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Orientador: Iakov Veniaminovitch Kopelevitch / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-22T01:33:07Z (GMT). No. of bitstreams: 1 Baring_LuisAugustoGomes_D.pdf: 21081310 bytes, checksum: 275f0ba5ff80d6f9f19f53cf8316e1a6 (MD5) Previous issue date: 2012 / Resumo: No presente trabalho estudamos os semimetais bismuto Bi, antimônio Sb e Bi1-xSbx, materiais com propriedades topologicamente não triviais. Observamos a ocorrência de supercondutividade intrínseca em bismuto com TC »= 8:5K. Construímos, a partir dos dados de magnetização e resistência, o diagrama de fase do campo crítico H versus a temperatura T. Esse diagrama de fase, pode ser ajustado segundo modelos da literatura válidos para supercondutividade granular. Detectamos, no bismuto, o aumento da corrente Josephson e acoplamento intergranular no limite quântico devidos à quantização de Landau. Isso se manifesta como uma supercondutividade reentrante. Foi também encontrada transição tipo metal-isolante induzida por campo magnético em todos os materiais estudados. O diagrama de fase H versus T mostra uma extraordinária semelhança entre os três materiais. A amostra Bi1-xSbx, com x = 0:052, revelou a ocorrência de transição semimetal-isolante topológico já em campo magnético zero. Fizemos uma comparação com resultados anteriores da literatura, analisando a dependência da temperatura em que ocorre essa transição em relação à concentração de antimônio x e ao campo magnético B e demonstramos a similaridade entre eles. Observamos, também, supercondutividade nos semimetais bismuto, antimônio e no Bi1-xSbx, induzida por dopagem com os metais ouro e índio, e mostramos que a supercondutividade está associada à interface entre os metais e os semimetais. Finalmente, encontramos a indução de supercondutividade mediante a aplicação de campo magnético em bismuto, consistente com a ocorrência de férmions de Majorana na interface entre esse material e a tinta prata usada para os contatos. Tal observação pode ser devida, também, à ocorrência de um estado supercondutor fora do equilíbrio. / Abstract: In this work we studied the semimetals bismuth Bi, antimony Sb and Bi1-xSbx, all of them with non-trivial topologic properties. We observed an intrinsic superconductivity in bismuth, with TC »= 8:5 K. The phasediagram of the critical field H versus the temperature T, based upon the magnetization and resistance data, may be well fitted according to theoretical models valid for granular superconductivity. We also detected, in bismuth, the increase of the Josephson current and interganular coupling in the quantum limit due to Landau quantization. This manifests itself as a reentrant superconducting state. Our results revealed a metal-insulator transition triggered by magnetic field, for all the studied materials. The phase diagram H ¡T shows a striking similarity between them. The sample Bi1-xSbx with x = 0:052 demonstrated a semimetal-insulator transition even at zero field. We compared our results with previous results of other groups and analyzed the temperature dependence of the transition as a function of the antimony amount x and the magnetic field B and demonstrated their similarity. We also observed supeerconductivity in the semimetals bismuth, antimony and Bi1-xSbx, triggered by doping with the metals gold and indium, and showed that the superconductivity is associated to the interface between the metals and the semimetals. Finally, we found the superconductivity induced by the aplication of magnetic field in bismuth, consistent with the Majorana fermions present in the interface between this material and the silver paste contacts. This may also be related to a non-equilibrium superconduting state. / Doutorado / Física / Doutor em Ciências

[pt] Em um sistema de comunicações, procura-se representar a informação gerada de forma eficiente, de modo que a redundância da informação seja reduzida ou idealmente eliminada, com o propósito de armazenamento e/ou transmissão da mesma. Este interesse justifica portanto, o estudo e desenvolvimento de técnicas de compressão que vem sendo realizado ao longo dos anos. Este trabalho de pesquisa investiga o uso de códigos de permutação para codificação de fontes segundo um critério de fidelidade, mais especificamente de fontes sem memória, caracterizadas por uma distribuição uniforme e critério de distorção de erro médio quadrático. Examina-se os códigos de permutação sob a ótica de fontes compostas e a partir desta perspectiva, apresenta-se um esquema de compressão com duplo estágio. Realiza-se então uma análise desse esquema de codificação. Faz-se também uma extensão L- dimensional (L > 1) do esquema de permutação apresentado na literatura. Os resultados obtidos comprovam um melhor desempenho da versão em duas dimensões, quando comparada ao caso unidimensional, sendo esta a principal contribuição do presente trabalho. A partir desses resultados, busca-se a aplicação de um esquema que utiliza códigos de permutação para a compressão de imagens. / [en] In communications systems the information must be represented in an efficient form, in such a way that the redundancy of the information is either reduced or ideally eliminated, with the intention of storage or transmission of the same one. This interest justifies the study and development of compression techniques that have been realized through the years. This research investigates the use of permutation codes for source encoding with a fidelity criterion, more specifically of memoryless uniform sources with mean square error fidelity criterion. We examine the permutation codes under the view of composed sources and from this perspective, a project of double stage source encoder is presented. An analysis of this project of codification is realized then. A L-dimensional extension (L > 1) of permutation codes from previous research is also introduced. The results prove a better performance of the version in two dimensions, when compared with the unidimensional case and this is the main contribution of the present study. From these results, we investigate an application for permutation codes in image compression.

