Intraspeaker Comparisons of Acoustic and Articulatory Variability in American English /r/ Productions

The purpose of this report is to test the hypothesis that speakers utilize an acoustic, rather than articulatory, planning space for speech production. It has been well-documented that many speakers of American English use different tongue configurations to produce /r/ in different phonetic contexts. The acoustic planning hypothesis suggests that although the /r/ configuration varies widely in different contexts, the primary acoustic cue for /r/, a dip in the F3 trajectory, will be less variable due to tradeoffs in articulatory variability, or trading relations, that help maintain a relatively constant F3 trajectory across phonetic contexts. Acoustic data and EMMA articulatory data from seven speakers producing /r/ in different phonetic contexts were analyzed. Visual inspection of the EMMA data at the point of F3 minimum revealed that each speaker appeared to use at least two of three trading relation strategies that would be expected to reduce F3 variability. Articulatory covariance measures confirmed that all seven speakers utilized a trading relation between tongue back height and tongue back horizontal position, six speakers utilized a trading relation between tongue tip height and tongue back height, and the speaker who did not use this latter strategy instead utilized a trading relation between tongue tip height and tongue back horizontal position. Estimates of F3 variability with and without the articulatory covariances indicated that F3 would be much higher for all speakers if the articulatory covariances were not utilized. These conclusions were further supported by a comparison of measured F3 variability to F3 variabilities estimated from the pellet data with and without articulatory covariances. In all subjects, the actual F3 variance was significantly lower than the F3 variance estimated without articulatory covariances, further supporting the conclusion that the articulatory trading relations were being used to reduce F3 variability. Together, these results strongly suggest that the neural control mechanisms underlying speech production make elegant use of trading relations between articulators to maintain a relatively invariant acoustic trace for /r/ across phonetic contexts

Intraspeaker Comparisons of Acoustic and Articulatory Variability in American English /r/ Productions

The purpose of this report is to test the hypothesis that speakers utilize an acoustic, rather than articulatory, planning space for speech production. It has been well-documented that many speakers of American English use different tongue configurations to produce /r/ in different phonetic contexts. The acoustic planning hypothesis suggests that although the /r/ configuration varies widely in different contexts, the primary acoustic cue for /r/, a dip in the F3 trajectory, will be less variable due to tradeoffs in articulatory variability, or trading relations, that help maintain a relatively constant F3 trajectory across phonetic contexts. Acoustic data and EMMA articulatory data from seven speakers producing /r/ in different phonetic contexts were analyzed. Visual inspection of the EMMA data at the point of F3 minimum revealed that each speaker appeared to use at least two of three trading relation strategies that would be expected to reduce F3 variability. Articulatory covariance measures confirmed that all seven speakers utilized a trading relation between tongue back height and tongue back horizontal position, six speakers utilized a trading relation between tongue tip height and tongue back height, and the speaker who did not use this latter strategy instead utilized a trading relation between tongue tip height and tongue back horizontal position. Estimates of F3 variability with and without the articulatory covariances indicated that F3 would be much higher for all speakers if the articulatory covariances were not utilized. These conclusions were further supported by a comparison of measured F3 variability to F3 variabilities estimated from the pellet data with and without articulatory covariances. In all subjects, the actual F3 variance was significantly lower than the F3 variance estimated without articulatory covariances, further supporting the conclusion that the articulatory trading relations were being used to reduce F3 variability. Together, these results strongly suggest that the neural control mechanisms underlying speech production make elegant use of trading relations between articulators to maintain a relatively invariant acoustic trace for /r/ across phonetic contexts

Processing Images of Craters for Spacecraft Navigation

A crater-detection algorithm has been conceived to enable automation of what, heretofore, have been manual processes for utilizing images of craters on a celestial body as landmarks for navigating a spacecraft flying near or landing on that body. The images are acquired by an electronic camera aboard the spacecraft, then digitized, then processed by the algorithm, which consists mainly of the following steps: 1. Edges in an image detected and placed in a database. 2. Crater rim edges are selected from the edge database. 3. Edges that belong to the same crater are grouped together. 4. An ellipse is fitted to each group of crater edges. 5. Ellipses are refined directly in the image domain to reduce errors introduced in the detection of edges and fitting of ellipses. 6. The quality of each detected crater is evaluated. It is planned to utilize this algorithm as the basis of a computer program for automated, real-time, onboard processing of crater-image data. Experimental studies have led to the conclusion that this algorithm is capable of a detection rate >93 percent, a false-alarm rate <5 percent, a geometric error <0.5 pixel, and a position error <0.3 pixel

Articulatory Tradeoffs Reduce Acoustic Variability During American English /r/ Production

Acoustic and articulatory recordings reveal that speakers utilize systematic articulatory tradeoffs to maintain acoustic stability when producing the phoneme /r/. Distinct articulator configurations used to produce /r/ in various phonetic contexts show systematic tradeoffs between the cross-sectional areas of different vocal tract sections. Analysis of acoustic and articulatory variabilities reveals that these tradeoffs act to reduce acoustic variability, thus allowing large contextual variations in vocal tract shape; these contextual variations in turn apparently reduce the amount of articulatory movement required. These findings contrast with the widely held view that speaking involves a canonical vocal tract shape target for each phoneme.National Institute on Deafness and Other Communication Disorders (1R29-DC02852-02, 5R01-DC01925-04, 1R03-C2576-0l); National Science Foundation (IRI-9310518

Chaos in the Takens-Bogdanov bifurcation with O(2) symmetry

The Takens–Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation invariant in one spatial dimension with no left-right preference the imposition of periodic boundary conditions leads to the Takens–Bogdanov bifurcation with O(2) symmetry. This bifurcation, analyzed by G. Dangelmayr and E. Knobloch, Phil. Trans. R. Soc. London A 322, 243 (1987), describes the interaction between steady states and traveling and standing waves in the nonlinear regime and predicts the presence of modulated traveling waves as well. The analysis reveals the presence of several global bifurcations near which the averaging method (used in the original analysis) fails. We show here, using a combination of numerical continuation and the construction of appropriate return maps, that near the global bifurcation that terminates the branch of modulated traveling waves, the normal form for the Takens–Bogdanov bifurcation admits cascades of period-doubling bifurcations as well as chaotic dynamics of Shil’nikov type. Thus chaos is present arbitrarily close to the codimension two point

Efficient Analysis of High Dimensional Data in Tensor Formats

In this article we introduce new methods for the analysis of high dimensional data in tensor formats, where the underling data come from the stochastic elliptic boundary value problem. After discretisation of the deterministic operator as well as the presented random fields via KLE and PCE, the obtained high dimensional operator can be approximated via sums of elementary tensors. This tensors representation can be effectively used for computing different values of interest, such as maximum norm, level sets and cumulative distribution function. The basic concept of the data analysis in high dimensions is discussed on tensors represented in the canonical format, however the approach can be easily used in other tensor formats. As an intermediate step we describe efficient iterative algorithms for computing the characteristic and sign functions as well as pointwise inverse in the canonical tensor format. Since during majority of algebraic operations as well as during iteration steps the representation rank grows up, we use lower-rank approximation and inexact recursive iteration schemes

Distribution of Eigenvalues for the Modular Group

The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.Comment: 72 pages, Latex, the fiogures mentioned in the text are not vital, but can be obtained upon request from the first Autho

Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504