Roman Unger

Language shift, bilingualism and the future of Britain's Celtic languages

‘Language shift’ is the process whereby members of a community in which more than one language is spoken abandon their original vernacular language in favour of another. The historical shifts to English by Celtic language speakers of Britain and Ireland are particularly well-studied examples for which good census data exist for the most recent 100–120 years in many areas where Celtic languages were once the prevailing vernaculars. We model the dynamics of language shift as a competition process in which the numbers of speakers of each language (both monolingual and bilingual) vary as a function both of internal recruitment (as the net outcome of birth, death, immigration and emigration rates of native speakers), and of gains and losses owing to language shift. We examine two models: a basic model in which bilingualism is simply the transitional state for households moving between alternative monolingual states, and a diglossia model in which there is an additional demand for the endangered language as the preferred medium of communication in some restricted sociolinguistic domain, superimposed on the basic shift dynamics. Fitting our models to census data, we successfully reproduce the demographic trajectories of both languages over the past century. We estimate the rates of recruitment of new Scottish Gaelic speakers that would be required each year (for instance, through school education) to counteract the ‘natural wastage’ as households with one or more Gaelic speakers fail to transmit the language to the next generation informally, for different rates of loss during informal intergenerational transmission.

A New Methodology for Modeling, Analysis, Synthesis, and Simulation of Time-Optimal Train Traffic in Large Networks

From a system-theoretic standpoint, a constrained state-space model for train traffic in a large railway network is developed. The novelty of the work is the transformation or rather reduction of the directed graph of the network to some parallel lists. Mathematization of this sophisticated problem is thus circumvented. All the aspects of a real network (such as that of the German rail) are completely captured by this model. Some degrees of freedom, as well as some robustness can be injected into the operation of the system. The problem of time-optimal train traffic in large networks is then defined and solved using the maximum principle. The solution is obtained by reducing the boundary value problem arising from the time-optimality criterion to an initial value problem for an ordinary differential equation. A taxonomy of all possible switching points of the control actions is presented. The proposed approach is expected to result in faster-than-real-time simulation of time-optimal traffic in large networks and, thus, facilitation of real-time control of the network by dispatchers. This expectation is quantitatively justified by analysis of simulation results of some small parts of the German rail network.

Time-Optimal Train Traffic in Large Networks Based on a New Model

Abstract From a system-theoretic standpoint, a constrained state-space model for train traffic in a railway network is developed. It is based on transforming the directed graph of the network to some parallel lists. All the aspects of a real network (such as that of the German Rail) are completely captured by this model. It is generic and can be used to establish an operating system for other large railway networks. By way of this model, some degrees of freedom as well as some robustness can be injected into the operation of the system. The problem of time-optimal train traffic in large networks is then defined and solved. The solution is obtained by reducing the boundary value problem arising from the time-optimality criterion to an initial value problem for an ordinary differential equation (ODE) whereby all the static switching points are computed offline.

Numerical Studies of Recovery Chances for a Simplified EIT Problem

This study investigates a simplified discretized EIT model with eight electrodes distributed equally spaced at the boundary of a disc covered with a small number of material ‘stripes’ of varying conductivity. The goal of this paper is to evaluate the chances of identifying the conductivity values of each stripe from rotating measurements of potential differences. This setting comes from an engineering background, where the used EIT model is exploited for the detection of conductivities in carbon nanotubes (CNT) and carbon nanofibers (CNF). Connections between electrical conductivity and mechanical strain have been of major interest within the engineering community and has motivated the investigation of such a ‘stripe’ structure. Up to five conductivity values can be recovered from noisy 8 × 8 data matrices in a stable manner by a least squares approach. Hence, this is a version of regularization by discretization and additional tools for stabilizing the recovery seem to be superfluous. To our astonishment, no local minima of the squared misfit functional were observed, which seems to indicate uniqueness of the recovery if the number of stripes is quite small.

Nonparametric Copula Density Estimation Using a Petrov–Galerkin Projection

Nonparametrical copula density estimation is a meaningful tool for analyzing the dependence structure of a random vector from given samples. Usually kernel estimators or penalized maximum likelihood estimators are considered. We propose solving the Volterra integral equation

Obstacle Description with Radial Basis Functions for Contact Problems in Elasticity

\begin{aligned} \int \limits _0^{u_1} \cdots \int \limits _0^{u_d} \mathrm{c}(s_1,\ldots , s_d) d s_1 \cdots d s_d = \mathrm{C}(u_1, \ldots , u_d) \end{aligned}

Unterraum-CG-Techniken zur Bearbeitung von Kontaktproblemen

to find the copula density \(\mathrm{c}(u_1, \ldots , u_d) = \frac{\partial ^d \mathrm{C}}{\partial u_1 \cdots \partial u_d}\) of the given copula \(\mathrm{C}\). In the statistical framework, the copula \(\mathrm{C}\) is not available and we replace it by the empirical copula of the pseudo samples, which converges to the unobservable copula \(\mathrm{C}\) for large samples. Hence, we can treat the copula density estimation from given samples as an inverse problem and consider the instability of the inverse operator, which has an important impact if the input data of the operator equation are noisy. The well-known curse of high dimensions usually results in huge nonsparse linear equations after discretizing the operator equation. We present a Petrov–Galerkin projection for the numerical computation of the linear integral equation. A special choice of test and ansatz functions leads to a very special structure of the linear equations, such that we are able to estimate the copula density also in higher dimensions.