Recent work on fractionally-supervised classification (FSC), an approach that allows classification to be carried out with a fractional amount of weight given to the unla- belled points, is extended in two important ways. First, and of fundamental impor- tance, the question over how to choose the amount of weight given to the unlabelled points is addressed. Then, the FSC approach is extended to mixtures of multivariate t-distributions. The first extension is essential because it makes FSC more readily applicable to real problems. The second, although less fundamental, demonstrates the efficacy of FSC beyond Gaussian mixture models. / Thesis / Master of Science (MSc)

Blind equalization schemes are used to cancel the effects of a channel on the received signal when the transmission of a training sequence in a predefined time slot is not possible. In the absence of a training sequence, blind equalization schemes can also increase the throughput of the overall system. A general problem with blind adaptation techniques is that they have poor convergence properties compared to the traditional techniques using training sequences. Having a multi-modal cost surface, blind adaptation techniques may force the equalizer to converge to a false minimum, depending on the initialization. The most commonly used blind adaptation algorithm is the Constant Modulus Algorithm (CMA). It is shown by simulation that a logarithmic error equation can make CMA converge to a global minimum, if a differential encoding scheme is used. The performance of CMA with different error equations is also investigated for different channel conditions. For a time varying channel, the performance of an equalizer not only depends on the convergence behavior but also on the tracking property, which indicates the ability of an equalizer to track changes in the channel. The tracking property of a blind equalizer with CMA has been investigated under different channel conditions. It is also shown that the tracking property of a blind equalizer can be improved by using a recursive linear predictor at the output of the equalizer to predict the amplitude of the equalizer output. The predicted value of the amplitude is then used to adjust the instantaneous gain of the overall system. A recursive linear predictor is designed to predict a colored signal without having a priori knowledge about the correlation function of the input sequence. The performance of the designed predictor is also investigated by predicting the envelope of a flat fading channel under constant mobile velocity and constant acceleration conditions. / Master of Science

Many empirical studies show that both equity volatility and its trading volume have long range dependence and can be modeled as fractional integrated processes. The objective of this study is to investigate relationship between volatility and volume.We adopt four estimators of volatility, which includes the squared log returns, historical volatility, iterative t estimators and $GARCH$ estimators. The results show that among the four estimators squared log returns usually have the largest integration orders and produce hightest ratios of fractional cointegration. The fractional integrated orders are estimated separately and jointly, and the cointegration parameters are estimated by ordinary least squares, a narrow band frequency domain least squares method and a semiparametric estimator of Whittle likelihood. Models are also established when volatility and volume are not fractional cointegrated.

Darbe atlikta integruoto ugdymo ir nežymiai protiškai atsilikusių mokinių, ugdymą integruotose klasėse analizė. Iškelta hipotezė, kad nežymiai protiškai atsilikusių mokinių darbas per matematikos pamokas yra ne visada produktyvus. Anketinės apklausos metodu bei stebint pamokas buvo atliktas tyrimas, kurio tikslas – išanalizuoti nežymiai protiškai atsilikusių mokinių, integruotų į bendrojo lavinimo mokyklas, veiklą per matematikos pamokas. Atlikta kokybinė ir kiekybinė atvejų analizė. Tyrime dalyvavo 5 mokiniai ir mokytojai, ugdantys mokinius, turinčius nežymų protinį atsilikimą, integruotose klasėse. Empirinėje dalyje nagrinėjamas nežymiai protiškai atsilikusių mokinių ugdymas bendrojo lavinimo mokykloje, jų užimtumas ir darbo produktyvumas, mokytojų darbas su jais. Svarbiausios empirinio tyrimo išvados: • Nežymiai protiškai atsilikęs mokinys pamokoje vidutiniškai buvo užimtas 39 minutes, iš jų 35 minutes dirbo aktyviai, o medžiaga pamokoje atitiko mokinio gebėjimus 31 minutę Šie rezultatai parodo, kad mokinys ne visą pamokos laiką būna užimtas. Mokytoja mokiniui skiria 2,6 minučių pamokos laiko ir prieina du kartus. • Ne visada aktyvus darbas rodo, kad pamokoje mokinys dirba produktyviai, taip pat medžiaga gali atitikti mokinio gebėjimus, bet darbas gali būti neproduktyvus dėl įvairiausių priežasčių. Pirmasis mokinys vidutiniškai pamokoje produktyviai dirbo tik 16 minučių, nors kitos temos ir atitiko mokinio gebėjimus, bet trūko mokytojos aiškinimo ir... [toliau žr. visą tekstą] / The paper deals with the analysis of integrated education and fractionally subnormal in intelli-gence pupils of integrated classes. Hypothesis: work with fractionally subnormal in intelligence pupils in Mathematic is not always productive. It is important to note that observing lessons the interrogatory by filling in the form is also under the consideration with its purpose to investigate activity of fractionally subnormal in intelligence pupils that are integrated into comprehensive school. Pupils and teachers, who educate fractionally subnormal in intelligence pupils in integrated classes, took part in this investigation. The empirical part of this work deals with fractionally subnormal in intelligence pupils that are integrated into comprehensive school, their occupation, efficiency and teachers work with them. Conclusions of empirical investigation are: • On the average, fractionally subnormal in intelligence pupil during the class was busy for 39 minutes. 35 minutes of the lesson, he was working and the teaching material has fitted the ability of the pupil for 31 minute. These results show that the pupil is not busy the en-tire lesson. Teacher gives attention to the pupil for 2,6 minutes of the lesson and goes up to him twice. • Active work not always shows that the pupils work is productive. Teaching material could fit the ability of the pupil, but the efficiency may not be good for different reasons. On the average, the first pupil has been working productively... [to full text]

