Wireless networks become more and more important in modern information systems as the last mile/meter solutions, thanks to the flexibility of mobile access to facilitate Internet access anytime, anywhere. Given the limited resources, e.g., spectrum and energy supplies, to meet the ever increasing demand for wireless data services, new approaches are beckoned to enhance the spectrum and energy efficiency. We investigate this problem from three important aspects, digital modulation, clock synchronization and concurrent transmission scheduling. The contributions of this dissertation are four-fold. First, we employ the cross-layer design to explore the spatial diversity and broadcast nature of wireless links and propose a novel network modulation scheme that can superpose the information bits of different priorities into one symbol. It offers a new dimension to improve the network throughput since we can flexibly configure the transmission according to the channels among transceivers. Moreover, it is compatible with the main-stream hardware and we just need a software upgrade to implement the idea. Second, we propose modulation schemes based on hexagonal tiling, which is known to be the most compact way of two-dimensional regular tiling. In order to fully utilize the advantage of hexagonal constellation, we employ the non-binary error controlcoding since the number of constellation points of hexagonal constellation is not necessarily to be an integer power-of-two. The feasibility of these new modulation schemes is verified by the prototype system based on the software defined radio platform USRP2 and GNU Radio. Third, to facilitate a wide range of wireless communications technologies and protocols, clock synchronization among several wireless devices is a fundamental requirement. We investigated this problem by tracing to the source of clock desynchronization, which is the clock skew. However, as shown by measurement results, the clock skew is not constant and related to the working temperature. We propose a novel clock skew estimation algorithm that can leverage the temperature information to accurately estimate the clock skew. Based on the estimation results, we propose a clock synchronization scheme that can directly remove the clock skew according to the working temperature. Fourth, the traditional time-sharing based scheduling schemes usually schedule one transmission within certain area. The emerging broadband wireless devices can dynamically adjust the transmitted data rate according to the received signal to interference and noise ratio (SINR). Allowing concurrent transmissions may be more efficient, while optimal scheduling problem for concurrent transmissions is an NP-hard problem. We propose simple yet effective heuristic algorithms that can significantly improve the system throughput with moderate computational complexity. / Graduate / 0544 / yangzhe2007@gmail.com

In recent work, N. Hitchin described special geometries in terms of a variational problem for closed generic $p$-forms. In particular, he introduced on 8-manifolds the notion of an integrable $PSU(3)$-structure which is defined by a closed and co-closed 3-form. In this thesis, we first investigate this $PSU(3)$-geometry further. We give necessary conditions for the existence of a topological $PSU(3)$-structure (that is, a reduction of the structure group to $PSU(3)$ acting through its adjoint representation). We derive various obstructions for the existence of a topological reduction to $PSU(3)$. For compact manifolds, we also find sufficient conditions if the $PSU(3)$-structure lifts to an $SU(3)$-structure. We find non-trivial, (compact) examples of integrable $PSU(3)$-structures. Moreover, we give a Riemannian characterisation of topological $PSU(3)$-structures through an invariant spinor valued 1-form and show that the $PSU(3)$-structure is integrable if and only if the spinor valued 1-form is harmonic with respect to the twisted Dirac operator. Secondly, we define new generalisations of integrable $G_2$- and $Spin(7)$-manifolds which can be transformed by the action of both diffeomorphisms and 2-forms. These are defined by special closed even or odd forms. Contraction on the vector bundle $Toplus T^*$ defines an inner product of signature $(n,n)$, and even or odd forms can then be naturally interpreted as spinors for a spin structure on $Toplus T^*$. As such, the special forms we consider induce reductions from $Spin(7,7)$ or $Spin(8,8)$ to a stabiliser subgroup conjugate to $G_2 times G_2$ or $Spin(7) times Spin(7)$. They also induce a natural Riemannian metric for which we can choose a spin structure. Again we state necessary and sufficient conditions for the existence of such a reduction by means of spinors for a spin structure on $T$. We classify topological $G_2 times G_2$-structures up to vertical homotopy. Forms stabilised by $G_2 times G_2$ are generic and an integrable structure arises as the critical point of a generalised variational principle. We prove that the integrability conditions on forms imply the existence of two linear metric connections whose torsion is skew, closed and adds to 0. In particular we show these integrability conditions to be equivalent to the supersymmetry equations on spinors in supergravity theory of type IIA/B with NS-NS background fields. We explicitly determine the Ricci-tensor and show that over compact manifolds, only trivial solutions exist. Using the variational approach we derive weaker integrability conditions analogous to weak holonomy $G_2$. Examples of generalised $G_2$- and $Spin(7)$ structures are constructed by the device of T-duality.

