A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explicitly known only to leading order in perturbation theory, but at that order is positive semi-definite, as follows from Perelman's work on the Ricci flow. This gives rise to a monotonicity formula for the flow which is expected to fail only if the beta function perturbation series fails to converge, which can happen if curvatures or their derivatives grow large. We test the validity of the monotonicity formula at next-to-leading order in perturbation theory by explicitly computing the second-order terms in the metric on the space of coupling constants. At this order, this metric is found not to be positive semi-definite. In situations where this might spoil monotonicity, derivatives of curvature become large enough for higher order perturbative corrections to be significant.Comment: 15 pages; Erroneous sentence in footnote 14 removed; this version therefore supersedes the published version (our thanks to Dezhong Chen for the correction

Compact representation of wall-bounded turbulence using compressive sampling

Compressive sampling is well-known to be a useful tool used to resolve the energetic content of signals that admit a sparse representation. The broadband temporal spectrum acquired from point measurements in wall-bounded turbulence has precluded the prior use of compressive sampling in this kind of flow, however it is shown here that the frequency content of flow fields that have been Fourier transformed in the homogeneous spatial (wall-parallel) directions is approximately sparse, giving rise to a compact representation of the velocity field. As such, compressive sampling is an ideal tool for reducing the amount of information required to approximate the velocity field. Further, success of the compressive sampling approach provides strong evidence that this representation is both physically meaningful and indicative of special properties of wall turbulence. Another advantage of compressive sampling over periodic sampling becomes evident at high Reynolds numbers, since the number of samples required to resolve a given bandwidth with compressive sampling scales as the logarithm of the dynamically significant bandwidth instead of linearly for periodic sampling. The combination of the Fourier decomposition in the wall-parallel directions, the approximate sparsity in frequency, and empirical bounds on the convection velocity leads to a compact representation of an otherwise broadband distribution of energy in the space defined by streamwise and spanwise wavenumber, frequency, and wall-normal location. The data storage requirements for reconstruction of the full field using compressive sampling are shown to be significantly less than for periodic sampling, in which the Nyquist criterion limits the maximum frequency that can be resolved. Conversely, compressive sampling maximizes the frequency range that can be recovered if the number of samples is limited, resolving frequencies up to several times higher than the mean sampling rate. It is proposed that the approximate sparsity in frequency and the corresponding structure in the spatial domain can be exploited to design simulation schemes for canonical wall turbulence with significantly reduced computational expense compared with current techniques

Vacuum Spacetimes with Future Trapped Surfaces

In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat. Further, this initial data will contain an annular region which is foliated by two-surfaces of topology $S^2$. These two-surfaces are future trapped in the language of Penrose. The Penrose singularity theorem guarantees that the vacuum spacetime which evolves from this initial data is future null incomplete.Comment: 19 page

A lymphoma plasma membrane-associated protein with ankyrin-like properties.

In this study we have used several complementary techniques to isolate and characterize a 72-kD polypeptide that is tightly associated with a major mouse T-lymphoma membrane glycoprotein, gp 85 (a wheat germ agglutinin-binding protein), in a 16 S complex. These two proteins do not separate in the presence of high salt but can be dissociated by treatment with 2 M urea. Further analysis indicates that the 72-kD protein has ankyrin-like properties based on the following criteria: (a) it cross-reacts with specific antibodies raised against erythrocyte and brain ankyrin; (b) it displays a peptide mapping pattern and a pI (between 6.5 and 6.8) similar to that of the 72-kD proteolytic fragment of erythrocyte ankyrin; (c) it competes with erythrocyte ghost membranes (spectrin-depleted preparations) for spectrin binding; and (d) it binds to purified spectrin and fodrin molecules. Most importantly, in intact lymphoma cells this ankyrin-like protein is localized directly underneath the plasma membrane and is found to be preferentially accumulated beneath receptor cap structures as well as associated with a membrane-cytoskeleton complex preparation. It is proposed that the ankyrin-like 72-kD protein may play an important role in linking certain surface glycoprotein(s) to fodrin which, in turn, binds to actin filaments required for lymphocyte cap formation

Shear-Wave Elastography Assessments of Quadriceps Stiffness Changes prior to, during and after Prolonged Exercise: A Longitudinal Study during an Extreme Mountain Ultra-Marathon.

