We studied invariant measures and invariant densities for dynamical systems with random switching (switching systems, in short). These switching systems can be described by a two-component Markov process whose first component is a stochastic process on a finite-dimensional smooth manifold and whose second component is a stochastic process on a finite collection of smooth vector fields that are defined on the manifold. We identified sufficient conditions for uniqueness and absolute continuity of the invariant measure associated to this Markov process. These conditions consist of a Hoermander-type hypoellipticity condition and a recurrence condition. In the case where the manifold is the real line or a subset of the real line, we studied regularity properties of the invariant densities of absolutely continuous invariant measures. We showed that invariant densities are smooth away from critical points of the vector fields. Assuming in addition that the vector fields are analytic, we derived the asymptotically dominant term for invariant densities at critical points.

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

No description available.

No description available.

No description available.

<p> Embedded deterministic test (EDT) is a manufacturing test paradigm that combines the compression advantage of built-in self-test with the high fault coverage of deterministic stimuli inherent to methods based on automatic test pattern generation and external testers. Despite enabling the use of low cost testers for rapidly achieving high fault coverage, EDT must consciously use the available tester channels to ensure non-disruptive scaling to future devices of increased complexity. The focus of this thesis is to introduce a new EDT approach for systems-on-a-chip (SOCs) that are designed using embedded cores that are intellectual property (IP)-protected.</p> <p> Following an introduction to integrated circuit testing and an overview of the related work, we define the criteria that must be satisfied by the EDT approaches for the future SOCs of ever growing complexity. Then we observe that the necessary amount of compressed volume of test data transferred from the tester to the embedded cores in an SOC varies significantly during the testing process. This motivates a novel approach to compressed SOC testing based on time-multiplexing the tester channels. It is shown how the introduction of test control channels will reduce the number of required test data channels which will then have increased usage, as the embedded cores will receive compressed test data only when necessary. Through the use of modular and scalable hardware for on-chip test control and test data decompression, we define a new algorithmic framework for test data compression that is applicable to SOCs comprising IP-protected blocks. Experimental results indicate that our approach compares to the existing approaches for EDT that have similar design criteria and methodology constraints, while providing a seamless integration to low cost test equipment.</p> / Thesis / Master of Applied Science (MASc)

The cell cycle of budding yeast is controlled by a complex chemically reacting network of a large group of species, including mRNAs and proteins. Many mathematical models have been proposed to unravel its molecular mechanism. However, it is hard for people with less training to visually interpret the dynamics from the simulation results of these models. In this thesis, we use the visualization toolkit D3 and jQuery to design a web-based interface and help users to visualize the cell cycle simulation results. It is essentially a website where the proliferation of the wild-type and mutant cells can be visualized as dynamical animation. With the help of this visualization tool, we can easily and intuitively see many key steps in the budding yeast cell cycle procedure, such as bud emergence, DNA synthesis, mitosis, cell division, and the current populations of species. / Master of Science / The cell cycle of budding yeast is controlled by a complex chemically reacting network. Many mathematical models have been proposed to unravel its molecular mechanism. However, it is hard to visually interpret the dynamics from the simulation results of these models. In this thesis, we use the visualization toolkit D3 and jQuery to design a web-based interface and help users to visualize the cell cycle simulation results. It is essentially a webpage where the proliferation of the wild-type and mutant cells can be visualized as dynamical animation.

State Machine Replication (SMR) has become the de-facto methodology of building a replication based fault-tolerance system. Current SMR systems usually have multiple machines involved, each of the machines in the SMR system acts as the replica of others. However having multiple machines leads to more cost to the infrastructure, in both hardware cost and power consumption. For tolerating non-critical CPU and memory failure that will not crash the entire machine, there is no need to have extra machines to do the job. As a result, intra-machine replication is a good fit for this scenario. However, current intra-machine replication approaches do not provide strong isolation among the replicas, which allows the faults to be propagated from one replica to another. In order to provide an intra-machine replication technique with strong isolation, in this thesis we present a SMR system on a multi-kernel OS. We implemented a replication system that is capable of replicating concurrent applications on different kernel instances of a multi-kernel OS. Modern concurrent application can be deployed on our system with minimal code modification. Additionally, our system provides two different replication modes that allows the user to switch freely according to the application type. With the evaluation of multiple real world applications, we show that those applications can be easily deployed on our system with 0 to 60 lines of code changes to the source code. From the performance perspective, our system only introduces 0.23\% to 63.39\% overhead compared to non-replicated execution. / Master of Science

