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     

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.     

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.     

The effect of polyamine homologation on the transport and cytotoxicity properties of polyamine-(DNA-intercalator) conjugates

An efficient five-step synthetic method was developed to access a homologous series of spermidine-acridine and spermidine-anthracene conjugates. The derivatives were comprised of a spermidine fragment covalently tethered at its N4 position to either an acridine or anthracene nucleus via an aliphatic chain (e.g., spermidine-[aliphatic tether]-acridine). The distance separating the spermidine and aromatic nucleus was altered by using different tethers comprised of four or five methylene units, respectively. These ligands (2-5) were shown to inhibit human DNA topoisomerase-II (TOPO-II) activity at 10 microM. Enzymatic activity was assessed as the ability to unknot (decatenate) and cleave kinetoplast DNA (kDNA). Polyamine conjugation did not disrupt the ability of the acridine-spermidine conjugates 2 and 3 to inhibit TOPO-II activity as compared with the 9-aminoacridine and 9-(N-butyl)aminoacridine controls (at 10 microM). In general, the acridine derivatives (2 and 3) showed higher TOPO-II inhibitory activity than their anthracene counterparts (4 and 5). However, this trend was reversed in a whole cell assay with L1210 (murine leukemia) cells, wherein the anthracene analogues were more potent than their acridine counterparts. In this regard the qualitative enzyme-based assay did not predict the trends in the corresponding IC(50) values. Within either series insertion of an additional methylene unit did not significantly alter activity. While the appended spermidine unit did not disrupt TOPO II inhibition by the tethered DNA intercalator, it did provide an alternative mode of entry into the cell as demonstrated by spermidine protection assays. These results were compared with a spermine-intercalator analogue. Of all the conjugates tested the N(4)-(4-(9-aminoacridinyl)butyl)spermine hexahydrochloride (conjugate 16)resulted in the highest degree of L1210 cell rescue upon cotreatment of the cells with exogenous spermidine. It was concluded that the monoalkylated spermine motif present in 16 holds promise as a better vector than its N4 monoalkylated spermidine counterpart.