Variações ambientais e de processo representam um grande desafio a ser vencido pelas redes de distribuição de relógio. O efeito das variações nos atrasos da rede de distribuição de relógio não pode ser previsto com precisão e portanto não podem ser diretamente considerados no projeto das redes de distribuição de relógio. Estruturas baseadas em clock meshes (i.e. clock mesh, clock spines e crosslinks) são a maneira mais eficiente de proteger a rede de relógio do efeito das variações nos atrasos. Clock meshes tem sido utilizados por bastante tempo no projeto de microprocessadores e recentemente foram incluídos no fluxo de síntese de ASICs. Embora o uso de clock meshes esteja aumentando há uma grande necessidade por métodos de analise e otimização dos mesmos. Essa tese propõe soluções para ambos os problemas. Uma metodologia para permitir a simulação elétrica de clock meshes grandes é proposta. O método proposto permite que a simulação dos clock meshes seja paralelizada com um erro menor que 1%. Duas metodologias de otimização também são propostas nessa tese. A primeira consiste em um algoritmo para dimensionamento para os mesh buffers. Esse algoritmo permite que o clock skew e o consumo de potência sejam reduzidos ao custo de aumentar o clock slew. O segundo método de otimização proposto consiste em um novo projeto para os mesh buffers. O novo mesh buffer é capaz de reduzir o clock skew em 22% e o consumo de potencia em 59%. / Process and environmental variations are a great challenge to clock network designers. Variations effect on the clock network delays can not be predicted, hence it can not be directly accounted in the design stage. Clock mesh-based structures (i.e. clock mesh, clock spines and crosslinks) are the most effective way to tolerate variation effects on delays. Clock meshes have been used for a long time in microprocessor designs and recently became supported by commercial tools in the ASIC design flow. Although clock meshes have been known for some time and its use in ASIC design is increasing, there is a lack of good analysis and optimization strategies for clock meshes. This thesis tackles both problems. Chapter 1 presents a basic introduction to clock distribution and important definitions. A review of existent clock dsitribution design strategies is presented in chapter 2. A study about the clock distribution architecture used in several microprocessor and a comparison between mesh-based and pure tree clock distribution architectures is shown in chapter 3.2. A methodology for enabling and speeding up the simulation of large clock meshes is presented in chapter 4. The proposed analysis methodology was shown to enable the parallel evaluation of large clock meshes with an error smaller than 1%. Chapter 5 presents two optimization strategies, a new mesh buffer design and a mesh buffer sizing algorithm. The new mesh buffer design was proposed improving clock skew by 22% and clock power by 59%. The mesh buffer sizing algorithm can reduce clock skew by 33%, power consumption by 20% with at the cost of a 26% slew increase. At last conclusions are presented on chapter 6.

Variações ambientais e de processo representam um grande desafio a ser vencido pelas redes de distribuição de relógio. O efeito das variações nos atrasos da rede de distribuição de relógio não pode ser previsto com precisão e portanto não podem ser diretamente considerados no projeto das redes de distribuição de relógio. Estruturas baseadas em clock meshes (i.e. clock mesh, clock spines e crosslinks) são a maneira mais eficiente de proteger a rede de relógio do efeito das variações nos atrasos. Clock meshes tem sido utilizados por bastante tempo no projeto de microprocessadores e recentemente foram incluídos no fluxo de síntese de ASICs. Embora o uso de clock meshes esteja aumentando há uma grande necessidade por métodos de analise e otimização dos mesmos. Essa tese propõe soluções para ambos os problemas. Uma metodologia para permitir a simulação elétrica de clock meshes grandes é proposta. O método proposto permite que a simulação dos clock meshes seja paralelizada com um erro menor que 1%. Duas metodologias de otimização também são propostas nessa tese. A primeira consiste em um algoritmo para dimensionamento para os mesh buffers. Esse algoritmo permite que o clock skew e o consumo de potência sejam reduzidos ao custo de aumentar o clock slew. O segundo método de otimização proposto consiste em um novo projeto para os mesh buffers. O novo mesh buffer é capaz de reduzir o clock skew em 22% e o consumo de potencia em 59%. / Process and environmental variations are a great challenge to clock network designers. Variations effect on the clock network delays can not be predicted, hence it can not be directly accounted in the design stage. Clock mesh-based structures (i.e. clock mesh, clock spines and crosslinks) are the most effective way to tolerate variation effects on delays. Clock meshes have been used for a long time in microprocessor designs and recently became supported by commercial tools in the ASIC design flow. Although clock meshes have been known for some time and its use in ASIC design is increasing, there is a lack of good analysis and optimization strategies for clock meshes. This thesis tackles both problems. Chapter 1 presents a basic introduction to clock distribution and important definitions. A review of existent clock dsitribution design strategies is presented in chapter 2. A study about the clock distribution architecture used in several microprocessor and a comparison between mesh-based and pure tree clock distribution architectures is shown in chapter 3.2. A methodology for enabling and speeding up the simulation of large clock meshes is presented in chapter 4. The proposed analysis methodology was shown to enable the parallel evaluation of large clock meshes with an error smaller than 1%. Chapter 5 presents two optimization strategies, a new mesh buffer design and a mesh buffer sizing algorithm. The new mesh buffer design was proposed improving clock skew by 22% and clock power by 59%. The mesh buffer sizing algorithm can reduce clock skew by 33%, power consumption by 20% with at the cost of a 26% slew increase. At last conclusions are presented on chapter 6.