Cette thèse porte sur quelques problèmes de codage de source dans lesquels on souhaite préserver la confidentialité vis à vis d’une écoute du canal. Dans la première partie, nous fournissons des nouveaux résultats fondamentaux sur le codage de source pour la détection (utilisateur légitime) et la confidentialité (vis à vis d’une écoute du canal) en présence d'informations secondaires aux terminaux de réception. Nous proposons plusieurs nouveaux résultats d'optimisation de la région de débit-erreur-équivocation réalisable, et proposons des algorithmes pratiques pour obtenir des solutions aussi proches que possible de l'optimal, ce qui nécessite la conception de quantificateurs en présence d'un eavesdropper. Dans la deuxième partie, nous étudions le problème de l'estimation sécurisée dans un cadre d'utilité-confidentialité où l'utilisateur recherche soit à extraire les aspects pertinents de données complexes ou bien à les cacher vis à vis d'un eavesdropper potentiel. L'objectif est principalement axé sur l'élaboration d'un cadre général qui combine la théorie de l'information et la théorie de la communication, visant à fournir un nouvel outil pour la confidentialité dans les Smart Grids. D'un point de vue théorique, cette recherche a permis de quantifier les limites fondamentales et donc le compromis entre sécurité et performance (estimation / détection). / This thesis investigates source coding problems in which some secrecy should be ensured with respect to eavesdroppers. In the first part, we provide some new fundamental results on both detection and secrecy oriented source coding in the presence of side information at the receiving terminals. We provide several new results of optimality and single-letter characterization of the achievable rate-error-equivocation region, and propose practical algorithms to obtain solutions that are as close as possible to the optimal, which requires the design of optimal quantization in the presence of an eavesdropper In the second part, we study the problem of secure estimation in a utility-privacy framework where the user is either looking to extract relevant aspects of complex data or hide them from a potential eavesdropper. The objective is mainly centered on the development of a general framework that combines information theory with communication theory, aiming to provide a novel and powerful tool for security in Smart Grids. From a theoretical perspective, this research was able to quantify fundamental limits and thus the tradeoff between security and performance (estimation/detection).

Cette thèse explore plusieurs sujets fondamentaux pour les circuits mésoscopiques qui incorporent un faible nombre de canaux de conduction électroniques. Les premières expériences concernent le caractère quantifié (discret) de la charge dans les circuits. Nous démontrons le critère de quantification de la charge, nous observons la loi d’échelle prédite pour cette quantification ainsi qu’une transition vers comportement universel à mesure que la température augmente. Le second ensemble d’expériences concerne la physique critique quantique non-conventionnelle qui émerge du modèle Kondo à multi-canaux. Par l’implémentation d’une impureté Kondo avec un pseudo-spin de valeur ½ constitué de deux états de charge dégénérés d’un circuit, nous explorons la physique Kondo à deux- et trois-canaux. Au point critique quantique symétrique, nous observons les points fixes Kondo universels prédits, des exposants universels de lois d’échelle et nous validons les courbes complètes obtenues par le groupe de renormalisation numérique. En s’écartant du point critique quantique, nous explorons la transition depuis la zone critique quantique : par une visualisation directe du development d’une transition de phase quantique, par l’espace des paramètres de la zone critique quantique ainsi que par les comportements d’universalité et d’échelle. / This thesis explores several fundamental topics in mesoscopic circuitry that incorporates few electronic conduction channels. The first experiments address the quantized character (the discreteness) of charge in circuits. We demonstrate the charge quantization criterion, observe the predicted charge quantization scaling and demonstrate a crossover toward a universal behavior as temperature is increased. The second set of experiments addresses the unconventional quantum critical physics that arises in the multichannel Kondo model. By implementing a Kondo impurity with a pseudo-spin of ½ constituted by two degenerate charge states of a circuit, we explore the two- and three-channel Kondo physics. At the symmetric quantum critical point, we observe the predicted universal Kondo fixed points, scaling exponents and validate the full numerical renormalization group scaling curves. Away from the quantum critical point, we explore the crossover from quantum criticality: direct visualization of the development of a quantum phase transition, the parameter space for quantum criticality, as well as universality and scaling behaviors.

