Nonnegative Least-squares Method Research Articles

Fault Slip Distribution of the 1999 Mw 7.1 Hector Mine, California, Earthquake, Estimated from Satellite Radar and GPS Measurements

We use a combination of satellite radar and GPS data to estimate the slip distribution of the 1999 M w 7.1 Hector Mine Earthquake, a right-lateral strikeslip earthquake that occurred on a northwest–southeast striking fault in the southern California Mojave Desert. The data include synthetic aperture radar interferograms (InSAR) from both ascending and descending orbits, radar amplitude image offset fields (SARIO) for both ascending and descending azimuth directions, and campaign GPS observations from 55 stations provided by Agnew et al. (2002). We model the fault with nine segments derived from the field-mapped fault rupture, the SARIO data, and aftershock locations. We first estimate the dip of each fault segment, as well as a single constant strike-slip component across each segment, resulting in an average dip of 83° to the northeast and slip of up to 5.6 m. Then, we fix the optimal fault segment dip, discretize the fault segments into 1.5 km × 1.5 km patches, and solve for the variable slip distribution using a nonnegative least-squares method that includes an appropriate degree of smoothing. Our preferred solution has both right-lateral strike-slip and reverse faulting. The estimated geodetic moment is 5.93 × 10 19 N m ( M w 7.1), similar to seismological estimates, indicating that there are insignificant interseismic and postseismic deformation signals in the data. We find strike-slip displacements of up to 6.0 m and reverse faulting of up to 1.6 m, with the maximum slip located just northwest of the epicenter. Most of the slip is concentrated northwest and south of the epicenter; little slip is found on the northeastern branch of the fault. The SARIO data and our modeling indicate that the amount and extent of surface fault rupture were underestimated in the field.

Dwell time algorithm for computer-controlled polishing of small axis-symmetrical aspherical lens mold

SAMSUNG Electronics Co.Opto-Mechatronics LabDigital Media R&D Center416 Maetan-3Dong, Paldal-GuSuwon City, Kyungki-DoKorea 442-742E-mail: hocheol@samsung.comMinyang YangKorea Advanced Institute of Science andTechnologyDepartment of Mechanical Engineering373-1 Kusong-dong, Yusong-guTaejonKorea 305-701E-mail: myyang@kaist.ac.krAbstract. We describe a dwell time algorithm for the polishing of smallaxis-symmetrical aspherical surfaces. The dwell time distribution of thescanning polishing tool on the rotating workpiece is calculated to reducethe residual surface error. The dwell time at each discrete grid is calcu-lated as an integer multiple of the workpiece rotation period, which isalso useful for the spatially varying case in the local polishing area. Aspherical polyurethane tool with abrasives is adopted for a computer-controlled polishing process. A linear algebraic equation of removaldepth, removal matrix, and dwell time is derived by convolution of theremoval depth at the dwell positions. The nonnegative least-squaresmethod gives a solution to minimize residual error. Parametric effectssuch as the dwell grid interval are simulated. Finally, an experiment fortool mark removal is performed and the dwell time algorithm is evaluatedto be valid.

Muscle synergies encoded within the spinal cord: evidence from focal intraspinal NMDA iontophoresis in the frog.

This paper relates to the problem of the existence of muscle synergies, that is whether the CNS command to muscles is simplified by controlling their activity in subgroups or synergies, rather than individually. We approach this problem with two methods that have been recently introduced: intraspinal N-methyl-D-aspartate (NMDA) microstimulation and a synergy-extracting algorithm. To search for a common set of synergies encoded for by the spinal cord whose combinations would account for a large range of electromyographic (EMG) patterns, we chose, rather than examining a large range of natural behaviors, to chemically microstimulate a large number of spinal cord interneuronal sites in different frogs. A possible advantage of this complementary method is that it is task-independent. Visual inspection suggested that the NMDA-elicited EMG patterns recorded from 12 leg muscles might indeed be constructed from smaller subgroups of muscles whose activity co-varied, suggestive of synergies. We used a modification of our extracting computational algorithm whereby a nonnegative least-squares method was employed to iteratively update both the synergies and their coefficients of activation in reconstructing the EMG patterns. Using this algorithm, a limited set of seven synergies was found whose linear combinations accounted for more than 91% of the variance in the pooled EMG data from 10 frogs, and more than 96% in individual frogs. The extracted synergies were similar among frogs. Further, preferred combinations of these synergies were clearly identified. This was found by extracting smaller sets of four, five, or six synergies and fitting each synergy from those sets as a combination from the set of seven synergies extracted from the same frog; the synergy combinations from each frog were then pooled together to examine their frequency of occurrence. Concordance with this method of identifying synergy combinations was found by examining how the synergies from the set of seven correlated pair-wise as they reconstructed the EMG data. These results support the existence of muscle synergies encoded within the spinal cord, which through preferred combinations, account for a large repertoire of spinal cord motor output. These findings are contrasted with previous approaches to the problem of synergies.

Decomposition of laser altimeter waveforms

The authors develop a method to decompose a laser altimeter return waveform into a series of components assuming that the position of each component within the waveform can be used to calculate the mean elevation of a specific reflecting surface within the laser footprint. For simplicity, they assume each component is Gaussian in nature. They estimate the number of Gaussian components from the number of inflection points of a smoothed copy of the laser waveform and obtain initial estimates of the Gaussian half-widths and positions from the positions of its consecutive inflection points. Initial amplitude estimates are obtained using a nonnegative least-squares method (LSM). To reduce the likelihood of fitting the background noise within the waveform and to minimize the number of Gaussians needed in the approximation, we rank the importance of each Gaussian in the decomposition using its initial half-width and amplitude estimates. The initial parameter estimates of all Gaussians ranked important are optimized using the Levenburg-Marquardt method. If the sum of the Gaussians does not approximate the return waveform to a prescribed accuracy, then additional Gaussians can be included in the optimization procedure or initial parameters can be recalculated. The Gaussian decomposition method is demonstrated on data collected by the airborne laser vegetation imaging sensor (LVIS) in October 1997 over the Sequoia National Forest, California.

Comparison of Various Numerical Procedures for Analysis of Structural Heterogeneity

Several methods (condensation approximation, regularization, and non-negative least-squares (NNLS)) have been applied for calculating the pore size distribution (PSD) function from simulated isotherms. It has been shown that two near by peaks in the low size region may be recovered well by both regularization and NNLS method only for isotherms without experimental error. Wide peaks may be recovered by numerical methods almost independently on a number of experimental points and error inherent in input data. Condensation approximation is the most insensitive to the experimental errors. However it gives a distorted one peak distribution shifted to low values of micropore size and having a long tail at large values. In the case ofisotherms with large errors (10% for regularization and 5% for NNLS), both numerical methods give PSD functions close to that obtained by the CA method.

Principal component calibration models in the acoustic evaluation of zooplankton size spectra

The theoretical basis of application of PCR (principal components regression) methods to the estimation of zooplankton size spectra by multifrequency acoustical methods is presented. Preliminary performance studies on simulated data are preformed to test the capacities of this technique as a function of the acoustic signal‐to‐noise ratio (SNR) and the type of acoustic scattering model. The results are compared with those obtained with a non‐negative least squares (NNLS) algorithm, and finally, an application to a real data matrix is shown. The main advantage over the NNLS method is that it avoids the knowledge of the scattering responses for each class of particles. The results obtained on simulated data indicate that PCR calibration models are good alternatives for the estimation of size spectra, in the range tested. For all the conditions analyzed, the error estimators and correlation coefficients show a better fit than NNLS models. The real data matrix tested is particularly complex, avoiding the use o...