abstract: Improving energy efficiency has always been the prime objective of the custom and automated digital circuit design techniques. As a result, a multitude of methods to reduce power without sacrificing performance have been proposed. However, as the field of design automation has matured over the last few decades, there have been no new automated design techniques, that can provide considerable improvements in circuit power, leakage and area. Although emerging nano-devices are expected to replace the existing MOSFET devices, they are far from being as mature as semiconductor devices and their full potential and promises are many years away from being practical. The research described in this dissertation consists of four main parts. First is a new circuit architecture of a differential threshold logic flipflop called PNAND. The PNAND gate is an edge-triggered multi-input sequential cell whose next state function is a threshold function of its inputs. Second a new approach, called hybridization, that replaces flipflops and parts of their logic cones with PNAND cells is described. The resulting \hybrid circuit, which consists of conventional logic cells and PNANDs, is shown to have significantly less power consumption, smaller area, less standby power and less power variation. Third, a new architecture of a field programmable array, called field programmable threshold logic array (FPTLA), in which the standard lookup table (LUT) is replaced by a PNAND is described. The FPTLA is shown to have as much as 50% lower energy-delay product compared to conventional FPGA using well known FPGA modeling tool called VPR. Fourth, a novel clock skewing technique that makes use of the completion detection feature of the differential mode flipflops is described. This clock skewing method improves the area and power of the ASIC circuits by increasing slack on timing paths. An additional advantage of this method is the elimination of hold time violation on given short paths. Several circuit design methodologies such as retiming and asynchronous circuit design can use the proposed threshold logic gate effectively. Therefore, the use of threshold logic flipflops in conventional design methodologies opens new avenues of research towards more energy-efficient circuits. / Dissertation/Thesis / Doctoral Dissertation Computer Science 2015

A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.