La première partie de la thèse traite des déformations et quantification de bialgèbres de Lie. L'existence d'une quantification pour chaque bialgèbre de Lie a été démontrée par Etingof et Kazhdan. Dans ce travail, on s'intéresse au cas des bialgèbres de Lie colorée, c'est à dire une structure de bialgèbres de Lie sur un espace gradué par un groupe quelconque et un bicaractère. A cet effet, on adapte la preuve de Etingof et Kazhdan et on introduit une généralisation au cas coloré du grand crochet introduit par Lecomte et Roger. Par ailleurs nous définissons une cohomologie pour les algèbres et bialgèbres de Lie colorées. Dans le deuxième partie de la thèse, on considère les algèbres Hom-associatives et algèbres Hom-Lie. Une algèbre Hom-associative est définie par une multiplication et une application linéaire alpha modifiant l'associativité. On commence cette partie par rappeler des définitions et propriétés des algèbres de type Hom. Ensuite, on définit la cohomologie de Hochschild de type alpha, en donnant ses propriétés. Une étude similaire est faite dans le cas des algèbres Hom-Lie et la cohomologie de Chevalley-Eilenberg, ainsi que pour les Hom-bialgèbres et bialgèbres Hom-Lie. La théorie de déformations formelles introduite par Gerstenhaber met en lien les déformations et la cohomologie. Dans cette thèse on établit une théorie de déformations des algèbres Hom-associatives basée sur la cohomologie de Hochschild de type alpha. Il s'agit de déformer simultanément la multiplication et l'application linéaire. Par ailleurs, on explore la structure d’algèbre de Lie à homotopie près correspondante, telle que les éléments de Maurer-Cartan sont des Hom-algèbres. / In the first part of this thesis, we provide a proof that any color Lie bialgebra can be quantized. This was proved for Lie bialgebras by Etingof and Kazhdan. Here we generalize this proof to color Lie bialgebras, which are Lie bialgebras graded by an arbitrary abelian group and symmetry given by a bicharacter. Before giving the details of the proof, we first recall the definitions and basic properties of color Lie algebras and bialgebras. Also a generalization of the Grand Crochet introduced by Lecomte and Roger to the color setting is given. Using the Grand Crochet, we also provide a cohomology for color Lie bialgebras. In the second part, we study different type of Hom-algebras, especially Hom-Lie and Hom-associative algebras. Hom-algebras are algebras were the defining relations, e.g. the associativity, are twisted by a linear map alpha called structure map. We first recall the relevant definitions. Then we define a new cohomology for Hom-associative and Hom-Lie algebras called alpha-type Hochschild and Chevalley-Eilenberg cohomology respectively. We also show how these cohomologies can be used to study formal deformations, in the sense of Gerstenhaber, of Hom-associative and Hom-Lie algebras. We allow the deformation of the multiplication and the structure map. We also consider alpha type cohomologies for Hom-bialgebras. Moreover, we explore the corresponding homotopy Lie algebra structure such that the Maurer-Cartan elements are Hom-algebras.

In this paper we improve the rate-distortion performance of a previously proposed video coder based on frame replenishment and adaptive mean-removed vector quantization. This is realized by determining for each block of a given frame the optimal encoding mode in the rate-distortion sense. The algorithm is a new contribution to very low bit rate video coding with adaptive vector quantization suitable for videophone applications. Experimental results comparing the two coders for several test sequences at different bit rates are provided.

