerung von CO und O2 auf allen drei Metallzentren verstärkt die jeweilige Adsorptionsstärke durch kooperative Effekte. Das Ausbleiben einer katalytischen Oxidation von CO unter thermischen Bedingungen wird durch die Ergebnisse unterstützt, vor allem wegen des Widerspruchs, sowohl gleichzeitig einen Bindungsbruch zu ermöglichen, ohne dabei die Metallatome zu größeren Clustern zusammenzuführen. Für die Simulation von Oberflächenprozesse wurde eine präzise Beschreibung des Potentials von CO auf defektfreien MgO(001)-Oberflächen unter Einbezug reaktiver Kraftfelder entwickelt. Es sind quasi-klassische Streusimulationen von CO durchgeführt und dessen Streuverhalten bei verschiedenen Einschlagsenergien und Rotationsschwingungszuständen untersucht worden. Besonderes Augenmerk fällt dabei auf die Bewegungsmöglichkeit der Oberflächenatome. Die Spektren der Flugzeit und Verteilung der Streuwinkel deuten auf zwei verschiedene Streukanäle hin, welche sich vor allem bei schwachen Einschlagsenergien deutlich hervorheben. Dies ist im Einklang mit der schwachen Natur der Gas-Oberflächen-Wechselwirkung. Der Streuprozess hängt deutlich von der Orientierung des Kohlenmonoxids beim Einschlag ab, was an der Anisotropie der Potentialenergiefläche ersichtlich wird. Die Beobachtungen, vor allem bei kleinen Einschlagsenergien, stimmen mit den Vorhersagen des etablierten Baule-Modells überein

Linear and nonlinear approaches to unravel dynamics and connectivity in neuronal cultures

[eng] In the present thesis, we propose to explore neuronal circuits at the mesoscale, an approach in which one monitors small populations of few thousand neurons and concentrates in the emergence of collective behavior. In our case, we carried out such an exploration both experimentally and numerically, and by adopting an analysis perspective centered on time series analysis and dynamical systems. Experimentally, we used neuronal cultures and prepared more than 200 of them, which were monitored using fluorescence calcium imaging. By adjusting the experimental conditions, we could set two basic arrangements of neurons, namely homogeneous and aggregated. In the experiments, we carried out two major explorations, namely development and disintegration. In the former we investigated changes in network behavior as it matured; in the latter we applied a drug that reduced neuronal interconnectivity. All the subsequent analyses and modeling along the thesis are based on these experimental data. Numerically, the thesis comprised two aspects. The first one was oriented towards a simulation of neuronal connectivity and dynamics. The second one was oriented towards the development of linear and nonlinear analysis tools to unravel dynamic and connectivity aspects of the measured experimental networks. For the first aspect, we developed a sophisticated software package to simulate single neuronal dynamics using a quadratic integrate–and–fire model with adaptation and depression. This model was plug into a synthetic graph in which the nodes of the network are neurons, and the edges connections. The graph was created using spatial embedding and realistic biology. We carried out hundreds of simulations in which we tuned the density of neurons, their spatial arrangement and the characteristics of the fluorescence signal. As a key result, we observed that homogeneous networks required a substantial number of neurons to fire and exhibit collective dynamics, and that the presence of aggregation significantly reduced the number of required neurons. For the second aspect, data analysis, we analyzed experiments and simulations to tackle three major aspects: network dynamics reconstruction using linear descriptions, dynamics reconstruction using nonlinear descriptors, and the assessment of neuronal connectivity from solely activity data. For the linear study, we analyzed all experiments using the power spectrum density (PSD), and observed that it was sufficiently good to describe the development of the network or its disintegration. PSD also allowed us to distinguish between healthy and unhealthy networks, and revealed dynamical heterogeneities across the network. For the nonlinear study, we used techniques in the context of recurrence plots. We first characterized the embedding dimension m and the time delay δ for each experiment, built the respective recurrence plots, and extracted key information of the dynamics of the system through different descriptors. Experimental results were contrasted with numerical simulations. After analyzing about 400 time series, we concluded that the degree of dynamical complexity in neuronal cultures changes both during development and disintegration. We also observed that the healthier the culture, the higher its dynamic complexity. Finally, for the reconstruction study, we first used numerical simulations to determine the best measure of ‘statistical interdependence’ among any two neurons, and took Generalized Transfer Entropy. We then analyzed the experimental data. We concluded that young cultures have a weak connectivity that increases along maturation. Aggregation increases average connectivity, and more interesting, also the assortativity, i.e. the tendency of highly connected nodes to connect with other highly connected node. In turn, this assortativity may delineates important aspects of the dynamics of the network. Overall, the results show that spatial arrangement and neuronal dynamics are able to shape a very rich repertoire of dynamical states of varying complexity.[cat] L’habilitat dels teixits neuronals de processar i transmetre informació de forma eficient depèn de les propietats dinàmiques intrínseques de les neurones i de la connectivitat entre elles. La present tesi proposa explorar diferents tècniques experimentals i de simulació per analitzar la dinàmica i connectivitat de xarxes neuronals corticals de rata embrionària. Experimentalment, la gravació de l’activitat espontània d’una població de neurones en cultiu, mitjançant una càmera ràpida i tècniques de fluorescència, possibilita el seguiment de forma controlada de l’activitat individual de cada neurona, així com la modificació de la seva connectivitat. En conjunt, aquestes eines permeten estudiar el comportament col.lectiu emergent de la població neuronal. Amb l’objectiu de simular els patrons observats en el laboratori, hem implementat un model mètric aleatori de creixement neuronal per simular la xarxa física de connexions entre neurones, i un model quadràtic d’integració i dispar amb adaptació i depressió per modelar l’ampli espectre de dinàmiques neuronals amb un cost computacional reduït. Hem caracteritzat la dinàmica global i individual de les neurones i l’hem correlacionat amb la seva estructura subjacent mitjançant tècniques lineals i no–lineals de series temporals. L’anàlisi espectral ens ha possibilitat la descripció del desenvolupament i els canvis en connectivitat en els cultius, així com la diferenciació entre cultius sans dels patològics. La reconstrucció de la dinàmica subjacent mitjançant mètodes d’incrustació i l’ús de gràfics de recurrència ens ha permès detectar diferents transicions dinàmiques amb el corresponent guany o pèrdua de la complexitat i riquesa dinàmica del cultiu durant els diferents estudis experimentals. Finalment, a fi de reconstruir la connectivitat interna hem testejat, mitjançant simulacions, diferents quantificadors per mesurar la dependència estadística entre neurona i neurona, seleccionant finalment el mètode de transferència d’entropia gereralitzada. Seguidament, hem procedit a caracteritzar les xarxes amb diferents paràmetres. Malgrat presentar certs tres de xarxes tipus ‘petit món’, els nostres cultius mostren una distribució de grau ‘exponencial’ o ‘esbiaixada’ per, respectivament, cultius joves i madurs. Addicionalment, hem observat que les xarxes homogènies presenten la propietat de disassortativitat, mentre que xarxes amb un creixent nivell d’agregació espaial presenten assortativitat. Aquesta propietat impacta fortament en la transmissió, resistència i sincronització de la xarxa