This master’s thesis deals with the restoration of audio signals damaged by quantization. The theoretical part starts with a description of quantization and dequantization in general, few existing methods of dequantization of audio signals and theory of sparse representations of signals are also presented. The next part introduces algorithms suitable for dequantization, specifically Douglas–Rachford, Chambolle–Pock, SPADEQ and implementation of these algorithms in MATLAB application in the next chapter. In the last part of this thesis, testing of reconstructed signals using the algorithms takes place and results are evaluated by objective measures SDR, PEMO-Q, PEAQ and subjective listening test MUSHRA.

Massive MU-MIMO (Multiuser-Multiple Input and Multple Output) is a promising technology for 5G wireless communications because of its spectrum and energy efficiency. To combat the distortion from multipath fading channel, the acquisition of channel state information is essential, which generally requires the training signal that lowers the data rate. In addition, coarse quantization can reduce the high computational energy and cost, yet results in the loss of information. In this thesis, an iterative decision feedback receiver, including iterative Channel Estimation (CE) and equalization, is constructed for a Massive MU-MIMO uplink system. The impact of multipath distortion and coarse quantization can be gradually reduced due to the iterative structure that exploits extrinsic feedback to improve the CE and data detection, so that the data rate is improved by reducing training signals for CE and by using low precision quantization. To observe and evaluate the convergence behaviour, an Extrinsic Information Transfer (EXIT) chart method is utilized to visualize the performance of the iterative receiver. / Graduate

We investigate field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest. Within the quasistatic framework, we represent the nanostructure material domains with frequency-dependent dielectric functions. Quantities associated with the normal modes of the electronic systems, the nonretarded plasmon dispersion relations, eigenmodes, and fields are then calculated for several geometric entities of use in nanoscience and nanotechnology. From the classical energy of the charge density oscillations in the modeled nanoparticle, we then derive the Hamiltonian of the system, which is used for quantization. The quantized plasmon field is obtained and, employing an interaction Hamiltonian derived from the first-order perturbation theory within the hydrodynamic model of an electron gas, we obtain an analytical expression for the radiative decay rate of the plasmons. The established treatment is applied to multiple geometries to investigate the quantized charge density oscillations on their bounding surfaces. Specifically, using one sheet of a two-sheeted hyperboloid of revolution, paraboloid of revolution, and cylindrical domains, all with one infinite dimension, and the finite spheroidal and toroidal domains are treated. In addition to a comparison of the paraboloidal and hyperboloidal results, interesting similarities are observed for the paraboloidal domains with respect to the surface modes and radiation patterns of a prolate spheroid, a finite geometric domain highly suitable for modeling of nanoparticles such as quantum dots. The prolate and oblate spheroidal calculations are validated by comparison to the spherical case, which is obtained as a special case of a spheroid. In addition to calculating the potential and field distributions, and dispersion relations, we study the angular intensity and the relation between the emission angle with the rate of radiative decay. The various morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent. For the specific case of a nanoring, modeled in the toroidal geometry, significant complexity arises due to an inherent coupling among the various modes. Within reasonable approximations to decouple the modes, we study the radiative decay channel for a vacuum bounded single solid nanoring by quantizing the fields associated with charge density oscillations on the nanoring surface. Further suggestions are made for future studies. The obtained results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.

In this thesis, structures defined via modular operads and properads are generalized to their non-commutative analogs. We define the connected sum for modular operads. This way we are able to construct the graded commutative product on the algebra over Feynman transform of the modular operad. This forms a Batalin-Vilkovisky algebra with symmetry given by the modular operad. We transfer this structure to the cohomology via the Homological perturbation lemma. In particular, we consider these constructions for Quantum closed and Quantum open modular operad. As a parallel project we introduce associative analog of Frobenius properad, called Open Frobenius properad. We construct the cobar complex over it and in the spirit of Barannikov interpret algebras over cobar complex as homological differential operators. Furthermore we present the IBA∞-algebras as analog of well-known IBL∞-algebras. 1