Los sistemas de comunicaciones con múltiples antenas o sistemas MIMO (multiple-input multiple-output) se presentan como una de las tecnologías más prometedoras en el campo de las comunicaciones inalámbricas, ya que permiten aprovechar la dimensión espacial además de las dimensiones de frecuencia y tiempo. De esta forma, se pueden obtener tasas de transmisión más elevadas usando el mismo ancho de banda, que es un recurso escaso, y manteniendo una potencia de transmisión baja, lo cual es crucial para dispositivos alimentados por baterías. Por estas razones, la tecnología MIMO ha sido adoptada en muchos estándares como Long-Term Evolution (LTE), LTE Advanced y Worldwide Interoperability for Microwave Access (WiMAX). Las técnicas MIMO también pueden se pueden emplear en un escenario multiusuario, donde varios usuarios comparten la dimensión espacial provocando una interferencia multiusuario. A través de la precodificación y del uso de múltiples antenas en el transmisor, la señal de los diferentes usuarios puede ser multiplexada espacialmente de forma que se mitigue la interferencia multiusuario incluso con usuarios de una sola antena. Estos sistemas, conocidos como sistemas MU-MISO (multiuser multiple-input single-output), han atraído mucho la atención en los últimos años ya que permiten el desarrollo de terminales pequeños y baratos, manteniendo así el equipamiento más caro en el transmisor. Sin embargo, estos beneficios conllevan un sistema más complejo. Por una parte, el multiplexado espacial requiere una carga de procesado considerable, que depende del tamaño del sistema: número de antenas transmisoras, número de receptores y ancho de banda. Por otra parte, las técnicas MIMO requieren un conocimiento del canal en transmisión o CSIT (channel state information at the transmitter) preciso. En sistemas con duplexación por división en frecuencia o FDD (frequency-division duplex), la información de canal o CSI (channel state information) debe ser estimada en el receptor y proporcionada al transmisor a través del enlace de realimentación, reduciendo así la eficiencia del sistema. Por lo tanto, esta tesis se centra en la mejora de la eficiencia de las implementaciones de precodificación y en el rendimiento de los esquemas de realimentación de canal en sistemas MU-MISO. El problema de la precodificación se aborda en primer lugar. Se ha llevado a cabo un análisis de algunas de las técnicas de precodificación más usadas, prestando especial atención a su rendimiento y a su complejidad. Este análisis revela que aquellas técnicas que hacen uso de lattice reduction (LR) obtienen un mejor rendimiento. Sin embargo, la complejidad computacional de la técnica LR dificulta su implementación en la práctica. El análisis también revela que las técnicas zero-forcing (ZF), Tomlinson-Harashima precoding (THP) y LR-THP son las técnicas más adecuadas para cubrir todo el rango de rendimiento y complejidad computacional. Asimismo, se ha llevado a cabo un análisis de estas técnicas bajo CSIT imperfecto. Dicho análisis ha demostrado que LR es una técnica muy importante también para el caso de CSIT imperfecto. A continuación, se han presentado implementaciones paralelas de técnicas de precodificación sobre unidades de procesamiento gráfico o GPUs (graphic processing unit), comparándose con implementaciones en unidades de procesamiento central o CPU (central processing unit). Dado que las implementaciones de THP y LR-THP han demostrado ser las que mejor se adaptan a la arquitectura de la GPU y ya que tienen muchas operaciones comunes, se ha propuesto una implementación sobre GPU de un esquema THP reconfigurable combinado con LR. La reconfigurabilidad de las GPUs permite desactivar la etapa de LR cuando los requisitos de los usuarios están garantizados por el esquema THP, combinando complejidad computacional con rendimiento. Aunque esta implementación consigue una mejora significativa respecto a la implementación sobre CPU, su paralelismo viene limitado por la naturaleza secuencial del problema LR. Por ello, se han propuesto varias estrategias para la paralelización del problema LR que han sido evaluadas en distintas plataformas: CPU multi-núcleo, GPU y plataforma heterogénea que consiste en CPU+GPU. Los resultados revelan que la arquitectura GPU permite reducir considerablemente el tiempo de computación del problema LR, especialmente en la plataforma heterogénea. La segunda parte de la tesis trata el problema de la realimentación de canal en sistemas FDD. En estos sistemas, los receptores normalmente proporcionan una versión cuantificada del canal a través del canal de realimentación. Con el objetivo de mantener una eficiencia alta, el canal debe ser cuantificado con los mínimos bits posibles. En primer lugar, se explora el uso de la correlación en frecuencia para reducir el volumen de información de realimentación. Se han presentado dos esquemas diferentes basados en cuantificación vectorial o VQ (vector quantization) y en la transformación Karhunen-Loève, respectivamente, y se han comparado con esquemas existentes en términos de rendimiento y complejidad computacional. Los resultados