Today, a large amount of time series data is being produced from a variety of different devices such as smart speakers, cell phones and vehicles. This data can be used to make inferences and predictions. Neural network based methods are among one of the most popular ways to model time series data. The field of neural networks is constantly expanding and new methods and model variants are frequently introduced. In 2018, a new family of neural networks was introduced. Namely, Neural Ordinary Differential Equations (Neural ODEs). Neural ODEs have shown great potential in modelling the dynamics of temporal data. Here we present an investigation into using Neural Ordinary Differential Equations for anomaly detection. We tested two model variants, LSTM-ODE and latent-ODE. The former model utilises a neural ODE to model the continuous-time hidden state in between observations of an LSTM model, the latter is a variational autoencoder that uses the LSTM-ODE as encoding and a Neural ODE as decoding. Both models are suited for modelling sparsely and irregularly sampled time series data. Here, we test their ability to detect anomalies on various sparsity and irregularity ofthe data. The models are compared to a Gaussian mixture model, a vanilla LSTM model and an LSTM variational autoencoder. Experimental results using the Human Activity Recognition dataset showed that the Neural ODEbased models obtained a better ability to detect anomalies compared to their LSTM based counterparts. However, the computational training cost of the Neural ODE models were considerably higher than for the models that onlyutilise the LSTM architecture. The Neural ODE based methods were also more memory consuming than their LSTM counterparts. / Idag produceras en stor mängd tidsseriedata från en mängd olika enheter som smarta högtalare, mobiltelefoner och fordon. Denna datan kan användas för att dra slutsatser och förutsägelser. Neurala nätverksbaserade metoder är bland de mest populära sätten att modellera tidsseriedata. Mycket forskning inom området neurala nätverk pågår och nya metoder och modellvarianter introduceras ofta. Under 2018 introducerades en ny familj av neurala nätverk. Nämligen, Neurala Ordinära Differentialekvationer (NeuralaODE:er). Neurala ODE:er har visat en stor potential i att modellera dynamiken hos temporal data. Vi presenterar här en undersökning i att använda neuralaordinära differentialekvationer för anomalidetektion. Vi testade två olika modellvarianter, en som kallas LSTM-ODE och en annan som kallas latent-ODE.Den förstnämnda använder Neurala ODE:er för att modellera det kontinuerliga dolda tillståndet mellan observationer av en LSTM-modell, den andra är en variational autoencoder som använder LSTM-ODE som kodning och en Neural ODE som avkodning. Båda dessa modeller är lämpliga för att modellera glest och oregelbundet samplade tidsserier. Därför testas deras förmåga att upptäcka anomalier på olika gleshet och oregelbundenhet av datan. Modellerna jämförs med en gaussisk blandningsmodell, en vanlig LSTM modell och en LSTM variational autoencoder. Experimentella resultat vid användning av datasetet Human Activity Recognition (HAR) visade att de Neurala ODE-baserade modellerna erhöll en bättre förmåga att upptäcka avvikelser jämfört med deras LSTM-baserade motsvarighet. Träningstiden förde Neurala ODE-baserade modellerna var dock betydligt långsammare än träningstiden för deras LSTM-baserade motsvarighet. Neurala ODE-baserade metoder krävde också mer minnesanvändning än deras LSTM motsvarighet.

This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost. / Ph. D.

Submitted by CLAYTON EDUARDO LENTE DA SILVA null (claedu@gmail.com) on 2016-06-02T17:41:44Z No. of bitstreams: 1 TeseFinalClayton.pdf: 1339813 bytes, checksum: 78fb3fb4fd37414af7b1a14dd1d3a122 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-06-06T16:37:20Z (GMT) No. of bitstreams: 1 silva_cel_dr_sjrp.pdf: 1339813 bytes, checksum: 78fb3fb4fd37414af7b1a14dd1d3a122 (MD5) / Made available in DSpace on 2016-06-06T16:37:20Z (GMT). No. of bitstreams: 1 silva_cel_dr_sjrp.pdf: 1339813 bytes, checksum: 78fb3fb4fd37414af7b1a14dd1d3a122 (MD5) Previous issue date: 2016-05-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta tese estudamos sistemas dinâmicos não suaves autônomos e não autônomos. Consideramos inicialmente sistemas quadráticos positivamente limitados autônomos planares e damos condições sobre os campos para que o sistema de Filippov correspondente seja limitado. Também estudamos uma classe de sistemas quadráticos e provamos que, sob algumas restrições nos coeficientes da parte linear, os sistemas de Filippov relacionados são limitados. Em seguida, consideramos sistemas não autônomos e damos condições para a existência de soluções periódicas de uma classe de equações diferenciais ordinárias não autônomas. Por fim, consideramos equações diferenciais ordinárias não autônomas de segunda ordem genéricas, relacionadas a sistemas não suaves e não autônomos, estudamos o conceito de solução destas equações e damos condições analíticas que são satisfeitas por soluções típicas, como as soluções deslizantes, por exemplo. A unicidade de soluções para estas equações também é estudada. / In this thesis we study autonomous and non-autonomous non-smooth dynamical systems. We initially consider planar autonomous positively bounded quadratic systems. We give conditions on the vector fields for that the correspondent Filippov system be bounded. We also study a class of quadratic systems and we prove that, under some restrictions on the coefficients of linear part, the related Filippov systems are bounded. We then consider non-autonomous systems and we give conditions for the existence of periodic solutions of a certain class of non-autonomous ordinary differential equations. Finally we consider generic non-autonomous second order differential equations and we study the concept of solution of these equations and determine analytical conditions that are satisfied by typical solutions, sliding solutions for instance. Moreover, the uniqueness of solutions for these equations is studied.

