On tubular neighborhoods of piecewise linear and topological manifolds.

Analogues of the smooth tubular neighborhood theorem are developed for the topological and piecewise linear categories.

A new construction of Calabi–Yau manifolds: Generalized CICYs

We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi–Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility stems from the fact that they can be simply described in terms of a ‘configuration matrix’, a matrix of integers from which many of the details of the geometries can be easily extracted. The generalization we present is to allow negative integers in the configuration matrices which were previously taken to have positive semi-definite entries. This broadening of the complete intersection construction leads to a larger class of Calabi–Yau manifolds than that considered in previous work, which nevertheless enjoys much of the same degree of calculational control. These new Calabi–Yau manifolds are complete intersections in (not necessarily Fano) ambient spaces with an effective anticanonical class. We find examples with topology distinct from any that has appeared in the literature to date. The new manifolds thus obtained have many interesting features. For example, they can have smaller Hodge numbers than ordinary CICYs and lead to many examples with elliptic and K3-fibration structures relevant to F-theory and string dualities.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Dielectron Mass Spectra From Au+au Collisions At √[s(nn)]=200 gev.

We report the STAR measurements of dielectron (e(+)e(-)) production at midrapidity (|y(ee)|<1) in Au+Au collisions at √[s(NN)]=200  GeV. The measurements are evaluated in different invariant mass regions with a focus on 0.30-0.76 (ρ-like), 0.76-0.80 (ω-like), and 0.98-1.05 (ϕ-like)   GeV/c(2). The spectrum in the ω-like and ϕ-like regions can be well described by the hadronic cocktail simulation. In the ρ-like region, however, the vacuum ρ spectral function cannot describe the shape of the dielectron excess. In this range, an enhancement of 1.77±0.11(stat)±0.24(syst)±0.33(cocktail) is determined with respect to the hadronic cocktail simulation that excludes the ρ meson. The excess yield in the ρ-like region increases with the number of collision participants faster than the ω and ϕ yields. Theoretical models with broadened ρ contributions through interactions with constituents in the hot QCD medium provide a consistent description of the dilepton mass spectra for the measurement presented here and the earlier data at the Super Proton Synchrotron energies.

Convergence Of Soil Nitrogen Isotopes Across Global Climate Gradients.

Quantifying global patterns of terrestrial nitrogen (N) cycling is central to predicting future patterns of primary productivity, carbon sequestration, nutrient fluxes to aquatic systems, and climate forcing. With limited direct measures of soil N cycling at the global scale, syntheses of the (15)N:(14)N ratio of soil organic matter across climate gradients provide key insights into understanding global patterns of N cycling. In synthesizing data from over 6000 soil samples, we show strong global relationships among soil N isotopes, mean annual temperature (MAT), mean annual precipitation (MAP), and the concentrations of organic carbon and clay in soil. In both hot ecosystems and dry ecosystems, soil organic matter was more enriched in (15)N than in corresponding cold ecosystems or wet ecosystems. Below a MAT of 9.8°C, soil δ(15)N was invariant with MAT. At the global scale, soil organic C concentrations also declined with increasing MAT and decreasing MAP. After standardizing for variation among mineral soils in soil C and clay concentrations, soil δ(15)N showed no consistent trends across global climate and latitudinal gradients. Our analyses could place new constraints on interpretations of patterns of ecosystem N cycling and global budgets of gaseous N loss.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

Photophysical properties of a photocytotoxic fluorinated chlorin conjugated to four beta-cyclodextrins

A meso-tetrakis(pentafluorophenyl)-chlorin with the reduced pyrrole ring linked to an isoxazolidine ring (FC) has been conjugated to four beta-cyclodextrins (CDFC). The CDFC exhibits excellent water solubility and is a potent photosensitizer towards proliferating NCTC 2544 human keratinocytes. The study by conventional steady state absorption and fluorescence spectroscopies and by time-resolved femto- and nanosecond laser flash spectroscopies suggests that in ethanol and pH 7 buffer the beta-cyclodextrins embed the highly hydrophobic tetrakis(pentafluorophenyl)-chlorin macrocycle and strongly interact with the chlorin rings in the singlet and triplet manifolds. In these solvents, femtosecond spectroscopy suggests that the conjugate undergoes a rapid relaxation in the upper excited singlet states induced by photochemical and/or conformation change(s) at a rate of about 5 ps(-1) to fluorescent states whose lifetime is similar to 8 ns. This interaction is destroyed upon addition of Triton X100 to buffer. Both FC and CDFC strongly fluoresce (Phi(F) similar to 0.5) in micelles. Similar behavior is observed at the triplet level. In ethanol and water, the initial transient triplet state absorbance decays within 1-3 mu s yielding a longer lived triplet with spectral properties indistinguishable from that of original difference absorbance spectra. The determination of the molar absorbance in the 440-460 nm region (similar to 35 000 M(-1) cm(-1)) leads to an estimate of similar to 0.2 for the triplet formation quantum yield of FC in toluene and of FC and CDFC in Triton X100 micelles. Quenching of the CDFC triplets by dioxygen in buffer produces (1)O(2) in a good yield consistent with the effective photocytotoxicity of the chlorin-cyclodextrins conjugate towards cultured NCTC 2544 human keratinocytes. By contrast, FC which aggregates in buffer produces little if any (1)O(2).

The non-equilibrium nature of culinary evolution

Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here, we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural 'founder effect' produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes.

Comparative Analysis of Activation Phenotype, Proliferation, and IFN-gamma Production by Spleen NK1.1(+) and NK1.1(-) T Cells During Plasmodium chabaudi AS Malaria

The NK1.1 molecule participates in NK, NKT, and T-cell activation, contributing to IFN-gamma production and cytotoxicity. To characterize the early immune response to Plasmodium chabaudi AS, spleen NK1.1(+) and NK1.1(-) T cells were compared in acutely infected C57BL/6 mice. The first parasitemia peak in C57BL/6 mice correlated with increase in CD4(+)NK1.1(+)TCR-alpha beta(+), CD8(+)NK1.1(+)TCR-alpha beta(+), and CD4(+)NK1.1(-)TCR-alpha beta(+) cell numbers per spleen, where a higher increment was observed for NK1.1(+) T cells compared to NK1.1(-) T cells. According to the ability to recognize the CD1d-alpha-GalCer tetramer, CD4(+)NK1.1(+) cells in 7-day infected mice were not predominantly invariant NKT cells. At that time, nearly all NK1.1(+) T cells and around 30% of NK1.1(-) T cells showed an experienced/activated (CD44(HI)CD69(HI)CD122(HI)) cell phenotype, with high expression of Fas and PD-L1 correlating with their low proliferative capacity. Moreover, whereas IFN-gamma production by CD4(+)NK1.1(+) cells peaked at day 4 p.i., the IFN-gamma response of CD4(+)NK1.1(-) cells continued to increase at day 5 of infection. We also observed, at day 7 p.i., 2-fold higher percentages of perforin(+) cells in CD8(+)NK1.1(+) cells compared to CD8(+)NK1.1(-) cells. These results indicate that spleen NK1.1(+) and NK1.1(-) T cells respond to acute P. chabaudi malaria with different kinetics in terms of activation, proliferation, and IFN-gamma production.