Linear Connections on Graphs

In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the differential algebras for graphs by extending the work of Dimakis et al and discuss linear connections and curvatures on graphs. Especially, we calculate connections and curvatures explicitly for the general nonzero torsion case. There is a metric, but no metric-compatible connection in general except the complete symmetric graph with two vertices.Comment: 22pages, Latex file, Some errors corrected, To appear in J. Math. Phy

Experimental study of planetary gases with applications to planetary interior models

High-pressure experimental data on planetary materials are critical in developing planetary models and in addressing otherwise insoluble problems of the internal structure of the major planets. Progress in the last five years has been particularly marked. Maximum static pressure of 550 GPa was achieved. For the first time, X-ray diffraction of solidified gases (Ne, Xe) and ices (H2O) were obtained at pressures above one megabar, single-crystal diffraction of ultralight elements (H2, He) were detected up to 25 GPa, pressures over 200 GPa at 77 K were reached in solid hydrogen, including the discovery of a phase transformation in the molecular solid. Advances in instrumentation and new measurements performed during 1983 to 1988 are summarized

Behavioral ontogeny in larvae and early juveniles of the giant trevally (Caranx ignobilis) (Pisces: Carangidae)

Behavior of young (8−18 mm SL) giant trevally (Caranx ignobilis), a large coral-reef−associated predator, was observed in the laboratory and the ocean. Size was a better predictor of swimming speed and endurance than was age. Critical speed increased with size from 12 to 40 cm/s at 2.7 cm/s for each mm increase in size. Mean scaled critical speed was 19 body lengths/s and was not size related. Swimming speed in the ocean was 4 to 20 cm/s (about half of critical speed) and varied among areas, but within each area, it increased at 2 cm/s for each mm increase in size. Swimming endurance in the laboratory increased from 5 to 40 km at 5 km for each mm increase in size. Vertical distribution changed ontogenetically: larvae swam shallower, but more variably, and then deeper with growth. Two-thirds of individuals swam directionally with no ontogenetic increase in orientation precision. Larvae swam offshore off open coasts, but not in a bay. In situ observations of C. ignobilis feeding, interacting with pelagic animals, and reacting to reefs are reported. Manus

Single-Cell Transcriptomes Reveal a Complex Cellular Landscape in the Middle Ear and Differential Capacities for Acute Response to Infection.

Single-cell transcriptomics was used to profile cells of the normal murine middle ear. Clustering analysis of 6770 transcriptomes identified 17 cell clusters corresponding to distinct cell types: five epithelial, three stromal, three lymphocyte, two monocyte, two endothelial, one pericyte and one melanocyte cluster. Within some clusters, cell subtypes were identified. While many corresponded to those cell types known from prior studies, several novel types or subtypes were noted. The results indicate unexpected cellular diversity within the resting middle ear mucosa. The resolution of uncomplicated, acute, otitis media is too rapid for cognate immunity to play a major role. Thus innate immunity is likely responsible for normal recovery from middle ear infection. The need for rapid response to pathogens suggests that innate immune genes may be constitutively expressed by middle ear cells. We therefore assessed expression of innate immune genes across all cell types, to evaluate potential for rapid responses to middle ear infection. Resident monocytes/macrophages expressed the most such genes, including pathogen receptors, cytokines, chemokines and chemokine receptors. Other cell types displayed distinct innate immune gene profiles. Epithelial cells preferentially expressed pathogen receptors, bactericidal peptides and mucins. Stromal and endothelial cells expressed pathogen receptors. Pericytes expressed pro-inflammatory cytokines. Lymphocytes expressed chemokine receptors and antimicrobials. The results suggest that tissue monocytes, including macrophages, are the master regulators of the immediate middle ear response to infection, but that virtually all cell types act in concert to mount a defense against pathogens

On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators

The spectra of the Schr\"odinger operators with periodic potentials are studied. When the potential is real and periodic, the spectrum consists of at most countably many line segments (energy bands) on the real line, while when the potential is complex and periodic, the spectrum consists of at most countably many analytic arcs in the complex plane. In some recent papers, such operators with complex $\mathcal{PT}$-symmetric periodic potentials are studied. In particular, the authors argued that some energy bands would appear and disappear under perturbations. Here, we show that appearance and disappearance of such energy bands imply existence of nonreal spectra. This is a consequence of a more general result, describing the local shape of the spectrum.Comment: 5 pages, 2 figure

Anomalous frequency and intensity scaling of collective and local modes in a coupled spin tetrahedron system

We report on the magnetic excitation spectrum of the coupled spin tetrahedral system Cu$_{2}$Te$_{2}$O$_{5}$Cl$_{2}$ using Raman scattering on single crystals. The transition to an ordered state at T$_{N}^{Cl}$=18.2 K evidenced from thermodynamic data leads to the evolution of distinct low-energy magnetic excitations superimposed by a broad maximum. These modes are ascribed to magnons with different degree of localization and a two-magnon continuum. Two of the modes develop a substantial energy shift with decreasing temperature similar to the order parameter of other Neel ordered systems. The other two modes show only a negligible temperature dependence and dissolve above the ordering temperature in a continuum of excitations at finite energies. These observations point to a delicate interplay of magnetic inter- and intra-tetrahedra degrees of freedom and an importance of singlet fluctuations in describing a spin dynamics.Comment: 7pages, 6figures, 1tabl

Group V Phospholipase A2 Induces Leukotriene Biosynthesis in Human Neutrophils through the Activation of Group IVA Phospholipase A2

We reported previously that exogenously added human group V phospholipase A2 (hVPLA2) could elicit leukotriene B4 (LTB4) biosynthesis in human neutrophils (Han, S. K., Kim, K. P., Koduri, R., Bittova, L., Munoz, N. M., Leff, A. R., Wilton, D. C., Gelb, M. H., and Cho, W. (1999) J. Biol. Chem. 274, 11881-11888). To determine the mechanism of the hVPLA2-induced LTB4 biosynthesis in neutrophils, we thoroughly examined the effects of hVPLA2 and their lipid products on the activity of group IVA cytosolic PLA2 (cPLA2) and LTB4 biosynthesis under different conditions. As low as 1 nM exogenous hVPLA2 was able to induce the release of arachidonic acid (AA) and LTB4. Typically, AA and LTB4 were released in two phases, which were synchronized with a rise in intracellular calcium concentration ([Ca2+]i) near the perinuclear region and cPLA2 phosphorylation. A cellular PLA2 assay showed that hVPLA2 acted primarily on the outer plasma membrane, liberating fatty acids and lysophosphatidylcholine (lyso-PC), whereas cPLA2 acted on the perinuclear membrane. Lyso-PC and polyunsaturated fatty acids including AA activated cPLA2 and 5-lipoxygenase by increasing [Ca2+]i and inducing cPLA2 phosphorylation, which then led to LTB4 biosynthesis. The delayed phase was triggered by the binding of secreted LTB4 to the cell surface LTB4 receptor, which resulted in a rise in [Ca2+]i and cPLA2 phosphorylation through the activation of mitogen-activated protein kinase, extracellular signal-regulated kinase 1/2. These results indicate that a main role of exogenous hVPLA2 in neutrophil activation and LTB4 biosynthesis is to activate cPLA2 and 5-lipoxygenase primarily by liberating from the outer plasma membrane lyso-PC that induces [Ca2+]i increase and cPLA2 phosphorylation and that hVPLA2-induced LTB4 production is augmented by the positive feedback activation of cPLA2 by LTB4