In J.D. Jackson's Classical Electrodynamics textbook, the analysis of Dirac's charge quantization condition in the presence of a magnetic monopole has a mathematical omission and an all-too-brief physical argument that might mislead some students. This paper presents a detailed derivation of Jackson's main result, explains the significance of the missing term, and highlights the close connection between Jackson's findings and Dirac's original argument. (C) 2016 Sharif University of Technology. All rights reserved.

A área de reconhecimento de objetos tem assistido a um impressionante progresso na última década. O estudo de descritores, aliado à estratégias de amostragem usando quantizações espaciais e a combinação de classificadores têm permeado o estado da arte nos últimos anos. Neste trabalho é proposta uma nova quantização espacial com número arbitrário de níveis e subdivisões arbitrárias de regiões. Regiões adjacentes possuem sobreposição gerando redundância na representação destas regiões de fronteiras e, assim, evitando as quebras que acontecem nas pirâmides espaciais tradicionais que prejudicam a interpretação das formas. Apesar de melhorar o desempenho da abordagem do saco de palavras, as pirâmides espaciais não são robustas a variações na orientação dos objetos na imagem. Foi também proposto neste trabalho, uma divisão espacial utilizando regiões circulares concêntricas que aumentam a robustez a rotação dos objetos na imagem em aproximadamente 80% quando comparada às pirâmides espaciais. Além das novas divisões espaciais, é proposto neste trabalho um novo descritor baseado na aplicação de granulometria morfológica no mapa de bordas da imagem original. Este descritor foi utilizado na criação de modelos de classes em aplicações de categorização de objetos utilizando uma base de dados pública com resultados superiores aos do melhor descritor baseado em bordas reportado pela literatura. Todas estas novas técnicas propostas foram utilizadas em um problema desafiador de categorização de objetos de classes muito parecidas. Foi utilizado um subconjunto da base de pássaros Caltech-UCSD Birds-200 2011 com resultados comparáveis aos melhores resultados reportados pela literatura. A abordagem proposta cria uma classificação de dois níveis e utiliza modelos específicos por classe o que é intuitivo, pois cada espécie de pássaro possui características muito sutis que as diferenciam das demais espécies testadas. Vários descritores são utilizados na criação dos modelos de classes e uma combinação de classificadores gera a rotulação final para a amostra. O descritor proposto neste trabalho esteve presente no melhor modelo de 11 das 13 classes testadas e o resultado final obtido pela técnica de categorização proposta é o melhor resultado utilizando a abordagem do saco de palavras. / The object recognition area has experienced an impressive progress in the last decade. The study of descriptors, together with a sampling strategy using spatial quantization and the combination of classifiers have been presented in the state of art in recent years. This work proposes a new spatial quantizations with an arbitrary number of levels and divisions in each level. Adjacent regions have overlapping areas that generate redundant representation and avoid breakages in the structures that are in their border regions as it happens in the traditional spatial pyramids and impairs the correct interpretation of these structures. Despite spatial pyramids to improve the performance of the bag-of-words approach in object recognition, they are not robust to changes in object orientation in the image. It was also proposed, in this work, a spatial division using concentric circular regions that is almost 80% more robust to rotation of objects when compared to the spatial pyramids using rectangular divisions. In addition to the new spatial division of the image, it is proposed a new granulometric-based descriptor that it is applied to the map of edges of the original image. This descriptor was used in the building of categorys models for object categorization in a public database and showed a better performance than the most used edge-based descriptor reported in literature. All these new proposed techniques were used in a challenge problem of object categorization of very similar classes. It was used a subset of the public database Caltech-UCSD Birds-200 2011 and the method obtained results compared to the best results reported in the literature. The proposed approach uses a 2-level classification and builds class-specific models that are an intuitive way to model the species of birds as very subtle characteristics differ in each tested class of birds. Many descriptors are used in the building of models of species and a combination of classifiers generates the final label for a tested sample. The descriptor proposed here were presented in 11 of 13 best models of birds classes. The final result obtained by the proposed object categorization method is the best one using the bag-of-words approach.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis studies control systems with communication constraints. Such constraints arise due to the fact that practical control systems often use non-transparent communication links, i.e., links subject to data-rate constraints, random data-dropouts or random delays. Traditional control theory cannot deal with such constraints and the need for new tools and insights arises. We study two problems: control with average data-rate constraints and control over analog erasure channels with i.i.d. dropout profiles. When focusing on average data-rate constraints, it is natural to ask whether information theoretic ideas may assist the study of networked control systems. In this thesis we show that it is possible to use fundamental information theoretic concepts to arrive at a framework that allows one to tackle performance related control problems. In doing so, we show that there exists an exact link between control systems subject to average data-rate limits, and control systems which are closed over additive i.i.d. noise channels subject to a signal-to-noise ratio constraint. On the other hand, in the case of control systems subject to i.i.d. data-dropouts, we show that there exists a second-order moments equivalence between a linear feedback system which is interconnected over an analog erasure channel, and the same system when it is interconnected over an additive i.i.d. noise channel subject to a signal-to-noise ratio constraint. From the results foreshadowed above, it follows that the study of control systems closed over signal-to-noise ratio constrained additive i.i.d. noise channels is a task of relevance to many networked control problems. Moreover, the interplay between signal-to-noise ratio constraints and control objectives is an interesting issue in its own right. This thesis starts with such a study. Then, we use the resultant insights to address performance issues in control systems subject to either average data-rate constraints or i.i.d. data-dropouts. Our approach shows that, once key equivalences are exposed, standard control intuition and synthesis machinery can be used to tackle networked control problems in an exact manner. It also sheds light into fundamental results in the literature and gives (partial) answers to several previously open questions. We believe that the insights in this thesis are of fundamental importance and, to the best of the author's knowledge, novel.

