Variational derivation of two-component Camassa-Holm shallow water system

By a variational approach in the Lagrangian formalism, we derive the nonlinear integrable two-component Camassa-Holm system (1). We show that the two-component Camassa-Holm system (1) with the plus sign arises as an approximation to the Euler equations of hydrodynamics for propagation of irrotational shallow water waves over a flat bed. The Lagrangian used in the variational derivation is not a metric.Comment: to appear in Appl. Ana

The a-number of hyperelliptic curves

It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by $g<\frac{3p}{2}$. In this paper, we show that this bound can be lowered to $g <p$. The method of proof is to force the Cartier-Manin matrix to have rank one and examine what restrictions that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when $p=3,5$ and $7$.Comment: 7 pages. v2: revised and improved the proof of the main theorem based on suggestions from the referee. To appear in the proceedings volume of Women in Numbers Europe-

A gene regulatory network armature for T lymphocyte specification

Choice of a T lymphoid fate by hematopoietic progenitor cells depends on sustained Notch–Delta signaling combined with tightly regulated activities of multiple transcription factors. To dissect the regulatory network connections that mediate this process, we have used high-resolution analysis of regulatory gene expression trajectories from the beginning to the end of specification, tests of the short-term Notch dependence of these gene expression changes, and analyses of the effects of overexpression of two essential transcription factors, namely PU.1 and GATA-3. Quantitative expression measurements of >50 transcription factor and marker genes have been used to derive the principal components of regulatory change through which T cell precursors progress from primitive multipotency to T lineage commitment. Our analyses reveal separate contributions of Notch signaling, GATA-3 activity, and down-regulation of PU.1. Using BioTapestry (www.BioTapestry.org), the results have been assembled into a draft gene regulatory network for the specification of T cell precursors and the choice of T as opposed to myeloid/dendritic or mast-cell fates. This network also accommodates effects of E proteins and mutual repression circuits of Gfi1 against Egr-2 and of TCF-1 against PU.1 as proposed elsewhere, but requires additional functions that remain unidentified. Distinctive features of this network structure include the intense dose dependence of GATA-3 effects, the gene-specific modulation of PU.1 activity based on Notch activity, the lack of direct opposition between PU.1 and GATA-3, and the need for a distinct, late-acting repressive function or functions to extinguish stem and progenitor-derived regulatory gene expression

Automorphic Instanton Partition Functions on Calabi-Yau Threefolds

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that whenever the low-energy theory in D=3 exhibits an arithmetic "U-duality" symmetry G(Z) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function can be realized as a holomorphic section on the twistor space Z over M. We also offer some comments on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra, Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201

The APOB insertion/deletion polymorphism (rs17240441) influences postprandial lipaemia in healthy adults

BACKGROUND: Apolipoprotein (apo)B is the structural apoprotein of intestinally- and liver- derived lipoproteins and plays an important role in the transport of triacylglycerol (TAG) and cholesterol. Previous studies have examined the association between the APOB insertion/deletion (ins/del) polymorphism (rs17240441) and postprandial lipaemia in response to a single meal; however the findings have been inconsistent with studies often underpowered to detect genotype-lipaemia associations, focused mainly on men, or with limited postprandial characterisation of participants. In the present study, using a novel sequential test meal protocol which more closely mimics habitual eating patterns, we investigated the impact of APOB ins/del polymorphism on postprandial TAG, non-esterified fatty acids, glucose and insulin levels in healthy adults. FINDINGS: Healthy participants (n = 147) consumed a standard test breakfast (0 min; 49 g fat) and lunch (330 min; 29 g fat), with blood samples collected before (fasting) and on 11 subsequent occasions until 480 min after the test breakfast. The ins/ins homozygotes had higher fasting total cholesterol, LDL-cholesterol, TAG, insulin and HOMA-IR and lower HDL-cholesterol than del/del homozygotes (P < 0.017). A higher area under the time response curve (AUC) was evident for the postprandial TAG (P < 0.001) and insulin (P = 0.032) responses in the ins/ins homozygotes relative to the del/del homozygotes, where the genotype explained 35% and 7% of the variation in the TAG and insulin AUCs, respectively. CONCLUSIONS: In summary, our findings indicate that the APOB ins/del polymorphism is likely to be an important genetic determinant of the large inter-individual variability in the postprandial TAG and insulin responses to dietary fat intake

