Constructing monotone homotopies and sweepouts

This article investigates when homotopies can be converted to monotone homotopies without increasing the lengths of curves. A monotone homotopy is one which consists of curves which are simple or constant, and in which curves are pairwise disjoint. We show that, if the boundary of a Riemannian disc can be contracted through curves of length less than $L$, then it can also be contracted monotonously through curves of length less than $L$. This proves a conjecture of Chambers and Rotman. Additionally, any sweepout of a Riemannian $2$-sphere through curves of length less than $L$ can be replaced with a monotone sweepout through curves of length less than $L$. Applications of these results are also discussed.Comment: 16 pages, 6 figure

On the complexity of optimal homotopies

In this article, we provide new structural results and algorithms for the Homotopy Height problem. In broad terms, this problem quantifies how much a curve on a surface needs to be stretched to sweep continuously between two positions. More precisely, given two homotopic curves $\gamma_1$ and $\gamma_2$ on a combinatorial (say, triangulated) surface, we investigate the problem of computing a homotopy between $\gamma_1$ and $\gamma_2$ where the length of the longest intermediate curve is minimized. Such optimal homotopies are relevant for a wide range of purposes, from very theoretical questions in quantitative homotopy theory to more practical applications such as similarity measures on meshes and graph searching problems. We prove that Homotopy Height is in the complexity class NP, and the corresponding exponential algorithm is the best one known for this problem. This result builds on a structural theorem on monotonicity of optimal homotopies, which is proved in a companion paper. Then we show that this problem encompasses the Homotopic Fr\'echet distance problem which we therefore also establish to be in NP, answering a question which has previously been considered in several different settings. We also provide an O(log n)-approximation algorithm for Homotopy Height on surfaces by adapting an earlier algorithm of Har-Peled, Nayyeri, Salvatipour and Sidiropoulos in the planar setting

Effects of repeated consumption on sensory-enhanced satiety

Previous research suggests that sensory characteristics of a drink modify the acute satiating effects of its nutrients, with enhanced satiety evident when a high energy drink was thicker and tasted creamier. The present study tested whether this modulation of satiety by sensory context was altered by repeated consumption. Participants (n=48) consumed one of four drinks mid-morning on seven non-consecutive days with satiety responses measured pre-exposure (day 1), post-exposure (day 6) and at a one month follow-up. Drinks combined two levels of energy (lower energy, LE, 326 KJ: higher energy, HE, 1163KJ) with two levels of satiety-predictive sensory characteristics (low-sensory, LS, or enhanced sensory, ES). Test lunch intake 90 minutes after drink consumption depended on both the energy content and sensory characteristics of the drink before exposure, but on energy content alone at post-exposure and the follow-up. The largest change was an increase in test meal intake over time in the LE/LS condition. Effects on intake were reflected in appetite ratings, with rated hunger and expected filling affected by sensory characteristics and energy content pre-exposure, but were largely determined by energy content post exposure and at follow up. In contrast, a measure of expected satiety reflected sensory characteristics regardless of energy content on all three test days. Overall these data suggest that some aspects of the sensory-modulation of satiety are changed by repeated consumption, with covert energy becoming more effective in suppressing appetite over time, but also suggest that these behavioural changes are not readily translated into expectations of satiety

The development of magmatism along the Cameroon Volcanic Line: evidence from seismicity and seismic anisotropy

The Cameroon Volcanic Line (CVL) straddles the continent-ocean boundary in West Africa but exhibits no clear age progression. This renders it difficult to explain by traditional plume/plate motion hypotheses; thus, there remains no consensus on the processes responsible for its development. To understand better the nature of asthenospheric flow beneath the CVL, and the effects of hotspot tectonism on the overlying lithosphere, we analyze mantle seismic anisotropy and seismicity. Cameroon is relatively aseismic compared to hotspots elsewhere, with little evidence for magmatism-related crustal deformation away from Mount Cameroon, which last erupted in 2000. Low crustal Vp/Vs ratios (?1.74) and a lack of evidence for seismically anisotropic aligned melt within the lithosphere both point toward a poorly developed magmatic plumbing system beneath the CVL. Null SKS splitting observations dominate the western continental portion of the CVL; elsewhere, anisotropic fast polarization directions parallel the strike of the Precambrian Central African Shear Zone (CASZ). The nulls may imply that the convecting upper mantle beneath the CVL is isotropic, or characterized by a vertically oriented olivine lattice preferred orientation fabric, perhaps due to a mantle plume or the upward limb of a small-scale convection cell. Precambrian CASZ fossil lithospheric fabrics along the CVL may have been thermomechanically eroded during Gondwana breakup ?130?Ma, with an isotropic lower lithosphere subsequently reforming due to cooling of the slow-moving African plate. Small-scale lithospheric delamination during the 30?Ma recent development of the line may also have contributed to the erosion of the CASZ lithospheric fossil anisotropy, at the same time as generating the low-volume alkaline basaltic volcanism along the CV

PBP4: A New Perspective on Staphylococcus aureus β-Lactam Resistance.