The high frequency (HF) band lies within 2-30 MHz of the electromagnetic spectrum. For decades, the HF band has been recognized as the primary means of long-range wireless communications. When satellite communication first emerged in 1960s, HF technology was considered to be obsolete. However, with its enduring qualities, HF communication survived through this competition and positioned itself as a powerful complementary and/or alternative technology to satellite communications. HF systems have been traditionally associated with low-rate data transmission. With the shift from analog to digital in voice communication, and increasing demands for high-rate data transmission (e.g., e-mail, Internet, FTP), HF communication has been going through a renaissance. Innovative techniques are required to push the capacity limits of the HF band. In this dissertation, we consider cooperative communication as an enabling technology to meet the challenging expectations of future generation HF communication systems. Cooperative communication exploits the broadcast nature of wireless transmission and relies on the cooperation of users relaying the information to one another. We address the design, analysis, and optimization of cooperative HF communication systems considering both multi-carrier and single-carrier architectures. As the multi-carrier HF system, we consider the combination of the orthogonal frequency division multiplexing (OFDM) with the bit interleaved coded modulation (BICM) as the underlying physical layer platform. It is assumed that cooperating nodes may use different HF propagation mechanisms, such as near-vertical-incidence sky wave (NVIS) and surface wave, to relay their received signals to the destination in different environmental scenarios. Diversity gain analysis, optimum relay selection strategy and power allocation between the source and relays are investigated for the proposed cooperative HF system. For single-carrier HF systems, we first derive a matched-filer-bound (MFB) on the error rate performance of the non-regenerative cooperative systems. The results from the MFB analysis are also used for relay selection and power allocation in the multi-relay cooperative systems. To overcome the intersymbol interference impairment induced by frequency-selectivity of the HF channel, equalization is inevitable at the destination in a single-carrier system. In this work, we investigate the minimum-mean-square-error (MMSE) based linear/decision-feedback frequency domain equalizers (FDEs). Both symbol-spaced and fractionally-spaced implementations of the proposed FDEs are considered and their performance is compared under different channel conditions and sampling phase errors at the relay and destination nodes.

Three different algorithms for the generation of stationary Gaussian time series with given autocorrelation function are presented in this paper. The algorithms have already been suggested in the literature but are not well known and have never been compared before. Interrelations between the different methods, advantages and disadvantages with respect to speed and memory requirements and the range of autocorrelation functions for which the different methods are stable are discussed. The time-complexity of the algorithms and the comparisons of their implementations show that the method twice using the Fourier transform is by far the most efficient if time series of moderate or large length are generated. A tested C-code of the latter algorithm is included as this method is tricky to implement and very difficult to find in the literature. (We know only one reference, that gives a correct algorithm, but there the description is very short and no proof is included.) (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