<p>The thesis demonstrates a low-cost, low-bandwidth and low-resolution Analog-to- Digital Converter(ADC) in 0.35 um CMOS Process. A second-order Sigma-Delta modulator is used as the basis of the A/D Converter. A Semi-Uniform quantizer is used with the modulator to take advantage of input distributions that are dominated by smaller-amplitude signals e.g. Audio, Voice and Image-sensor signals. A Single-bit feedback topology is used with a multi-bit quantizer in the modulator. This topology avoids the use of a multi-bit DAC in the feedback loop – hence the system does not need to use digital correction techniques to compensate for a multi-bit DAC nonlinearity. </p><p>High-Level Simulations of the second-order Sigma-Delta modulator single-bit feedback topology along with a Semi-Uniform quantizer are performed in Cadence. Results indicate that a 5-bit Semi-Uniform quantizer with a Over-Sampling Ratio of 32, can achieve a resolution of 10 bits, in addition, a semi-uniform quantizer exhibits a 5-6 dB gain in SNR over its uniform counterpart for input amplitudes smaller than –10 dB. Finally, this system is designed in 0.35um CMOS process.</p>

<p>This master thesis consists of implementation and evaluation of an AEC, Acoustic Echo Canceller, algorithm in a floating-point architecture. The most important question this thesis will try to answer is to determine benefits or drawbacks of using a floating-point architecture, relative a fixed-point architecture, to do AEC. In a telephony system there is two common forms of echo, line echo and acoustic echo. Acoustic echo is introduced by sound emanating from a loudspeaker, e.g. in a handsfree or speakerphone, being picked up by a microphone and then sent back to the source. The problem with this feedback is that the far-end speaker will hear one, or multiple, time-delayed version(s) of her own speech. This time-delayed version of speech is usually perceived as both confusing and annoying unless removed by the use of AEC. In this master thesis the performance of a floating-point version of a normalized least-mean-square AEC algorithm was evaluated in an environment designed and implemented to approximate live telephony calls. An instruction-set simulator and assembler available at the initiation of this master thesis were extended to enable; zero-overhead loops, modular addressing, post-increment of registers and register-write forwarding. With these improvements a bit-true assembly version was implemented capable of real-time AEC requiring 15 million instructions per second. A solution using as few as eight mantissa bits, in an external format used when storing data in memory, was found to have an insignificant effect on the selected AEC implementation’s performance. Due to the relatively low memory requirement of the selected AEC algorithm, the use of a small external format has a minor effect on the required memory size. In total this indicates that the possible reduction of the memory requirement and related energy consumption, does not justify the added complexity and energy consumption of using a floating-point architecture for the selected algorithm. Use of a floating-point format can still be advantageous in speech-related signal processing when the introduced time delay by a subband, or a similar frequency domain, solution is unacceptable. Speech algorithms that have high memory use and small introduced delay requirements are a good candidate for a floating-point digital signal processor architecture.</p>

Real-time rendering of static volumetric data is generally known to be a memory and computationally intensive process. With the advance of graphic hardware, especially GPU, it is now possible to do this using desktop computers. However, with the evolution of real-time CT and MRI technologies, volumetric rendering is an even bigger challenge. The first one is how to reduce the data transmission between the main memory and the graphic memory. The second one is how to efficiently take advantage of the time redundancy which exists in the time-varying volumetric data. Most previous researches either focus on one problem or the other. In this thesis, we implemented a system which efficiently deals with both of the challenges. We proposed an optimized compression scheme that explores the time redundancy as well as space redundancy of time-varying volumetric data. The compressed data is then transmitted to graphic memory and directly rendered by GPU, so the data transfer between main memory and graphic memory is significantly reduced. With our implemented system, we successfully reduce more than half of the time of transferring the whole data directly. We also compare our proposed compression scheme with the one without exploiting time redundancy. The optimized compression scheme shows a reduce compression distortion over time. With usability, portability and extensibility in mind, the implemented system is also quite flexible.

