This dissertation studies the diversity multiplexing tradeoff and the capacity of wireless multiple-relay network. In part 1, we study the setup of the parallel Multi-Input Multi-Output (MIMO) relay network. An amplify-and-forward relaying scheme, Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of either the number of relays or the power of each relay goes to infinity. In part 2, we study the general setup of multi-antenna multi-hop multiple- relay network. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. Furthermore, we derive diversity- multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple- access multiple-relay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. In part 3, we characterize the maximum achievable diversity gain of the multi- antenna multi-hop relay network and we show that the proposed RS scheme achieves the maximum diversity gain. In part 4, RS scheme is utilized to investigate DMT of the general multi-antenna multiple-relay networks. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Furthermore, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme. Finally, in part 5, we study the multiplexing gain of the general multi-antenna multiple-relay networks. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks. KPP networks can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable. Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.

This dissertation studies the diversity multiplexing tradeoff and the capacity of wireless multiple-relay network. In part 1, we study the setup of the parallel Multi-Input Multi-Output (MIMO) relay network. An amplify-and-forward relaying scheme, Incremental Cooperative Beamforming, is introduced and shown to achieve the capacity of the network in the asymptotic case of either the number of relays or the power of each relay goes to infinity. In part 2, we study the general setup of multi-antenna multi-hop multiple- relay network. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. Furthermore, we derive diversity- multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple- access multiple-relay (K > 1) networks (without direct link between the source(s) and the destination), the proposed RS scheme achieves the optimum DMT. In part 3, we characterize the maximum achievable diversity gain of the multi- antenna multi-hop relay network and we show that the proposed RS scheme achieves the maximum diversity gain. In part 4, RS scheme is utilized to investigate DMT of the general multi-antenna multiple-relay networks. First, we study the case of a multi-antenna full-duplex single-relay two-hop network, for which we show that the RS achieves the optimum DMT. Applying this result, we derive a new achievable DMT for the case of multi-antenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multi-antenna two parallel non-interfering half-duplex relays. Furthermore, we show that random unitary matrix multiplication also improves the DMT of the Non-Orthogonal AF relaying scheme in the case of a multi-antenna single relay channel. Finally, we study the general case of multi-antenna full-duplex relay networks and derive a new lower-bound on its DMT using the RS scheme. Finally, in part 5, we study the multiplexing gain of the general multi-antenna multiple-relay networks. We prove that the traditional amplify-forward relaying achieves the maximum multiplexing gain of the network. Furthermore, we show that the maximum multiplexing gain of the network is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes. Finally, the argument is extended to the multicast and multi-access scenarios.

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Sheet and film forming processes refer to a set of processes that have a 2-dimensional sheet or film as their output. They are typically characterized by a scanning sensor which moves between the edges of the sheet in a periodic manner. This work is concerned with control and monitoring of such processes. There are three main contributions in this study. The first and foremost contribution is the reformulation of the Linear Quadratic Gaussian (LQG) objective function to give one the ability to trade-off between control over either dimension of the sheet. The second contribution is a method to derive the LQG trade-off surface between output variability in either dimension and input variance. The third contribution is a set of data driven techniques for performance assessment of these processes. Simulation results using the model used by Bergh and MacGregor (1987) are provided to support the proposed methods. / Process Control

Speed-accuracy tradeoffs, velocity profiles, and physiological tremor are fundamental characteristics of human movement. The principles underlying these phenomena have long attracted major interest and controversy. Each is well established experimentally but as yet they have no common theoretical basis. It is proposed that these three phenomena occur as the direct consequence of a movement response planning system that acts as an intermittent optimal controller operating at discrete intervals of ~100 ms. The BUMP model of response planning describes such a system. It forms the kernel of adaptive model theory which defines, in computational terms, a basic unit of motor production or BUMP. Each BUMP consists of three processes: (i) analysing sensory information, (ii) planning a desired optimal response, and (iii) executing that response. These processes operate in parallel across successive sequential BUMPs. The response planning process requires a discrete time interval in which to generate a minimum acceleration trajectory of variable duration, or horizon, to connect the actual response with the predicted future state of the target and compensate for executional error. BUMP model simulation studies show that intermittent adaptive optimal control employing two extremes of variable horizon predictive control reproduces almost exactly findings from several authoritative human experiments. On the one extreme, simulating spatially-constrained movements, a receding horizon strategy results in a logarithmic speed-accuracy tradeoff and accompanying asymmetrical velocity profiles. On the other extreme, simulating temporally-constrained movements, a fixed horizon strategy results in a linear speed-accuracy tradeoff and accompanying symmetrical velocity profiles. Furthermore, simulating ramp movements, a receding horizon strategy closely reproduces experimental observations of 10 Hz physiological tremor. A 100 ms planning interval yields waveforms and power spectra equivalent to those of joint-angle, angular velocity and electromyogram signals recorded for several speeds, directions, and skill levels of finger movement. While other models of response planning account for one or other set of experimentally observed features of speed-accuracy tradeoffs, velocity profiles, and physiological tremor, none accounts for all three. The BUMP model succeeds in explaining these disparate movement phenomena within a single framework, strengthening this approach as the foundation for a unified theory of motor control and planning.

