An analytical solution for the coupled telegrapher’s equations in terms of the voltage and current on a homogeneous lossy transmission line and multiconductor transmission line is presented. The resulting telegrapher’s equation solution is obtained in the form of an exact time domain propagator operating on the line voltage and current. It is shown that the analytical equations lead to a stable numerical method that can be used in the analysis of both homogeneous and inhomogeneous transmission lines. A numerical dispersion relation is derived proving that this method has no numerical dispersion down to the two points per wavelength Nyquist limit. Examples are presented showing that exceptionally accurate results are obtained for lossy single and multiconductor transmission lines. The method is extended to represent the general solution to Maxwell’s differential equations in vector matrix form. It is shown that, given the electromagnetic field and boundary conditions at a given instant in time, the free space time domain propagator and corresponding dyadic Green’s functions in 1-, 2-, and 3-dimensions can be used to calculate the field at all subsequent times.

In large multiprocessors, the access to shared memory is often nonuniform, and may vary as much as ten times for some distributed shared-memory architectures (DSMs). This dissertation identifies another important nonuniform property of DSM systems: nonuniform communication architecture, NUCA. High-end hardware-coherent machines built from large nodes, or from chip multiprocessors, are typical NUCA systems, since they have a lower penalty for reading recently written data from a neighbor's cache than from a remote cache. This dissertation identifies node affinity as an important property for scalable general-purpose locks. Several software-based hierarchical lock implementations exploiting NUCAs are presented and evaluated. NUCA-aware locks are shown to be almost twice as efficient for contended critical sections compared to traditional lock implementations. The shared-memory “illusion”' provided by some large DSM systems may be implemented using either hardware, software or a combination thereof. A software-based implementation can enable cheap cluster hardware to be used, but typically suffers from poor and unpredictable performance characteristics. This dissertation advocates a new software-hardware trade-off design point based on a new combination of techniques. The two low-level techniques, fine-grain deterministic coherence and synchronous protocol execution, as well as profile-guided protocol flexibility, are evaluated in isolation as well as in a combined setting using all-software implementations. Finally, a minimum of hardware trap support is suggested to further improve the performance of coherence protocols across cluster nodes. It is shown that all these techniques combined could result in a fairly stable performance on par with hardware-based coherence.

Signal acquisition, signal reconstruction and analysis of spectrum of the signal are the three most important steps in signal processing and they are found in almost all of the modern day hardware. In most of the signal processing hardware, the signal of interest is sampled at uniform intervals satisfying some conditions like Nyquist rate. However, in some cases the privilege of having uniformly sampled data is lost due to some constraints on the hardware resources. In this thesis an important problem of signal reconstruction and spectral analysis from nonuniformly sampled data is addressed and a variety of methods are presented. The proposed methods are tested via numerical experiments on both artificial and real-life data sets. The thesis starts with a brief review of methods available in the literature for signal reconstruction and spectral analysis from non uniformly sampled data. The methods discussed in the thesis are classified into two broad categories - dense and sparse methods, the classification is based on the kind of spectra for which they are applicable. Under dense spectral methods the main contribution of the thesis is a non-parametric approach named LIMES, which recovers the smooth spectrum from non uniformly sampled data. Apart from recovering the spectrum, LIMES also gives an estimate of the covariance matrix. Under sparse methods the two main contributions are methods named SPICE and LIKES - both of them are user parameter free sparse estimation methods applicable for line spectral estimation. The other important contributions are extensions of SPICE and LIKES to multivariate time series and array processing models, and a solution to the grid selection problem in sparse estimation of spectral-line parameters. The third and final part of the thesis contains applications of the methods discussed in the thesis to the problem of radial velocity data analysis for exoplanet detection. Apart from the exoplanet application, an application based on Sudoku, which is related to sparse parameter estimation, is also discussed.