muestran que ambas técnicas son capaces de reducir significativamente el volumen de información de realimentación aprovechando la correlación en frecuencia. Finalmente, la correlación espacial también se aprovecha para reducir la información de realimentación. Se ha presentado una caracterización espacial estadística del modelo de canal SCM (spatial channel model) del 3GPP (3rd Generation Partnership Project) para un entorno de alta correlación. Basado en esta caracterización, se propone un esquema de cuantificación de canal para entornos de alta correlación. Con el objetivo de obtener una caracterización para alta y baja correlación, se considera un modelo de correlación más sencillo como el modelo de Kronecker. Basado en esta caracterización, se proponen dos esquemas de cuantificación y se evalúan con un modelo de canal realista como el SCM. Los resultados muestran que ambos esquemas son capaces de reducir la información de realimentación en ambientes con correlación alta y moderada. / Multiple-input multiple-output (MIMO) communication systems have emerged as one of the most promising technologies in the field of wireless communications, allowing to exploit the spatial dimension as well as the time and frequency dimensions. Thus, higher rates can be obtained by using the same bandwidth, which is a scarce resource, and keeping a low transmit power, which is crucial in battery-operated devices. For these reasons, MIMO technologies have been adopted by many standards such as Long-Term Evolution (LTE), LTE advanced (LTE-A) and Worldwide Interoperability for Microwave Access (WiMAX). MIMO techniques can also be used in a multiuser scenario, where several usersshare the spatial dimension causing multiuser interference. By means of precoding and the use of multiple antennas at the transmitter, the signal of the different users can be spatially multiplexed so that multiuser interference is mitigated even for single-antenna users. These systems, known as multiuser multiple-input singular-output (MU-MISO) systems, have attracted much attention in recent years since they allow the development of small and inexpensive terminals, keeping the most expensive hardware at the transmitter. However, these benefits come at the cost of having a more complex system. On the one hand, spatial multiplexing requires a considerable processing load that depends on the size of the system: number of transmit antennas, number of receivers and bandwidth. On the other hand, MIMO techniques require accurate channel state information at the transmitter (CSIT). In frequency-division duplex (FDD) systems, channel state information (CSI) has to be estimated at the receiver and provided to the transmitter through the feedback link, hence reducing the efficiency of the system. Therefore, this thesis is primarily focused on improving the efficiency of precoding implementations and the performance of feedback schemes in MU-MISO systems. First, the problem of precoding is addressed. An analysis of some of the most utilized precoding techniques is conducted, paying special attention to their performance and computational complexity. The analysis reveals that those techniques that make use of lattice reduction (LR) achieve the best performance. However, the computational complexity of LR makes its implementation difficult for practical systems. The analysis reveals that zero-forcing (ZF), Tomlinson-Harashima precoding (THP) and lattice reduction Tomlinson-Harashima precoding (LR-THP) are the most suitable techniques for covering the entire range of performance and computational complexity. An analysis of these techniques with imperfect CSIT has also been performed. In this analysis, LR has proven to be a key technique also when imperfect CSIT is available. Next, parallel implementations of the precoding techniques on a graphic processing unit (GPU) are presented and compared to implementations that use a central processing unit (CPU). Since the implementations of THP and LR-THP have shown to best fit the GPU architecture and since they also share many operations, a GPU implementation of a reconfigurable THP scheme combined with LR has been proposed. The reconfigurable nature of GPUs allows gating the LR stage off when the user requirements are sufficiently guaranteed by the THP scheme, trading computational cost and performance. Although this implementation achieves a significant speed-up compared to its CPU implementation, its parallelism is limited by the sequential nature of LR. Therefore, several strategies for the parallelization of the LR problem are proposed and evaluated on different platforms: multicore CPU, GPU and a heterogeneous platform consisting of CPU+GPU. Results reveal that a GPU architecture allows a considerable reduction of the computational time of the LR problem, especially in the heterogeneous platform. The second part of this thesis addresses the problem of feedback in FDD systems. In these systems, a quantized version of the channel is usually provided by the receivers through the feedback link. In order to keep a high efficiency, the channel must be quantized using as few bits