In under 6 decades dengue has emerged from South East Asia to become the most widespread arbovirus affecting human populations. Recent dramatic increases in epidemic dengue fever have mainly been attributed to factors such as vector expansion and ongoing ecological, climate and socio-demographic changes. The failure to control the virus in endemic regions and prevent global spread of its mosquito vectors and genetic variants, underlines the urgency to reassess previous research methods, hypotheses and empirical observations. This thesis comprises a set of studies that integrate currently neglected and emerging epidemiological, ecological and evolutionary factors into unified mathematical frameworks, in order to better understand the contemporary population biology of the dengue virus. The observed epidemiological dynamics of dengue are believed to be driven by selective forces emerging from within-host cross-immune reactions during sequential, heterologous infections. However, this hypothesis is mainly supported by modelling approaches that presume all hosts to contribute equally and significantly to the selective effects of cross-immunity both in time and space. In the research presented in this thesis it is shown that the previously proposed effects of cross-immunological reactions are weakened in agent-based modelling approaches, which relax the common deterministic and homogeneous mixing assumptions in host-host and host-pathogen interactions. Crucially, it is shown that within these more detailed models, previously reported universal signatures of dengue's epidemiology and population genetics can be reproduced by demographic and natural stochastic processes alone. While this contrasts with the proposed role of cross-immunity, it presents demographic stochasticity as a parsimonious mechanism that integrates, for the first time, multi-scale features of dengue's population biology. The implications of this research are applicable to many other pathogens, involving challenging new ways of determining the underlying causes of the complex phylodynamics of antigenically diverse pathogens.

During human immunodeficiency virus 1 (HIV-1) infection, the viral population is in constant battle with the host immune system. The cytotoxic T-lymphocyte (CTL) response, a branch of the adaptive immune response, is implicated in viral control and can drive viral evolution in the infected host population. Endogenous viral peptides, or ‘epitopes’, are presented to CTLs by human leukocyte antigen (HLA) class I molecules on the surface of infected cells where they may be identified as non-self. Mutations in or proximal to a viral epitope can result in ‘escape’ from CTLs targeting that epitope. The repertoire of epitopes which may be presented is dependent upon host class I HLA types. As such, reversion may occur after transmission due to changes in viral fitness and selection in the context of a new HLA background. Thus, parameters describing the dynamics of CTL escape and reversion are key to understanding how CTL responses within individuals relate to HIV-1 sequence evolution in the infected host population. Escape and reversion can be studied directly using biological assays and longitudinal viral sequence data, or indirectly by considering viral sequences across multiple hosts. Indirect approaches include tree based methods which detect associations between host HLA and viral sequence but do not estimate rates of escape and reversion, and ordinary differential equation (ODE) models which estimate these rates but do not consider the dependency structure inherent in viral sequence data. We introduce two models which estimate escape and reversion rates whilst accounting for the shared ancestry of viral sequence data. For our first model, we lay out an integrated Bayesian approach which combines genealogical inference and an existing epidemiological model to inform escape and reversion rate estimates. Using this model, we find evidence for correlation between escape rate estimates across widely separated geographical regions. We also observe a non-linear negative correlation between in vitro replicative capacity and escape rate. Both findings suggest that epistasis does not play a strong role in the escape process. Although our first model worked well, it had some key limitations which we address in our second method. Notably, by making a series of approximations, we are able account for recombination and analyse very large datasets which would be computationally infeasible under the first model. We verify our second approach through extensive simulations, and use the method to estimate both drug and HLA associated selection along portions of the HIV-1 genome. We test the results of the model using existing knowledge, and determine a collection of putative selected sites which warrant further investigation. Finally, we find evidence to support the notion that the CTL response played a role in HIV-1 subtype diversification.

