Truncated Newton method for sparse unconstrained optimization using automatic differentiation

When solving large complex optimization problems, the user is faced with three major problems. These are (i) the cost in human time in obtaining accurate expressions for the derivatives involved; (ii) the need to store second derivative information; and (iii), of lessening importance, the time taken to solve the problem on the computer. For many problems, a significant part of the latter can be attributed to solving Newton-like equations. In the algorithm described, the equations are solved using a conjugate direction method that only needs the Hessian at the current point when it is multiplied by a trial vector. In this paper, we present a method that finds this product using automatic differentiation while only requiring vector storage. The method takes advantage of any sparsity in the Hessian matrix and computes exact derivatives. It avoids the complexity of symbolic differentiation, the inaccuracy of numerical differentiation, the labor of finding analytic derivatives, and the need for matrix store. When far from a minimum, an accurate solution to the Newton equations is not justified, so an approximate solution is obtained by using a version of Dembo and Steihaug's truncated Newton algorithm (Ref. 1).This paper was presented at the SIAM National Meeting, Boston, Massachusetts, 1986.     

On practical metrology and chemical analysis: etalons and traceability systems

 National measurement systems are infrastructures to ensure, for each nation, a consistent and internationally recognised basis for measurement. Such complex systems have historical, technical, legal, organisational and institutional aspects to connect scientific metrology with practical measurements. Underlying any valid measurement is a chain of comparisons linking the measurement to an accepted standard. The ways the links are forged and the etalons (measurement standards) to which they connect are defining characteristics of all measurement systems. This is often referred to as traceability which aims at basing measurements in common measurement units – a key issue for the integration of quantitative chemical analysis with the evolving physical and engineering measurement systems. Adequate traceability and metrological control make possible new technical capabilities and new levels of quality assurance and confidence by users in the accuracy and integrity of quantitative analytical results. Traceability for chemical measurements is difficult to achieve and harder to demonstrate. The supply of appropriate etalons is critical to the development of metrology systems for chemical analysis. An approach is suggested that involves the development of networks of specialised reference laboratories able to make matrix-independent reference measurements on submitted samples, which may then be used as reference materials by an originating laboratory using its practical measurement procedures. Received: 31 July 1995 Accepted: 19 August 1995     

Corn stover fractions and bioenergy

Information is presented on structure, composition, and response to enzymes of corn stover related to barriers for bioconversion to ethanol. Aromatic compounds occurred in most tissue cell walls. Ferulic acid esterase treatment before cellulase treatment significantly improved dry weight loss and release of phenolic acids and sugars in most fractions over cellulase alone. Leaf fractions were considerably higher in dry weight loss and released sugars with esterase treatment, but stem pith cells gave up the most phenolic acids. Results help identify plant fractions more appropriate for coproducts and bioconversion and those more suitable as residues for soil erosion control.     

640 × 512 pixel narrow-band, four-band, and broad-band quantum well infrared photodetector focal plane arrays

A 9 μm cutoff 640 × 512 pixel hand-held quantum well infrared photodetector (QWIP) camera has been demonstrated with excellent imagery. A noise equivalent differential temperature (NEDT) of 10.6 mK is expected at a 65 K operating temperature with f/2 optics at a 300 K background. This focal plane array has shown background limited performance at a 72 K operating temperature with the same optics and background conditions. In this paper, we discuss the development of this very sensitive long-wavelength infrared camera based on a GaAs/AlGaAs QWIP focal plane array and its performance in quantum efficiency, NEDT, uniformity, and operability. In the second section of this paper, we discuss the first demonstration of a monolithic spatially separated four-band 640 × 512 pixel QWIP focal plane array and its performance. The four spectral bands cover 4–5.5, 8.5–10, 10–12, and 13.5–15 μm spectral regions with 640 × 128 pixels in each band. In the last section, we discuss the array performance of a 640 × 512 pixel broad-band (10–16 μm full-width at half-maximum) QWIP focal plane.     

The Post-Hopf-Bifurcation Response of a Loosely Supported Cylinder in an Array Subjected to Cross-Flow. Part II: Theoretical Model and Comparison with Experiments

A nonlinear quasi-steady model for the analysis of the dynamics of a loosely supported cylinder, which takes into account position-dependent nonlinear fluid forces as well as nonuniform flow, is formulated. The model includes an approximation for the equivalent viscous damping associated with energy dissipation on impact at the support. The nonlinear model shows reasonably good agreement with experiments, in predicting the observed bifurcations in the cylinder response. Comparison criteria include the standard orbital plots, time traces and response spectra. A borderline chaotic response is found to be predominant over the test velocity range. In this chaotic regime, the theoretical results were verified via attractor fractal-dimension calculations and saddle orbit distributions; theoretical values of these invariant measures compare reasonably well with their experimental counterparts. Two mechanisms leading to chaos have been identified for this system. The first is a switching mechanism , at the onset of impacting. The second, and more prevalent, is the type I intermittency route to chaos.     

Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

Identification by high-performance liquid chromatography of tyrosine ammonia-lyase activity in purified fractions of Phaseolus vulgaris phenylalanine ammonia-lyase.

Activities of phenylalanine ammonia-lyase (PAL) and tyrosine ammonia-lyase (TAL) were assessed at each stage of a three-step purification of PAL. Assays were performed by high-performance liquid chromatographic (HPLC) separation and ultraviolet detection of reaction products. Use of HPLC permitted assay of low activities of PAL and TAL for periods up to approximately four and two days, respectively. HPLC also facilitated the accurate quantitation of the product of the TAL reaction, trans-p-coumaric acid, which was observed to isomerize readily under experimental conditions. PAL and TAL were associated throughout the purification procedure, with TAL activity at 0.6-1.3% of PAL activity. It was concluded that, contrary to previous reports, TAL and PAL activities are mediated by the same enzyme, or else by chromatographically very similar enzymes.     

Crystallization of Arthrobacter sp. strain 1C N-(1-D-carboxyethyl)-L-norvaline dehydrogenase and its complex with NAD+

The novel NAD+-linked opine dehydrogenase from a soil isolate Arthrobacter sp. strain 1C belongs to an enzyme superfamily whose members exhibit quite diverse substrate specificites. Crystals of this opine dehydrogenase, obtained in the presence or absence of co-factor and substrates, have been shown to diffract to beyond 1.8 ? resolution. X-ray precession photographs have established that the crystals belong to space group P21212, with cell parameters a = 104.9, b = 80.0, c = 45.5 ? and a single subunit in the asymmetric unit. The elucidation of the three-dimensional structure of this enzyme will provide a structural framework for this novel class of dehydrogenases to enable a comparison to be made with other enzyme families and also as the basis for mutagenesis experiments directed towards the production of natural and synthetic opine-type compounds containing two chiral centres.