Direct one-index transformations in multiconfiguration response calculations

The evaluation of gradient vectors of a general operator with one-index, double-one-index, or higher-order one-index transformed integrals is a key operation in multiconfiguration response theory calculations. We describe an integral-driven direct algorithm that carries out this operation efficiently without pretransforming the integrals. The use of this algorithm leads to a considerable reduction in disk space and timing. © 1994 by John Wiley & Sons, Inc.     

Occupational and environmental laboratory medicine: A network of EQAS organisers

Most people in any community come into contact with chemicals that are potentially harmful to their health. Some elements are essential to health and inadequate amounts in food may also lead to ill health. Measurement of chemicals in blood, urine or other specimens is a fundamental feature of studies undertaken in the field of Occupational and Environmental Laboratory Medicine (OELM). Results are used to assess the risk for either overexposure or deficiency of essential nutrients. External Quality Assessment Schemes (EQAS) aid laboratories to achieve accurate and consistent data and 11 organisers of EQAS in Europe and North America are working to improve the effectiveness of their activities.The aims of the Network of EQAS Organisers in OELM are to stimulate improvements in analytical results, establish equivalence of assessment among Schemes, collaborate to enhance the practice of EQA including whenever possible to warrant traceability of EQAS to primary standards.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia.     

Tracking individual fish from a moving platform using a split-beam transducer

Tracking of individual fish targets using a split-beam echosounder is a common method for investigating fish behavior. When mounted on a floating platform like a ship or a buoy, the transducer movement often complicates the process. This paper presents a framework for tracking single targets from such a platform. A filter based on the correlated fish movements between pings is developed to estimate the platform movement, and an extended Kalman filter is used to combine the split-beam measurements and the platform-position estimates. Different methods for gating and data association are implemented and tested with respect to data-association errors, using manually tracked data from a free-floating buoy as a reference. The data association was improved by utilizing the estimated velocity for each track to predict the location of the next observation. The data association was more robust when estimates of platform tilt/roll were used. Other techniques to estimate position and velocity, like linear regression and smoothing splines, were implemented and tested on a simulated data set. The platform-state estimation improved the estimates for methods like the Kalman filter and a smoothing spline with cross validation, but not for robust methods like linear regression and smoothing spline with a fixed degree of smoothing.     

Symmetries on random arrays and set-indexed processes

A processX on the setÑ of all finite subsetsJ ofN is said to be spreadable, if for all subsequencesp=(p ₁,p ₂,...) ofN, wherepJ={p _j ;jJ}. Spreadable processes are characterized in this paper by a representation formula, similar to those obtained by Aldous and Hoover for exchangeable arrays of r.v.'s. Our representation is equivalent to the statement that a process onÑ is spreadable, iff it can be extended to an exchangeable process indexed by all finite sequences of distinct elements fromN. The latter result may be regarded as a multivariate extension of a theorem by Ryll-Nardzewski, stating that, for infinite sequences of r.v.'s, the notions of exchangeability and spreadability are equivalent.     

A Favard theorem for orthogonal rational functions on the unit circle

We consider forn=0, 1,... the nested spaces _n of rational functions of degreen at most with given poles . Given a finite measure supported on the unit circle, we associate with it a nested orthogonal basis of rational functions ₀,..., _n for _n ,n=0, 1,.... These _n satisfy a recurrence relation that generalizes the recurrence for Szeg polynomials.In this paper we shall prove a Favard type theorem which says that if one has a sequence of rational functions _{n n} which are generated by such a recurrence, then there will be a measure supported on the unit circle to which they are orthogonal. We shall give a sufficient condition for the uniqueness of this measure.     

Discrete-continuous reaction-diffusion model with mobile point-like sources and sinks

The European Physical Journal E - We study rotating stratified turbulence (RST) making use of numerical data stemming from a large parametric study varying the Reynolds, Froude and Rossby numbers,...     

Phase Spaces and Deformation Theory

In the papers (Laudal in Contemporary Mathematics, vol. 391, [2005]; Geometry of time-spaces, Report No. 03, [2006/2007]), we introduced the notion of (non-commutative) phase algebras (spaces) Ph ⁿ (A), n=0,1,…,∞ associated to any associative algebra A (space), defined over a field k. The purpose of this paper is to study this construction in some more detail. This seems to give us a possible framework for the study of non-commutative partial differential equations. We refer to the paper (Laudal in Phase spaces and deformation theory, Report No. 09, [2006/2007]), for the applications to non-commutative deformation theory, Massey products and for the construction of the versal family of families of modules. See also (Laudal in Homology, Homotopy, Appl. 4:357–396, [2002]; Proceedings of NATO Advanced Research Workshop, Computational Commutative and Non-Commutative Algebraic Geometry, [2004]).      

Stationary and invariant densities and disintegration kernels

Let \(G\) be a locally compact topological group, acting measurably on some Borel spaces \(S\) and \(T\) , and consider some jointly stationary random measures \(\xi \) on \(S\times T\) and \(\eta \) on \(S\) such that \(\xi (\cdot \times T)\ll \eta \) a.s. Then there exists a stationary random kernel \(\zeta \) from \(S\) to \(T\) such that \(\xi =\eta \otimes \zeta \) a.s. This follows from the existence of an invariant kernel \(\varphi \) from \(S\times {\mathcal {M}}_{S\times T}\times {\mathcal {M}}_S\) to \(T\) such that \(\mu =\nu \otimes \varphi (\cdot ,\mu ,\nu )\) whenever \(\mu (\cdot \times T)\ll \nu \) . Also included are some related results on stationary integration, absolute continuity, and ergodic decomposition.