Large Silicon Abundance in Photodissociation Regions

We have made one-dimensional raster-scan observations of the rho Oph and sigma Sco star-forming regions with two spectrometers (SWS and LWS) on board the ISO. In the rho Oph region, [SiII] 35um, [OI] 63um, 146um, [CII] 158um, and the H2 pure rotational transition lines S(0) to S(3) are detected, and the PDR properties are derived as the radiation field scaled by the solar neighborhood value G_0~30-500, the gas density n~250--2500 /cc, and the surface temperature T~100-400 K. The ratio of [SiII] 35um to [OI] 146um indicates that silicon of 10--20% of the solar abundance must be in the gaseous form in the photodissociation region (PDR), suggesting that efficient dust destruction is undergoing even in the PDR and that part of silicon atoms may be contained in volatile forms in dust grains. The [OI] 63um and [CII] 158um emissions are too weak relative to [OI] 146um to be accounted for by standard PDR models. We propose a simple model, in which overlapping PDR clouds along the line of sight absorb the [OI] 63um and [CII] 158um emissions, and show that the proposed model reproduces the observed line intensities fairly well. In the sigma Sco region, we have detected 3 fine-structure lines, [OI] 63um, [NII] 122um, and [CII] 158um, and derived that 30-80% of the [CII] emission comes from the ionized gas. The upper limit of the [SiII] 35um is compatible with the solar abundance relative to nitrogen and no useful constraint on the gaseous Si is obtained for the sigma Sco region.Comment: 25 pages with 7 figures, accepted in Astrophysical Journa

Interstellar Turbulence II: Implications and Effects

Interstellar turbulence has implications for the dispersal and mixing of the elements, cloud chemistry, cosmic ray scattering, and radio wave propagation through the ionized medium. This review discusses the observations and theory of these effects. Metallicity fluctuations are summarized, and the theory of turbulent transport of passive tracers is reviewed. Modeling methods, turbulent concentration of dust grains, and the turbulent washout of radial abundance gradients are discussed. Interstellar chemistry is affected by turbulent transport of various species between environments with different physical properties and by turbulent heating in shocks, vortical dissipation regions, and local regions of enhanced ambipolar diffusion. Cosmic rays are scattered and accelerated in turbulent magnetic waves and shocks, and they generate turbulence on the scale of their gyroradii. Radio wave scintillation is an important diagnostic for small scale turbulence in the ionized medium, giving information about the power spectrum and amplitude of fluctuations. The theory of diffraction and refraction is reviewed, as are the main observations and scintillation regions.Comment: 46 pages, 2 figures, submitted to Annual Reviews of Astronomy and Astrophysic

Off-shell superconformal nonlinear sigma-models in three dimensions

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear on JHE

Functional role of T-cell receptor nanoclusters in signal initiation and antigen discrimination

Antigen recognition by the T-cell receptor (TCR) is a hallmark of the adaptive immune system. When the TCR engages a peptide bound to the restricting major histocompatibility complex molecule (pMHC), it transmits a signal via the associated CD3 complex. How the extracellular antigen recognition event leads to intracellular phosphorylation remains unclear. Here, we used single-molecule localization microscopy to quantify the organization of TCR–CD3 complexes into nanoscale clusters and to distinguish between triggered and nontriggered TCR–CD3 complexes. We found that only TCR–CD3 complexes in dense clusters were phosphorylated and associated with downstream signaling proteins, demonstrating that the molecular density within clusters dictates signal initiation. Moreover, both pMHC dose and TCR–pMHC affinity determined the density of TCR–CD3 clusters, which scaled with overall phosphorylation levels. Thus, TCR–CD3 clustering translates antigen recognition by the TCR into signal initiation by the CD3 complex, and the formation of dense signaling-competent clusters is a process of antigen discrimination