La course à la miniaturisation des circuits électroniques pousse à développer des systèmes faible coût, quece soit en terme de consommation d’énergie ou de ressources de calcul. Il est ainsi possible de réduire la consommationen diminuant la tension d’alimentation et/ou la fréquence d’horloge, mais ceci a pour conséquence de diminuer aussila vitesse de fonctionnement du circuit. Une commande prédictive rapide permet alors de gérer dynamiquement un telcompromis, de manière à ce que la consommation d’énergie soit minimisée tout en garantissant de bonnes performances.Les stratégies de commande proposées ont notamment l’avantage d’être très robustes aux dispersions technologiquesqui sont un problème récurrent dans les nanopuces. Des solutions sont également proposées afin de réduire le coût decalcul du contrôleur. Les systèmes à échantillonnage non-uniforme, dont la loi de commande est calculée et mise à jourlorsqu’un événement est déclenché, sont ainsi étudiés. Ce principe permet de réduire le nombre d’échantillons et, parconséquent, d’économiser des ressources de calcul, tout en garantissant de bonnes performances du système commandé.Des résultats de simulation, et surtout expérimentaux, valident finalement l’intérêt d’utiliser une telle approche. / The demand of electronic components in all embedded and miniaturized applications encourages to developlow-cost components, in term of energy consumption and computational resources. Actually, the power consumption canbe reduced when decreasing the supply voltage and/or the clock frequency, but with the effect that the device runs moreslowly in return. Nevertheless, a fast predictive control strategy allows to dynamically manage this tradeoff in order tominimize the energy consumption while ensuring good performance of the device. Furthermore, the proposals are highlyrobust to tackle variability which is a real problem in nanometric systems on chip. Some issues are also suggested inthis thesis to reduce the control computational cost. Contrary to a time-triggered system where the controller calculatesthe control law at each (constant and periodic) sampling time, an event-based controller updates the control signalonly when the measurement sufficiently changes. Such a paradigm hence calls for resources whenever they are indeednecessary, that is when required from a performance or stability point of view for instance. The idea is to soften thecomputational load by reducing the number of samples and consequently the CPU utilization. Some simulation andexperimental results eventually validate the interest of such an approach.

abstract: The combination of rapid urban growth and climate change places stringent constraints on multisector sustainability of cities. Green infrastructure provides a great potential for mitigating anthropogenic-induced urban environmental problems; nevertheless, studies at city and regional scales are inhibited by the deficiency in modelling the complex transport coupled water and energy inside urban canopies. This dissertation is devoted to incorporating hydrological processes and urban green infrastructure into an integrated atmosphere-urban modelling system, with the goal to improve the reliability and predictability of existing numerical tools. Based on the enhanced numerical tool, the effects of urban green infrastructure on environmental sustainability of cities are examined. Findings indicate that the deployment of green roofs will cool the urban environment in daytime and warm it at night, via evapotranspiration and soil insulation. At the annual scale, green roofs are effective in decreasing building energy demands for both summer cooling and winter heating. For cities in arid and semiarid environments, an optimal trade-off between water and energy resources can be achieved via innovative design of smart urban irrigation schemes, enabled by meticulous analysis of the water-energy nexus. Using water-saving plants alleviates water shortage induced by population growth, but comes at the price of an exacerbated urban thermal environment. Realizing the potential water buffering capacity of urban green infrastructure is crucial for the long-term water sustainability and subsequently multisector sustainability of cities. Environmental performance of urban green infrastructure is determined by land-atmosphere interactions, geographic and meteorological conditions, and hence it is recommended that analysis should be conducted on a city-by-city basis before actual implementation of green infrastructure. / Dissertation/Thesis / Doctoral Dissertation Civil and Environmental Engineering 2016