Deep learning has proven to be a major leap in machine learning, allowing completely new problems to be solved. While flexible and powerful, neural networks have the disadvantage of being large and demanding high performance from the devices on which they are run. In order to deploy neural networks on more, and simpler, devices, techniques such as quantization, sparsification and tensor decomposition have been developed. These techniques have shown promising results, but their effects on model robustness against attacks remain largely unexplored. In this thesis, Universal Adversarial Perturbations (UAP) and the Fast Gradient Sign Method (FGSM) are tested against VGG-19 as well as versions of it compressed using 8-bit quantization, TensorFlow’s float16 quantization, and 8-bit and 4-bit single layer quantization as introduced in this thesis. The results show that UAP transfers well to all quantized models, while the transferability of FGSM is high to the float16 quantized model, lower to the 8-bit models, and high to the 4-bit SLQ model. We suggest that this disparity arises from the universal adversarial perturbations’ having been trained on multiple examples rather than just one, which has previously been shown to increase transferability. The results also show that quantizing a single layer, the first layer in this case, can have a disproportionate impact on transferability. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

京都大学 / 0048 / 新制・論文博士 / 博士(工学) / 乙第13240号 / 論工博第4178号 / 新制||工||1720(附属図書館) / (主査)教授 木本 恒暢, 教授 藤田 静雄, 教授 山田 啓文 / 学位規則第4条第2項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Résumé: Ce travail se veut une analyse conceptuelle de certains développements récents dans les fondements mathématiques de la Mécanique Classique et de la Mécanique Quantique qui ont permis de formuler ces deux théories dans un même langage. Du point de vue algébrique, l’ensemble des observables d’un système physique, soit-il classique ou quantique, est décrit par une algèbre de Jordan-Lie. Du point de vue géométrique, l’espace des états de tout système est décrit par un espace uniforme de Poisson avec transition de probabilité. Ces deux structures mathématiques sont ici interprétées comme une manifestation du double rôle constitutif des propriétés en physique : elles sont à la fois des quantités et des transformations. Il s’agit alors de comprendre l’articulation précise entre ces deux rôles. Au cours de l’analyse, il apparaîtra que la Mécanique Quantique peut être vue comme se distinguant de la Mécanique Classique par une condition de compatibilité entres les quantités et les transformations.D’autre part, cette thèse met en évidence l’existence d’une tension fondamentale entre une certaine façon abstraite de concevoir les structures mathématiques, présente dans la pratique de la physique mathématique, et la nécessité de spécifier des états ou des observables particulières. Il devient alors important de comprendre comment, dans le formalisme, se construit un schéma d’indexation. La “poursuite de l’individuation” est l’analyse de différentes techniques mathématiques vues comme tentatives de résolution ce problème. En particulier,nous discuterons comment la théorie des groupes permet d’y apporter une solution partielle. / This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these structures are here perceived as formal translations of the fundamental two fold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics canbe thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. Moreover, this dissertation shows the existence of a tension between a certain ‘abstractway’ of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chasefor Individuation” is the analysis of diferent mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution

No description available.