Considere um meio desordenado formado por $N$ pontos cujas coordenadas são geradas aleatoriamente com probabilidade uniforme ao longo das arestas unitárias de um hipercubo de $d$ dimensões. Um caminhante, partindo de um ponto qualquer desse meio, se desloca seguindo a regra determinista de dirigir-se sempre ao ponto mais próximo que não tenha sido visitado nos últimos $\\mu$ passos. Esta dinâmica de movimentação, denominada caminhada determinista do turista, leva a trajetórias formadas por uma parte inicial transiente de $t$ pontos, e uma parte final cíclica de $p$ pontos. A exploração do meio se limita aos $t+p$ pontos percorridos na trajetória. O sucesso da exploração depende do valor da memória $\\mu$ do viajante. Para valores pequenos de $\\mu$ a exploração é altamente localizada e o sistema não é satisfatoriamente explorado. Já para $\\mu$ da ordem de $N$, aparecem ciclos longos, permitindo a exploração global do meio. O objetivo deste estudo é determinar o valor de memória $\\mu_1$ para o qual ocorre uma transição abrupta no comportamento exploratório do turista em meios unidimensionais. Procuramos também entender a distribuição da posição final do turista após atingir um estado estacionário que é atingido quando o turista fica aprisionado nos ciclos. Os resultados obtidos por simulações numéricas e por um tratamento analítico mostram que $\\mu_1 = \\log_2 N$. O estudo também mostrou a existência de uma região de transição com largura $\\varepsilon = e/ \\ln 2$ constante, caracterizando uma transição aguda de fase no comportamento exploratório do turista em uma dimensão. A análise do estado estacionário da caminhada em função da memória mostrou que, para $\\mu$ distante de $\\mu_1$, a dinâmica de exploração ocorre como um processo difusivo tradicional (distribuição gaussiana). Já para $\\mu$ próximo de $\\mu_1$ (região de transição), essa dinâmica segue um processo superdifusivo não-linear, caracterizado por distribuições $q$-gaussianas e distribuições $\\alpha$-estáveis de Lévy. Neste processo, o parâmetro $q$ funciona como parâmetro de ordem da transição. / Consider a disordered medium formed by $N$ point whose coordinates are randomly generated with uniform probability along the unitary edges of a $d$-dimensional hypercube. A walker, starting to walk from any point of that medium, moves following the deterministic rule of always going to the nearest point that has not been visited in the last $\\mu$ steps. This dynamic of moving, called deterministic tourist walk, leads to trajectories formed by a initial transient part of $t$ points and a final cycle of $p$ points. The exploration of the medium is limited to the $t+p$ points covered. The success of the exploration depends on the traveler\'s memory value $\\mu$. For small values of $\\mu$, the exploration is highly localized and the whole system remains unexplored. For values of $\\mu$ of the order of $N$, however, long cycles appear, allowing global exploration of the medium. The objective of this study is to determine the memory value $\\mu_1$ for which a sharp transition in the exploratory behavior of the tourist in one-dimensional media occurs. We also want to understand the distribution of the final position of the tourist after reaches a steady state in exploring the medium. That steady state is reached when the tourist is trapped in cycles. The results achieved by numerical simulations and analytical treatment has shown that $\\mu_1 = \\log_2 N$. The study has also shown the existence of a transition region, with a constant width of $\\varepsilon = e/ \\ln 2$, characterizing a phase transition in the exploratory behavior of the tourist in one dimension. The analysis of the walk steady state as a function of the memory has shown that for $\\mu$ far from $\\mu_1$, the exploratory dynamic follows a traditional diffusion process (with gaussian distribution). In the other hand, for $\\mu$ near $\\mu_1$ (transition region), the dynamic follows a non-linear superdiffusion process, characterized by $q$-gaussian distributions and Lèvy $\\alpha$-stable distributions. In this process, the parameter $q$ plays the role of a transition order parameter.

