No description available.

Cette thèse se compose de trois chapitres constituant des contributions distinctes mais reliées au même centre d'intérêt, la théorie de la décision dans le risque. Le premier chapitre traite de préférences additivement séparable par rapport aux probabilités. Il en est déduit une axiomatisation simple de préférences variationnelles représentées par une fonctionnelle se décomposant en un terme d'espérance d'utilité et un terme entropique. Le second chapitre consiste en une fondation axiomatique de préférences interdépendantes en présence d'interactions sociales, sur la base du modèle initialement élaboré par Blume, Brock et Durlauf. Le troisième chapitre pose la question de l'apport du modèle probabiliste de la physique quantique à la théorie de la décision et de son application pour prendre en compte la perception subjective des évènements par les individus. / This thesis consists of three separate chapters related to economic decisions under risk. The first chapter presents axioms for an additively separable representation of preferences over probabilities. A simple axiomatization of variational preferences represented by the sum of an expected utility term and an entropic term is deduced. The second chapter consists of an axiomatic foundation of other-regarding preferences under social interactions, based on the model originally developed by Blume, Brock and Durlauf. The third chapter introduces the probabilistic model of quantum physics to decision theory. In this context, individuals have a private representation of the set of events.

Let (b$_{i,j}$) be a bounded matrix on extit{ l}$^{2}$, $Bbb T={zinBbb C:|z|=1}$, and A be a bounded matrix on L$^{ 2}(mathbb{T)}$ satisfying the conditions 1.$langle Az^{2j},z^{2i} angle =sigma ^{-1}b_{ij}+|alpha |^{2}sigma ^{-1}langle Az^{j},z^{i} angle $; 2.$langle Az^{2j},z^{2i-1} angle =-alpha sigma ^{-1}b_{ij}+alpha sigma ^{-1}langle Az^{j},z^{i} angle $; 3.$langle Az^{2j-1},z^{2i} angle =-overline{alpha }sigma ^{-1}b_{ij}+overline{alpha }sigma ^{-1}langle Az^{j},z^{i} angle$; 4.$langle Az^{2j-1},z^{2i-1} angle =|alpha |^{2}sigma ^{-1}b_{ij}+sigma ^{-1}langle Az^{j},z^{i} angle $ hspace{-0.76cm} for all $i,jin mathbb{Z}$, where $sigma =1+|alpha |^{2},,alpha in mathbb{C},alpha eq0$. The above conditions evidently suggests that there is a "dyadic" relation in the entries of $A$. Here in the following picture illustrates how each $ij-$th entry of $A$ generates the 2 by 2 block in $A$ with entries ${a_{2i 2j}, a_{2i-1 2j}, a_{2i 2j-1}, a_{2i-1 2j-1}}.$ vspace{-0.3cm} egin{figure}[hp] egin{center} includegraphics[scale=0.42]{cubic.pdf} end{center} vspace{-0.8cm}caption{The dyadic recurrent form} end{figure} It has been shown [2] that $displaystyle A=sum_{n=0}^{infty }S^{n}BS^{ast n}$, where $Sz^i=sigma ^{-1/2}(overline{alpha }z^{2i}+z^{2i-1})$ and $$B=sumlimits_{i=-infty}^infty sumlimits_{j=-infty}^infty b_{ij}(u_{i}otimes u_{j}), u_{i}(z)=sigma ^{-1/2}z^{2i-1}(alpha -z).$$ In this paper, we shall use the above relations to compute $langle a_{i,j} angle $ explicitly. ewline Key words: shift operator, bounded matrix, dyadic recurrent formula, slant Toeplitz operator, separable Hilbert space 2.$langle Az^{2j},z^{2i-1} angle =-alpha sigma ^{-1}b_{ij}+alpha sigma ^{-1}langle Az^{j},z^{i} angle $ 3.$langle Az^{2j-1},z^{2i} angle =-overline{alpha }sigma ^{-1}b_{ij}+overline{alpha }sigma ^{-1}langle Az^{j},z^{i} angle $ 4.$langle Az^{2j-1},z^{2i-1} angle =|alpha |^{2}sigma ^{-1}b_{ij}+sigma ^{-1}langle Az^{j},z^{i} angle $ for all $i,jin mathbb{Z}$, where $sigma =1+|alpha |^{2},,alpha in mathbb{C},alpha eq0$ egin{figure}[hp] egin{center} includegraphics[scale=0.42]{cubic.pdf} end{center} caption{The dyadic recurrent form} end{figure} Since it has been shown [2] that $displaystyle A=sum_{n=0}^{infty }S^{n}BS^{ast n}$, where $ Sz^i=sigma ^{-1/2}(overline{alpha }z^{2i}+z^{2i-1})$ $ B=sum sum b_{ij}(u_{i}otimes u_{j})$ ;;; which $u_{i}(z)=sigma ^{-1/2}z^{2i-1}(alpha -z)$ Then we can use it to compute $langle Az^{j},z^{i} angle $ explicity if A satisfies the previous condition. ewline Key words: shift operator, bounded matrix, dyadic recurrent formula, slant Toeplitz operator, separable Hilbert space

