This thesis consists of two parts, a first part on computations in algebraic geometry, and a second part on deformation quantization. More specifically, it is a collection of four papers. In the papers I, II and III, we present algorithms and an implementation for the computation of degrees of characteristic classes in algebraic geometry. Paper IV is a contribution to the field of deformation quantization and actions of the Grothendieck-Teichmüller group. In Paper I, we present an algorithm for the computation of degrees of Segre classes of closed subschemes of complex projective space. The algorithm is based on the residual intersection theorem and can be implemented both symbolically and numerically. In Paper II, we describe an algorithm for the computation of the degrees of Chern-Schwartz-MacPherson classes and the topological Euler characteristic of closed subschemes of complex projective space, provided an algorithm for the computation of degrees of Segre classes. We also explain in detail how the algorithm in Paper I can be implemented numerically. Together this yields a symbolical and a numerical version of the algorithm. Paper III describes the Macaulay2 package CharacteristicClasses. It implements the algorithms from papers I and II, as well as an algorithm for the computation of degrees of Chern classes. In Paper IV, we show that L-infinity-automorphisms of the Schouten algebra T_poly(R^d) of polyvector fields on affine space R^d which satisfy certain conditions can be globalized. This means that from a given L-infinity-automorphism of T_poly(R^d) an L-infinity-automorphism of T_poly(M) can be constructed, for a general smooth manifold M. It follows that Willwacher's action of the Grothendieck-Teichmüller group on T_poly(R^d) can be globalized, i.e., the Grothendieck-Teichmüller group acts on the Schouten algebra T_poly(M) of polyvector fields on a general manifold M. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Accepted.</p>

In this work, our goal is to track visual targets using residual vector quantization (RVQ). We compare our results with principal components analysis (PCA) and tree structured vector quantization (TSVQ) based tracking. This work is significant since PCA is commonly used in the Pattern Recognition, Machine Learning and Computer Vision communities. On the other hand, TSVQ is commonly used in the Signal Processing and data compression communities. RVQ with more than two stages has not received much attention due to the difficulty in producing stable designs. In this work, we bring together these different approaches into an integrated tracking framework and show that RVQ tracking performs best according to multiple criteria on publicly available datasets. Moreover, an advantage of our approach is a learning-based tracker that builds the target model while it tracks, thus avoiding the costly step of building target models prior to tracking.

<p>This thesis treats the problem of source coding in situations where the encoded data is subject to errors. The typical scenario is a communication system, where source data such as speech or images should be transmitted from one point to another. A problem is that most communication systems introduce some sort of error in the transmission. A wireless communication link is prone to introduce individual bit errors, while in a packet based network, such as the Internet, packet losses are the main source of error.</p><p>The traditional approach to this problem is to add error correcting codes on top of the encoded source data, or to employ some scheme for retransmission of lost or corrupted data. The source coding problem is then treated under the assumption that all data that is transmitted from the source encoder reaches the source decoder on the receiving end without any errors. This thesis takes another approach to the problem and treats source and channel coding jointly under the assumption that there is some knowledge about the channel that will be used for transmission. Such joint source--channel coding schemes have potential benefits over the traditional separated approach. More specifically, joint source--channel coding can typically achieve better performance using shorter codes than the separated approach. This is useful in scenarios with constraints on the delay of the system.</p><p>Two different flavors of joint source--channel coding are treated in this thesis; multiple description coding and channel optimized vector quantization. Channel optimized vector quantization is a technique to directly incorporate knowledge about the channel into the source coder. This thesis contributes to the field by using channel optimized vector quantization in a couple of new scenarios. Multiple description coding is the concept of encoding a source using several different descriptions in order to provide robustness in systems with losses in the transmission. One contribution of this thesis is an improvement to an existing multiple description coding scheme and another contribution is to put multiple description coding in the context of channel optimized vector quantization. The thesis also presents a simple image coder which is used to evaluate some of the results on channel optimized vector quantization.</p>