Abstract This thesis is devoted to studying two wireless relay network models, namely wireless tandem multiple-input-multiple-output (MIMO) relay networks and wireless two-hop multicast relay networks. Regarding wireless tandem MIMO relay networks, we develop a systematic approach to analyze their fundamental diversity-multiplexing tradeoff (DMT) under the assumption that the relays implement a class of practical full-duplex techniques that enable them to opt for either full-duplex or half-duplex mode. Based on the analysis, we make contribution from the following aspects: First of all, we thoroughly compare the performance of full-duplex and half-duplex mode operations in the framework of wireless tandem relay networks. We find that both full-duplex and half-duplex modes have opportunity to outperform each other. Specifically, for many tandem relay networks, in the low multiplexing gain region, the best relay-mode configuration is to let all the relays operate in half-duplex mode since this relay-mode configuration achieves the best diversity gain in the low multiplexing gain region. However, in the high multiplexing gain region, the best diversity gain is usually achieved by switching some relays to full-duplex mode. Furthermore, we study how residual interference at relays working in full-duplex mode affects the DMT of a tandem network. We find that residual interference not only derogates the performance of full-duplex mode, but also affects the optimal power allocation of the network. Specifically, if residual interference is zero or has a sufficiently low power level, a linear power allocation scheme can achieve the optimal DMT of the network. Otherwise, the optimal DMT is achieved by a nonlinear power allocation scheme. Finally, the DMT analysis illustrates an effective principle to deal with general multi-hop wireless networks, which is to break them down into small scale subnetworks with certain key structures. Then, studying the general multi-hop wireless networks essentially becomes studying those small scale subnetworks and the relationship among them. Regarding wireless two-hop multicast relay networks, we focus on a case study where a single source multicasts to two destinations through the assistance of two relays. We propose and analyze the performance of a partial decode-and-forward protocol for the network, which includes the full decode-and-forward protocol as a special case and achieves a better performance in general. Specifically, we prove that the achievable rate of the partial decode-and-forward protocol can either reach arbitrarily close to the cut-set upper bound of the network or reach within 1 bit/s/Hz to that, asymptotically with respect to the transmit power. We also show that the partial decode-and-forward protocol can achieve the optimal DMT of the network. Then, we discuss the perspective of implementing the partial decode-and-forward strategy to more general multicast relay networks. / Tiivistelmä Tämä opinnäytetyö tutkii kahta langatonta välitysverkkomallia, nimittäin langatonta tandem multiple-input-multiple-output (MIMO) välitysverkkoa ja langatonta monilähetysvälitysverkkoa kahdelle hypylle. Kehitämme systemaattisen lähestymistavan diversiteetti-multipleksointi vaihtokaupan (DMT) analysointiin langattomiin tandem MIMO välitysverkkoihin, olettaen välittäjien käyttävän käytännöllisiä full-duplex lähetystekniikoita, jotka mahdollistavat valinnan joko full-duplex tai half-duplex lähetystilan välillä. Analyysin perusteella kontribuoimme seuraavilla tavoilla: Ensinnäkin, vertailemme perusteellisesti full-duplex sekä half-duplex lähetystiloja langattomissa tandem välitysverkoissa. Huomaamme, että molemmat full-duplex ja half-duplex lähetystilat voivat suoriutua toinen toistaan paremmin. Tarkemmin sanoen, monissa tandem välitysverkoissa silloin kun multipleksoinnin hyöty on alhainen, paras välitystapa on antaa kaikkien välittäjien käyttää half-duplex lähetystilaa, koska silloin saavutetaan paras diversiteettilisäys. Toisaalta, kun multipleksointilisäys on suuri, paras diversiteettilisäys saadaan yleensä asettamalla jotkin välittäjät full-duplex lähetystilaan. Lisäksi, tutkimme kuinka full-duplex lähetystilaa käyttävien välittäjien jäljelle jäävä interferenssi vaikuttaa tandemverkon DMT:aan. Huomaamme, että jäljelle jäävä interferenssi vähentää full-duplex mallin tehokkuutta ja lisäksi vaikuttaa optimaaliseen tehonjakamiseen verkossa. Tarkemmin sanoen, jos jäljelle jäävä interferenssin tehotaso on nolla tai tarpeeksi lähellä sitä, lineaarisella tehojaolla voi saavuttaa verkon optimaalisen DMT:n. Muutoin, optimaalinen DMT saavutetaan epälineaarisella tehojaolla. Lopuksi, DMT analyysi havainnollistaa tehokkaan periaatteen yleisluontoisten monihyppyverkkojen käsittelemiseen, eli verkon jakamisen pienempiin osiin erilaiin avainrakenteisiin. Tämän jälkeen yleisluntoisten langattoimen monihyppyverkkojen tutkiminen tapahtuu tutkimalla näitä pieniä osia ja niiden välisiä vuorovaikutussuhteita. Langattomaan kahden hypyn monilähetysvälitysverkkon osalta keskitymme tapaustutkimukseen, jossa yksi lähettäjä monilähettää kahdelle vastaanottajalle kahden välittäjän avulla. Ehdotamme tälle verkolle osittaista decode-and-forward protokollaa, joka sisältää täyden decode-and-forward protokollan erikoistapauksena ja saavuttaa yleisesti tätä protokollaa paremman tehokkuuden. Tarkemmin sanoen, todistamme että tällä protokollalla siirtonopeus lähetystehon suhteen joko lähenee asymptoottisesti verkon cut-set ylärajaa mielivaltaisen lähelle tai saavuttaa sen 1 bit/s/Hz sisään. Osoitamme myös, että osittainen decode-and-forward protokolla voi saavuttaa verkon optimaalisen DMT:n. Tämän jälkeen, käsittelemme osittaisen decode-and-forward strategian impelentointia yleisluontoisille monilähetysvälitysverkoille.