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

In this thesis we study the subset of quantum operations that can be implemented using only local quantum operations and classical communication (LOCC). This restricted paradigm serves as a tool to study not only quantum correlations and other nonlocal quantum effects, but also resource transformations such as channel capacities. The mathematical structure of LOCC is complex and difficult to characterize. In the first part of this thesis we provide a precise description of LOCC and related operational classes in terms of quantum instruments. Our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds. This perspective allows us to measure the distance between two LOCC instruments and hence discuss the closure of LOCC in a rigorous way. While the set of LOCC is not topologically closed, we show that the operations that can be implemented using some fixed number rounds of communication constitute a compact subset of all quantum operations. We also exhibit a subset of LOCC measurements that is closed. Additionally we establish the existence of an open ball around the completely depolarizing map consisting entirely of LOCC implementable maps. In the second part of this thesis we focus on the task of discriminating states from some known set S by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement", we provide a framework for lower bounding the error probability of any LOCC protocol aiming at discriminating the states from S. We apply our framework to an orthonormal product basis known as the domino states. This gives an alternative and simplified bound quantifying how well these states can be discriminated using LOCC. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question. These results give new examples of quantitative gaps between the classes of separable and LOCC operations. In the last part of this thesis, we ask what differentiates separable from LOCC operations. Both of these classes play a key role in the study of entanglement. Separable operations are known to be strictly more powerful than LOCC ones, but no simple explanation of this phenomenon is known. We show that, in the case of bipartite von Neumann measurements, the ability to interpolate is an operational principle that separates LOCC and separable operations.

Shooter localization systems are used to detect and locate the origin of gunfire. A wireless sensor network is one possible implementation of such a system. A wireless sensor network is sensitive to synchronization errors. Localization techniques that rely on the timing will give less accurate or even useless results if the synchronization errors are too large. This thesis focuses on the influence of synchronization errors on the abilityto localize a shooter using a wireless sensor network. A localization algorithm is developed and implemented and the effect of synchronization errors is studied. The localization algorithm is evaluated using numerical experiments, simulations, and data from real gunshots collected at field trials. The results indicate that the developed localization algorithm is able to localizea shooter with quite good accuracy. However, the localization performance is to a high degree influenced by the geographical configuration of the network as well as the synchronization error. / Skottlokaliseringssystem används för att upptäcka och lokalisera ursprunget för avlossade skott. Ett trådlöst sensornätverk är ett sätt att utforma ett sådant system.Trådlösa sensornätverk är känsliga för synkroniseringsfel. Lokaliseringsmetoder som bygger på tidsobservationer kommer med för stora synkroniseringsfel ge dåliga eller helt felaktiga resultat. Detta examensarbete fokuserar på vilken inverkan synkroniseringsfel har på möjligheterna att lokalisera en skytt i ett trådlöst sensornätverk. En lokaliseringsalgoritm utvecklas och förmågan att korrekt lokalisera en skytt vid olika synkroniseringsfel undersöks. Lokaliseringsalgoritmen prövas med numeriska experiment, simuleringar och även för data från riktiga skottljud, insamlade vid fältförsök. Resultaten visar att lokaliseringsalgoritmen fungerar tillfredställande, men att lokaliseringsförmågan till stor del påverkas av synkroniseringsfel men även av sensornätverkets geografiska utseende.

