Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

Viscoelastic crustal deformation by magmatic intrusion: A case study in the Kutcharo caldera, eastern Hokkaido, Japan

Geodetic signals observed at volcanoes, particularly their temporal patterns, have required us to make the correlation between the surface displacement and magmatic process at depth in terms of viscoelastic crustal rheology. Here we use a parallelized 3-D finite element model to examine the response of the linear Maxwell viscoelastic crust and mantle to the inflation of a sill in order to show the characteristics of a long-term volcano deformation. In the model, an oblate-spheroidal sill is instantaneously or gradually inflated in a two-layered medium that consists of an elastic layer underlain by a viscoelastic layer. Our numerical experiments show that syn-inflation surface uplift is followed by post-inflation surface subsidence as the viscoelastic substrate relaxes. For gradual inflation events, the magnitude of inflation-induced uplift is reduced by the relaxation, through which the volume of a magma inferred by matching the prediction of an elastic model with observed surface uplift could be underestimated. For a given crustal viscosity, sill depth is the principal factor controlling subsidence caused by viscoelastic relaxation. The subsidence rate is highest when the inflation occurs at the boundary between the elastic and the viscoelastic layers. The mantle viscosity has an insignificant impact unless the depth of the inflation is greater than a half the crustal thickness. We apply the viscoelastic model to the interferometric synthetic aperture radar (InSAR) data in the Kutcharo caldera, eastern Hokkaido, Japan, where the surface has slowly subsided over a period of approximately three years following about a two-year period of inflation. The emplacement of a magmatic sill is constrained to occur at a depth of 4.5 km, which is significantly shallower than the geophysically imaged large-scale magma chamber. The geodetically detected deformation in the caldera reflects the small-scale emplacement of a magma that ascended from the deeper chamber, but not the inflation of the chamber itself. The observed ground displacement is controlled by a lower-crustal viscosity of 4 × 1017 Pa s, which is lower than that inferred from some studies of post-seismic deformation, perhaps due to higher temperatures beneath the active caldera. Our results suggest that geodetic signals observed during and following magmatic intrusions need to be revisited

Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction

We study the extended supersymmetric integrable hierarchy underlying the Pohlmeyer reduction of superstring sigma models on semi-symmetric superspaces F/G. This integrable hierarchy is constructed by coupling two copies of the homogeneous integrable hierarchy associated to the loop Lie superalgebra extension f of the Lie superalgebra f of F and this is done by means of the algebraic dressing technique and a Riemann-Hilbert factorization problem. By using the Drinfeld-Sokolov procedure we construct explicitly, a set of 2D spin \pm1/2 conserved supercharges generating supersymmetry flows in the phase space of the reduced model. We introduce the bi-Hamiltonian structure of the extended homogeneous hierarchy and show that the two brackets are of the Kostant-Kirillov type on the co-adjoint orbits defined by the light-cone Lax operators L_\pm. By using the second symplectic structure, we show that these supersymmetries are Hamiltonian flows, we compute part of the supercharge algebra and find the supersymmetric field variations they induce. We also show that this second Poisson structure coincides with the canonical Lorentz-Invariant symplectic structure of the WZNW model involved in the Lagrangian formulation of the extended integrable hierarchy, namely, the semi-symmetric space sine-Gordon model (SSSSG), which is the Pohlmeyer reduced action functional for the transverse degrees of freedom of superstring sigma models on the cosets F/G. We work out in some detail the Pohlmeyer reduction of the AdS_2xS^2 and the AdS_3xS^3 superstrings and show that the new conserved supercharges can be related to the supercharges extracted from 2D superspace. In particular, for the AdS_2xS^2 example, they are formally the same.Comment: V2: Two references added, V3: Modifications in section 2.6, V4: Published versio

The influence of elastic thickness non-uniformity on viscoelastic crustal response to magma emplacement: application to the Kutcharo caldera, eastern Hokkaido, Japan

An elastic layer plays an important role in deformation of the crust. At active volcanoes, its thickness would be effectively thinned by a higher geothermal gradient, particularly in a region beneath which magmatic activity is relatively high. This study examines the influence of elastic thickness non-uniformity on viscoelastic crustal deformation by magma emplacement. A 3-D linear Maxwell viscoelastic model is employed, in which an elastic layer underlain by a viscoelastic layer with a spatially uniform viscosity is thinned to be hi in the volcano centre, compared with hi + Δh in the peripheral regions, and a sill-like magma emplacement occurs in the upper layer beneath the centre. It is found that the post-emplacement viscoelastic subsidence is diminished or enhanced by the elastic thickness non-uniformity, depending on whether or not the horizontal width of the magma emplacement (ωs) is greater than the horizontal width (ωe) over which the elastic layer is thinner. The available signature of the non-uniformity is explored by comparison with a model that has a spatially uniform elastic thickness (UET) of hi. If an apparent viscosity (ηa) of the UET model is adjusted so that the difference in post-emplacement subsidence is minimized at the deformation centre, the non-uniformity appears in the overall deformation field as a displacement anomaly over the perimeter of the sill in which viscoelastic subsidence is greater for the non-uniform model. The anomaly is, however, by no more than the magnitude of ∼15 per cent of the maximal syn-emplacement uplift, though ηa is necessarily modified to be ∼0.2–10 times the non-uniform model viscosity (ηc). If ωe is larger than a few times ωs, a weak signature is no longer expected in the deformation field, and ηa is not significantly deviated from ηc. Since the signature appears so faintly in a displacement field, the InSAR data in the Kutcharo caldera for a period from 1993 August 13 to 1998 June 9 do not allow us to capture the non-uniformity. However, it can be concluded that if ωe beneath the caldera is comparable with or greater than the topographic caldera diameter (ωc) as implied by the spatial variation of the geothermal gradient, the non-uniformity has no significant influence. Otherwise, if ωe < ωc, the non-uniformity influences the estimation of the crustal viscosity, but does not affect the overall deformation field. The elastic thickness non-uniformity can be theoretically captured in the deformation field, but in practice, its influence, particularly on estimating crustal viscosity, cannot be properly inferred without other geophysical data such as the geothermal gradient in and around the caldera

