Linguistic interfaces and language acquisition in childhood: introduction to the special issue

Much contemporary L1 acquisition theory and empirical research are guided by the hypothesis that acquisition delays in children are often related to the integration of information across grammatical and other cognitive modules, such as syntax and discourse-pragmatics (see e.g., Grinstead, 2010). This special issue brings together cutting edge research from all relevant paradigms addressing interface issues in child language acquisition and provides a platform for the study of the interaction between different levels of linguistic knowledge. In this introduction, we present the reader with the tools needed to best understand the contributions of the individual studies and what they bring to bear on larger theoretical questions as a collective.

Spectra of a class of non-self-adjoint matrices

We consider a new class of non-self-adjoint matrices that arise from an indefinite self- adjoint linear pencil of matrices, and obtain the spectral asymptotics of the spectra as the size of the matrices diverges to infinity. We prove that the spectrum is qualitatively different when a certain parameter c equals 0, and when it is non-zero, and that certain features of the spectrum depend on Diophantine properties of c.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

RMetS special interest group meeting: high resolution data assimilation

Data assimilation (DA) systems are evolving to meet the demands of convection-permitting models in the field of weather forecasting. On 19 April 2013 a special interest group meeting of the Royal Meteorological Society brought together UK researchers looking at different aspects of the data assimilation problem at high resolution, from theory to applications, and researchers creating our future high resolution observational networks. The meeting was chaired by Dr Sarah Dance of the University of Reading and Dr Cristina Charlton-Perez from the MetOffice@Reading. The purpose of the meeting was to help define the current state of high resolution data assimilation in the UK. The workshop assembled three main types of scientists: observational network specialists, operational numerical weather prediction researchers and those developing the fundamental mathematical theory behind data assimilation and the underlying models. These three working areas are intrinsically linked; therefore, a holistic view must be taken when discussing the potential to make advances in high resolution data assimilation.