Numerical applications of the generalized method of steepest descents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1992.Includes bibliographical references (leaves 268-272).by Jean-Marie Clarisse.Ph.D

Reflections Inspired by My Critics

The crucial idea in constitutional law is legitimacy; the crucial idea in jurisprudence is justification. For some time, the academic debate about U.S. constitutionalism has looked for justifications for our practices, believing this would confer legitimacy on them. In my work, I have endeavored to derive legitimacy from the practices themselves, reserving the task of justification for other purposes. By showing the way in which legitimacy is established and maintained in a constitutional system like ours, I hoped to derive solutions to a number of classical questions, all of which, I believe, are at bottom questions about legitimacy and legitimation. These questions were the principal subject of Constitutional Fate, although there are many views expressed there that bear on other contemporary legal issues. At the same time, I also wished to propose a way of understanding constitutional law that changed its relationship to jurisprudence, as practiced nowadays, rendering some jurisprudential questions far less insistent and some largely unexplored questions central. As such, this work is also thus directed to a description of how a constitutional system is evaluated, and how our responsibilities within that system are discharged – a system that depends so greatly on the exercise of conscience. This description, I believed, is mainly a matter of justification, and it is the principal subject of Constitutional Interpretation. If one believes, as I do, that justification does not assure legitimacy, whenever one evaluates a proposed system one must ask not only whether it is easier to justify, but also whether it will be able to achieve and maintain legitimacy

Bayesian nonparametric learning of complex dynamical phenomena

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 257-270).The complexity of many dynamical phenomena precludes the use of linear models for which exact analytic techniques are available. However, inference on standard nonlinear models quickly becomes intractable. In some cases, Markov switching processes, with switches between a set of simpler models, are employed to describe the observed dynamics. Such models typically rely on pre-specifying the number of Markov modes. In this thesis, we instead take a Bayesian nonparametric approach in defining a prior on the model parameters that allows for flexibility in the complexity of the learned model and for development of efficient inference algorithms. We start by considering dynamical phenomena that can be well-modeled as a hidden discrete Markov process, but in which there is uncertainty about the cardinality of the state space. The standard finite state hidden Markov model (HMM) has been widely applied in speech recognition, digital communications, and bioinformatics, amongst other fields. Through the use of the hierarchical Dirichlet process (HDP), one can examine an HMM with an unbounded number of possible states. We revisit this HDPHMM and develop a generalization of the model, the sticky HDP-HMM, that allows more robust learning of smoothly varying state dynamics through a learned bias towards self-transitions. We show that this sticky HDP-HMM not only better segments data according to the underlying state sequence, but also improves the predictive performance of the learned model. Additionally, the sticky HDP-HMM enables learning more complex, multimodal emission distributions.(cont.) We demonstrate the utility of the sticky HDP-HMM on the NIST speaker diarization database, segmenting audio files into speaker labels while simultaneously identifying the number of speakers present. Although the HDP-HMM and its sticky extension are very flexible time series models, they make a strong Markovian assumption that observations are conditionally independent given the discrete HMM state. This assumption is often insufficient for capturing the temporal dependencies of the observations in real data. To address this issue, we develop extensions of the sticky HDP-HMM for learning two classes of switching dynamical processes: the switching linear dynamical system (SLDS) and the switching vector autoregressive (SVAR) process. These conditionally linear dynamical models can describe a wide range of complex dynamical phenomena from the stochastic volatility of financial time series to the dance of honey bees, two examples we use to show the power and flexibility of our Bayesian nonparametric approach. For all of the presented models, we develop efficient Gibbs sampling algorithms employing a truncated approximation to the HDP that allows incorporation of dynamic programming techniques, greatly improving mixing rates. In many applications, one would like to discover and model dynamical behaviors which are shared among several related time series. By jointly modeling such sequences, we may more robustly estimate representative dynamic models, and also uncover interesting relationships among activities.(cont.) In the latter part of this thesis, we consider a Bayesian nonparametric approach to this problem by harnessing the beta process to allow each time series to have infinitely many potential behaviors, while encouraging sharing of behaviors amongst the time series. For this model, we develop an efficient and exact Markov chain Monte Carlo (MCMC) inference algorithm. In particular, we exploit the finite dynamical system induced by a fixed set of behaviors to efficiently compute acceptance probabilities, and reversible jump birth and death proposals to explore new behaviors. We present results on unsupervised segmentation of data from the CMU motion capture database.by Emily B. Fox.Ph.D

The development of speech coding and the first standard coder for public mobile telephony

