Gene expression time delays & Turing pattern formation systems

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning

Schubert calculus of Richardson varieties stable under spherical Levi subgroups

We observe that the expansion in the basis of Schubert cycles for $H^*(G/B)$ of the class of a Richardson variety stable under a spherical Levi subgroup is described by a theorem of Brion. Using this observation, along with a combinatorial model of the poset of certain symmetric subgroup orbit closures, we give positive combinatorial descriptions of certain Schubert structure constants on the full flag variety in type $A$. Namely, we describe $c_{u,v}^w$ when $u$ and $v$ are inverse to Grassmannian permutations with unique descents at $p$ and $q$, respectively. We offer some conjectures for similar rules in types $B$ and $D$, associated to Richardson varieties stable under spherical Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as suggested by referees. Final version, to appear in Journal of Algebraic Combinatoric

On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

Streaming instability of slime mold amoebae: An analytical model

During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed

Detection, evaluation, and management of preoperative anaemia in the elective orthopaedic surgical patient: NATA guidelines

Previously undiagnosed anaemia is common in elective orthopaedic surgical patients and is associated with increased likelihood of blood transfusion and increased perioperative morbidity and mortality. A standardized approach for the detection, evaluation, and management of anaemia in this setting has been identified as an unmet medical need. A multidisciplinary panel of physicians was convened by the Network for Advancement of Transfusion Alternatives (NATA) with the aim of developing practice guidelines for the detection, evaluation, and management of preoperative anaemia in elective orthopaedic surgery. A systematic literature review and critical evaluation of the evidence was performed, and recommendations were formulated according to the method proposed by the Grades of Recommendation Assessment, Development and Evaluation (GRADE) Working Group. We recommend that elective orthopaedic surgical patients have a haemoglobin (Hb) level determination 28 days before the scheduled surgical procedure if possible (Grade 1C). We suggest that the patient's target Hb before elective surgery be within the normal range, according to the World Health Organization criteria (Grade 2C). We recommend further laboratory testing to evaluate anaemia for nutritional deficiencies, chronic renal insufficiency, and/or chronic inflammatory disease (Grade 1C). We recommend that nutritional deficiencies be treated (Grade 1C). We suggest that erythropoiesis-stimulating agents be used for anaemic patients in whom nutritional deficiencies have been ruled out, corrected, or both (Grade 2A). Anaemia should be viewed as a serious and treatable medical condition, rather than simply an abnormal laboratory value. Implementation of anaemia management in the elective orthopaedic surgery setting will improve patient outcome

Wainwright’s West Yorkshire: affect and landscape in the television drama of Sally Wainwright

Over the past two decades RED Production Company's key presence in British television drama has been grounded in its regional focus on the North of England. It shares this commitment with Sally Wainwright, whose work with and outside of RED is built around a strong affective engagement with its characters’ experiences. These stories offer intimate explorations of family dynamics and female relationships, situated within and interwoven with the spaces and places of West Yorkshire. From her adaptation of Wuthering Heights in Sparkhouse (BBC, 2002) to her 2016 Christmas biopic of the Brontë sisters To Walk Invisible (BBC, 2016), through Last Tango in Halifax (BBC, 2012–16) and Happy Valley (BBC, 2014–) these are distinctly regional narratives whose female-led familial melodrama, psychodrama and romance are embedded within and return to the landscapes of the region, spaces which blend the stolid and torrid. Wide and spectacular aerial shots follow cars that track through the green and brown expanses between the Harrogate and Halifax families of the elderly couple in Last Tango, the beauty of the Calder Valley pens in the stark bleakness that is foundational to Happy Valley, and the Brontë sisters stride across heathered hills and are silhouetted against grey skies in To Walk Invisible. This article explores the visual dynamics of Wainwright's work and her engagement with the landscapes of the region in both her writing and direction, evoking their numerous literary and cultural connotations in her interweaving of West Yorkshire's stark, dynamic beauty with her stories of intimate female affect

Strength in diversity: enhancing learning in vocationally-orientated, master's level courses

Postgraduate education in geography, especially at the Master’s level, is undergoing significant changes in the developed world. There is an expansion of vocationally-oriented degree programmes, increasing recruitment of international students, integration of work place skills, and the engagement of non-traditional postgraduate students as departments respond to policies for a more ‘inclusive’ higher education. This paper sets the context by outlining some programmatic changes in selected countries (Australia, the UK, and the USA). We briefly reflect on how postgraduate ‘bars’ or ‘levels’ are defined and explore in detail what ‘diversity’ or ‘heterogeneity’ means in these new postgraduate settings. The paper then explores some examples of practice drawn from our own experiences, whilst recognising that relevance will vary in other contexts. Finally we consider how diversity can be harnessed as a strength that has potential to enhance taught elements of contemporary postgraduate education in and beyond the discipline

Chemical Abundances of Planetary Nebulae in the Sagittarius Dwarf Elliptical Galaxy

Spectrophotometry and imaging of the two planetary nebulae He2-436 and Wray16-423, recently discovered to be in the Sagittarius dwarf elliptical galaxy, are presented. Wray16-423 is a high excitation planetary nebula (PN) with a hot central star. In contrast He2-436 is a high density PN with a cooler central star and evidence of local dust, the extinction exceeding that for Wray16-423 by E(B-V)=0.28. The extinction to Wray16-423, (E(B-V)=0.14), is consistent with the extinction to the Sagittarius (Sgr) Dwarf. Both PN show Wolf-Rayet features in their spectra, although the lines are weak in Wray16-423. Images in [O III] and H-alpha+[N II], although affected by poor seeing, yield a diameter of 1.2'' for Wray16-423 after deconvolution; He~2-436 was unresolved. He2-436 has a luminosity about twice that of Wray16-423 and its size and high density suggest a younger PN. In order to reconcile the differing luminosity and nebular properties of the two PN with similar age progenitor stars, it is suggested that they are on He burning tracks The abundance pattern is very similar in both nebulae and shows an oxygen depletion of -0.4 dex with respect to the mean O abundance of Galactic PN and [O/H] = -0.6. The Sgr PN progenitor stars are representative of the higher metallicity tail of the Sgr population. The pattern of abundance depletion is similar to that in the only other PN in a dwarf galaxy companion of the Milky Way, that in Fornax, for which new spectra are presented. However the abundances are larger than for Galactic halo PN suggesting a later formation age. The O abundance of the Sgr galaxy deduced from its PN, shows similarities with that of dwarf ellipticals around M31, suggesting that this galaxy was a dwarf elliptical before its interaction with the Milky Way.Comment: 24 pages, Latex (aas2pp4.sty) including 5 postscript figures. To appear in Ap