Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U -> infinity and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U -> 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.

Dynamics of phytoplankton associations in three reservoirs in northeastern Brazil assessed using Reynolds' theory

The aim of the present study was to evaluate the influence of seasonality on the behavior of phytoplankton associations in eutrophic reservoirs with different depths in northeastern Brazil. Five collections were carried out at each of the reservoirs at two depths (0.1 m and near the sediment) at three-month intervals in each season (dry and rainy). The phytoplankton samples were preserved in Lugol's solution and quantified under an inverted microscope for the determination of density values, which were subsequently converted to biomass values based on cellular biovolume and classified in phytoplankton associations. The following abiotic variables were analyzed: water temperature, dissolved oxygen, pH, turbidity, water transparency, total phosphorus, total dissolved phosphorus, orthophosphate and total nitrogen. The data were investigated using canonical correspondence analysis. The influence of seasonality on the dynamics of the phytoplankton community was lesser in the deeper reservoirs. Depth affected the behavior of the algal associations. Variation in light availability was a determinant of changes in the phytoplankton structure. Urosolenia and Anabaena associations were more abundant in shallow ecosystems with a larger eutrophic zone, whereas the Microcystis association was more related to deep ecosystems with adequate availability of nutrients. The distribution of Cyclotella, Geitlerinema, Planktothrix, Pseudanabaena and Cylindrospermopsis associations was different from that seen in subtropical regions and the substitution of these associations was related to a reduction in the eutrophic zone rather than the mixture zone. Published by Elsevier GmbH.

URANS calculations for smooth circular cylinder flow in a wide range of Reynolds Numbers: solution verification and validation

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and Re 5 x 10(5) will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 k - omega SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature. [DOI: 10.1115/1.4007571]

Remarks on the classification of a pair of commuting semilinear operators

Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators. (C) 2011 Elsevier Inc. All rights reserved.

Classifying A-field and B-field configurations in the presence of D-branes. Part II: Stacks of D-branes

In the paper of Bonora et al. (2008) [3] we have shown, in the context of type II superstring theory, the classification of the allowed B-field and A-field configurations in the presence of anomaly-free D-branes, the mathematical framework being provided by the geometry of gerbes. Here we complete the discussion considering in detail the case of a stack of D-branes, carrying a non-abelian gauge theory, which was just sketched in Bonora et al. (2008) [3]. In this case we have to mix the geometry of abelian gerbes, describing the B-field, with the one of higher-rank bundles, ordinary or twisted. We describe in detail the various cases that arise according to such a classification, as we did for a single D-brane, showing under which hypotheses the A-field turns out to be a connection on a canonical gauge bundle. We also generalize to the non-abelian setting the discussion about "gauge bundles with non-integral Chern classes", relating them to twisted bundles with connection. Finally, we analyze the geometrical nature of the Wilson loop for each kind of gauge theory on a D-brane or stack of D-branes.

High temperature limit in static backgrounds

We prove that the hard thermal loop contribution to static thermal amplitudes can be obtained by setting all the external four-momenta to zero before performing the Matsubara sums and loop integrals. At the one-loop order we do an iterative procedure for all the one-particle irreducible one-loop diagrams, and at the two-loop order we consider the self-energy. Our approach is sufficiently general to the extent that it includes theories with any kind of interaction vertices, such as gravity in the weak field approximation, for d space-time dimensions. This result is valid whenever the external fields are all bosonic.

Coherent states and related quantizations for unbounded motions

We discuss the construction of coherent states (CS) for systems with continuous spectra. First, we propose to adopt the Malkin-Manko approach, developed for systems with discrete spectra, to the case under consideration. Following this approach, we consider two examples, a free particle and a particle in a linear potential. Second, we generalize the approach of action-angle CS to systems with continuous spectra. In the first approach we start with a well-defined quantum formulation (canonical quantization) of a physical system and the construction of CS follows from such a quantization. In the second approach, the quantization procedure is inherent to the CS construction itself.

Period determination in the food-entrainable and methamphetamine-sensitive circadian oscillator(s)

Daily rhythmic processes are coordinated by circadian clocks, which are present in numerous central and peripheral tissues. In mammals, two circadian clocks, the food-entrainable oscillator (FEO) and methamphetamine-sensitive circadian oscillator (MASCO), are "black box" mysteries because their anatomical loci are unknown and their outputs are not expressed under normal physiological conditions. In the current study, the investigation of the timekeeping mechanisms of the FEO and MASCO in mice with disruption of all three paralogs of the canonical clock gene, Period, revealed unique and convergent findings. We found that both the MASCO and FEO in Per1(-/-)/Per2(-/-)/Per3(-/-) mice are circadian oscillators with unusually short (similar to 21 h) periods. These data demonstrate that the canonical Period genes are involved in period determination in the FEO and MASCO, and computational modeling supports the hypothesis that the FEO and MASCO use the same timekeeping mechanism or are the same circadian oscillator. Finally, these studies identify Per1(-/-)/Per2(-/-)/Per3(-/-) mice as a unique tool critical to the search for the elusive anatomical location(s) of the FEO and MASCO.

