Robust Non-Linear Regression Using The Dogleg Algorithm

What are the statistical and computational problems associated with robust nonlinear regression? This paper presents a number of possible approaches to these problems and develops a particular algorithm based on the work of Powell and Dennis.

The Singular Value Analysis in Matrix Computation

This paper discusses the robustness and the computational stability of the singular value decomposition algorithm used at the NBER Computer Research Center. The effect of perturbations on input data is explored. Suggestions are made for using the algorithm to get information about the rank of a real square or rectangular matrix. The algorithm can also be used to compute the best approximate solution of linear system of equations in the least squares sense, to solve linear systems of equations with equality constraints, and to determine dependencies or near dependencies among the rows or columns of a matrix. A copy of the subroutine that is used and some examples on which it has been tested are included in the appendixes.

Mechanical Behavior of SLS Components in Relation to the Build Orientation During the Sintering Process as Measured by ESPI

Selective Laser Sintering (SLS) allows producing real parts from CAD data from materials with different characteristics compared to the final model, presenting dissimilar mechanical properties between the prototype and the product. The purpose of this work is to correlate the mechanical behavior of beam-type specimens produced by SLS with build orientation angle used as a process parameter, also attempting to demonstrate how this parameter affects the accuracy of the Empirical Similitude Method (ESM). ESM presents itself as a valuable tool when creating scale models with SLS, specifically in the framework of evolutionary product design. More specifically, the Young modulus variation of test specimens of well-known dimensions and material (DuraformTM PA2 ), will be characterized by loading them within the elastic range. The resulting elastic deformations will be measured using the technique of Electronic Speckle Pattern Interferometry (ESPI) for small deformations in an out-of-plane configuration, contrasting these results with the elastic theory of deformations. As a main result, it was found that there exists a linear correlation between the build angle and the elastic modulus of the parts. Secondly, it was demonstrated empirically that the ESM predicts better the mechanical response of the part than TSM. Moreover, a 30% error reduction can be achieved within the ESM when using the build orientation angle as a process parameter.Mechanical Engineerin

Hubble Advanced Camera for Surveys Observations of the z=6.42 Quasar SDSS 1148+5251: A Leak in the Gunn-Peterson Trough

The Hubble Advanced Camera for Surveys has been used to obtain a narrow-band image of the weak emission peak seen at lambda=7205 A in the Gunn-Peterson Ly beta absorption trough of the highest redshift quasar, SDSS J1148+5251. The emission looks perfectly point-like; there is no evidence for the intervening galaxy that we previously suggested might be contaminating the quasar spectrum. We derive a more accurate astrometric position for the quasar in the two filters and see no indication of gravitational lensing. We conclude that the light in the Ly beta trough is leaking through two unusually transparent, overlapping windows in the IGM absorption, one in the Ly beta forest at z ~ 6 and one in the Ly alpha forest at z ~ 5. If there are significant optical depth variations on velocity scales small compared with our spectral resolution (~150 km/s), the Ly alpha trough becomes more transparent for a given Ly beta optical depth. Such variations can only strengthen our conclusion that the fraction of neutral hydrogen in the IGM increases dramatically at z>6. We argue that the transmission in the Ly beta trough is not only a more sensitive measure of the neutral fraction than is Ly alpha, it also provides a less biased estimator of the neutral hydrogen fraction than does the Ly alpha transmission.Comment: Submitted to the Astronomical Journa

Probing the Ionization State of the Universe at z>6

We present high signal-to-noise ratio Keck ESI spectra of the two quasars known to have Gunn-Peterson absorption troughs, SDSS J1030+0524 (z=6.28) and SDSS J1148+5251 (z=6.37). The Ly alpha and Ly beta troughs for SDSS J1030+0524 are very black and show no evidence for any emission over a redshift interval of ~0.2 starting at z=6. On the other hand, SDSS J1148+5251 shows a number of emission peaks in the Ly beta Gunn-Peterson trough along with a single weak peak in the Ly alpha trough. The Ly alpha emission has corresponding Ly beta emission, suggesting that it is indeed a region of lower optical depth in the intergalactic medium at z=6.08. The stronger Ly beta peaks in the spectrum of SDSS J1148+5251 could conceivably also be the result of "leaks" in the IGM, but we suggest that they are instead Ly alpha emission from an intervening galaxy at z=4.9. This hypothesis gains credence from a strong complex of C IV absorption at the same redshift and from the detection of continuum emission in the Ly alpha trough at the expected brightness. If this proposal is correct, the quasar light has probably been magnified through gravitational lensing by the intervening galaxy. The Stromgren sphere observed in the absorption spectrum of SDSS J1148+5251 is significantly smaller than expected based on its brightness, which is consistent with the hypothesis that the quasar is lensed. If our argument for lensing is correct, the optical depths derived from the troughs of SDSS J1148+5251 are only lower limits (albeit still quite strong, with tau(LyA)>16 inferred from the Ly beta trough.) The Ly beta absorption trough of SDSS J1030+0524 gives the single best measurement of the IGM transmission at z>6, with an inferred optical depth tau(LyA)>22.Comment: To appear in July 2003 AJ, 34 pages, 11 figures; minor changes/typos fixe

A Synopsis of the 1979 Amendments to the Federal Rules of Criminal Procedure

On April 30, 1979, the Supreme Court of the United States ordered the amendment of the Federal Rules of Criminal Procedure. The modifications ordered by the Court promise to bring about significant changes in the Rules, clarify ambiguous sections, eliminate confusion in application, and bring the Rules into conformity with recent case law. The process of amending the Federal Rules of Criminal Procedure began with the Advisory Committee on Criminal Rules of the Judicial Conference of the United States. The Advisory Committee was responsible for drafting the text of the proposed amendments and submitting explanatory comments. The proposed changes and additions were then sent to the Committee on Rules of Practice and Procedure of the Judicial Conference, which solicited comments from the bench and bar before submitting the amendments to the Judicial Conference. Subsequently, the Judicial Conference approved the proposed amendments and transmitted them to the Supreme Court. The Supreme Court then ordered these amendments to take effect on August 1, 1979. Upon receipt by Congress, the amendments to the Rules were referred to the House Subcommittee on Criminal Justice. Currently engaged in a major effort to overhaul the Federal Criminal Code, the Subcommittee was unable to study the proposed changes in detail. Consequently, the Subcommittee acted to delay the passage of those amendments that it regarded as particularly controversial or far-reaching. Accordingly, Congress delayed the effective dates of the modifications to rules 11(e)(6), 17(h), 32(f), and 44(c) and the enactment of rules 26.2 and 32.1 until a study of the changes could be made, or until December 1, 1980, whichever comes first. This comment will analyze the changes made in the Federal Rules, particularly noting the rationale for the various amendments and the intended effects of those changes