Stock market crashes are outliers

We call attention against what seems to be a widely held misconception according to which large crashes are the largest events of distributions of price variations with fat tails. We demonstrate on the Dow Jones Industrial Average that with high probability the three largest crashes in this century are outliers. This result supports the suggestion that large crashes result from specific amplification processes that might lead to observable pre-cursory signatures. Received and Revised: 30 November 1997 / Accepted: 8 December 1997     

Non-deterministic programming

This paper presents some results of R. W. Floyd (1966). He proposes inclusion of additional features in present programming languages to be able to express in a convenient way algorithms based on the technique of backtrack described by Golomb and Baumert (1965). Floyd proposes a way of implementation. Here we suggest an alternative method and present results obtained from an experimental implementation.     

Enzymatic degradation of model cellulose films

Enzymatic degradation of model cellulose films prepared by a spin-coating technique was investigated by ellipsometry. The cellulose films were prior to degradation characterized by ellipsometry, contact angle measurements, ESCA (electron spectroscopy for chemical analysis) and AFM (atomic force microscopy). At enzyme addition to preformed cellulose films an initial adsorption was observed, which was followed by a total interfacial mass decrease due to enzymatic degradation of the cellulose films. The degradation rate was found to be constant during an extended time of hours, whereafter the degradation leveled off. In parallel to the decreased interfacial mass, the cellulose degradation resulted in a thinner and more dilute interfacial film. At long degradation times, however, there was an expansion of the cellulose film. The enzyme concentration affected the degradation rate significantly, with a faster degradation at a higher enzyme concentration. The effects of pH, temperature, ionic strength and stirring rate in the cuvette were also investigated.     

Pointwise convergence in probability of general smoothing splines

Establishing the convergence of splines can be cast as a variational problem which is amenable to a \(\Gamma \)-convergence approach. We consider the case in which the regularization coefficient scales with the number of observations, n, as \(\lambda _n=n^{-p}\). Using standard theorems from the \(\Gamma \)-convergence literature, we prove that the general spline model is consistent in that estimators converge in a sense slightly weaker than weak convergence in probability for \(p\le \frac{1}{2}\). Without further assumptions, we show this rate is sharp. This differs from rates for strong convergence using Hilbert scales where one can often choose \(p>\frac{1}{2}\).     

Natural dualities for three classes of relational structures

Motivated by the work of Hofmann [14] and Davey [7] on dualities for structures, we will construct natural dualities for the classes of quasi-ordered sets, equivalence-relationed sets, and reflexive (undirected) graphs. We describe the dual structures by giving finite sets of quasi-equations that axiomatise the dual categories. We also show that there is a natural connection between the duality we construct for finite quasi-ordered sets and Birkhoff’s representation theorem for finite ordered sets [2], and between the dualities constructed for quasi-ordered sets and equivalence-relationed sets.     

Modellrechnungen zur Isotopentrennung durch Multiphotonen-Photodissoziation von Molekülen

Für stoßfreie SF₆-Moleküle werden Mulltiphotonen-Photofragmentierungswahrscheinlichkeiten im intensiven IR-LASER-Feld berechnet einschließlich der Isotopenselektivität derartiger Prozesse in Abhängigkeit von der eingestrahlten LASER-Linie, der Leistungsdichte, dem Impulsprofil und der Temperatur. Über ein quantenmechanisches Modell werden die Rotationsschtwingungsniveaus des SF₆-Moleküls, die Verstimmung zwischen LASER- und Molekülschwin-gungsfrequenz und die intramolekulare Schwingungsrelaxation berücksichtigt.     

Reviews

Ion Implantation, Proceedings from the European Conference on Ion Implanatation, Reading, September 7–9 1970 Peter Peregrinus Limited, Southgate House, Stevenage Herts, England. England 1970, 241 pages. Price: $6.00

Lectures in Theoretical Physics Volume XI-C: Atomic Collision Processes Editors: S. Geltman, K. T. Mahanthappa and W. E. Brittin. Gordon and Breach 1969, pp xiii + 337.