A six sensor method for measuring acoustic properties in ducts.

An accurate description of sound propagation in a duct is important to obtain the sound power radiating from a source in both near and far fields. A technique has been developed and applied to decompose higher-order modes of sound emitted into a duct. Traditional experiments and theory based on two-sensor methods are limited to the plane-wave contribution to the sound field at low frequency. Due to the increase in independent measurements required, a computational method has been developed to simulate sensitivities of real measurements (e.g., noise) and optimize the set-up. An experimental rig has been constructed to decompose the first two modes using six independent measurements from surface, flush-mounted microphones. Experiments were initially performed using a loudspeaker as the source for validation. Subsequently, the sound emitted by a mixed-flow fan has been investigated and compared to measurements made in accordance with the internationally standardized in-duct fan measurement method. This method utilizes large anechoic terminations and a procedure involving averaging over measurements in space and time to account for the contribution from higher-order modes. The new method does not require either of these added complications and gives detail about the underlying modal content of the emitted sound.

Low-rank optimization for distance matrix completion

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. © 2011 IEEE.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

From subspace learning to distance learning: A geometrical optimization approach

In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates the subspace of the matrix and its projection onto that subspace. A proper weighting of the two iterations enables to continuously interpolate between the problem of learning a subspace and learning a distance when the subspace is fixed. © 2009 IEEE.

Riemannian geometry of Grassmann manifolds with a view on algorithmic computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in ℝn. In these formulas, p-planes are represented as the column space of n × p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications - computing an invariant subspace of a matrix and the mean of subspaces - are worked out.

Nonlinear analysis of cardiac rhythm fluctuations using DFA method

An approach by which the detrented fluctuation analysis (DFA) method can be used to help diagnose heart failure was demonstrated. DFA was applied to patients suffering from congestive heart failure (CHF) to check correlations between DFA indices and CHF, and determine a correlation between DFA indices and mortality, with a particular attention to the residue parameter, which is a measure of the departure of the DFA from its power law approximation. DFA parameters proved to be useful as a complement to the physiological parameters weber and FE to sort out the patients into three prognostic group.

Optimization Algorithms on Matrix Manifolds

This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms.

A high throughput Nile red method for quantitative measurement of neutral lipids in microalgae

Isolation of high neutral lipid-containing microalgae is key to the commercial success of microalgae-based biofuel production. The Nile red fluorescence method has been successfully applied to the determination of lipids in certain microalgae, but has been unsuccessful in many others, particularly those with thick, rigid cell walls that prevent the penetration of the fluorescence dye. The conventional "one sample at a time" method was also time-consuming. In this study, the solvent dimethyl sulfoxide (DMSO) was introduced to microalgal samples as the stain carrier at an elevated temperature. The cellular neutral lipids were determined and quantified using a 96-well plate on a fluorescence spectrophotometer with an excitation wavelength of 530 nm and an emission wavelength of 575 run. An optimized procedure yielded a high correlation coefficient (R-2 = 0.998) with the lipid standard triolein and repeated measurements of replicates. Application of the improved method to several green algal strains gave very reproducible results with relative standard errors of 8.5%, 3.9% and 8.6%, 4.5% for repeatability and reproducibility at two concentration levels (2.0 mu g/mL and 20 mu g/mL), respectively. Moreover, the detection and quantification limits of the improved Nile red staining method were 0.8 mu g/mL and 2.0 mu g/mL for the neutral lipid standard triolein, respectively. The modified method and a conventional gravimetric determination method provided similar results on replicate samples. The 96-well plate-based Nile red method can be used as a high throughput technique for rapid screening of a broader spectrum of naturally-occurring and genetically-modified algal strains and mutants for high neutral lipid/oil production. (C) 2009 Published by Elsevier B.V.

Decoupling method for vector control of the brushless doubly-fed machine

The brushless doubly-fed machine exhibits rotor-speed-dependent, cross-coupling effects between inputs and outputs when vector control is implemented. Manipulation of the model equations shows that these effects are represented by rotation angles. A parameter-independent decoupling method is presented which reduces these cross-coupling disturbances by estimating the rotation angle and applying it back to the controller. © 2013 IEEE.

Validation of a method of estimating age, modelling growth, and describing the age composition of Coilia mystus from the Yangtze Estuary, China

A collection of 577 Coilia mystus was made during April 2006 and 2007 from China's Yangtze Estuary to estimate the age structure and growth patterns of the population. Examination of sectioned sagittal otoliths revealed a periodic straight/curved growth pattern. The straight zone was from April to November, and the curved zone from October to May, indicating annual periodicity. Annual periodicity was also verified by margin zone analysis. The shift from a curved-zone to the next straight-zone stanza was defined as an annulus. The fish from which the otoliths were taken were 0-5 years old. The von Bertalanffy growth function was fitted to standard length (LS)-at-age data as L-S = 215.16 (1 - e(-0.53(t+0.30))) (n = 577, r(2) = 0.81, p < 0.05). The mature females included five age classes, ages 1 and 2 accounting for 74.3% of the population. The mature males included fish aged 1 and 2, those at age 1 accounting for 86.4% of the population. Mean length was smaller, and annual growth less, for mature males than for females of comparable age. The study demonstrated that the Yangtze population of C. mystus consists of more age classes than previously thought and that the age structure of the population needs to be considered in management decisions.