Categorical quantum computation

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Piecewise Linearization Technique for Compact Charge Modeling of Independent DG MOSFET

Charge linearization techniques have been used over the years in advanced compact models for bulk and double-gate MOSFETs in order to approximate the position along the channel as a quadratic function of the surface potential (or inversion charge densities) so that the terminal charges can be expressed as a compact closed-form function of source and drain end surface potentials (or inversion charge densities). In this paper, in case of the independent double-gate MOSFETs, we show that the same technique could be used to model the terminal charges quite accurately only when the 1-D Poisson solution along the channel is fully hyperbolic in nature or the effective gate voltages are same. However, for other bias conditions, it leads to significant error in terminal charge computation. We further demonstrate that the amount of nonlinearity that prevails between the surface potentials along the channel actually dictates if the conventional charge linearization technique could be applied for a particular bias condition or not. Taking into account this nonlinearity, we propose a compact charge model, which is based on a novel piecewise linearization technique and shows excellent agreement with numerical and Technology Computer-Aided Design (TCAD) simulations for all bias conditions and also preserves the source/drain symmetry which is essential for Radio Frequency (RF) circuit design. The model is implemented in a professional circuit simulator through Verilog-A, and simulation examples for different circuits verify good model convergence.

Deciding Isomorphisms of Simple Types in Polynomial Time

The isomorphisms holding in all models of the simply typed lambda calculus with surjective and terminal objects are well studied - these models are exactly the Cartesian closed categories. Isomorphism of two simple types in such a model is decidable by reduction to a normal form and comparison under a finite number of permutations (Bruce, Di Cosmo, and Longo 1992). Unfortunately, these normal forms may be exponentially larger than the original types so this construction decides isomorphism in exponential time. We show how using space-sharing/hash-consing techniques and memoization can be used to decide isomorphism in practical polynomial time (low degree, small hidden constant). Other researchers have investigated simple type isomorphism in relation to, among other potential applications, type-based retrieval of software modules from libraries and automatic generation of bridge code for multi-language systems. Our result makes such potential applications practically feasible.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Closed-form design equations for decoupling networks of small arrays

Small element spacing in compact arrays results in strong mutual coupling between the array elements. A decoupling network consisting of reactive cross-coupling elements can alleviate problems associated with the coupling. Closed-form design equations for the decoupling networks of symmetrical arrays with two or three elements are presented.

The effect of cooling rate on the structure and properties of closed-cell aluminium foams

The application of different cooling rates as a strategy to enhance the structure of aluminium foams is studied. The potential to influence the level of morphological defects and cell size non-uniformities is investigated. AlSi6Cu4 alloy was foamed through the powder compact route and then solidified, applying three different cooling rates. Foam development was monitored in situ by means of X-ray radioscopy while foaming inside a closed mould. The macro-structure of the foams was analysed in terms of cell size distribution as determined by X-ray tomography. Compression tests were conducted to assess the mechanical performance of the foams and measured properties were correlated with structural features of the foams. Moreover, possible changes in the ductile brittle nature of deformation with cooling rate were analysed by studying the initial stages of deformation. We observed improvements in the cell size distributions, reduction in microporosity and grain size at higher cooling rates, which in turn led to a notable enhancement in compressive strength. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

An Improved Compact Compliant Mechanism for an External Pipe-Crawler

An external pipe-crawling device presented in this paper aids the inspection of pipes in hazardous environments and areas inaccessible to humans. The principal component of our design, which uses inchworm type motion, is a compliant ring mechanism actuated using shape memory alloy (SMA) wire. It was fabricated and tested and was reported in our earlier work. But this device had a drawback of low crawling speed (about 1 mm/min) owing to the delay in heating and cooling of the SMA strips in the linear actuation. Additionally, that design also had the difficulties of mounting on pipes with closed ends, large radial span, and the need for housing for electrical insulation and guiding of the SMA wire. In this paper we present a compact design that overcomes the difficulties of the earlier design. In particular, we present a compact compliant mechanism with two halves so as to enable mounting and un-mounting on any closed or open pipe. Another feature is the presence of insulation and guiding of the SMA wire without housing. This design results in a reduction of the radial span of the ring from 22 mm to 12 mm, and the stiffness of the mechanism and the SMA wire are matched. An SMA helical spring is to used in the place of an SMA strip to increase the crawling speed of the device. A microcontroller-based circuitry is also fitted to cyclically.activate the SMA wires and springs.

Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Three constructive examples of separable pre-Hilbert spaces nonisomorphic to their closed hyperplanes

An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Design and Control of a Closed-Loop Brushless Torque Actuator

This report explores the design and control issues associated with a brushless actuator capable of achieving extremely high torque accuracy. Models of several different motor - sensor configurations were studied to determine dynamic characteristics. A reaction torque sensor fixed to the motor stator was implemented to decouple the transmission dynamics from the sensor. This resulted in a compact actuator with higher bandwidth and precision than could be obtained with an inline or joint sensor. Testing demonstrated that closed-loop torque accuracy was within 0.1%, and the mechanical bandwidth approached 300 Hz.

Image classification for a large number of object categories

L'increment de bases de dades que cada vegada contenen imatges més difícils i amb un nombre més elevat de categories, està forçant el desenvolupament de tècniques de representació d'imatges que siguin discriminatives quan es vol treballar amb múltiples classes i d'algorismes que siguin eficients en l'aprenentatge i classificació. Aquesta tesi explora el problema de classificar les imatges segons l'objecte que contenen quan es disposa d'un gran nombre de categories. Primerament s'investiga com un sistema híbrid format per un model generatiu i un model discriminatiu pot beneficiar la tasca de classificació d'imatges on el nivell d'anotació humà sigui mínim. Per aquesta tasca introduïm un nou vocabulari utilitzant una representació densa de descriptors color-SIFT, i desprès s'investiga com els diferents paràmetres afecten la classificació final. Tot seguit es proposa un mètode par tal d'incorporar informació espacial amb el sistema híbrid, mostrant que la informació de context es de gran ajuda per la classificació d'imatges. Desprès introduïm un nou descriptor de forma que representa la imatge segons la seva forma local i la seva forma espacial, tot junt amb un kernel que incorpora aquesta informació espacial en forma piramidal. La forma es representada per un vector compacte obtenint un descriptor molt adequat per ésser utilitzat amb algorismes d'aprenentatge amb kernels. Els experiments realitzats postren que aquesta informació de forma te uns resultats semblants (i a vegades millors) als descriptors basats en aparença. També s'investiga com diferents característiques es poden combinar per ésser utilitzades en la classificació d'imatges i es mostra com el descriptor de forma proposat juntament amb un descriptor d'aparença millora substancialment la classificació. Finalment es descriu un algoritme que detecta les regions d'interès automàticament durant l'entrenament i la classificació. Això proporciona un mètode per inhibir el fons de la imatge i afegeix invariança a la posició dels objectes dins les imatges. S'ensenya que la forma i l'aparença sobre aquesta regió d'interès i utilitzant els classificadors random forests millora la classificació i el temps computacional. Es comparen els postres resultats amb resultats de la literatura utilitzant les mateixes bases de dades que els autors Aixa com els mateixos protocols d'aprenentatge i classificació. Es veu com totes les innovacions introduïdes incrementen la classificació final de les imatges.

Chaos of Wolbachia Sequences Inside the Compact Fig Syconia of Ficus benjamina (Ficus: Moraceae)

Figs and fig wasps form a peculiar closed community in which the Ficus tree provides a compact syconium (inflorescence) habitat for the lives of a complex assemblage of Chalcidoid insects. These diverse fig wasp species have intimate ecological relationships within the closed world of the fig syconia. Previous surveys of Wolbachia, maternally inherited endosymbiotic bacteria that infect vast numbers of arthropod hosts, showed that fig wasps have some of the highest known incidences of Wolbachia amongst all insects. We ask whether the evolutionary patterns of Wolbachia sequences in this closed syconium community are different from those in the outside world. In the present study, we sampled all 17 fig wasp species living on Ficus benjamina, covering 4 families, 6 subfamilies, and 8 genera of wasps. We made a thorough survey of Wolbachia infection patterns and studied evolutionary patterns in wsp (Wolbachia Surface Protein) sequences. We find evidence for high infection incidences, frequent recombination between Wolbachia strains, and considerable horizontal transfer, suggesting rapid evolution of Wolbachia sequences within the syconium community. Though the fig wasps have relatively limited contact with outside world, Wolbachia may be introduced to the syconium community via horizontal transmission by fig wasps species that have winged males and visit the syconia earlier.