Insights into multivariate calibration using errors-in-variables modeling

A {ital q}-vector of responses, y, is related to a {ital p}-vector of explanatory variables, x, through a causal linear model. In analytical chemistry, y and x might represent the spectrum and associated set of constituent concentrations of a multicomponent sample which are related through Beer`s law. The model parameters are estimated during a calibration process in which both x and y are available for a number of observations (samples/specimens) which are collectively referred to as the calibration set. For new observations, the fitted calibration model is then used as the basis for predicting the unknown values of the new x`s (concentrations) form the associated new y`s (spectra) in the prediction set. This prediction procedure can be viewed as parameter estimation in an errors-in-variables (EIV) framework. In addition to providing a basis for simultaneous inference about the new x`s, consideration of the EIV framework yields a number of insights relating to the design and execution of calibration studies. A particularly interesting result is that predictions of the new x`s for individual samples can be improved by using seemingly unrelated information contained in the y`s from the other members of the prediction set. Furthermore, motivated by this EIV analysis, this result can be extended beyond the causal modeling context to a broader range of applications of multivariate calibration which involve the use of principal components regression

Tunable Low Density Palladium Nanowire Foams

Nanostructured palladium foams offer exciting potential for applications in diverse fields such as catalyst, fuel cell, and particularly hydrogen storage technologies. We have fabricated palladium nanowire foams using a cross-linking and freeze-drying technique. These foams have a tunable density down to 0.1% of the bulk, and a surface area to volume ratio of up to 1,540,000:1. They exhibit highly attractive characteristics for hydrogen storage, in terms of loading capacity, rate of absorption and heat of absorption. The hydrogen absorption/desorption process is hysteretic in nature, accompanied by substantial lattice expansion/contraction as the foam converts between Pd and PdHx.Comment: 17 pages, 4 figure

Notes on Recent Cases

Notes on recent cases by Edward P. McGuire, Henry Hasley, Thomas V. Happer, W. F. Craig, John P. Bersheid, Marc Wonderlin, Herbert J. Nester

Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital-signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized even when the coupling between them is changing unpredictably.Comment: 24 pages, 13 figures. To appear in Phil. Trans. R. Soc. A (special theme issue to accompany 2009 International Workshop on Delayed Complex Systems

Spaceborne Processor Array

A Spaceborne Processor Array in Multifunctional Structure (SPAMS) can lower the total mass of the electronic and structural overhead of spacecraft, resulting in reduced launch costs, while increasing the science return through dynamic onboard computing. SPAMS integrates the multifunctional structure (MFS) and the Gilgamesh Memory, Intelligence, and Network Device (MIND) multi-core in-memory computer architecture into a single-system super-architecture. This transforms every inch of a spacecraft into a sharable, interconnected, smart computing element to increase computing performance while simultaneously reducing mass. The MIND in-memory architecture provides a foundation for high-performance, low-power, and fault-tolerant computing. The MIND chip has an internal structure that includes memory, processing, and communication functionality. The Gilgamesh is a scalable system comprising multiple MIND chips interconnected to operate as a single, tightly coupled, parallel computer. The array of MIND components shares a global, virtual name space for program variables and tasks that are allocated at run time to the distributed physical memory and processing resources. Individual processor- memory nodes can be activated or powered down at run time to provide active power management and to configure around faults. A SPAMS system is comprised of a distributed Gilgamesh array built into MFS, interfaces into instrument and communication subsystems, a mass storage interface, and a radiation-hardened flight computer

Implications of the ALEPH tau-Lepton Decay Data for Perturbative and Non-Perturbative QCD

We use ALEPH data on hadronic $\tau$ decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination $V-A$ receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of $V+A$ the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of $\alpha_s$. We also analyze the range of validity of the Operator Product Expansion (OPE). In the $V-A$ channel we find a dimension $d=6$ contribution which is comparable to the original SVZ estimate, but the instanton model provides a different non-singular term of the same magnitude. In the $V+A$ case both the OPE and the instanton model predict the same $d=4$ power correction induced by the gluon condensate, but it is masked by much larger perturbative contributions. We conclude that the range of validity of the OPE is limited to x\lsim0.3 fm, whereas the instanton model describes the data over the entire range.Comment: 4 pages, 6 figure

Superhumps in Cataclysmic Binaries. XXII. 1RXS J232953.9+062814

We report photometry of 1RXS J232953.9+062814, a recently discovered dwarf nova with a remarkably short 64.2-minute orbital period. In quiescence, the star's light curve is that of a double sinusoid, arising from the "ellipsoidal" distortion of the Roche-lobe-filling secondary. During superoutburst, common superhumps develop with a period 3-4% longer than P_orb. This indicates a mass ratio M_2/M_1=0.19+-0.02, a surprisingly large value in so compact a binary. This implies that the secondary star has a density 2-3 times higher than that of other short-period dwarf novae, suggesting a secondary enriched by H-burning prior to the common-envelope phase of evolution. We estimate i=50+-5 deg, M_1=0.63 (+0.12, -0.09) M_sol, M_2=0.12 (+0.03, -0.02) M_sol, R_2=0.121 (+0.010, -0.007) R_sol, and a distance to the binary of 180+-40 pc.Comment: PDF, 17 pages, 3 tables, 5 figures; accepted, in press, to appear June 2002, PASP; more info at http://cba.phys.columbia.edu

A Black Hole in the X-Ray Nova Velorum 1993

We have obtained 17 moderate-resolution (~2.5 A) optical spectra of the Galactic X-ray Nova Velorum 1993 in quiescence with the Keck-II telescope. The orbital period (P) is 0.285206 +/- 0.0000014 d, and the semiamplitude (K_2) is 475.4 +/- 5.9 km/s. Our derived mass function, f(M_1) = PK_2^3 /2 pi G = 3.17 +/- 0.12 M_sun, is close to the conventional absolute limiting mass for a neutron star (~ 3.0-3.2 M_sun) -- but if the orbital inclination i is less than 80 degrees (given the absences of eclipses), then M_1 is greater than 4.2-4.4 M_sun for nominal secondary-star masses of 0.5 M_sun (M0) to 0.65 M_sun (K6). The primary star is therefore almost certainly a black hole rather than a neutron star. The velocity curve of the primary from H-alpha emission has a semiamplitude (K_1) of 65.3 +/- 7.0 km/s, but with a phase offset by 237 degrees (rather than 180 degrees) from that of the secondary star. The nominal mass ratio q = M_2/M_1 = K_1/K_2 = 0.137 +/- 0.015, and hence for M_2 = 0.5-0.65 M_sun we derive M_1 = 3.64-4.74 M_sun. An adopted mass M_1 ~ 4.4 M_sun is significantly below the typical value of ~ 7 M_sun found for black holes in other low-mass X-ray binaries. Keck observations of MXB 1659-29 (V2134 Oph) in quiescence reveal a probable optical counterpart at R = 23.6 +/- 0.4 mag.Comment: 16 pages, 9 figures, added references, revised per. referee's comments Accepted for publication in August 1999 issue of PAS