The index of symmetry of compact naturally reductive spaces

We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type. We also study several examples where the leaf of symmetry is not of the group type. Interesting examples arise from the unit tangent bundle of the sphere of curvature 2, and two metrics in an Aloff-Wallach 7-manifold and the Wallach 24-manifold.submittedVersionFil: Olmos, Carlos Enrique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Reggiani, Silvio Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Tamuru, Hiroshi. Universidad de Hiroshima. Escuela de Ciencias. Departamento de Matemática; Japón.Matemática Pur

Geodesic flows on Riemannian g.o. spaces

We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.Comment: 12 pages, minor corrections, final versio

A Broadly Applicable Strategy for Entry into Homogeneous Nickel(0) Catalysts from Air-Stable Nickel(II) Complexes

A series of air-stable nickel complexes of the form L[subscript 2]Ni(aryl) X (L = monodentate phosphine, X = Cl, Br) and LNi(aryl)X (L = bis-phosphine) have been synthesized and are presented as a library of precatalysts suitable for a wide variety of nickel-catalyzed transformations. These complexes are easily synthesized from low-cost NiCl[subscript 2]·6H[subscript 2]O or NiBr[subscript 2]·3H[subscript 2]O and the desired ligand followed by addition of 1 equiv of Grignard reagent. A selection of these complexes were characterized by single-crystal X-ray diffraction, and an analysis of their structural features is provided. A case study of their use as precatalysts for the nickel-catalyzed carbonyl-ene reaction is presented, showing superior reactivity in comparison to reactions using Ni(cod)[subscript 2]. Furthermore, as the precatalysts are all stable to air, no glovebox or inert-atmosphere techniques are required to make use of these complexes for nickel-catalyzed reactions.National Institute of General Medical Sciences (U.S.) (GM63755)National Science Foundation (U.S.). Graduate Research Fellowshi

DNA Methylation and Normal Chromosome Behavior in Neurospora Depend on Five Components of a Histone Methyltransferase Complex, DCDC

Methylation of DNA and of Lysine 9 on histone H3 (H3K9) is associated with gene silencing in many animals, plants, and fungi. In Neurospora crassa, methylation of H3K9 by DIM-5 directs cytosine methylation by recruiting a complex containing Heterochromatin Protein-1 (HP1) and the DIM-2 DNA methyltransferase. We report genetic, proteomic, and biochemical investigations into how DIM-5 is controlled. These studies revealed DCDC, a previously unknown protein complex including DIM-5, DIM-7, DIM-9, CUL4, and DDB1. Components of DCDC are required for H3K9me3, proper chromosome segregation, and DNA methylation. DCDC-defective strains, but not HP1-defective strains, are hypersensitive to MMS, revealing an HP1-independent function of H3K9 methylation. In addition to DDB1, DIM-7, and the WD40 domain protein DIM-9, other presumptive DCAFs (DDB1/CUL4 associated factors) co-purified with CUL4, suggesting that CUL4/DDB1 forms multiple complexes with distinct functions. This conclusion was supported by results of drug sensitivity tests. CUL4, DDB1, and DIM-9 are not required for localization of DIM-5 to incipient heterochromatin domains, indicating that recruitment of DIM-5 to chromatin is not sufficient to direct H3K9me3. DIM-7 is required for DIM-5 localization and mediates interaction of DIM-5 with DDB1/CUL4 through DIM-9. These data support a two-step mechanism for H3K9 methylation in Neurospora

Interactions of nanorod particles in the strong coupling regime

The plasmon coupling in a nanorod dimer obeys the exponential size dependence according to the Universal Plasmon Ruler Equation. However, it was shown recently that such a model does not hold at short nanorod distance (Nano Lett. 2009, 9, 1651). Here we study the nanorod coupling in various cases, including nanorod dimer with the asymmetrical lengths and symmetrical dimer with the varying gap width. The asymmetrical nanorod dimer causes two plasmon modes: one is the attractive lower- energy mode and the other the repulsive high-energy mode. Using a simple coupled LC-resonator model, the position of dimer resonance has been determined analytically. Moreover, we found that the plasmon coupling of symmetrical cylindrical (or rectangular) nanorod dimer is governed uniquely by gap width scaled for the (effective) rod radius rather than for the rod length. A new Plasmon Ruler Equation without using the fitting parameters has been proposed, which agrees well with the FDTD calculations. The method has also been extended to study the plasmonic wave-guiding in a linear chain of gold nanorod particles. A field decay length up to 2700nm with the lateral mode size about 50nm (~wavelength/28) has been suggested.Comment: 31 pages, 6 figures, 58 reference

