Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness.

Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices.

Results: On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8% plus or minus 2.0%. The true positive classification performance is 95.4% plus or minus 3.2%, and the true negative performance is 91.5% plus or minus 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools.

Conclusions: Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.
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Functional Structure and Approximation in Econometrics (book front matter)

This is the front matter from the book, William A. Barnett and Jane Binner (eds.), Functional Structure and Approximation in Econometrics, published in 2004 by Elsevier in its Contributions to Economic Analysis monograph series. The front matter includes the Table of Contents, Volume Introduction, and Section Introductions by Barnett and Binner and the Preface by W. Erwin Diewert. The volume contains a unified collection and discussion of W. A. Barnett's most important published papers on applied and theoretical econometric modelling.consumer demand, production, flexible functional form, functional structure, asymptotics, nonlinearity, systemwide models

A topological approximation of the nonlinear Anderson model

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance-overlap in phase space, ranging from a fully developed chaos involving Levy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on a Cayley tree. It is found in vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t\rightarrow+\infty. The second moment grows with time as a powerlaw t^\alpha, with \alpha = 1/3. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of stripes propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.Comment: 20 pages, 2 figures; improved text with revisions; accepted for publication in Physical Review

Gaussian approximations in filters and smoothers for data assimilation

We present mathematical arguments and experimental evidence that suggest that Gaussian approximations of posterior distributions are appropriate even if the physical system under consideration is nonlinear. The reason for this is a regularizing effect of the observations that can turn multi-modal prior distributions into nearly Gaussian posterior distributions. This has important ramifications on data assimilation (DA) algorithms in numerical weather prediction because the various algorithms (ensemble Kalman filters/smoothers, variational methods, particle filters (PF)/smoothers (PS)) apply Gaussian approximations to different distributions, which leads to different approximate posterior distributions, and, subsequently, different degrees of error in their representation of the true posterior distribution. In particular, we explain that, in problems with medium' nonlinearity, (i) smoothers and variational methods tend to outperform ensemble Kalman filters; (ii) smoothers can be as accurate as PF, but may require fewer ensemble members; (iii) localization of PFs can introduce errors that are more severe than errors due to Gaussian approximations. In problems with strong' nonlinearity, posterior distributions are not amenable to Gaussian approximation. This happens, e.g. when posterior distributions are multi-modal. PFs can be used on these problems, but the required ensemble size is expected to be large (hundreds to thousands), even if the PFs are localized. Moreover, the usual indicators of performance (small root mean square error and comparable spread) may not be useful in strongly nonlinear problems. We arrive at these conclusions using a combination of theoretical considerations and a suite of numerical DA experiments with low- and high-dimensional nonlinear models in which we can control the nonlinearity.Office of Naval Research [N00173-17-2-C003, PE-0601153N]; Alfred P. Sloan Research Fellowship; National Science Foundation [DMS-1619630]Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]