This thesis deals with several statistical and probabilistic aspects of symmetry and asymmetry, both in a univariate and multivariate context, and is divided into three distinct parts.<p><p>The first part, composed of Chapters 1, 2 and 3 of the thesis, solves two conjectures associated with multivariate skew-symmetric distributions. Since the introduction in 1985 by Adelchi Azzalini of the most famous representative of that class of distributions, namely the skew-normal distribution, it is well-known that, in the vicinity of symmetry, the Fisher information matrix is singular and the profile log-likelihood function for skewness admits a stationary point whatever the sample under consideration. Since that moment, researchers have tried to determine the subclasses of skew-symmetric distributions who suffer from each of those problems, which has led to the aforementioned two conjectures. This thesis completely solves these two problems.<p><p>The second part of the thesis, namely Chapters 4 and 5, aims at applying and constructing extremely general skewing mechanisms. As such, in Chapter 4, we make use of the univariate mechanism of Ferreira and Steel (2006) to build optimal (in the Le Cam sense) tests for univariate symmetry which are very flexible. Actually, their mechanism allowing to turn a given symmetric distribution into any asymmetric distribution, the alternatives to the null hypothesis of symmetry can take any possible shape. These univariate mechanisms, besides that surjectivity property, enjoy numerous good properties, but cannot be extended to higher dimensions in a satisfactory way. For this reason, we propose in Chapter 5 different general mechanisms, sharing all the nice properties of their competitors in Ferreira and Steel (2006), but which moreover can be extended to any dimension. We formally prove that the surjectivity property holds in dimensions k>1 and we study the principal characteristics of these new multivariate mechanisms.<p><p>Finally, the third part of this thesis, composed of Chapter 6, proposes a test for multivariate central symmetry by having recourse to the concepts of statistical depth and runs. This test extends the celebrated univariate runs test of McWilliams (1990) to higher dimensions. We analyze its asymptotic behavior (especially in dimension k=2) under the null hypothesis and its invariance and robustness properties. We conclude by an overview of possible modifications of these new tests./<p><p>Cette thèse traite de différents aspects statistiques et probabilistes de symétrie et asymétrie univariées et multivariées, et est subdivisée en trois parties distinctes.<p><p>La première partie, qui comprend les chapitres 1, 2 et 3 de la thèse, est destinée à la résolution de deux conjectures associées aux lois skew-symétriques multivariées. Depuis l'introduction en 1985 par Adelchi Azzalini du plus célèbre représentant de cette classe de lois, à savoir la loi skew-normale, il est bien connu qu'en un voisinage de la situation symétrique la matrice d'information de Fisher est singulière et la fonction de vraisemblance profile pour le paramètre d'asymétrie admet un point stationnaire quel que soit l'échantillon considéré. Dès lors, des chercheurs ont essayé de déterminer les sous-classes de lois skew-symétriques qui souffrent de chacune de ces problématiques, ce qui a mené aux deux conjectures précitées. Cette thèse résoud complètement ces deux problèmes.<p><p>La deuxième partie, constituée des chapitres 4 et 5, poursuit le but d'appliquer et de proposer des méchanismes d'asymétrisation très généraux. Ainsi, au chapitre 4, nous utilisons le méchanisme univarié de Ferreira and Steel (2006) pour construire des tests de symétrie univariée optimaux (au sens de Le Cam) qui sont très flexibles. En effet, leur méchanisme permettant de transformer une loi symétrique donnée en n'importe quelle loi asymétrique, les contre-hypothèses à la symétrie peuvent prendre toute forme imaginable. Ces méchanismes univariés, outre cette propriété de surjectivité, possèdent de nombreux autres attraits, mais ne permettent pas une extension satisfaisante aux dimensions supérieures. Pour cette raison, nous proposons au chapitre 5 des méchanismes généraux alternatifs, qui partagent toutes les propriétés de leurs compétiteurs de Ferreira and Steel (2006), mais qui en plus sont généralisables à n'importe quelle dimension. Nous démontrons formellement que la surjectivité tient en dimension k > 1 et étudions les caractéristiques principales de ces nouveaux méchanismes multivariés.<p><p>Finalement, la troisième partie de cette thèse, composée du chapitre 6, propose un test de symétrie centrale multivariée en ayant recours aux concepts de profondeur statistique et de runs. Ce test étend le célèbre test de runs univarié de McWilliams (1990) aux dimensions supérieures. Nous en analysons le comportement asymptotique (surtout en dimension k = 2) sous l'hypothèse nulle et les propriétés d'invariance et de robustesse. Nous concluons par un aperçu sur des modifications possibles de ces nouveaux tests. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

A 3D nonlinear finite element analysis was developed for simulating the behavior of skewed concrete slabs and to identify the response of the slab with different angles and element sizes. The purpose of this research is helping the engineering and construction industry to utilize the FEM study and results more in different structural applications.Simulations performed in ABAQUS for skewed slabs are also compared to straight and skewed slabs according to the analytical formulation by Timoshenko.The result showed that when the distance increases, the load capacity measured by reaction forces decreases for all different skew angles except angle 0° and 15° which show a stable reaction force along the entire path. .The study reveals that depending on the skew angle and the element size, the stress distribution and vertical displacements in the slab vary significantly from those in a straight slab. It is shown that the displacement decreases with the increase of the skew angle while the stresses increase with the decrease of the skew angle.There are small differences in the vertical displacements and stress distribution between the results obtained by this study and the results obtained by Timoshenko regarding the plates with skews of 0°, 30° and 45°.

Can we capture the explosive nature of volatility skew observed in the market, without resorting to non-Markovian models? We show that, in terms of skew, the Heston model cannot match the market at both long and short maturities simultaneously. We introduce Abi Jaber (2019)'s Lifted Heston model and explain how to price options with it using both the cosine method and standard Monte-Carlo techniques. This allows us to back out implied volatilities and compute skew for both models, confirming that the Lifted Heston nests the standard Heston model. We then produce and analyze the skew for Lifted Heston models with a varying number N of mean reverting terms, and give an empirical study into the time complexity of increasing N. We observe a weak increase in convergence speed in the cosine method for increased N, and comment on the number of factors to implement for practical use.