There are situations in the framework of quasi-Monte Carlo integration where nonuniform low-discrepancy sequences are required. Using the inversion method for this task usually results in the best performance in terms of the integration errors. However, this method requires a fast algorithm for evaluating the inverse of the cumulative distribution function which is often not available. Then a smoothed version of transformed density rejection is a good alternative as it is a fast method and its speed hardly depends on the distribution. It can easily be adjusted such that it is almost as good as the inversion method. For importance sampling it is even better to use the hat distribution as importance distribution directly. Then the resulting algorithm is as good as using the inversion method for the original importance distribution but its generation time is much shorter. / Series: Preprint Series / Department of Applied Statistics and Data Processing

The aim of this paper is to investigate the known nonuniform version of Esseen''s inequality in the Lp-metric, to get a numerical bound for the appearing constant L. For a long time the results given by several authors constate the impossibility of a nonuniform estimation in the most interesting case δ=1, because the effect L=L(δ)=O(1/(1-δ)), δ->1-0, was observed, where 2+δ, 0<δ<1, is the order of the assumed moments of the considered independent random variables X_k, k=1,2,...,n. Again making use of the method of conjugated distributions, we improve the well-known technique to show in the most interesting case δ=1 the finiteness of the absolute constant L and to prove L=L(1)=<127,74*7,31^(1/p), p>1. In the case 0<δ<1 we only give the analytical structure of L but omit numerical calculations. Finally an example on normal approximation of sums of l_2-valued random elements demonstrates the application of the nonuniform mean central limit bounds obtained here.:1. Introduction S. 3 2. The nonuniform version of ESSEEN''s Inequality in the Lp-metrie S. 4 3. The partition of the domain of integration S. 5 4. The domain of moderate x S. 8 5. An error bound for large values of L2+δ,n S. 12 6. The proof of the inequality (2.1) S. 13 7. An application to normalapproximation of sums of l2-valued random elements S. 14 References S. 18 / Das Anliegen dieses Artikels besteht in der Untersuchung einer bekannten Variante der Esseen''schen Ungleichung in Form einer ungleichmäßigen Fehlerabschätzung in der Lp-Metrik mit dem Ziel, eine numerische Abschätzung für die auftretende absolute Konstante L zu erhalten. Längere Zeit erweckten die Ergebnisse, die von verschiedenen Autoren angegeben wurden, den Eindruck, dass die ungleichmäßige Fehlerabschätzung im interessantesten Fall δ=1 nicht möglich wäre, weil auf Grund der geführten Beweisschritte der Einfluss von δ auf L in der Form L=L(δ)=O(1/(1-δ)), δ->1-0, beobachtet wurde, wobei 2+δ, 0<δ<1, die Ordnung der vorausgesetzten Momente der betrachteten unabhängigen Zufallsgrößen X_k, k=1,2,...,n, angibt. Erneut wird die Methode der konjugierten Verteilungen angewendet und die gut bekannte Beweistechnik verbessert, um im interessantesten Fall δ=1 die Endlichkeit der absoluten Konstanten L nachzuweisen und um zu zeigen, dass L=L(1)=<127,74*7,31^(1/p), p>1, gilt. Im Fall 0<δ<1 wird nur die analytische Struktur von L herausgearbeitet, jedoch ohne numerische Berechnungen. Schließlich wird mit einem Beispiel zur Normalapproximation von Summen l_2-wertigen Zufallselementen die Anwendung der gewichteten Fehlerabschätzung im globalen zentralen Grenzwertsatz demonstriert.:1. Introduction S. 3 2. The nonuniform version of ESSEEN''s Inequality in the Lp-metrie S. 4 3. The partition of the domain of integration S. 5 4. The domain of moderate x S. 8 5. An error bound for large values of L2+δ,n S. 12 6. The proof of the inequality (2.1) S. 13 7. An application to normalapproximation of sums of l2-valued random elements S. 14 References S. 18

<p> A method for tlie dynamic analysis· of planar coupled shear walls subjected to ground motions is developed herein. The method is capable of application to nonuniform coupled shear walls resting on flexible foundations. The possibility-of development of yield hinges at the ends of the connecting beams is included in the analysis . Also P-& Effect is incorporated in the stiffness of the structure. </p> <p> The method is based on the transfer matrix technique in combination with the continuum method. A step-by-step integration approach is used in solving the equation of motion. The response to a number of earthquake records are obtained. The effect of the rotational ductility factor of connecting beams is studied. </p> / Thesis / Master of Engineering (MEngr)

<p>Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. </p><p>A method for performing <i>ab initio </i>MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored.</p><p>Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. </p><p>Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as <i>N log N</i>, where <i>N </i>is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs.</p><p>Finally, an outlook is given and some directions for further developments are suggested.</p>

Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. A method for performing ab initio MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored. Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as N log N, where N is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs. Finally, an outlook is given and some directions for further developments are suggested.