For the fractional-N frequency synthesizers using delta-sigma modulation (DSM) techniques, higher PLL bandwidth is highly desirable in order to achieve faster settling time. As the PLL bandwidth is increased, more quantization noises pass through the PLL so that the output phase noise performance is degraded. There is a tradeoff between phase-noise performance and PLL bandwidth. To improve the problem, the thesis studies the quantization noise cancellation technique. With this technique, the PLL bandwidth can be increased without the cost of degrading phase-noise performance. With the help of Agilent EEsof¡¦s ADS, the phase-noise performance of the studied fractional-N frequency synthesizers can be predicted. For demonstration, this research implements a 2.6 GHz fractional-N frequency synthesizer hybrid module, and compares the measured phase noises with and without the technique under considering various combinations of MASH DSM orders and PLL bandwidth. Another demonstration of this thesis is to design a PLL IC using TSMC 0.18 £gm CMOS process, and make a discussion on the testing performance of the PLL IC.

Let $M$ be a smooth compact manifold equipped with a co-oriented subbundle $E\subset TM$. We suppose that a compact Lie group $G$ acts on $M$ preserving $E$, such that the $G$-orbits are transverse to $E$. If the fibres of $E$ are equipped with a complex structure then it is possible to construct a $G$-invariant Dirac operator $\dirac$ in terms of the resulting almost CR structure. We show that there is a canonical equivariant differential form with generalized coefficients $\mathcal{J}(E,X)$ defined on $M$ that depends only on the $G$-action and the co-oriented subbundle $E$. Moreover, the group action is such that $\dirac$ is a $G$-transversally elliptic operator in the sense of Atiyah \cite{AT}. Its index is thus defined as a generalized function on $G$. Beginning with the equivariant index formula of Paradan and Vergne \cite{PV3}, we obtain an index formula for $\dirac$ computed as an integral over $M$ that is free of choices and growth conditions. This formula necessarily involves equivariant differential forms with generalized coefficients and we show that the only such form required is the canonical form $\mathcal{J}(E,X)$. In certain cases the index of $\dirac$ can be interpreted in terms of a CR analogue of the space of holomorphic sections, allowing us to view our index formula as a character formula for the $G$-equivariant quantization of the almost CR manifold $(M,E)$. In particular, we obtain the ``almost CR'' quantization of a contact manifold, in a manner directly analogous to the almost complex quantization of a symplectic manifold.

Multi-user wireless systems with multiple antennas can drastically increase the capac- ity while maintaining the quality of service requirements. The best performance of these systems is obtained at the presence of instantaneous channel knowledge. Since uplink-downlink channel reciprocity does not hold in frequency division duplex and broadband time division duplex systems, efficient channel quantization becomes important. This thesis focuses on different quantization techniques in a linearly precoded multi-user wireless system. Our work provides three major contributions. First, we come up with an end-to-end transceiver design, incorporating precoder, receive combining and feedback policy, that works well at low feedback overhead. Second, we provide optimal bit allocation across the gain and shape of a complex vector to reduce the quantization error and investigate its effect in the multiuser wireless system. Third, we design an adaptive differential quantizer that reduces feedback overhead by utilizing temporal correlation of the channels in a time varying scenario.

Multi-user wireless systems with multiple antennas can drastically increase the capac- ity while maintaining the quality of service requirements. The best performance of these systems is obtained at the presence of instantaneous channel knowledge. Since uplink-downlink channel reciprocity does not hold in frequency division duplex and broadband time division duplex systems, efficient channel quantization becomes important. This thesis focuses on different quantization techniques in a linearly precoded multi-user wireless system. Our work provides three major contributions. First, we come up with an end-to-end transceiver design, incorporating precoder, receive combining and feedback policy, that works well at low feedback overhead. Second, we provide optimal bit allocation across the gain and shape of a complex vector to reduce the quantization error and investigate its effect in the multiuser wireless system. Third, we design an adaptive differential quantizer that reduces feedback overhead by utilizing temporal correlation of the channels in a time varying scenario.