Fast method to compute the scalar product of gradient and given vector

The paper deals with a special problem in Automatic Differentiation. Letf be a rational function ofn variables, let #(f) denote the number of operations to evaluatef(x), letg denote the gradient off. Many algorithms for minimizingf(x) require the scalar productg(u) ^tv. In the standard method for computingg(u) ^tv the amount of work grows withn·#(f). In this note a new method for computingg(u) ^tv is presented. The new method is considerably faster, its amount of work only grows with #(f).     

HOW EVOLUTIONARY IS SCHUMPETER'S THEORY OF ECONOMIC DEVELOPMENT?

The generic features of an evolutionary theory which are identified in the conceptional discussion of the present paper can be shown to be present already in Schumpeter's 1912 work, The Theory of Economic Development . None the less, it is argued that Schumpeter fell short of a level of generality by which he would have succeeded in providing a true foundation for evolutionary economics. The reason is his eagerness--very clearly visible in the "lost" seventh chapter--to align his theory with the economic reasoning of contemporary "pure" economic theory that was moulded in an equilibrium-oriented heuristic and the methodology of comparative statics. Schumpeter's conception--which, in opposing the idea of borrowing from Darwinian thought, he called "development"--is rather a special theory of the unsteady capitalist growth process passing through booms and crises. Throughout all of Schumpeter's writings the notion of development is therefore closely related to the business cycle phenomenon. The paper argues that this special framing implies not only some arbitrary hypotheses which are difficult to accept in an evolutionary interpretation, but also some limitations in his understanding of (what he refused to call) economic evolution, particularly with respect to its driving forces.     

Analysis and design of Hermite subdivision schemes

Published online: 14 May 2002     

The content of asbestos bodies in the bronchoalveolar fluid as a parameter of an increased pulmonary asbestos load

Pulmonary asbestos burdens are usually determined by quantitative pulmonary dust analysis. The aim of this study was to investigate the value of bronchoalveolar lavage (BAL) for this purpose. First, the upper limit of normal for asbestos bodies (AB) in BAL fluid was established using a reference group of 371 patients with no evidence of increased exposure to asbestos. 99% of these patients had less than 0.5 AB/ml. In order to see whether BAL fluid AB concentration reflected pulmonary tissue content, BAL fluid and lung tissue from a further 64 patients with diverse histories of asbestos exposure were investigated. There was a positive association between AB concentration in BAL fluid and lung tissue only for the overall group of 64 patients (r = 0.86; P < 0.001). Twelve of 13 patients with more than 1 AB/ml and ten patients with more than 5 AB/ml had more than 1000 AB/cm3 lung tissue, a value that is usually exceeded in asbestosis. When the upper concentration limit was set at 0.5 AB/ml for BAL fluid and 50 AB/cm3 for lung tissue, only two out of 64 patients had a false positive value (specificity 95%), but eleven patients had false negative results (sensitivity 58%). These investigations establish that concentrations of > or = 0.5 AB/ml are a reliable indicator of increased asbestos exposure and concentrations > 1 AB/ml are associated with a higher probability of having more than 1000 AB/cm3 lung tissue. However, exclusion of increased asbestos exposure is not possible on the basis of negative BAL findings, since the sensitivity of the method is too low.     

A numerical investigation on the geometry dependence of the crack growth resistance in CT specimens

The influence of the specimen thickness B and the ligament length b on the J _R -curves is numerically investigated for CT specimens. The thickness effect is taken into account with 2-D analyses by dividing a plain sided specimen into a plane stress part and a plane strain part. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement for crack growth initiation (CTOD_i) and the crack tip opening angle for stable crack growth (CTOA_C). It is shown that for the global behaviour of a plain sided specimen, the B/b ratio is essential. The difference between the geometry dependence of the initiation value of the J-integral and the geometry dependence of the slope of the J _R -curves is also shown.