En s'appuyant sur une connaissance précise du temps, sur la réservation de ressources et l'application distribuée de règles d'admission strictes, un réseau déterministe permet de transporter des flux pré-spécifiés avec un taux de perte extrêmement bas et une latence maximale majorée, ouvrant la voie au support d'applications critiques et/ou temps-réel sur une infrastructure de réseau convergée. De nos jours, la Technologie Opérationnelle (OT) s'appuie sur des réseaux déterministes mais conçus à façon, en général propriétaires, utilisant typiquement des liens série spécifiques, et opérés en isolation les uns des autres, ce qui multiplie la complexité physique et les coûts d'achat et de déploiement (CAPEX), ainsi que d'opération et maintenance (OPEX), et empêche l'utilisation agile des ressources. En apportant le déterminisme dans les réseaux des Technologies de l'Information (IT), une nouvelle génération de réseaux commutés de l'IT va permettre l'émulation de ces liens série et la convergence de réseaux autrefois dédiés sur une infrastructure commune à base d'IP. En retour, la convergence de l'IT et de l'OT permettra de nouvelles optimisations industrielles, en introduisant des technologies héritées de l'IT, comme le BigData et la virtualisation des fonctions du réseau (NFV), en support des opérations de l'OT, améliorant les rendements tout en apportant une réduction supplémentaire des coûts. Les solutions de réseaux déterministes réclament des possibilités nouvelles de la part des équipements, possibilités qui vont bien au-delà de celles demandées pour les besoins classiques de la QoS. Les attributs-clé sont : - la synchronisation précise de tous les n'uds, en incluant souvent la source et la destination des flux- le calcul centralisé de chemins de bout en bout à l'échelle du réseau- de nouveaux filtres de mise en forme du trafic à l'intérieur comme à l'entrée du réseau afin de le protéger en tous points- des moyens matériels permettant l'accès au medium à des échéances précises. Au travers de multiples papiers, de contributions à des standards, et de publication de propriété industrielle, le travail présenté ici repousse les limites des réseaux industriels sans fils en offrant : 1. Le calcul centralisé de chemin complexes basé sur une technologie innovante appelée ARC 2. La signalisation de ces chemins complexes et la traçabilité des paquets par une extension de la technologie BIER-TE 3. Réplication, Renvoi et Elimination des doublons le long de ces chemins complexes 4. Un temps-réel basé sur un échéancier qui assure un haut taux de délivrance et garantit une latence bornée 5. La capacité de transporter à la fois des flux déterministes et du trafic IPv6 à multiplexage statistique sur un maillage 6TiSCH partagéCe manuscrit rapporte des améliorations apportées aux techniques existantes des réseaux sans fils à basse puissance (LoWPAN) comme Zigbee, WirelessHART'et ISA100.11a, afin d'amener ces nouveaux bénéfices jusqu'aux réseaux opérationnels sans fil. Elle a été implémentée en programme et sur du matériel open-source, et évaluée face à du IEEE Std. 802.15.4 classique ainsi que du 802.15.4 TSCH, utilisés en topologie maillée. L'expérience menée montre que notre nouvelle proposition permet d'éviter les à-coups et de garantir des taux élevés de délivrance, même face à des évènements exceptionnels comme la perte d'un relais ou la dégradation temporaire d'un lien radio. / Based on time, resource reservation, and policy enforcement by distributed shapers, Deterministic Networking provides the capability to carry specified unicast or multicast data streams for real-time applications with extremely low data loss rates and bounded latency, so as to support time-sensitive and mission-critical applications on a converged enterprise infrastructure.As of today, deterministic Operational Technology (OT) networks are purpose-built, mostly proprietary, typically using serial point-to-point wires, and operated as physically separate networks, which multiplies the complexity of the physical layout and the operational (OPEX) and capital (CAPEX) expenditures, while preventing the agile reuse of the compute and network resources.Bringing determinism in Information Technology (IT) networks will enable the emulation of those legacy serial wires over IT fabrics and the convergence of mission-specific OT networks onto IP. The IT/OT convergence onto Deterministic Networks will in turn enable new process optimization by introducing IT capabilities, such as the Big Data and the network functions virtualization (NFV), improving OT processes while further reducing the associated OPEX.Deterministic Networking Solutions and application use-cases require capabilities of the converged network that is beyond existing QOS mechanisms.Key attributes of Deterministic Networking are: - Time synchronization on all the nodes, often including source and destination - The centralized computation of network-wide deterministic paths - New traffic shapers within and at the edge to protect the network- Hardware for scheduled access to the media.Through multiple papers, standard contribution and Intellectual Property publication, the presented work pushes the limits of wireless industrial standards by providing: 1. Complex Track computation based on a novel ARC technology 2. Complex Track signaling and traceability, extending the IETF BIER-TE technology 3. Replication, Retry and Duplicate Elimination along the Track 4. Scheduled runtime enabling highly reliable delivery within bounded time 5. Mix of IPv6 best effort traffic and deterministic flows within a shared 6TiSCH mesh structureThis manuscript presents enhancements to existing low power wireless networks (LoWPAN) such as Zigbee, WirelessHART¿and ISA100.11a to provide those new benefits to wireless OT networks. It was implemented on open-source software and hardware, and evaluated against classical IEEE Std. 802.15.4 and 802.15.4 TSCH radio meshes. This manuscript presents and discusses the experimental results; the experiments show that the proposed technology can guarantee continuous high levels of timely delivery in the face of adverse events such as device loss and transient radio link down.