W Z plus missing-E-T signal from gaugino pair production at LHC7

LHC searches for supersymmetry currently focus on strongly produced sparticles, which are copiously produced if gluinos and squarks have masses of a few hundred GeV. However, in supersymmetric models with heavy scalars, as favored by the decoupling solution to the SUSY flavor and CP problems, and m((g) over tilde) greater than or similar to 500 GeV as indicated by recent LHC results, chargino-neutralino ((W) over tilde (+/-)(1)(Z) over tilde (2)) production is the dominant cross section for m((W) over tilde1) similar to m((Z) over tilde2) < m(<(g)over tilde>)/3 at LHC with root s = 7 TeV (LHC7). Furthermore, if m((Z) over tilde1) + (m (Z) over tilde) less than or similar to m((Z) over tilde2) less than or similar to m((Z) over tilde1) + m(h), then (Z) over tilde (2) dominantly decays via (Z) over tilde (2) -> (Z) over tilde (1)Z, while (W) over tilde (1) decays via (W) over tilde (1) -> (Z) over tilde W-1. We investigate the LHC7 reach in the W Z + (sic)T channel (for both leptonic and hadronic decays of the W boson) in models with and without the assumption of gaugino mass universality. In the case of the mSUGRA/CMSSM model with heavy squark masses, the LHC7 discovery reach in the W Z+ (sic)T channel becomes competetive with the reach in the canonical (sic)T + jets channel for integrated luminosities similar to 30 fb(-1). We also present the LHC7 reach for a simplified model with arbitrary m((Z) over tilde1) and m((W) over tilde1) similar to m((Z) over tilde2). Here, we find a reach of up to m((W) over tilde1) similar to 200 (250) GeV for 10 (30) fb(-1).

Effect of the thermostat in the molecular dynamics simulation on the folding of the model protein chignolin

Molecular dynamics simulations of the model protein chignolin with explicit solvent were carried out, in order to analyze the influence of the Berendsen thermostat on the evolution and folding of the peptide. The dependence of the peptide behavior on temperature was tested with the commonly employed thermostat scheme consisting of one thermostat for the protein and another for the solvent. The thermostat coupling time of the protein was increased to infinity, when the protein is not in direct contact with the thermal bath, a situation known as minimally invasive thermostat. In agreement with other works, it was observed that only in the last situation the instantaneous temperature of the model protein obeys a canonical distribution. As for the folding studies, it was shown that, in the applications of the commonly utilized thermostat schemes, the systems are trapped in local minima regions from which it has difficulty escaping. With the minimally invasive thermostat the time that the protein needs to fold was reduced by two to three times. These results show that the obstacles to the evolution of the extended peptide to the folded structure can be overcome when the temperature of the peptide is not directly controlled.

Gene Expression Profile in Response to Doxorubicin-Rapamycin Combined Treatment of HER-2-Overexpressing Human Mammary Epithelial Cell Lines

HER-2-positive breast cancers frequently sustain elevated AKT/mTOR signaling, which has been associated with resistance to doxorubicin treatment. Here, we investigated whether rapamycin, an mTOR inhibitor, increased the sensitivity to doxorubicin therapy in two HER-2-overexpressing cell lines: C5.2, which was derived from the parental HB4a by transfection with HER-2 and SKBR3, which exhibits HER-2 amplification. The epithelial mammary cell line HB4a was also analyzed. The combined treatment using 20 nmol/L of rapamycin and 30 nmol/L of doxorubicin arrested HB4a and C5.2 cells in S to G(2)-M, whereas SKBR3 cells showed an increase in the G(0)-G(1) phase. Rapamycin increased the sensitivity to doxorubicin in HER-2-overexpressing cells by approximately 2-fold, suggesting that the combination displayed a more effective antiproliferative action. Gene expression profiling showed that these results might reflect alterations in genes involved in canonical pathways related to purine metabolism, oxidative phosphorylation, protein ubiquitination, and mitochondrial dysfunction. A set of 122 genes modulated by the combined treatment and specifically related to HER-2 overexpression was determined by finding genes commonly regulated in both C5.2 and SKBR3 that were not affected in HB4a cells. Network analysis of this particular set showed a smaller subgroup of genes in which coexpression pattern in HB4a cells was disrupted in C5.2 and SKBR3. Altogether, our data showed a subset of genes that might be more robust than individual markers in predicting the response of HER-2-overexpressing breast cancers to doxorubicin and rapamycin combination. Mol Cancer Ther; 11(2); 464-74. (C) 2011 AACR.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

Bose glass and Mott glass of quasiparticles in a doped quantum magnet

The low-temperature states of bosonic fluids exhibit fundamental quantum effects at the macroscopic scale: the best-known examples are Bose-Einstein condensation and superfluidity, which have been tested experimentally in a variety of different systems. When bosons interact, disorder can destroy condensation, leading to a 'Bose glass'. This phase has been very elusive in experiments owing to the absence of any broken symmetry and to the simultaneous absence of a finite energy gap in the spectrum. Here we report the observation of a Bose glass of field-induced magnetic quasiparticles in a doped quantum magnet (bromine-doped dichloro-tetrakis-thiourea-nickel, DTN). The physics of DTN in a magnetic field is equivalent to that of a lattice gas of bosons in the grand canonical ensemble; bromine doping introduces disorder into the hopping and interaction strength of the bosons, leading to their localization into a Bose glass down to zero field, where it becomes an incompressible Mott glass. The transition from the Bose glass (corresponding to a gapless spin liquid) to the Bose-Einstein condensate (corresponding to a magnetically ordered phase) is marked by a universal exponent that governs the scaling of the critical temperature with the applied field, in excellent agreement with theoretical predictions. Our study represents a quantitative experimental account of the universal features of disordered bosons in the grand canonical ensemble.