Antibodies for Assessing Circadian Clock Proteins in the Rodent Suprachiasmatic Nucleus

Research on the mechanisms underlying circadian rhythmicity and the response of brain and body clocks to environmental and physiological challenges requires assessing levels of circadian clock proteins. Too often, however, it is difficult to acquire antibodies that specifically and reliably label these proteins. Many of these antibodies also lack appropriate validation. The goal of this project was to generate and characterize antibodies against several circadian clock proteins. We examined mice and hamsters at peak and trough times of clock protein expression in the suprachiasmatic nucleus (SCN). In addition, we confirmed specificity by testing the antibodies on mice with targeted disruption of the relevant genes. Our results identify antibodies against PER1, PER2, BMAL1 and CLOCK that are useful for assessing circadian clock proteins in the SCN by immunocytochemistry

Imaging the dephasing of spin wave modes in a square thin film magnetic element

Copyright © 2004 The American Physical SocietyWe have used time-resolved scanning Kerr effect microscopy to study dephasing of spin wave modes in a square Ni81Fe19 element of 10 μm width and 150 nm thickness. When a static magnetic field H was applied parallel to an edge of the square, demagnetized regions appeared at the edges orthogonal to the field. When H was applied along a diagonal, a demagnetized region appeared along the opposite diagonal. Time-resolved images of the out-of-plane magnetization component showed stripes that lie perpendicular to H and indicate the presence of spin wave modes with wave vector parallel to the static magnetization. The transient Kerr rotation was measured at different positions along an axis parallel to H, and the power spectra revealed a number of different modes. Micromagnetic simulations reproduce both the observed images and the mode frequencies. This study allows us to understand an anisotropic damping observed at the center of the square element in terms of dephasing of the resonant mode spectrum

High-Throughput Chemical Screen Identifies a Novel Potent Modulator of Cellular Circadian Rhythms and Reveals CKIα as a Clock Regulatory Kinase

A novel compound “longdaysin” was found to dramatically slow down the speed of the circadian clock through simultaneous inhibition of protein kinases CKIδ, CKIα, and ERK2

Co-existence of acute myeloid leukemia with multilineage dysplasia and Epstein-Barr virus-associated T-cell lymphoproliferative disorder in a patient with rheumatoid arthritis: a case report

Rheumatoid arthritis (RA) is an autoimmune disease mediated by inflammatory processes mainly at the joints. Recently, awareness of Epstein-Barr virus (EBV)-associated T-cell lymphoproliferative disorder (T-LPD) has been heightened for its association with methotraxate usage in RA patients. In the contrary, acute myeloid leukemia with multilineage dysplasia (AML-MLD) has never been documented to be present concomitantly with the above two conditions. In this report we present a case of an autopsy-proven co-existence of AML-MLD and EBV-associated T-LPD in a patient with RA

Regulation of BMAL1 Protein Stability and Circadian Function by GSK3β-Mediated Phosphorylation

Circadian rhythms govern a large array of physiological and metabolic functions. To achieve plasticity in circadian regulation, proteins constituting the molecular clock machinery undergo various post-translational modifications (PTMs), which influence their activity and intracellular localization. The core clock protein BMAL1 undergoes several PTMs. Here we report that the Akt-GSK3beta signaling pathway regulates BMAL1 protein stability and activity.GSK3beta phosphorylates BMAL1 specifically on Ser 17 and Thr 21 and primes it for ubiquitylation. In the absence of GSK3beta-mediated phosphorylation, BMAL1 becomes stabilized and BMAL1 dependent circadian gene expression is dampened. Dopamine D2 receptor mediated signaling, known to control the Akt-GSK3beta pathway, influences BMAL1 stability and in vivo circadian gene expression in striatal neurons.These findings uncover a previously unknown mechanism of circadian clock control. The GSK3beta kinase phosphorylates BMAL1, an event that controls the stability of the protein and the amplitude of circadian oscillation. BMAL1 phosphorylation appears to be an important regulatory step in maintaining the robustness of the circadian clock