Identification of parameters in amplitude equations describing coupled wakes

We study the flow behind an array of equally spaced parallel cylinders. A system of Stuart-Landau equations with complex parameters is used to model the oscillating wakes. Our purpose is to identify the 6 scalar parameters which most accurately reproduce the experimental data of Chauve and Le Gal [{Physica D {\bf 58}}, pp 407--413, (1992)]. To do so, we perform a computational search for the minimum of a distance \calj. We define \calj as the sum-square difference of the data and amplitudes reconstructed using coupled equations. The search algorithm is made more efficient through the use of a partially analytical expression for the gradient $\nabla \cal J$. Indeed $\nabla \cal J$ can be obtained by the integration of a dynamical system propagating backwards in time (a backpropagation equation for the Lagrange multipliers). Using the parameters computed via the backpropagation method, the coupled Stuart-Landau equations accurately predicted the experimental data from Chauve and Le Gal over a correlation time of the system. Our method turns out to be quite robust as evidenced by using noisy synthetic data obtained from integrations of the coupled Stuart-Landau equations. However, a difficulty remains with experimental data: in that case the several sets of identified parameters are shown to yield equivalent predictions. This is due to a strong discretization or ``round-off" error arising from the digitalization of the video images in the experiment. This ambiguity in parameter identification has been reproduced with synthetic data subjected to the same kind of discretization.Comment: 25 pages uuencoded compressed PostScript file (58K) with 13 figures (155K in separated file) Submitted to Physica

Visualization of Tonal Harmony for Jazz Lead Sheets

Jazz improvisation is the extemporaneous expression of melody, and musicians commonly base their performances on chord progressions given by lead sheets. It is standard practice to commit a progression to memory by analyzing it for common patterns. This paper presents a visualization design intended to help reduce the amount of cognitive work needed to assimilate a song’s chords and harmonic patterns. It does this using color, shapes, and glyphs as visual variables to convey meaning about tonal centers, chord functions, and harmonic structure

Estimating Nuisance Parameters in Inverse Problems

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.Comment: 16 pages, 5 figure

Random field modeling for interpretation and analysis of layered data

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1987.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 288-290.by Carey David Bunks.Ph.D

Direct temperature and salinity acoustic full waveform inversion

5 pages, 4 figuresRecent work has shown that Full Waveform Inversion could be suitable to extract physical properties such as sound speed (c), density (ρ), temperature (T), and salinity (S) from the weak impedance contrasts associated with the ocean's thermohaline fine structure.The seismic inversion approaches proposed so far are based on the iterative inversion of c from multichannel seismic data, while the rest of parameters (T,S, and ρ) are determined in a second step using two equations of state and a local T-S empirical relationship. In this work, we present an alternative to this approach. Using 1-D synthetic seismic data, we demonstrate that the direct full waveform inversion of T and S using adjoint methods is feasible without the use of any local T-S relationship and that the models of physical properties obtained with this approach are far more accurate than those inferred from c. Key Points T and S can be inverted simultaneously from ocean acoustic data using FWI Local T-S empirical relationships are not required for the inversion Our T and S results have a potential density error of 0.01 kg/m3. © 2013. American Geophysical Union. All Rights ReservedThis work has been fulfilled in the framework of the project POSEIDON (CTM2010-25169) and APOGEO (CTM2011-16001-E/MAR), both funded by the Spanish Ministry of Economy and Competitiveness (MINECO), and the Marie Curie project OCEANSEIS (FP7-PEOPLE-2010-IOF-271936-OCEANSEIS)Peer Reviewe