The fidelity of dynamic signaling by noisy biomolecular networks

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.We acknowledge support from a Medical Research Council and Engineering and Physical Sciences Council funded Fellowship in Biomedical Informatics (CGB) and a Scottish Universities Life Sciences Alliance chair in Systems Biology (PSS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Expression and DNA methylation of TNF, IFNG and FOXP3 in colorectal cancer and their prognostic significance.

BACKGROUND: Colorectal cancer (CRC) progression is associated with suppression of host cell-mediated immunity and local immune escape mechanisms. Our aim was to assess the immune function in terms of expression of TNF, IFNG and FOXP3 in CRC. METHODS: Sixty patients with CRC and 15 matched controls were recruited. TaqMan quantitative PCR and methylation-specific PCR was performed for expression and DNA methylation analysis of TNF, IFNG and FOXP3. Survival analysis was performed over a median follow-up of 48 months. RESULTS: TNF was suppressed in tumour and IFNG was suppressed in peripheral blood mononuclear cells (PBMCs) of patients with CRC. Tumours showed enhanced expression of FOXP3 and was significantly higher when tumour size was >38 mm (median tumour size; P=0.006, Mann-Whitney U-test). Peripheral blood mononuclear cell IFNG was suppressed in recurrent CRC (P=0.01). Methylated TNFpromoter (P=0.003) and TNFexon1 (P=0.001) were associated with significant suppression of TNF in tumours. Methylated FOXP3cpg was associated with significant suppression of FOXP3 in both PBMC (P=0.018) and tumours (P=0.010). Reduced PBMC FOXP3 expression was associated with significantly worse overall survival (HR=8.319, P=0.019). CONCLUSIONS: We have detected changes in the expression of immunomodulatory genes that could act as biomarkers for prognosis and future immunotherapeutic strategies

Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes

We study the effect of an order N^2 density of heavy quarks in strongly coupled N=4 SUSY Yang-Mills theory in the large N limit. This is achieved in the type IIB supergravity dual by introducing a uniformly smeared density of macroscopic string sources stretching to the boundary of AdS_5 x S^5. The backreacted system exhibits a flow from an AdS_5 "hedgehog" geometry to a scaling Lifshitz-like solution Lif_5 x S^5 with dynamical critical exponent z=7, wherein the scaling symmetry is broken by a logarithmic running dilaton. We find an exact black brane solution within the scaling regime which describes the low temperature thermodynamics of the system.Comment: 20 pages, 2 figures, references adde

Prenatal muscle development in a mouse model for the secondary dystroglycanopathies

The defective glycosylation of α-dystroglycan is associated with a group of muscular dystrophies that are collectively referred to as the secondary dystroglycanopathies. Mutations in the gene encoding fukutin-related protein (FKRP) are one of the most common causes of secondary dystroglycanopathy in the UK and are associated with a wide spectrum of disease. Whilst central nervous system involvement has a prenatal onset, no studies have addressed prenatal muscle development in any of the mouse models for this group of diseases. In view of the pivotal role of α-dystroglycan in early basement membrane formation, we sought to determine if the muscle formation was altered in a mouse model of FKRP-related dystrophy

Weak coupling large-N transitions at finite baryon density

We study thermodynamics of free SU(N) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (~ exp(N)) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.Comment: 38 pages, 7 figure

Holographic Roberge-Weiss Transitions

We investigate N=4 SYM coupled to fundamental flavours at nonzero imaginary quark chemical potential in the strong coupling and large N limit, using gauge/gravity duality applied to the D3-D7 system, treating flavours in the probe approximation. The interplay between Z(N) symmetry and the imaginary chemical potential yields a series of first-order Roberge-Weiss transitions. An additional thermal transition separates phases where quarks are bound/unbound into mesons. This results in a set of Roberge-Weiss endpoints: we establish that these are triple points, determine the Roberge-Weiss temperature, give the curvature of the phase boundaries and confirm that the theory is analytic in mu^2 when mu^2~0.Comment: 37 pages, 13 figures; minor comments added, to appear in JHE