<p>Deep ‘Analog Artificial Neural Networks’ (AANNs) perform complex classification problems with high accuracy. However, they rely on humongous amount of power to perform the calculations, veiling the accuracy benefits. The biological brain on the other hand is significantly more powerful than such networks and consumes orders of magnitude less power, indicating some conceptual mismatch. Given that the biological neurons are locally connected, communicate using energy efficient trains of spikes, and the behavior is non-deterministic, incorporating these effects in Artificial Neural Networks (ANNs) may drive us few steps towards a more realistic neural networks. </p> <p> </p> <p>Emerging devices can offer a plethora of benefits including power efficiency, faster operation, low area in a vast array of applications. For example, memristors and Magnetic Tunnel Junctions (MTJs) are suitable for high density, non-volatile Random Access Memories when compared with CMOS implementations. In this work, we analyze the possibility of harnessing the characteristics of such emerging devices, to achieve neuro-inspired solutions to intricate problems.</p> <p> </p> <p>We propose how the inherent stochasticity of nano-scale resistive devices can be utilized to realize the functionality of spiking neurons and synapses that can be incorporated in deep stochastic Spiking Neural Networks (SNN) for image classification problems. While ANNs mainly dwell in the aforementioned classification problem solving domain, they can be adapted for a variety of other applications. One such neuro-inspired solution is the Cellular Neural Network (CNN) based Boolean satisfiability solver. Boolean satisfiability (k-SAT) is an NP-complete (k≥3) problem that constitute one of the hardest classes of constraint satisfaction problems. We provide a proof of concept hardware based analog k-SAT solver that is built using MTJs. The inherent physics of MTJs, enhanced by device level modifications, is harnessed here to emulate the intricate dynamics of an analog, CNN based, satisfiability (SAT) solver. </p> <p> </p> <p>Furthermore, in the effort of reaching human level performance in terms of accuracy, increasing the complexity and size of ANNs is crucial. Efficient algorithms for evaluating neural network performance is of significant importance to improve the scalability of networks, in addition to designing hardware accelerators. We propose a scalable approach for evaluating Liquid State Machines: a bio-inspired computing model where the inputs are sparsely connected to a randomly interlinked reservoir (or liquid). It has been shown that biological neurons are more likely to be connected to other neurons in the close proximity, and tend to be disconnected as the neurons are spatially far apart. Inspired by this, we propose a group of locally connected neuron reservoirs, or an ensemble of liquids approach, for LSMs. We analyze how the segmentation of a single large liquid to create an ensemble of multiple smaller liquids affects the latency and accuracy of an LSM. In our analysis, we quantify the ability of the proposed ensemble approach to provide an improved representation of the input using the Separation Property (SP) and Approximation Property (AP). Our results illustrate that the ensemble approach enhances class discrimination (quantified as the ratio between the SP and AP), leading to improved accuracy in speech and image recognition tasks, when compared to a single large liquid. Furthermore, we obtain performance benefits in terms of improved inference time and reduced memory requirements, due to lower number of connections and the freedom to parallelize the liquid evaluation process.</p>

The polymerization of methyl methacrylate (MMA) was investigated in this dissertation. Selected kinetic models from the literature were reviewed, and two new, generalized models of diffusion-limited effects (gel- and glass effects), derived from the current models were proposed and tested for bulk and solution polymerization of MMA in batch and semi-batch reactors, under isothermal and non-isothermal conditions. The newly proposed models include the capability of modeling termination by combination, radical transfer to monomer and depropagation reaction. The new and previous models were compared with experimental data of bulk and solution polymerizations of MMA, under a selection of non-steady state processes conditions (initiator and monomer feed, step changes in temperature) and compositions (initiator and chain transfer agents, regarding both type and dosages). The particular case of a non-isothermal bulk polymerization was also investigated. A simulation program (Reactormodel) was developed in Matlab, and its algorithm is provided. / Sem resumo.