In the wheelchair family, a manual wheelchair is most commonly used by the lower-limb disabled, while its manual mode creates the lowest mechanical effi-ciency and the highest rate of upper-limb injury. Electric wheelchairs on the market are much more labor-saved; however, with their drive systems mostly combining with the bodies of the wheelchair, electric wheelchairs appear to be bulky and are not easily-carried. While in a limited space, on a short-distance moving, or in/off the elevator, electric wheelchairs cannot be practicably switched to manual ones. Thus, this text aims to develop a switchable dou-ble-action manual/electric wheelchair with an auxiliary driving wheel, expect-ing to increase the mechanical efficiency and not to enlarge the body of the wheelchair; the module-disassembled drive system is intended for the conven-ience of carrying. Besides, in order to keep both the manual and the electric functions, the caster contains a set of separable orientation control system, while enables the caster to be switched in both the modes of 360-degree rotation and of being controlled by the user. In this way, the use of the wheelchair would be-come much more multiple-choice.

In this thesis we study the subset of quantum operations that can be implemented using only local quantum operations and classical communication (LOCC). This restricted paradigm serves as a tool to study not only quantum correlations and other nonlocal quantum effects, but also resource transformations such as channel capacities. The mathematical structure of LOCC is complex and difficult to characterize. In the first part of this thesis we provide a precise description of LOCC and related operational classes in terms of quantum instruments. Our formalism captures both finite round protocols as well as those that utilize an unbounded number of communication rounds. This perspective allows us to measure the distance between two LOCC instruments and hence discuss the closure of LOCC in a rigorous way. While the set of LOCC is not topologically closed, we show that the operations that can be implemented using some fixed number rounds of communication constitute a compact subset of all quantum operations. We also exhibit a subset of LOCC measurements that is closed. Additionally we establish the existence of an open ball around the completely depolarizing map consisting entirely of LOCC implementable maps. In the second part of this thesis we focus on the task of discriminating states from some known set S by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement", we provide a framework for lower bounding the error probability of any LOCC protocol aiming at discriminating the states from S. We apply our framework to an orthonormal product basis known as the domino states. This gives an alternative and simplified bound quantifying how well these states can be discriminated using LOCC. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question. These results give new examples of quantitative gaps between the classes of separable and LOCC operations. In the last part of this thesis, we ask what differentiates separable from LOCC operations. Both of these classes play a key role in the study of entanglement. Separable operations are known to be strictly more powerful than LOCC ones, but no simple explanation of this phenomenon is known. We show that, in the case of bipartite von Neumann measurements, the ability to interpolate is an operational principle that separates LOCC and separable operations.

This thesis consists of four research papers. In the first paper we study whether certain properties of sets (functions) are separably determined. In our results we use the "method of elementary submodels". In the second paper we generalize some results concerning Valdivia compacta (equivalently spaces with a commutative retractional skeleton) to the context of spaces with a retractional skeleton (not necessarily commutative). The third paper further studies the structure of spaces with a projectional (resp. retractional) skeleton. Under certain conditions we prove the existence of a "simultaneous projectional skeleton" and we use this result to prove other statements concerning the structure of spaces with a projectional (resp. retractional) skeleton. In the last paper we study the method of elementary submodels in a greater detail and we compare it with the "method of rich families". 1

No description available.