<p> This thesis addresses the design of fractionally-spaced equalizers for a digital communication system which is susceptible to Adjacent Channel Interference (ACI). ACI can render an otherwise well designed system prone to excess bit errors. Algorithms for a trained adaptive FIR linear fractionally-spaced equalizer (FSE) with explicit sidelobe control are developed in order to provide robustness to ACI. The explicit sidelobe control is achieved by imposing a quadratic inequality constraint on the frequency response of the equalizer at a discrete set of frequency points in the sidelobe region.</p> <p> Algorithms are developed for both block adaptive and symbol-by-symbol adaptive modes. These algorithms use interior point optimization techniques to find the optimal equalizer coefficients. In the block adaptive mode, the problem is reformulated as a Second Order Cone Program (SOCP). In the symbol-by-symbol adaptive mode, the philosophy of the barrier approach to interior point methods is adopted. The concept of a central path and the Method of Analytic Centers (MAC) are used to develop two practically implementable algorithms, namely IPM2 and SBM, for performing symbol-by-symbol adaptive, fractionally-spaced equalization, with multiple quadratic inequality constraints.</p> <p> The performance of the proposed algorithms is compared to that of the Wiener filter, and the standard RLS algorithm with explicit diagonal loading. In the computer simulations, the proposed algorithms perform better in the sense that they provide the desired robustness when the communication model is prone to intermittent interferers in the sidelobe region of the frequency response of the FSE. Although the proposed algorithms have a moderately higher computational cost, their insensitivity to the deleterious effects of ACI make them an attractive choice in certain applications.</p> / Thesis / Master of Applied Science (MASc)

Les propriétés d'un gaz électronique bidimensionnel soumis à champs magnétiques intenses et à bas champs magnétiques sont étudiés par la spectroscopie optique: l'effet Hall quantique fractionnaire (FQHE) par photoluminescence et diffusion inélastique de la lumière, puis un nouvel effet oscillatoire de la résistance induit par micro-ondes (MIROs) par transport et absorption des micro-ondes. Les effets des interactions entre électrons du 2DEG sont à l'origine de FQHE. Jusqu'à maintenant, les expériences d'optiques n'ont pas permis les études des interactions entre électrons sur toute la gamme de fractions. Les fractions 1/3, 2/5, 3/7, 3/5, 2/3 et 1 sont clairement observées dans les spectres non traités et montrent une symétrie autour du facteur de remplissage 1/2. La symétrie des fermions composites ets observée dans les spectres. A bas champ magnétique, sous irradiation micro-onde, les propriétés de transport s'écartent nettement des oscillations bien connues de Shubnikov - de Haas pour évoluer vers une série d'états de résistance zéro. Les résultats des mesures d'absorption des micro-ondes sont présentés pour deux échantillons. L'échantillon de basse mobilité montre seulement une absorption autour de la résonance cyclotron (CR). L' échantillon de haute mobilité montre aussi des signaux d'absorption aux harmoniques de la CR. Les mesures ont permis d'inférer l'existence de deux processus d'absorption différents et séparés. L'absorption non résonante est mieux visible en transport et observée comme MIROs, et l'absorption résonante, mieux observée dans les mesures d'absorption, suit probablement les règles de polarisation de résonance cyclotron.

Rubber like materials find wide applications in damping treatment of structures, vibration isolations and they appear prominently in the form of hoses in many structures such as aircraft engines. The study reported in this thesis addresses a few issues in computational modeling of vibration of structures with some of its components made up of rubber like materials. Specifically, the study explores the use of fractional derivatives in representing the constitutive laws of such material and focuses its attention on problems of parameter identification in linear time invariant systems with fractional order damping models. The thesis is divided into four chapters and two annexures. A review of literature related to mathematical modeling of damping with emphasis on fractional order derivative models is presented in chapter 1. The review covers lternatives available for modeling energy dissipation that include viscous, structural and hybrid damping models. The advantages of using fractional order derivative models in this context is pointed out and papers dealing with solution of differential equations with fractional order derivatives are reviewed. Issues related to finite element modeling and random vibration analysis of systems with fractional order damping models are also covered. The review recognizes the problems of system parameter identification based on inverse eigensensitivity and inverse FRF sensitivity as problems requiring further research. The problem of determination of derivatives of eigensolutions and FRF-s with respect to system parameters of linear time invariant systems with fractional order damping models is considered in chapter 2. The eigensolutions here are obtained as solutions of a generalized asymmetric eigenvalue problem. The order of system matrices here depends upon the mechanical degrees of freedom and also somewhat artificially on the fractional order of the derivative terms. The formulary for first and second order eigenderivatives are developed taking account of these features. This derivation also takes into account the various orthogonality relations satisfied by the complex valued eigenvectors. The system FRF-s are obtained by a straight forward inversion of the system dynamic stiffness matrix and also by using a series solution in terms of system eigensolutions. As might be expected, the two solutions lead to identical results. The first and the second order derivatives of FRF-s are obtained based on system dynamic matrix and without taking recourse to modal summation. Numerical examples that bring out various facets of eigensolutions, FRF-s and their sensitivities are presented with reference to single and multi degree freedom systems. The application sensitivity analysis developed in chapter 2 to problems of system parameter identification is considered in chapter 3. Methods based on inverse eigensensitivity and inverse FRF sensitivity are outlined. The scope of these methods cover first and second order analyses and applications to single and multi degree freedom systems. While most illustrations are based on synthetic measurement data, limited efforts are also made to implement the identification methods using laboratory measurement data. The experimental work has involved the measurement of FRF-s on a system consisting of two steel tubes connected by a rubber hose. The two system identification methods are shown to perform well especially when information on second order sensitivity are included in the analysis. The method based on inverse eigensolution is shown to become increasingly unwieldy to apply as the order of the system matrices increases while the FRF based method does not suffer from this drawback. The FRF based method also has the advantage that the prior knowledge of order of fractional order derivative terms is not needed in its implementation while such knowledge is assumed in the method based on eigensolutions. While the methods are shown to perform satisfactorily when synthetic measurement data is used, their success is not uniformly good when laboratory measurement data are employed. Chapter 4 presents a summary of contributions made in the thesis and also enlists a few suggestions for further research. Annexure I provides a précis of elementary notion of fractional order derivatives and integrals. A case study on finite element analysis of aircraft engine component made up of metallic and rubber materials is outlined in Annexure II and the study points towards possible advantages of using fractional order damping models in the study of such structures.