Cette thèse est consacrée à l'étude de deux sujets de géométrie symplectique inspirés<p>de la physique mathématique. Les thèmes que nous développerons mettent en évidence certaines <p>connexions avec la topologie symplectique d'une part, la géométrie Riemannienne d'autre part.<p><p>Dans la partie 1, nous étudions la quantification par déformation formelle d'une variété <p>symplectique, à l'aide de produits star. Nous définissons le groupe des automorphimes<p>hamiltoniens d'un produit star formel. En nous inspirant d'idées de Banyaga, nous <p>identifions ce groupe comme étant le noyau d'un morphisme remarquable sur le groupe<p>des automorphismes du produit star. Nous relions certaines propriétés géométriques de <p>ce groupe d'automorphismes hamiltoniens à la topologie du groupe des difféomorphismes<p>hamiltoniens.<p><p>Dans la partie 2, nous étudions les opérateurs de Dirac symplectiques. Les ingrédients<p>nécessaires à leur construction (algèbre de Weyl, structures $Mp^c$, champs de spineurs <p>symplectiques, connexions symplectiques,) sont également utilisés en quantification géométrique et en<p>quantification par déformation formelle. Les opérateurs de Dirac symplectiques sont construits<p>de manière analogue à l'opérateur de Dirac de la géométrie Riemannienne. Une formule de Weitzenbock<p>lie les opérateurs de Dirac symplectiques à un opérateur elliptique $mathcal{P}$ d'ordre 2. Nous étudions<p>les noyaux de ces opérateurs de Dirac symplectiques et leur lien avec le noyau de P.<p>Sur l'espace hermitien symétrique $CP^n$, nous calculerons le spectre de $mathcal{P}$ et nous <p>prouverons un théorème de Hodge pour les opérateurs de Dirac-Dolbeault symplectiques.<p><p>/<p><p>In this thesis we study two topics of symplectic geometry inspired from mathematical physics.<p><p>Part 1 is devoted to the study of deformation quantization of symplectic manifolds. More precisely, we consider formal star products on a symplectic manifold. We define the group of Hamiltonian automorphisms of a formal star product. Following ideas of Banyaga, we describe this group as the kernel<p>of a morphism on the group of automorphisms of the star product. We relate geometric properties of the group of Hamiltonian automorphisms to the topology of the group of Hamiltonian diffeomorphisms. <p><p>Part 2 is devoted to the study of symplectic Dirac operators. The construction of those operators relies on many concepts used in geometric quantization and formal deformation quantization such as Weyl algebra, $Mp^c$ structures, symplectic spinors, symplectic connections, The construction of symplectic Dirac operators is analogous to the one of Dirac operators in Riemannian geometry. A Weitzenbock formula relates the symplectic Dirac operators to an elliptic operator $mathcal{P}$ of order 2. We study the kernels of the symplectic Dirac operators and relate them to the kernel of $mathcal{P}$. On the hermitian symmetric space <p>$CP^n$, we compute the spectrum of $mathcal{P}$ and we prove a Hodge theorem for the symplectic Dirac-Dolbeault operator. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

With the advancement of CMOS process and fabrication, it has been a trend to maximize digital design while minimize analog correspondents in mixed-signal system designs. So is the case for PLL. PLL has always been a traditional mixed-signal system limited by analog part performance. Around 2000, there emerged ADPLL of which all the blocks besides oscillator are implemented in digital circuits. There have been successful examples in application of Bluetooth, and it is moving to improve results for application of WiMax and ad-hoc frequency hopping communication link. Based on the theoretic and measurement results of existing materials, ADPLL has shown advantages such as fast time-to-market, low area, low cost and better system integration; but it also showed disadvantages in frequency resolution and phase noise, etc. Also this new topic still opens questions in many researching points important to PLL such as tracking behavior and quantization effect. In this thesis, a non-linear phase domain model for all digital phase-locked loop (ADPLL) was established and validated. Based on that, we analyzed that ADPLL phase noise prediction derived from traditional linear quantization model became inaccurate in non-linear cases because its probability density of quantization error did not meet the premise assumption of linear model. The phenomena of bandwidth expansion and in-band phase noise decreasing peculiar to integer-N ADPLL were demonstrated and explained by matlab and verilog behavior level simulation test bench. The expression of threshold quantization step was defined and derived as the method to distinguish whether an integer-N ADPLL was in non-linear cases or not, and the results conformed to those of matlab simulation. A simplified approximation model for non-linear integer-N ADPLL with noise sources was established to predict in-band phase noise, and the trends of the results conformed to those of matlab simulation. Other basic analysis serving for the conclusions above covered: ADPLL loop dynamics, traditional linear theory and its quantitative limitations and numerical analysis of random number. Finally, a present measurement setup was demonstrated and the results were analyzed for future work.

This thesis treats the problem of source coding in situations where the encoded data is subject to errors. The typical scenario is a communication system, where source data such as speech or images should be transmitted from one point to another. A problem is that most communication systems introduce some sort of error in the transmission. A wireless communication link is prone to introduce individual bit errors, while in a packet based network, such as the Internet, packet losses are the main source of error. The traditional approach to this problem is to add error correcting codes on top of the encoded source data, or to employ some scheme for retransmission of lost or corrupted data. The source coding problem is then treated under the assumption that all data that is transmitted from the source encoder reaches the source decoder on the receiving end without any errors. This thesis takes another approach to the problem and treats source and channel coding jointly under the assumption that there is some knowledge about the channel that will be used for transmission. Such joint source--channel coding schemes have potential benefits over the traditional separated approach. More specifically, joint source--channel coding can typically achieve better performance using shorter codes than the separated approach. This is useful in scenarios with constraints on the delay of the system. Two different flavors of joint source--channel coding are treated in this thesis; multiple description coding and channel optimized vector quantization. Channel optimized vector quantization is a technique to directly incorporate knowledge about the channel into the source coder. This thesis contributes to the field by using channel optimized vector quantization in a couple of new scenarios. Multiple description coding is the concept of encoding a source using several different descriptions in order to provide robustness in systems with losses in the transmission. One contribution of this thesis is an improvement to an existing multiple description coding scheme and another contribution is to put multiple description coding in the context of channel optimized vector quantization. The thesis also presents a simple image coder which is used to evaluate some of the results on channel optimized vector quantization. / QC 20101108