as possible. First, the use of the frequency correlation to reduce the feedback information is explored. Two different schemes based on vector quantization (VQ) and the Karhunen-Loève (KL) transform, respectively, are presented and compared with existing schemes in terms of performance and complexity. Results show that both techniques are able to significantly reduce the feedback overhead by taking advantage of the frequency correlation. Finally, the spatial correlation is leveraged to reduce the feedback information. A spatial statistical characterization of the spatial channel model (SCM) from the 3rd Generation Partnership Project (3GPP) for a highly correlated environment is presented. Based on this characterization, a channel quantization scheme for highly correlated environments is proposed. In order to obtain a statistical characterization for both high and low correlations, a simpler model such as the Kronecker correlation model is considered. Based on this characterization, two quantization schemes have been presented and evaluated using a realistic channel model such as the SCM. Results show that both schemes are able to reduce the feedback overhead in highly and moderately correlated scenarios. / Domene Oltra, F. (2015). Evaluation of precoding and feedback quantization schemes for multiuser communications systems [Tesis doctoral]. Editorial Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/46971 / Alfresco

Convolutional neural networks (CNN) are state of the art machine learning models used for various computer vision problems, such as image recognition. As these networks normally need a vast amount of parameters they can be computationally expensive, which complicates deployment on embedded hardware, especially if there are contraints on for instance latency, memory or power consumption. This thesis examines the CNN optimization methods pruning and quantization, in order to explore how they affect not only model accuracy, but also possible inference latency speedup. Four baseline CNN models, based on popular and relevant architectures, were implemented and trained on the CIFAR-10 dataset. The networks were then quantized or pruned for various optimization parameters. All models can be successfully quantized to both 5-bit weights and activations, or pruned with 70% sparsity without any substantial effect on accuracy. The larger baseline models are generally more robust and can be quantized more aggressively, however they are also more sensitive to low-bit activations. Moreover, for 8-bit integer quantization the networks were implemented on an ARM Cortex-A72 microprocessor, where inference latency was studied. These fixed-point models achieves up to 5.5x inference speedup on the ARM processor, compared to the 32-bit floating-point baselines. The larger models gain more speedup from quantization than the smaller ones. While the results are not necessarily generalizable to different CNN architectures or datasets, the valuable insights obtained in this thesis can be used as starting points for further investigations in model optimization and possible effects on accuracy and embedded inference latency.

<p>We investigate the Laplace transform in Komatsu ultradistributions and give conditions under which an analytic function is a Laplace transformation of an ultradistribution. We&nbsp; prove the equivalence of several denitions of convolu-tion of two Roumieu ultradistributions. For that purpose, we consider the _ ten-sor product of _~BfMpg<br />and a locally convex space. We dene specic global symbol classes of Shubin type and study the corresponding pseudodierential operators of innite order that act continuously on the spaces of tempered ultradistributions of Beurling and Roumieu type. For these classes, we develop symbolic calculus. We investigate the connection between the Anti-Wick and Weyl quantization when the symbols belong to these classes. We nd the largest subspace of ultradistri-butions for which the convolution with the gaussian kernel exists. This gives a way to extend the denition of Anti-Wick quantization for symbols that are not necessarily tempered ultradistributions.</p> / <p>Prouqavamo Laplasovu transformaciju u prostorima Komat-suove ultradistribucije i dajemo uslov pod kojim analitiqka funk-cija je Laplasova transformacija ultradistribucije. Dokazujemo ek-vivalentnost nekoliko definicija o konvoluciji dve Rumie ultradis-tribucije. Za &nbsp; ovu svrhu razmatramo &quot; tenzorski proizvod&nbsp; ~ B fMpg i lokalno konveksni prostor. Definiramo specifiqne globalne simbol klase Xubinovog tipa i prouqavamo odgovarajue psevdo diferenci-jalne operatore beskonaqnog reda koji neprekidno deluju na prosto-rima temperiranih ultradistribucija Berlineovog i Rumieovog tipa. Za ove klase gradimo simboliqki&nbsp; kalkulus. Prouqavamo vezu izmeu Anti-Wick-ove i Weyl-ove kvantizacije kad simboli pripadaju ove sim-bol klase. Nalazimo najvei podprostor ultradistribucija za koje konvolucija sa gausovog jezgra postoji. To prua mogunost da pro-xirimo definiciju Anti-Wick kvantizacije za simbole koje nemoraju da su temperirane ultradistribucije.</p>