On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

On the theory of self-similar parabolic optical pulses

Self-similar optical pulses (or “similaritons”) of parabolic intensity profile can be found as asymptotic solutions of the nonlinear Schr¨odinger equation in a gain medium such as a fiber amplifier or laser resonator. These solutions represent a wide-ranging significance example of dissipative nonlinear structures in optics. Here, we address some issues related to the formation and evolution of parabolic pulses in a fiber gain medium by means of semi-analytic approaches. In particular, the effect of the third-order dispersion on the structure of the asymptotic solution is examined. Our analysis is based on the resolution of ordinary differential equations, which enable us to describe the main properties of the pulse propagation and structural characteristics observable through direct numerical simulations of the basic partial differential equation model with sufficient accuracy.

Attitudes to language in literary sources:beyond post-colonialism in nigerian literature

All societies display attitudes to (varieties of) languages that tell us about the relative status of the groups that are associated to them. One method to document these is the systematic study of public discourses, including literary production. How (varieties of) languages are used, mentioned and characterised in a literary work tells us about their social status, and any change in this status should therefore be followed by changes in judgements on languages. This is demonstrated by the present paper with reference to the language attitudes in Nigeria, on the basis of two iconic Nigerian novels 2004 Purple Hibiscus and in 1958 classic postcolonial Things Fall Apart, separated by nearly fifty years. Ibo as well as Pidgin, Nigerian and European Englishes are presented in Purple Hibiscus in nuanced complementary configurations. A strong axiological polarisation is by contrast offered in Things Fall Apart between Ibo speakers and Ibo interpreters who are presented as cruel and ridiculous traitors siding with the English colonising power whose language, curiously, is not commented upon. Showing how a replicable method applied to language judgements can document social organisation and change, these results validate the view that the Nigerian society and culture has moved beyond the historically situated postcolonialist movement to embrace a globalised paradigm. © 2010 Taylor & Francis.

A comparative and longitudinal analysis of the evolving relationship between the environment and the strategy, structure and performance of selected organisations in the British carpet industry 1959-1986:a firms in sector perspective of organisational adaptation

Orthodox contingency theory links effective organisational performance to compatible relationships between the environment and organisation strategy and structure and assumes that organisations have the capacity to adapt as the environment changes. Recent contributions to the literature on organisation theory claim that the key to effective performance is effective adaptation which in turn requires the simultaneous reconciliation of efficiency and innovation which is afforded by an unique environment-organisation configuration. The literature on organisation theory recognises the continuing confusion caused by the fragmented and often conflicting results from cross-sectional studies. Although the case is made for longitudinal studies which comprehensively describe the evolving relationship between the environment and the organisation there is little to suggest how such studies should be executed in practice. Typically the choice is between the approaches of the historicised case study and statistical analysis of large populations which examine the relationship between environment and organisation strategy and/or structure and ignore the product-process relationship. This study combines the historicised case study and the multi-variable and ordinal scale approach of statistical analysis to construct an analytical framework which tracks and exposes the environment-organisation-performance relationship over time. The framework examines changes in the environment, strategy and structure and uniquely includes an assessment of the organisation's product-process relationship and its contribution to organisational efficiency and innovation. The analytical framework is applied to examine the evolving environment-organisation relationship of two organisations in the same industry over the same twenty-five year period to provide a sector perspective of organisational adaptation. The findings demonstrate the significance of the environment-organisation configuration to the scope and frequency of adaptation and suggest that the level of sector homogeneity may be linked to the level of product-process standardisation.

Bernstein's theory of pedagogic discourse: linguistics, educational policy and practice in the UK English/literacy classroom

In “The English Patient: English Grammar and teaching in the Twentieth Century”, Hudson and Walmsley (2005) contens that the decline of grammar in schools was linked to a similar decline in English universities, where no serious research or teaching on English grammar took place. This article argues that such a decline was due not only to a lack of research, but also because it suited educational policies of the time. It applies Bernstein’s theory of pedagogic discourse (1990 & 1996) to the case study of the debate surrounding the introduction of a national curriculum in English in England in the late 1980s and the National Literacy Strategy in the 1990s, to demonstrate the links between academic theory and educational policy.

The theory of on-line learning: a statistical physics approach

In this paper we review recent theoretical approaches for analysing the dynamics of on-line learning in multilayer neural networks using methods adopted from statistical physics. The analysis is based on monitoring a set of macroscopic variables from which the generalisation error can be calculated. A closed set of dynamical equations for the macroscopic variables is derived analytically and solved numerically. The theoretical framework is then employed for defining optimal learning parameters and for analysing the incorporation of second order information into the learning process using natural gradient descent and matrix-momentum based methods. We will also briefly explain an extension of the original framework for analysing the case where training examples are sampled with repetition.

Magnetization enumerator for LDPC codes - a statistical physics approach

We propose a method based on the magnetization enumerator to determine the critical noise level for Gallager type low density parity check error correcting codes (LDPC). Our method provides an appealingly simple interpretation to the relation between different decoding schemes, and provides more optimistic critical noise levels than those reported in the information theory literature.

Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

Statistical physics of error-correcting codes

In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

Are there theory of mind regions in the brain? A review of the neuroimaging literature

There have been many functional imaging studies of the brain basis of theory of mind (ToM) skills, but the findings are heterogeneous and implicate anatomical regions as far apart as orbitofrontal cortex and the inferior parietal lobe. The functional imaging studies are reviewed to determine whether the diverse findings are due to methodological factors. The studies are considered according to the paradigm employed (e.g., stories vs. cartoons and explicit vs. implicit ToM instructions), the mental state(s) investigated, and the language demands of the tasks. Methodological variability does not seem to account for the variation in findings, although this conclusion may partly reflect the relatively small number of studies. Alternatively, several distinct brain regions may be activated during ToM reasoning, forming an integrated functional "network." The imaging findings suggest that there are several "core" regions in the network-including parts of the prefrontal cortex and superior temporal sulcus-while several more "peripheral" regions may contribute to ToM reasoning in a manner contingent on relatively minor aspects of the ToM task. © 2008 Wiley-Liss, Inc.