The Morse-Witten complex via dynamical systems

Given a smooth closed manifold M, the Morse-Witten complex associated to a Morse function f and a Riemannian metric g on M consists of chain groups generated by the critical points of f and a boundary operator counting isolated flow lines of the negative gradient flow. Its homology reproduces singular homology of M. The geometric approach presented here was developed in [We-93] and is based on tools from hyperbolic dynamical systems. For instance, we apply the Grobman-Hartman theorem and the Lambda-Lemma (Inclination Lemma) to analyze compactness and define gluing for the moduli space of flow lines.Comment: 38 pages, 17 figures, minor modifications and correction

Open letter to Prime Minister David Cameron on food poverty in the UK

There is a worrying gap in health circumstances and outcomes between rich and poor people in the UK. Complex though the reasons for this inequality are, the reality is that many hardworking families in the UK are living in poverty and do not have enough income for a decent diet. UK food prices have risen by 12% in real terms since 2007, returning the cost of food relative to other goods to that in the 1990s

Asymptotics for Duration-Driven Long Range Dependent Processes

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an $iid$ process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized sample autocovariances at fixed lags. Finite collections of standardized sample autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter

Production and characterization of anti-human interferon γ receptor antibody fragments that inhibit cytokine binding to the receptor

Three single-chain antibody fragments that recognize the extracellular human interferon γ receptor α-chain (IFNγR), and inhibit the binding of human IFNγ, have been produced in Escherichia coli. These fragments are derived from murine anti-receptor monoclonal antibodies, and comprise the variable heavy (VH) domain linked to the variable light (VL) chain through a 15 amino acid linker [(GGGGS)3]. Using surface plasmon resonance technology (BIAcore), the soluble proteins were shown to retain a high affinity for recombinant IFNγR, and by radioimmunoassay to possess high inhibitory activity towards IFNγ-binding to human Raji cells. The antibody fragments most likely recognize epitopes that overlap the cytokine binding site on the receptor surface. Attempts to dissect further the antibodies to isolated VH- and VL-chains and to synthetic linear and cyclic peptides derived from the individual complementarity determining regions failed to afford fragments with significant IFNγR binding affinity. Nevertheless, these native-like variable region fragments and petidomimetics derived from them are of interest in the design of novel IFNγR antagonist

Photoconductance Quantization in a Single-Photon Detector

We have made a single-photon detector that relies on photoconductive gain in a narrow electron channel in an AlGaAs/GaAs 2-dimensional electron gas. Given that the electron channel is 1-dimensional, the photo-induced conductance has plateaus at multiples of the quantum conductance 2e$^{2}$/h. Super-imposed on these broad conductance plateaus are many sharp, small, conductance steps associated with single-photon absorption events that produce individual photo-carriers. This type of photoconductive detector could measure a single photon, while safely storing and protecting the spin degree of freedom of its photo-carrier. This function is valuable for a quantum repeater that would allow very long distance teleportation of quantum information.Comment: 4 pages, 4 figure

Rac1 GTPase-deficient mouse lens exhibits defects in shape, suture formation, fiber cell migration and survival

AbstractMorphogenesis and shape of the ocular lens depend on epithelial cell elongation and differentiation into fiber cells, followed by the symmetric and compact organization of fiber cells within an enclosed extracellular matrix-enriched elastic capsule. The cellular mechanisms orchestrating these different events however, remain obscure. We investigated the role of the Rac1 GTPase in these processes by targeted deletion of expression using the conditional gene knockout (cKO) approach. Rac1 cKO mice were derived from two different Cre (Le-Cre and MLR-10) transgenic mice in which lens-specific Cre expression starts at embryonic day 8.75 and 10.5, respectively, in both the lens epithelium and fiber cells. The Le-Cre/Rac1 cKO mice exhibited an early-onset (E12.5) and severe lens phenotype compared to the MLR-10/Rac1 cKO (E15.5) mice. While the Le-Cre/Rac1 cKO lenses displayed delayed primary fiber cell elongation, lenses from both Rac1 cKO strains were characterized by abnormal shape, impaired secondary fiber cell migration, sutural defects and thinning of the posterior capsule which often led to rupture. Lens fiber cell N-cadherin/β-catenin/Rap1/Nectin-based cell–cell junction formation and WAVE-2/Abi-2/Nap1-regulated actin polymerization were impaired in the Rac1 deficient mice. Additionally, the Rac1 cKO lenses were characterized by a shortened epithelial sheet, reduced levels of extracellular matrix (ECM) proteins and increased apoptosis. Taken together, these data uncover the essential role of Rac1 GTPase activity in establishment and maintenance of lens shape, suture formation and capsule integrity, and in fiber cell migration, adhesion and survival, via regulation of actin cytoskeletal dynamics, cell adhesive interactions and ECM turnover

Emotional valence and arousal affect reading in an interactive way: neuroimaging evidence for an approach-withdrawal framework

A growing body of literature shows that the emotional content of verbal material affects reading, wherein emotional words are given processing priority compared to neutral words. Human emotions can be conceptualised within a two-dimensional model comprised of emotional valence and arousal (intensity). These variables are at least in part distinct, but recent studies report interactive effects during implicit emotion processing and relate these to stimulus-evoked approach-withdrawal tendencies. The aim of the present study was to explore how valence and arousal interact at the neural level, during implicit emotion word processing. The emotional attributes of written word stimuli were orthogonally manipulated based on behavioural ratings from a corpus of emotion words. Stimuli were presented during an fMRI experiment while 16 participants performed a lexical decision task, which did not require explicit evaluation of a word's emotional content. Results showed greater neural activation within right insular cortex in response to stimuli evoking conflicting approach-withdrawal tendencies (i.e., positive high-arousal and negative low-arousal words) compared to stimuli evoking congruent approach vs. withdrawal tendencies (i.e., positive low-arousal and negative high-arousal words). Further, a significant cluster of activation in the left extra-striate cortex was found in response to emotional than neutral words, suggesting enhanced perceptual processing of emotionally salient stimuli. These findings support an interactive two-dimensional approach to the study of emotion word recognition and suggest that the integration of valence and arousal dimensions recruits a brain region associated with interoception, emotional awareness and sympathetic functions

Access to shops: The views of low-income shoppers

Concern is mounting as the retail stranglehold upon access to food grows. Research on the implications of restructuring retailing and health inequality has failed to involve low-income consumers in this debate. This paper reports on an exercise conducted for the UK Government's, Social Exclusion Unit's Policy Action Team on Access to Shops. The survey provides a useful baseline of the views of low-income groups in England. The choices that people on low income can make were found to be dominated by certain factors such as income and, most importantly, transport. Consumers reported varying levels of satisfaction with retail provision. The findings suggest gaps between what people have, what they want and what the planning process does and does not offer them. Better policy and processes are needed to include and represent the interests of low-income groups