This thesis describes in its core chapter (Chapter 4) the original algorithmic and design features of the ??rst coder for public mobile telephony, the GSM full-rate speech coder, as standardized in 1988. It has never been described in so much detail as presented here. The coder is put in a historical perspective by two preceding chapters on the history of speech production models and the development of speech coding techniques until the mid 1980s, respectively. In the epilogue a brief review is given of later developments in speech coding. The introductory Chapter 1 starts with some preliminaries. It is de- ??ned what speech coding is and the reader is introduced to speech coding standards and the standardization institutes which set them. Then, the attributes of a speech coder playing a role in standardization are explained. Subsequently, several applications of speech coders - including mobile telephony - will be discussed and the state of the art in speech coding will be illustrated on the basis of some worldwide recognized standards. Chapter 2 starts with a summary of the features of speech signals and their source, the human speech organ. Then, historical models of speech production which form the basis of di??erent kinds of modern speech coders are discussed. Starting with a review of ancient mechanical models, we will arrive at the electrical source-??lter model of the 1930s. Subsequently, the acoustic-tube models as they arose in the 1950s and 1960s are discussed. Finally the 1970s are reviewed which brought the discrete-time ??lter model on the basis of linear prediction. In a unique way the logical sequencing of these models is exposed, and the links are discussed. Whereas the historical models are discussed in a narrative style, the acoustic tube models and the linear prediction tech nique as applied to speech, are subject to more mathematical analysis in order to create a sound basis for the treatise of Chapter 4. This trend continues in Chapter 3, whenever instrumental in completing that basis. In Chapter 3 the reader is taken by the hand on a guided tour through time during which successive speech coding methods pass in review. In an original way special attention is paid to the evolutionary aspect. Speci??cally, for each newly proposed method it is discussed what it added to the known techniques of the time. After presenting the relevant predecessors starting with Pulse Code Modulation (PCM) and the early vocoders of the 1930s, we will arrive at Residual-Excited Linear Predictive (RELP) coders, Analysis-by-Synthesis systems and Regular- Pulse Excitation in 1984. The latter forms the basis of the GSM full-rate coder. In Chapter 4, which constitutes the core of this thesis, explicit forms of Multi-Pulse Excited (MPE) and Regular-Pulse Excited (RPE) analysis-by-synthesis coding systems are developed. Starting from current pulse-amplitude computation methods in 1984, which included solving sets of equations (typically of order 10-16) two hundred times a second, several explicit-form designs are considered by which solving sets of equations in real time is avoided. Then, the design of a speci??c explicitform RPE coder and an associated eÆcient architecture are described. The explicit forms and the resulting architectural features have never been published in so much detail as presented here. Implementation of such a codec enabled real-time operation on a state-of-the-art singlechip digital signal processor of the time. This coder, at a bit rate of 13 kbit/s, has been selected as the Full-Rate GSM standard in 1988. Its performance is recapitulated. Chapter 5 is an epilogue brie y reviewing the major developments in speech coding technology after 1988. Many speech coding standards have been set, for mobile telephony as well as for other applications, since then. The chapter is concluded by an outlook

Evaluation of glottal characteristics for speaker identification.

Based on the assumption that the physical characteristics of people's vocal apparatus cause their voices to have distinctive characteristics, this thesis reports on investigations into the use of the long-term average glottal response for speaker identification. The long-term average glottal response is a new feature that is obtained by overlaying successive vocal tract responses within an utterance. The way in which the long-term average glottal response varies with accent and gender is examined using a population of 352 American English speakers from eight different accent regions. Descriptors are defined that characterize the shape of the long-term average glottal response. Factor analysis of the descriptors of the long-term average glottal responses shows that the most important factor contains significant contributions from descriptors comprised of the coefficients of cubics fitted to the long-term average glottal response. Discriminant analysis demonstrates that the long-term average glottal response is potentially useful for classifying speakers according to their gender, but is not useful for distinguishing American accents. The identification accuracy of the long-term average glottal response is compared with that obtained from vocal tract features. Identification experiments are performed using a speaker database containing utterances from twenty speakers of the digits zero to nine. Vocal tract features, which consist of cepstral coefficients, partial correlation coefficients and linear prediction coefficients, are shown to be more accurate than the long-term average glottal response. Despite analysis of the training data indicating that the long-term average glottal response was uncorrelated with the vocal tract features, various feature combinations gave insignificant improvements in identification accuracy. The effect of noise and distortion on speaker identification is examined for each of the features. It is found that the identification performance of the long-term average glottal response is insensitive to noise compared with cepstral coefficients, partial correlation coefficients and the long-term average spectrum, but that it is highly sensitive to variations in the phase response of the speech transmission channel. Before reporting on the identification experiments, the thesis introduces speech production, speech models and background to the various features used in the experiments. Investigations into the long-term average glottal response demonstrate that it approximates the glottal pulse convolved with the long-term average impulse response, and this relationship is verified using synthetic speech. Furthermore, the spectrum of the long-term average glottal response extracted from pre-emphasized speech is shown to be similar to the long-term average spectrum of pre-emphasized speech, but computationally much simpler

Middle Atmosphere Program. Handbook for MAP. Volume 30: International School on Atmospheric Radar

Broad, tutorial coverage is given to the technical and scientific aspects of mesosphere stratosphere troposphere (MST) meteorological radar systems. Control issues, signal processing, atmospheric waves, the historical aspects of radar atmospheric dynamics, incoherent scatter radars, radar echoes, radar targets, and gravity waves are among the topics covered