In sports medicine, there is increasing interest in quantifying the elastic properties of skeletal muscle, especially during extreme muscular stimulation, to improve our understanding of the impact of alterations in skeletal muscle stiffness on resulting pain or injuries, as well as the mechanisms underlying the relationships between these parameters. Our main objective was to determine whether real-time shear-wave elastography (SWE) can monitor changes in quadriceps muscle elasticity during an extreme mountain ultra-marathon, a powerful mechanical stress model. Our study involved 50 volunteers participating in an extreme mountain marathon (distance: 330 km, elevation: +24,000 m). Quantitative SWE velocity and shear modulus measurements were performed in most superficial quadriceps muscle heads at the following 4 time points: before the race, halfway through the race, upon finishing the race and after recovery (+48 h). Blood biomarker levels were also measured. A significant decrease in the quadriceps shear modulus was observed upon finishing the race (3.31±0.61 kPa) (p<0.001) compared to baseline (3.56±0.63 kPa), followed by a partial recovery +48 h after the race (3.45±0.6 kPa) (p = 0.002) across all muscle heads, as well as for each of the following three muscle heads: the rectus femoris (p = 0.003), the vastus medialis (p = 0.033) and the vastus lateralis (p = 0.001). Our study is the first to assess changes in muscle stiffness during prolonged extreme physical endurance exercises based on shear modulus measurements using non-invasive SWE. We concluded that decreases in stiffness, which may have resulted from quadriceps overuse in the setting of supra-physiological stress caused by the extreme distance and unique elevation of the race, may have been responsible for the development of inflammation and muscle swelling. SWE may hence represent a promising tool for monitoring physiologic or pathological variations in muscle stiffness and may be useful for diagnosing and monitoring muscle changes

Micro-econometric and Micro-Macro Linked Models: Sequential Macro-Micro Modelling with Behavioral Microsimulations

Analyzing the poverty and distributional impact of macro events requires understanding how shocks or policy changes on the macro level affect household income and consumption. It is clear that this poses a formidable task, which of course raises the question of the appropriate methodology to address such questions. This paper presents one possible approach: A sequential methodology that combines a macroeconomic model with a behavioral micro-simulation. We discuss the merits and shortcomings of this approach with a focus on developing country applications with a short to medium run time horizon. - This chapter is a re-print of: Lay, J. (2010). Sequential macro-micro modelling with behavioural microsimulations. International Journal of Microsimulation, 3(1), 24-34

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

Dirac-harmonic maps from degenerating spin surfaces I: the Neveu-Schwarz case

We study Dirac-harmonic maps from degenerating spin surfaces with uniformly bounded energy and show the so-called generalized energy identity in the case that the domain converges to a spin surface with only Neveu-Schwarz type nodes. We find condition that is both necessary and sufficient for the $W^{1,2} \times L^{4}$ modulo bubbles compactness of a sequence of such maps.Comment: 24 page

Ant and termite communities in isolated and continuous forest fragments in Singapore

The conservation of tropical rainforest biodiversity is a pressing issue, due to the rapid rate of deforestation. Secondary forests may provide a useful alternative to old growth forests, as they often contain a substantial proportion of the original biodiversity. In this study, we investigate species richness, density and composition of ants and termites in six forest sites in Singapore, each differing in habitat isolation and land-use history. The six sites include an old growth forest, a selectively logged old growth forest, and four secondary forests: either located on abandoned agricultural lands or in abandoned villages, and either isolated or adjacent to old growth forests. We found that the old growth forest had significantly higher species density of ants and termites than any other site. Rarefaction curves showed that ant and termite species richness were highest in the old growth forest followed by the selectively logged forest albeit these results were not significantly different from other sites. Ant species composition changed along a gradient of fragment isolation. Termite community composition in the old growth forest shared a higher proportion of species with the adjacent secondary forest, than with the selectively logged old growth forest, suggesting that the species pool of adjacent habitats is important for species re-colonisation of regenerating habitats. Our results suggest, albeit without replications, that secondary forests differ in conservation value and that disturbed habitats in continuous forest fragments recover more rapidly than isolated ones. Further, we emphasise the importance of old growth forest fragments within man-made ecosystems as sources of original biodiversity