The Bose-Hubbard Model, a tight binding model within solid state theory can be solved exactly using a number theoretical approach. From this approach, in the two sited Bose-Hubbard model, the hopping term in the model takes the form of a Pauli x matrix. The hopping term can be interpreted as a two energy level system or a dimer with k+1 particles. The statistical properties of this dimer is investigated assuming Boltzmann distribution. The partition function and particle density on each site in the dimer is calculated for spin 1/2 system. The entropy and average energy is also calculated. The particle density is calculated and plotted as a function of temperature for the spin 1/2,1,3/2 and 2 system. At low temperature the particles are more likely to be found in the lower energy site and at high temperatures the particles is equally distributed at the both sites. / Bose-Hubbard modellen är en tight binding modell inom fasta tillstånd- ets fysik som kan lösas exakt genom att använda en talteoretisk lösning- smetod. Genom att göra detta med bara två interagerande platser i modellen tar hoppingtermen i modellen formen av en Pauli x-matris. Hopping modellen kan tolkas som ett system med två energinivåer eller en så kallad dimer med k+1 partiklar. Dimerens statistiska egenskaper undersöks utifrån Boltzmannfördelningen. Partitionsfunktionen och partikeldensiteten på varje plats i dimeren beräkn- as för ett spin 1/2 system, tillsammans med entropin och medelenergin. Vidare är partikeldensiteten  beräknad och plottad som funktion av temperaturen för spinn 1/2, 1, 3/2 och 2 system. Vid låg temperatur befinner sig partiklarna i dimeren i den lägre energinivån och vid hög temperatur är partiklarna jämt fördelade i de två energinivåerna

As the internet user base increases over the years, so do the logistic difficulties of handling higher and higher volumes of data. This large amount of information is now being exploited by Artificial Intelligence algorithms to deliver value to our society on a global scale. Among all the algorithms employed, the widespread adoption of Neural Networks in industrial settings is promoting the automation of tasks previously unsolvable by computers. As of today, efficiency limits the applicability of such technology on Big Data and efforts are being put to develop new acceleration solutions.In this project, we analyzes the computational capabilities of a multicore Digital Signal Processor called the EMCA (Ericsson Many-Core Architecture) when it comes to executing Neural Networks. The EMCA is a proprietary chip used for real-time processing of data in the pipeline of a Radio Base Station.We developed an inference engine to run Neural Networks on the EMCA. The software of such engine has been produced using a proprietary operating system called Flake OS, which runs on the EMCA. On top of the inference engine, we wrote a neural network squeezing pipeline based on quantization. On MNIST, the quantization algorithm can reduce the size of the networks by 4x folds with sub 1% accuracy degradation. The inference engine has been optimized to exploit the quantization utility and can run quantized neural networks. Tests have been done to understand the direct implications of using such algorithm. We show that the quantization is indeed beneficial for inference on DSPs.Finally, the EMCA has demonstrated state of the art computational capabilities for neural network inferencing. / Liksom antalet internetanvändare årligen ökar, så gör också de logistiska svårigheterna att hantera större och större volymer av data. Denna stora mängd av information används nu av artificiell intelligens algoritmer för att leverera värde till vårt samhälle på en global skala. Av alla använda algoritmer, så möjliggör det utbredda införandet av neurala nätverk i industriella omgivningar, att uppgifter som tidigare inte kunde lösas av datorer nu kan automatiseras. Idag så finns det effektivitetsfaktorer som begränsar användbarheten av dessa tekniker för stora datamängder och insatser görs därför för att utveckla nya accelererade lösningar. I det här projektet så analyserar vi beräkningsförmågan av en multicore digital signalprocessor kallad EMCA (Ericsson Many-Core Architecture) för att exekvera neurala nätverk. EMCAn är ett proprietärt mikro-chip som används för real-tids beräkningar av data i pipelinen av en radiobasstation. Vi utvecklade en inferensmotor för att köra neurala nätverk på EM-CAn. Mjukvaran för motorn använde ett proprietärt operativsystem, kallat Flake OS, som körs på EMCAn. Ovanpå inferensmotorn skrev vi en pipeline för att reducera storleken av det neurala nätverket med hjälp av kvantisering. På MNIST så kan kvantiseringsalgorit-men minska storleken av näten upp till 4 gånger med under 1% precisionsdegradering. Inferensmotorn har optimerats för att utnyttja kvantiseringsfunktionen och kan exekvera kvantiserade neurala nätverk. Tester har gjorts för att förstå de direkta följderna av att använda sådana algoritmer. Vi visar att kvantisering verkligen är till nytta för att göra inferens på DSPer. Slutligen, EMCAn har demonstrerat toppmodern beräkningsförmåga för inferens av neurala nätverk.