Based on different sampling theorem, for example classic Shannon’s sampling theorem and Papoulis’ generalized sampling theorem, signals are processed by the sampling devices without loss of information. As an interface between radio receiver front-ends and digital signal processing blocks, sampling devices play a dominant role in digital radio communications. Under the concept of Software Defined Radio (SDR), radio systems are going through the second evolution that mixes analog, digital and software technologies in modern radio designs. One design goal of SDR is to put the A/D converter as close as possible to the antenna. BandPass Sampling (BPS) enables one to have an interface between the RF or the higher IF signal and the A/D converter, and it might be a solution to SDR. However, three sources of performance degradation present in BPS systems, harmful signal spectral overlapping, noise aliasing and sampling timing jitter, hinder the conventional BPS theory from practical circuit implementations. In this thesis work, Generalized Quadrature BandPass Sampling (GQBPS) is first invented and comprehensively studied with focus on the noise aliasing problem. GQBPS consists of both BPS and FIR filtering that can use either real or complex coefficients. By well-designed FIR filtering, GQBPS can also perform frequency down-conversion in addition to noise aliasing reduction. GQBPS is a nonuniform sampling method in most cases. With respect to real circuit implementations, uniform sampling is easier to be realized compared to nonuniform sampling. GQBPS has been also extended to Generalized Uniform BandPass Sampling (GUBPS). GUBPS shares the same property of noise aliasing suppression as GQBPS besides that the samples are uniformly spaced. Due to the moving average operation of FIR filtering, the effect of sampling jitter is also reduced to a certain degree in GQBPS and GUBPS. By choosing a suitable sampling rate, harmful signal spectral overlapping can be avoided. Due to the property of quadrature sampling, the “self image” problem caused by I/Q mismatches is eliminated. Comprehensive theoretical analyses and program simulations on GQBPS and GUBPS have been done based on a general mathematic model. Circuit architecture to implementing GUBPS in Switched-Capacitor circuit technique has been proposed and analyzed. To improve the selectivity at the sampling output, FIR filtering is extended by adding a 1st order complex IIR filter in the implementation. GQBPS and GUBPS operate in voltage-mode. Besides voltage sampling, BPS can also be realized by charge sampling in current-mode. Most other research groups in this area are focusing on bandpass charge sampling. However, the theoretical analysis shows that our GQBPS and GUBPS in voltage mode are more efficient to suppress noise aliasing as compared to bandpass charge sampling with embedded filtering. The aliasing bands of sampled-data spectrum are always weighted by continuous-frequency factors for bandpass charge sampling with embedded filtering while discrete-frequency factors for GQBPS and GUBPS. The transmission zeros of intrinsic filtering will eliminate the corresponding whole aliasing bands of both signal and noise in GQBPS and GUBPS, while it will only cause notches at a limited set of frequencies in bandpass charge sampling. In addition, charge sampling performs an intrinsic continuous-time sinc function that always includes lowpass filtering. This is a drawback for a bandpass input signal. / QC 20100921

Der Beitrag stellt eine Verallgemeinerung der Ergebnisse dar, die in den Informationen/07; 1976,05 veröffentlicht wurden. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und nicht notwendig identisch verteilte Zufallsgrößen mit endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_m derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsatz explizit angeben können. Als Spezialfall ergibt sich die ungleichmäßige Fehlerschranke von A.BIKELIS (1966) im Fall der Existenz dritter absoluter Momente. Weiterhin werden Grenzwertsätze unter Voraussetzung einseitiger Momente betrachtet. Es werden einige Literaturhinweise angegeben. / The paper is a generalization of the results, published by the author in Informationen/07; 1976,05. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are non iid random variables with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_m are computed such that we have some error estimates in the nonuniform central limit theorem. A special case is the nonuniform error bound by A.BIKELIS (1966) in the case of existence of third absolute moments. Furthermore limit theorems with assumption of onesided moments are considered. Some references are given.