Quantization of Neural Networks is popular technique for adopting computation intensive Deep Learning applications to edge devices. In this work, low bit mixed precision quantization of FPN-Resnet18 model trained for the task of semantic segmentation is explored using Cityscapes and Arriver datasets. The Hessian information of each layer in the model is used to determine the bit precision for each layer and in some experiments the bit precision for the layers are determined randomly. The networks are quantization-aware trained with bit combinations 2, 4 and 8. The results obtained for both Cityscapes and Arriver datasets show that the quantization-aware trained networks with the low bit mixed precision technique offer a performance at par with the 8-bit quantization-aware trained networks and the segmentation performance degrades when the network activations are quantized below 8 bits. Also, it was found that the usage of the Hessian information had little effect on the network’s performance. / Kvantisering av Neurala nätverk är populär teknik för att införa beräknings-intensiva Deep Learning -applikationer till edge-enheter. I detta arbete utforskas låg bitmixad precisionskvantisering av FPN-Resnet18-modellen som är utbildad för uppgiften för semantisk segmentering med hjälp av Cityscapes och Arriverdatauppsättningar. Hessisk information från varje lager i modellen, används för att bestämma bitprecisionen för respektive lager. I vissa experiment bestäms bitprecision för skikten slumpmässigt. Nätverken är kvantiserings medvetna utbildade med bitkombinationer 2, 4 och 8. Resultaten som erhållits för både Cityscapes och Arriver datauppsättningar visar att de kvantiserings medvetna utbildade nätverken med lågbit blandad precisionsteknik erbjuder en prestanda i nivå med 8-bitars kvantiseringsmedvetna utbildade nätverk och segmenteringens prestationsgrader när nätverksaktiveringarna kvantiseras under 8 bitar. Det visade sig också att användningen av hessisk information hade liten effekt på nätets prestanda.

Le suivi de partition est défini comme étant la synchronisation sur ordinateur entre une partition musicale connue et le signal sonore de l'interprète de cette partition. Dans le cas particulier de la voix chantée, il y a encore place à l'amélioration des algorithmes existants, surtout pour le suivi de partition en temps réel. L'objectif de ce projet est donc d'arriver à mettre en oeuvre un logiciel suiveur de partition robuste et en temps-réel utilisant le signal numérisé de voix chantée et le texte des chansons. Le logiciel proposé utilise à la fois plusieurs caractéristiques de la voix chantée (énergie, correspondance avec les voyelles et nombre de passages par zéro du signal) et les met en correspondance avec la partition musicale en format MusicXML. Ces caractéristiques, extraites pour chaque trame, sont alignées aux unités phonétiques de la partition. En parallèle avec cet alignement à court terme, le système ajoute un deuxième niveau d'estimation plus fiable sur la position en associant une segmentation du signal en blocs de chant à des sections chantées en continu dans la partition. La performance du système est évaluée en présentant les alignements obtenus en différé sur 3 extraits de chansons interprétés par 2 personnes différentes, un homme et une femme, en anglais et en français.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / In this paper, we discuss a Block Adaptive Vector Quantization(BAVQ) Algorithm for Synthetic Aperture Radar(SAR). And we discuss a realization method of BAVQ algorithm for SAR raw data compressing in digital signal processor. Using the algorithm and the digital signal processor, we have compressed the SIR_C/X_SAR data.

The main focus of the thesis is to derive stability criteria for networked control system (NCS) models featuring imperfections such as time-varying and constant delays, quantization, packet dropouts, and non-uniform sampling intervals. The main method of proof is based on matrix algebra, as opposed to methods using Lyapunov functions or integral quadratic constraints (IQC). This work puts a particular focus on handling systems with a single integrator. This framework is elaborated in different specific directions as motivated by practical realizations of NCSs, as well as through numerical examples. A novel proof of the discrete time multivariate circle criterion and the Tsypkin criterion for systems including a single integrator is presented, as well as a stability criterion for linear systems with a single integrator subject to variable sampling periods and sector-bounded nonlinear feedback. Four stability criteria for different classes of systems subject to packet loss and time-varying delay are given. Stability criteria for a closed loop system switching between a set of linear time-invariant systems (LTIs) are proved. This result is applied to a single-link NCS with feedback subject to packet loss. Finally, necessary and sufficient conditions for delay-independent stability of an LTI system subject to nonlinear feedback are derived.