This thesis studies the design and implementation of a linear minimum mean-square error (LMMSE) receiver in asynchronous bandlimited direct-sequence code-division multiple-access (DS-CDMA) systems that employ long-code pseudo-noise (PN) sequences and operate in multipath environments. The receiver is shown to be capable of multiple-access interference (MAI) suppression and multipath diversity combining without the knowledge of other users' signature sequences. It outperforms any other linear receiver by maximizing output signal-to-noise ratio (SNR) with the aid of a new chip filter which exploits the cyclostationarity of the received signal and combines all paths of the desired user that fall within its supported time span. This work is motivated by the shortcomings of existing LMMSE receivers which are either incompatible with long-code CDMA or constrained by limitations in the system model. The design methodology is based on the concept of linear/conjugate linear (LCL) filtering and satisfying the orthogonality conditions to achieve the LMMSE filter response. Moreover, the proposed LMMSE receiver addresses two drawbacks of the coherent Rake receiver, the industry's current solution for multipath reception. First, unlike the Rake receiver which uses the chip-matched filter (CMF) and treats interference as additive white Gaussian noise (AWGN), the LMMSE receiver suppresses interference by replacing the CMF with a new chip pulse filter. Second, in contrast to the Rake receiver which only processes a subset of strongest paths of the desired user, the LMMSE receiver harnesses the energy of all paths of the desired user that fall within its time support, at no additional complexity. The performance of the proposed LMMSE receiver is analyzed and compared with that of the coherent Rake receiver with probability of bit error, <i>Pe</i>, as the figure of merit. The analysis is based on the accurate improved Gaussian approximation (IGA) technique. Closed form conditional <i>Pe</i> expressions for both the LMMSE and Rake receivers are derived. Furthermore, it is shown that if quadriphase random spreading, moderate to large spreading factors, and pulses with small excess bandwidth are used, the widely-used standard Gaussian Approximation (SGA) technique becomes accurate even for low regions of <i>Pe</i>. Under the examined scenarios tailored towards current narrowband system settings, the LMMSE receiver achieves 60% gain in capacity (1. 8 dB in output SNR) over the selective Rake receiver. A third of the gain is due to interference suppression capability of the receiver while the rest is credited to its ability to collect the energy of the desired user diversified to many paths. Future wideband systems will yield an ever larger gain. Adaptive implementations of the LMMSE receiver are proposed to rid the receiver from dependence on the knowledge of multipath parameters. The adaptive receiver is based on a fractionally-spaced equalizer (FSE) whose taps are updated by an adaptive algorithm. Training-based, pilot-channel-aided (PCA), and blind algorithms are developed to make the receiver applicable to both forward and reverse links, with or without the presence of pilot signals. The blind algorithms are modified versions of the constant modulus algorithm (CMA) which has not been previously studied for long-code CDMA systems. Extensive simulation results are presented to illustrate the convergence behavior of the proposed algorithms and quantify their performance loss under various levels of MAI. Computational complexities of the algorithms are also discussed. These three criteria (performance loss, convergence rate, and computational complexity) determine the proper choice of an adaptive algorithm with respect to the requirements of the specific application in mind.