L’objectif principal de cette thèse est de souligner que le compromis biais-variance n’est pas toujours vrai (p. ex. dans les réseaux neuronaux). Nous plaidons pour que ce manque d’universalité soit reconnu dans les manuels scolaires et enseigné dans les cours d’introduction qui couvrent le compromis. Nous passons d’abord en revue l’historique du compromis entre les biais et les variances, sa prévalence dans les manuels scolaires et certaines des principales affirmations faites au sujet du compromis entre les biais et les variances. Au moyen d’expériences et d’analyses approfondies, nous montrons qu’il n’y a pas de compromis entre la variance et le biais dans les réseaux de neurones lorsque la largeur du réseau augmente. Nos conclusions semblent contredire les affirmations de l’oeuvre historique de Geman et al. (1992). Motivés par cette contradiction, nous revisitons les mesures expérimentales dans Geman et al. (1992). Nous discutons du fait qu’il n’y a jamais eu de preuves solides d’un compromis dans les réseaux neuronaux lorsque le nombre de paramètres variait. Nous observons un phénomène similaire au-delà de l’apprentissage supervisé, avec un ensemble d’expériences d’apprentissage de renforcement profond. Nous soutenons que les révisions des manuels et des cours magistraux ont pour but de transmettre cette compréhension moderne nuancée de l’arbitrage entre les biais et les variances. / The main goal of this thesis is to point out that the bias-variance tradeoff is not always true (e.g. in neural networks). We advocate for this lack of universality to be acknowledged in textbooks and taught in introductory courses that cover the tradeoff. We first review the history of the bias-variance tradeoff, its prevalence in textbooks, and some of the main claims made about the bias-variance tradeoff. Through extensive experiments and analysis, we show a lack of a bias-variance tradeoff in neural networks when increasing network width. Our findings seem to contradict the claims of the landmark work by Geman et al. (1992). Motivated by this contradiction, we revisit the experimental measurements in Geman et al. (1992). We discuss that there was never strong evidence for a tradeoff in neural networks when varying the number of parameters. We observe a similar phenomenon beyond supervised learning, with a set of deep reinforcement learning experiments. We argue that textbook and lecture revisions are in order to convey this nuanced modern understanding of the bias-variance tradeoff.