Microhabitats of benthic foraminifera - a static concept or a dynamic adaption to optimize food aquisition?

In situ observations of microhabitat preferences of living benthic foraminifera are presented from sediments of the Norwegian-Greenland Sea, the upwelling area off northwestern Africa and the shallow-water Kiel Bight (Baltic Sea). Certain foraminiferal species (e.g.Cibicidoides wuellerstorfi andRupertina stabilis) can be regarded as strictly epibenthic species, colonizing elevated habitats that are strongly affected by bottom water hydrodynamics. Large epibenthic foraminifera (e.g.Rhabdammina abyssorum andHyperammina crassatina) colonize the sediment surface in areas where strong bottom currents occur and might have by virtue of their own size an impact on the small-scale circulation patterns of the bottom water. Motile species changing from epifaunal to infaunal habitats (e.g.Pyrgo rotalaria, Melonis barleeanum, Elphidium excavatum clavatum, Elphidium incertum, Ammotium cassis andSphaeroidina bulloides) are regarded here as highly adaptable to changes in food availability and/or changing environmental conditions. This flexible behaviour is regarded as a dynamic adaptation to optimize food acquisition, rather than a static concept leading to habitat classification of these ubiquitous rhizopods

Reverse accumulation and accurate rounding error estimates for taylor series coefficient

Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924~db=all Copyright Taylor and Francis/ Informa.We begin by extending the technique of reverse accumulation so as to obtain gradients of univariate Taylor series coefficients. This is done by re-interpreting the same formulae used to reverse accumulategradients in the conventional (scalar) case. Thus a carefully written implementation of conventional reverse accumulation can be extended to the Taylor series valued case by (further) overloading of the appropriate operators. Next, we show how to use this extended reverse accumulation technique so as to construct accurate (i.e. rigorous and sharp) error bounds for the numerical values of the Taylor series coefficients of the target function, again by re-interpreting the corresponding conventional (scalar) formulae. This extension can also be implemented simply by re-engineering existing code. The two techniques (reverse accumulation of gradients and accurate error estimates) each require only a small multiple of the processing time required to compute the underlying Taylor series coefficients. Space "requirements are comparable to those for conventional (scalar) reverse accumulation, and can be simply managed. We concluded with a discussion of possible implementation strategies and the implications for the re-use of code.Peer reviewe

Mathematica Connectivity to Interval Libraries filib++ and C-XSC

Abstract. Building interval software interoperability can be a good solution when re-using high-quality legacy code or when accessing functionalities unavailable natively in one of the software packages. In this work we present the integration of programs based on the interval libraries filib++ and C-XSC into Mathematica via MathLink communication protocol. On some small easily readable programs we demonstrate: i) some details of MathLink technology, ii) the transparency of numerical data communication without any conversion, iii) the advantage of symbolic manipulation interfaces — the access to the external compiled language functionality from within Mathematica is often even more convenient than from its own native environment

High-Order Stiff ODE Solvers via Automatic Differentiation and Rational Prediction

For solving potentially stiff initial value problems in ordinary differential equations numerically, we examine a class of high order methods that was last considered by Wanner in the sixties. These high order schemes may be viewed as implicit Taylor series methods based on Hermite quadratures. On linear problems the methods are equivalent to implicit Runge Kutta methods of the Legendre, Radau and Lobatto type and have therefore the same A- or L- stability properties. In contrast to earlier implementations we use improved automatic differentiation techniques for the calculation of Taylor coefficients and their Jacobian. To realize large steps on stiff problems we develop a new rational predictor that usually requires only a single correction by Newton's method to achieve solution accuracy at the discretization error level. Matrix sparsity is automatically detected and partly utilized, but other structural properties remain to be exploited. 1 Introduction The design and implementation ..

On implicit Taylor series methods for stiff ODEs

Several versions of implicit Taylor series methods (ITSM) are presented and evaluated. Criteria for the approximate solution of ODEs via ITSM are given. Some ideas, motivations, and remarks on the inclusion of the solution of stiff ODEs are outlined. 25 refs., 3 figs

Rationale for guaranteed ODE defect control

We introduce a modification of existing algorithms that allows easier analysis of numerical solutions of ordinary differential equations. We relax the requirement that the specified problem solved, and instead solve a nearby'' problem exactly, in Wilkinson's tradition of backward error analysis. The precise meaning of nearby'' is left to the user. This inexpensive algorithm sublimates the well-known difficulties associated with the propagation of accumulated error and avoids the difficulty of exponential growth of inclusion widths associated with internal techniques. No claim is made for the accuracy with which the specified problem is solved. It is shown that often no such claim is necessary. 14 refs., 4 figs

Operator overloading as an enabling technology for automatic differentiation

We present an example of the science that is enabled by object-oriented programming techniques. Scientific computation often needs derivatives for solving nonlinear systems such as those arising in many PDE algorithms, optimization, parameter identification, stiff ordinary differential equations, or sensitivity analysis. Automatic differentiation computes derivatives accurately and efficiently by applying the chain rule to each arithmetic operation or elementary function. Operator overloading enables the techniques of either the forward or the reverse mode of automatic differentiation to be applied to real-world scientific problems. We illustrate automatic differentiation with an example drawn from a model of unsaturated flow in a porous medium. The problem arises from planning for the long-term storage of radioactive waste

Multistep Filtering Operators for Ordinary Differential Equations

Interval methods for ordinary differential equations (ODEs) provide guaranteed enclosures of the solutions and numerical proofs of existence and unicity of the solution. Unfortunately, they may result in large over-approximations of the solution because of the loss of precision in interval computations and the wrapping effect. The main open issue in this area is to find tighter enclosures of the solution, while not sacrificing efficiency too much. This paper takes a constraint satisfaction approach to this problem, whose basic idea is to iterate a forward step to produce an initial enclosure with a pruning step that tightens it. The paper focuses on the pruning step and proposes novel multistep ltering operators for ODEs. These operators are based on interval extensions of amultistep solution that are obtained by using (Lagrange and Hermite) interpolation polynomials and their error terms. The paper also shows how traditional techniques (such as mean-value forms and coordinate transformations) can be adapted to this new context. Preliminary experimental results illustrate the potential of the approach, especially on stiff problems, well-known to be very difficult to solve