In this work, our goal is to prove results on prolongation of solutions, uniform boundedness of solutions, uniform stability as well uniform asymptotic stability (in the classical sense of Lyapunov) for measure differential equations and for dynamic equations on time scales. In order to get our results, we employ the theory of generalized ODEs, since these equations encompass measure differential equations and dynamic equations on time scales. Therefore, to get our results, we start by proving the expected result for abstract generalized ODEs. Then, using the correspondence between the solutions of these equations and the solutions of measure differential equations (see [38]), we extend all the results to these the latter. After that, using the correspondence between the solutions of measure differential equations and the solutions of dynamic equations on time scales (see [21]), we extend all the results to these last equations. Finally, we investigate autonomous generalized ODEs and show that these equations do not enlarge the class of classical autonomous ODEs, even when we consider a more general class of functions as right-hand sides. All the new results presented in this work are contained in papers [16, 17, 18, 19]. / Neste trabalho, nosso objetivo e provar resultados sobre prolongamento de soluções, limitação uniforme de soluções, estabilidade uniforme e estabilidade uniforme assintótica (no sentido clássico de Lyapunov) para equações diferenciais em medida e para equações dinâmicas em escalas temporais. A fim de obter os nossos resultados, empregamos a teoria de EDOs generalizadas, uma vez que estas equações abrangem equações diferenciais em medida e equações dinâmicas em escalas temporais. Portanto, para obter nossos resultados, vamos começar por provar, os resultados que queremos para EDOs generalizadas abstratas. Em seguida, usando a correspondência entre as soluções de EDOs generalizadas e soluções de equações diferenciais em medida (ver [38]), estenderemos os resultados para estas ultimas equações. Depois disso, usando a correspondência entre as soluções de equações diferenciais em medida e as soluções de equações dinâmicas em escalas temporais (ver [21]), estenderemos todos os resultados para estas ultimas equações. Finalmente, investigamos EDOs generalizadas autônomas e mostramos que estas equações não aumentam a classe de EDOs autônomas clássicas, mesmo quando consideramos uma classe mais geral de funções nos lados direitos das equações. Os novos resultados encontrados estão contidos em [16, 17, 18, 19].

Lors de l’infection par un pathogène intracellulaire, l’organisme déclenche une réponse immunitaire spécifique dont les acteurs principaux sont les lymphocytes T-CD8. Ces cellules sont responsables de l’éradication de ce type d’infections et de la constitution du répertoire immunitaire de l’individu. Les processus qui composent la réponse immunitaire se répartissent sur plusieurs échelles physiques inter-connectées (échelle intracellulaire, échelle d’une cellule, échelle de la population de cellules). La réponse immunitaire est donc un processus complexe, pour lequel il est difficile d’observer ou de mesurer les liens entre les différents phénomènes mis en jeu. Nous proposons trois modèles mathématiques multi-échelles de la réponse immunitaire, construits avec des formalismes différents mais liés par une même idée : faire dépendre le comportement des cellules TCD8 de leur contenu intracellulaire. Pour chaque modèle, nous présentons, si possible, sa construction à partir des hypothèses biologiques sélectionnées, son étude mathématique et la capacité du modèle à reproduire la réponse immunitaire au travers de simulations numériques. Les modèles que nous proposons reproduisent qualitativement et quantitativement la réponse immunitaire T-CD8 et constituent ainsi de bons outils préliminaires pour la compréhension de ce phénomène biologique. / Upon infection by an intracellular pathogen, the organism triggers a specific immune response,mainly driven by the CD8 T cells. These cells are responsible for the eradication of this type of infections and the constitution of the immune repertoire of the individual. The immune response is constituted by many processes which act over several interconnected physical scales (intracellular scale, single cell scale, cell population scale). This biological phenomenon is therefore a complex process, for which it is difficult to observe or measure the links between the different processes involved. We propose three multiscale mathematical models of the CD8 immune response, built with different formalisms but related by the same idea : to make the behavior of the CD8 T cells depend on their intracellular content. For each model, we present, if possible, its construction process based on selected biological hypothesis, its mathematical study and its ability to reproduce the immune response using numerical simulations. The models we propose succesfully reproduce qualitatively and quantitatively the CD8 immune response and thus constitute useful tools to further investigate this biological phenomenon.

