Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

TNF-α influences the lateral dynamics of TNF receptor I in living cells

In mammalian cells, inflammation is mainly mediated by the binding of tumor necrosis factor alpha to tumor necrosis factor receptor 1. In this study, we investigated lateral dynamics of TNF-R1 before and after ligand binding using high-density single-particle tracking in combination with photoactivated localization microscopy. Our single-molecule data indicates the presence of tumor necrosis factor receptor 1 with different mobilities in the plasma membrane, suggesting different molecular organizations. Cholesterol depletion led to a decrease of slow receptor species and a strong increase in the average diffusion coefficient. Moreover, as a consequence of tumor necrosis factor-alpha treatment, the mean diffusion coefficient moderately increased while its distribution narrowed. Based on our observation, we propose a refined mechanism on the structural arrangement and activation of tumor necrosis factor receptor 1 in the plasma membrane.

Further considerations of cosmic ray modulation of infra-red radiation in the atmosphere

Understanding effects of ionisation in the lower atmosphere is a new interdisciplinary area, crossing the traditionally distinct scientific boundaries between astro-particle and atmospheric physics and also requiring understanding of both heliospheric and magnetospheric influences on cosmic rays. Following the paper of Erlykin et al. (2014) we develop further the interpretation of our observed changes in long-wave (LW) radiation, Aplin and Lockwood (2013) by taking account of both cosmic ray ionisation yields and atmospheric radiative transfer. To demonstrate this, we show that the thermal structure of the whole atmosphere needs to be considered along with the vertical profile of ionisation. Allowing for, in particular, ionisation by all components of a cosmic ray shower and not just by the muons, reveals that the effect we have detected is certainly not inconsistent with laboratory observations of the LW absorption cross section. The analysis presented here, although very different from that of Erlykin et al., does come to the same conclusion that the events detected by AL were not caused by individual cosmic ray primaries – not because it is impossible on energetic grounds, but because events of the required energy are too infrequent for the 12 h_1 rate at which they were seen by the AL experiment. The present paper numerically models the effect of three different scenario changes to the primary GCR spectrum which all reproduce the required magnitude of the effect observed by AL. However, they cannot solely explain the observed delay in the peak effect which, if confirmed, would appear to open up a whole new and interesting area in the study of water oligomers and their effects on LW radiation. We argue that a technical artefact in the AL experiment is highly unlikely and that our initial observations merit both a wide-ranging follow-up experiment and more rigorous, self-consistent, three-dimensional radiative transfer modelling

Development and validation of the Morphing Fear Questionnaire (MFQ)

Morphing fears (also called transformation obsessions) involve concerns that a person may become contaminated by and acquire undesirable characteristics of others. These symptoms are found in patients with OCD and are thought to be related to mental contamination. Given the high levels of distress and interference morphing fears can cause, a reliable and valid assessment measure is needed. This article describes the development and evaluation of the Morphing Fear Questionnaire (MFQ), a 13-item measure designed to assess for the presence and severity of morphing fears. A sample of 900 participants took part in the research. Of these, 140 reported having a current diagnosis of OCD (SR-OCD) and 760 reported never having had OCD (N-OCD; of whom 24 reported a diagnosis of an anxiety disorder and 23 reported a diagnosis of depression). Factor structure, reliability, and construct and criterion related validity were investigated. Exploratory and confirmatory factor analyses supported a one-factor structure replicable across the N-OCD and SR-OCD group. The MFQ was found to have high internal consistency and good temporal stability, and showed significantly greater associations with convergent measures (assessing obsessive-compulsive symptoms, mental contamination, thought-action fusion and magical thinking) than with divergent measures (assessing depression and anxiety). Moreover, the MFQ successfully discriminated between the SR-OCD sample and the N-OCD group, anxiety disorder sample, and depression sample. These findings suggest that the MFQ has sound psychometric properties and that it can be used to assess morphing fear. Clinical implications are discussed.

Generic intertextuality in online social activism: the case of the It Gets Better project

The It Gets Better project has been held up as a model of successful social media activism. This article explores how narrators of It Gets Better videos make use of generic intertextuality, strategically combining the canonical narrative genres of the exemplum, the testimony, and the confession in a way that allows them to claim ‘textual authority’ and to make available multiple moral positions for themselves and their listeners. This strategy is further facilitated by the ambiguous participation frameworks associated with digital media, which make it possible for storytellers to tell different kinds of stories to different kinds of listeners at the same time, to simultaneously comfort the victims of anti-gay violence, confront its perpetrators, and elicit sympathy from ‘onlookers’. This analysis highlights the potential of new practices of online storytelling for social activism, and challenges notions that new media are contributing to the demise of common narrative traditions.

ENSO related variation of equatorial MRG and Rossby waves and forcing from higher latitudes

The contrasting behaviour of westward-moving mixed Rossby-gravity (WMRG) and the first Rossby (R1) waves in El Niño (EN) and La Niña (LN) seasons is documented with a focus on the Northern Hemisphere winter. The eastward-moving variance in the upper troposphere is dominated by WMRG and R1 structures that appear to be Doppler-shifted by the flow and are referred to as WMRG-E and R1-E. In the East Pacific and Atlantic the years with stronger equatorial westerly winds have the stronger WMRG and WMRG- E. In the East Pacific, R1 is also a maximum in LN. However, R1-E exhibits an eastward-shift between LN and EN. The changes with ENSO phase provide a test-bed for the understanding of these waves. In the East Pacific and Atlantic, the stronger WMRG-E and WMRG with stronger westerlies are in accord with the dispersion relation with simple Doppler-shifting by the zonal flow. The possible existence of free waves can also explain stronger R1 in EN in the Eastern Hemisphere. 1-D free wave propagation theory based on wave activity conservation is also important for R1. However, this theory is unable to explain the amplitude maxima for other waves observed in the strong equatorial westerly regions in the Western Hemisphere, and certainly not their ENSO-related variation. The forcing of equatorial waves by higher latitude wave activity and its variation with ENSO phase is therefore examined. Propagation of extratropical eastward-moving Rossby wave activity through the westerly ducts into the equatorial region where it triggers WMRG-E is favoured in the stronger westerlies, in LN in the East Pacific and EN in the Atlantic. It is also found that WMRG is forced by Southern Hemisphere westward-moving wavetrains arching into the equatorial region where they are reflected. The most significant mechanism for both R1 and R1-E appear to be lateral forcing by subtropical wavetrains.