Publications

Abstract

We introduce the Individual Differences in Language Skills (IDLaS-NL) web platform, which enables users to run studies on individual differences in Dutch language skills via the internet. IDLaS-NL consists of 35 behavioral tests, previously validated in participants aged between 18 and 30 years. The platform provides an intuitive graphical interface for users to select the tests they wish to include in their research, to divide these tests into different sessions and to determine their order. Moreover, for standardized administration the platform
provides an application (an emulated browser) wherein the tests are run. Results can be retrieved by mouse click in the graphical interface and are provided as CSV-file output via email. Similarly, the graphical interface enables researchers to modify and delete their study configurations. IDLaS-NL is intended for researchers, clinicians, educators and in general anyone conducting fundaental research into language and general cognitive skills; it is not intended for diagnostic purposes. All platform services are free of charge. Here, we provide a
description of its workings as well as instructions for using the platform. The IDLaS-NL platform can be accessed at www.mpi.nl/idlas-nl.

Abstract

This article addresses the problem of computing an upper bound of
the degree d of a polynomial solution P(x) of an algebraic differ-
ence equation of the form Gx)(P(x −τ1), . . . , P(x −τs) + G0(x) =

0 when such P(x) with the coefficients in a field K of character-
istic zero exists and where G is a non-linear s-variable polynomial
with coefficients in K[x] and G0 is a polynomial with coefficients
in K.
It will be shown that if G is a quadratic polynomial with constant
coefficients then one can construct a countable family of polynomi-
als fl(u0) such that if there exists a (minimal) index l0 with fl0(u0)
being a non-zero polynomial, then the degree d is one of its roots
or d ≤ l0, or d < deg(G0). Moreover, the existence of such l0 will
be proven for K being the field of real numbers. These results are
based on the properties of the modules generated by special fami-
lies of homogeneous symmetric polynomials.
A sufficient condition for the existence of a similar bound of the
degree of a polynomial solution for an algebraic difference equation
with G of arbitrary total degree and with variable coefficients will
be proven as well.

Abstract

For real-time and embedded systems, limiting the consumption of time and memory resources is often an important part of the requirements. Being able to predict bounds on the consumption of such resources during the development process of the code can be of great value. In this paper, we focus mainly on memory-related bounds. Recent research results have advanced the state of the art of resource consumption analysis. In this paper, we present a toolset that makes it possible to apply these research results in practice for (real-time) systems enabling JAVA developers to analyse symbolic loop bounds, symbolic bounds on heap size and both symbolic and numeric bounds on stack size. We describe which theoretical additions were needed in order to achieve this. We give an overview of the capabilities of the RESANA (Radboud University Nijmegen, The Netherlands) toolset that is the result of this effort. The toolset can not only perform generally applicable analyses, but it also contains a part of the analysis that is dedicated to the developers' (real-time) virtual machine, such that the results apply directly to the actual development environment that is used in practice

Abstract

Contrary to linear difference equations, there is no general theory of difference equations of the form G(P(x−τ1),…,P(x−τs))+G0(x)=0, with τi∈K, G(x1,…,xs)∈K[x1,…,xs] of total degree D⩾2 and G0(x)∈K[x], where K is a field of characteristic zero. This article is concerned with the following problem: given τi, G and G0, find an upper bound on the degree d of a polynomial solution P(x), if it exists. In the presented approach the problem is reduced to constructing a univariate polynomial for which d is a root. The authors formulate a sufficient condition under which such a polynomial exists. Using this condition, they give an effective bound on d, for instance, for all difference equations of the form G(P(x−a),P(x−a−1),P(x−a−2))+G0(x)=0 with quadratic G, and all difference equations of the form G(P(x),P(x−τ))+G0(x)=0 with G having an arbitrary degree.