La modélisation dynamique des systèmes écologiques constitue une méthode incontournable pour comprendre,prédire et contrôler la dynamique des écosystèmes semi-naturels, qui fait intervenir des processuscomplexes. Le principal objectif de cette thèse est de développer un modèle permettant de simuler la dynamiqueà moyen terme de la végétation herbacée dans les prairies permanentes, en tenant compte à lafois de la productivité et de la biodiversité. Les prairies sont des réservoirs présentant une forte biodiversitévégétale, qui soutiennent de nombreux services écosystémiques. Sur le plan agricole, cette importantediversité contribue à la qualité de la production fourragère, et de plus, elle permet une plus grande résistancede la végétation face à des changements climatiques (réchauffement moyen, vagues de chaleur etde sécheresse).Pourtant, cette notion clé de biodiversité n’est que faiblement prise en considération dans la modélisationde l’écosystème prairial : elle est souvent absente ou alors présente sous une forme très simplifiée. Enréponse à ces considérations, ces travaux de thèse présentent la construction d’un modèle de successionbasé sur des processus, décrit par un système d’équations différentielles ordinaires, qui représente ladynamique de la végétation aérienne des prairies tempérées. Ce modèle intègre les principaux facteursécologiques impactant la croissance et la compétition des espèces herbacées, et peut s’ajuster à n’importequel niveau de diversité, par le choix du nombre et de l’identité des espèces initialement présentes dansl’assemblage. Ce formalisme mécaniste de modélisation nous permet alors d’analyser les relations qui lientdiversité, productivité et stabilité, en réponse à différentes conditions climatiques et différents modes degestion agricole.[...]Ces résultats soulignent alors le besoin de prendre en compte le rôle clé joué par la biodiversité dansles modèles de l’écosystème prairial, de par son impact sur le comportement des dynamiques simulées.De plus, pour rendre correctement compte des interactions au sein de la végétation, le nombre d’espècesconsidéré dans le modèle doit être suffisamment important. Enfin, nous comparons les simulations devégétation de ce modèle à des mesures issues de deux sites expérimentaux, la prairie de fauche d’Oensingen,et le pâturage de Laqueuille. Les résultats de ces comparaisons sont encourageants et soulignentla pertinence du choix et de la représentation des processus écologiques clés qui composent ce modèlemécaniste.Ce travail de thèse propose donc un modèle, en total adéquation avec les besoins actuels en terme demodélisation de l’écosystème prairial, qui permet de mieux comprendre la dynamique de la végétationherbacée et les interactions entre productivité, diversité et stabilité. / Dynamic modelling of ecological systems is an essential method to understand, predict and control thedynamics of semi-natural ecosystems, which involves complex processes. The main objective of this PhDthesis is to develop a simulation model of the medium- and long-term dynamics of the herbaceous vegetationin permanent grasslands, taking into account both biodiversity and productivity. Grasslandecosystems are often hot spots of biodiversity, which contributes to the temporal stability of their services.On an agricultural perspective, this important biodiversity contributes to the forage quality, andbesides, it induces a higher ability of the vegetation cover to resist to different climatic scenarios (globalwarming, heat and drought waves).However, this key aspect of biodiversity is only poorly included in grassland models : often absent ofmodelling or included in a very simple form. Building on those considerations, this PhD work exposes thewriting of a process-based succession model, described by a system of Ordinary Differential Equationsthat simulates the aboveground vegetation dynamics of a temperate grassland. This model implementedthe main ecological factors involved in growth and competition processes of herbaceous species, and couldbe adjust to any level of diversity, by varying the number and the identity of species in the initial plantcommunity. This formalism of mechanistic models allows us to analyse relationships that link diversity,productivity and stability, in response to different climatic conditions and agricultural management.In mathematical grassland models, plant communities may be represented by a various number of statevariables, describing biomass compartments of some dominant species or plant functional types. The sizeof the initial species pool could have consequences on the outcome of the simulated ecosystem dynamicsin terms of grassland productivity, diversity, and stability. This choice could also influence the modelsensitivity to forcing parameters. To address these issues, we developed a method, based on sensitivityanalysis tools, to compare behaviour of alternative versions of the model that only differ by the identityand number of state variables describing the green biomass, here plant species. This method shows aninnovative aspect, by performing this model sensitivity analysis by using multivariate regression trees. Weassessed and compared the sensitivity of each instance of the model to key forcing parameters for climate,soil fertility, and defoliation disturbances. We established that the sensitivity to forcing parameters ofcommunity structure and species evenness differed markedly among alternative models, according tothe diversity level. We show a progressive shift from high importance of soil fertility (fertilisation level,mineralization rate) to high importance of defoliation (mowing frequency, grazing intensity) as the sizeof the species pool increased.These results highlight the need to take into account the role of species diversity to explain the behaviourof grassland models. Besides, to properly take into account those interactions in the grassland cover, theconsidered species pool size considered in the model needs to be high enough. Finally, we compare modelsimulations of the aboveground vegetation to measures from two experimental sites, the mowing grasslandof Oensingen, and the grazing grassland of Laqueuille. Results of these comparison are promising andhighlight the relevance of the choice and the representation of the different ecological processes includedin this mechanistic model.Thus, this PhD work offers a model, perfectly fitting with current needs on grassland modelling, whichcontribute to a better understanding of the herbaceous vegetation dynamics and interactions betweenproductivity, diversity and stability.