β-lactam antibiotics are excellent drugs for treatment of staphylococcal infections, due to their superior efficacy and safety compared to other drugs. Effectiveness of β-lactams is severely compromised due to resistance, which is widespread among clinical strains of Staphylococcus aureus. β-lactams inhibit bacterial cells by binding to penicillin binding proteins (PBPs), which perform the penultimate steps of bacterial cell wall synthesis. Among PBPs of S. aureus, PBP2a has received the most attention for the past several decades due to its preeminent role in conferring both high-level and broad-spectrum resistance to the entire class of β-lactam drugs. Studies on PBP2a have thus unraveled incredible details of its mechanism of action. We have recently identified that an uncanonical, low molecular weight PBP of S. aureus, PBP4, can also provide high-level and broad-spectrum resistance to the entire class of β-lactam drugs at a level similar to that of PBP2a. The role of PBP4 has typically been considered not so important for β-lactam resistance of S. aureus, and as a result its mode of action remains largely unknown. In this article, we review our current knowledge of PBP4 mediating β-lactam resistance in S. aureus

Deep VLT spectroscopy of the z=2.49 Radio Galaxy MRC 2104-242: Evidence for a metallicity gradient in its extended emission line region

We present spectroscopic observations of the rest-frame UV line emission around radio galaxy MRC 2104-242 at z=2.49, obtained with FORS1 on VLT Antu. The morphology of the halo is dominated by two spatially resolved regions. Lya is extended by >12 arcsec along the radio axis, CIV and HeII are extended by ~8 arcsec. The overall spectrum is typical for that of high redshift radio galaxies. The most striking spatial variation is that NV is present in the spectrum of the region associated with the center of the galaxy hosting the radio source, the northern region, while absent in the southern region. Assuming that the gas is photoionized by a hidden quasar, the difference in NV emission can be explained by a metallicity gradient within the halo. This is consistent with a scenario in which the gas is associated with a massive cooling flow or originates from the debris of the merging of two or more galaxies.Comment: Accepted for publication in A&A Letter

The impact of ageing on monocytes and macrophages

Ageing is a global burden. Increasing age is associated with increased incidence of infections and cancer and decreased vaccine efficacy. This increased morbidity observed with age, is believed to be due in part to a decline in adaptive immunity, termed immunosenescence. However not all aspects of immunity decrease with age as ageing presents with systemic low grade chronic inflammation, characterised by elevated concentrations of mediators such as IL-6, TNFα and C Reactive protein (CRP). Inflammation is a strong predictor of morbidity and mortality, and chronic inflammation is known to be detrimental to a functioning immune system. Although the source of the inflammation is much discussed, the key cells which are believed to facilitate the inflammageing phenomenon are the monocytes and macrophages. In this review we detail how macrophage and monocyte phenotype and function change with age. The impact of ageing on macrophages includes decreased phagocytosis and immune resolution, increased senescent-associated markers, increased inflammatory cytokine production, reduced autophagy, and a decrease in TLR expression. With monocytes there is an increase in circulating CD16+ monocytes, decreased type I IFN production, and decreased efferocytosis. In conclusion, we believe that monocytes and macrophages contribute to immunosenescence and inflammageing and as a result have an important role in defective immunity with age

Discrete random walk models for symmetric Levy-Feller diffusion processes

We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index $\alpha$ ($0< \alpha \le 2$), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the corresponding continuous Markovian stochastic processes, that we refer to as Levy-Feller diffusion processes.Comment: 13 pages, 3 figures, to be published in Physica

Monotone contractions of the boundary of the disc

In this paper, we study contractions of the boundary of a Riemannian 2-disc where the maximal length of the intermediate curves is minimized. We prove that with an arbitrarily small overhead in the lengths of the intermediate curves, there exists such an optimal contraction that is monotone, i.e., where the intermediate curves are simple closed curves which are pairwise disjoint. This proves a conjecture of Chambers and Rotman

Striking a balance between culture and fun: 'Quality' meets hitman genre in 'In Bruges'

This is an Author's Accepted Manuscript of an article published in New Review of Film and Television Studies, 9(2), 132 - 151, 2011, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/17400309.2011.556934.This paper gives an analysis of In Bruges (2008) that situates the film as a hybrid product offering a mixture of signifiers of cinematic ‘quality’ and ‘lower’ genre ingredients. This paper also considers the extent to which In Bruges offers a combination of tonal registers in which irony and detachment, as markers of distinction, are blended with a more mainstream-oriented appeal to emotional engagement on the part of the viewer, and considers how this might be related to the broader social and industrial contexts in which it appeared