Tautness for riemannian foliations on non-compact manifolds

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$ (relatively to a suitable riemannian metric $\mu$) is zero. In the transversally orientable case, tautness is equivalent to the non-vanishing of the top basic cohomology group $H^{^{n}}(M/\mathcal{F})$, where n = \codim \mathcal{F}. By the Poincar\'e Duality, this last condition is equivalent to the non-vanishing of the basic twisted cohomology group $H^{^{0}}_{_{\kappa_\mu}}(M/\mathcal{F})$, when $M$ is oriented. When $M$ is not compact, the tautness class is not even defined in general. In this work, we recover the previous study and results for a particular case of riemannian foliations on non compact manifolds: the regular part of a singular riemannian foliation on a compact manifold (CERF).Comment: 18 page

Intrinsic and Extrinsic Performance Limits of Graphene Devices on SiO2

The linear dispersion relation in graphene[1,2] gives rise to a surprising prediction: the resistivity due to isotropic scatterers (e.g. white-noise disorder[3] or phonons[4-8]) is independent of carrier density n. Here we show that acoustic phonon scattering[4-6] is indeed independent of n, and places an intrinsic limit on the resistivity in graphene of only 30 Ohm at room temperature (RT). At a technologically-relevant carrier density of 10^12 cm^-2, the mean free path for electron-acoustic phonon scattering is >2 microns, and the intrinsic mobility limit is 2x10^5 cm^2/Vs, exceeding the highest known inorganic semiconductor (InSb, ~7.7x10^4 cm^2/Vs[9]) and semiconducting carbon nanotubes (~1x10^5 cm^2/Vs[10]). We also show that extrinsic scattering by surface phonons of the SiO2 substrate[11,12] adds a strong temperature dependent resistivity above ~200 K[8], limiting the RT mobility to ~4x10^4 cm^2/Vs, pointing out the importance of substrate choice for graphene devices[13].Comment: 16 pages, 3 figure

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincar\'e duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad

Seed-mediated atomic-scale reconstruction of silver manganate nanoplates for oxygen reduction towards high-energy aluminum-air flow batteries

Aluminum-air batteries are promising candidates for next-generation high-energy-density storage, but the inherent limitations hinder their practical use. Here, we show that silver nanoparticle-mediated silver manganate nanoplates are a highly active and chemically stable catalyst for oxygen reduction in alkaline media. By means of atomic-resolved transmission electron microscopy, we find that the formation of stripe patterns on the surface of a silver manganate nanoplate originates from the zigzag atomic arrangement of silver and manganese, creating a high concentration of dislocations in the crystal lattice. This structure can provide high electrical conductivity with low electrode resistance and abundant active sites for ion adsorption. The catalyst exhibits outstanding performance in a flow-based aluminum-air battery, demonstrating high gravimetric and volumetric energy densities of similar to 2552 Wh kg(Al)(-1) and similar to 6890 Wh I-Al(-1) at 100 mA cm(-2), as well as high stability during a mechanical recharging process

Emergent Genome-Wide Control in Wildtype and Genetically Mutated Lipopolysaccarides-Stimulated Macrophages

Large-scale gene expression studies have mainly focused on highly expressed and ‘discriminatory’ genes to decipher key regulatory processes. Biological responses are consequence of the concerted action of gene regulatory network, thus, limiting our attention to genes having the most significant variations is insufficient for a thorough understanding of emergent whole genome response. Here we comprehensively analyzed the temporal oligonucleotide microarray data of lipopolysaccharide (LPS) stimulated macrophages in 4 genotypes; wildtype, Myeloid Differentiation factor 88 (MyD88) knockout (KO), TIR-domain-containing adapter-inducing interferon-β (TRIF) KO and MyD88/TRIF double KO (DKO). Pearson correlations computed on the whole genome expression between different genotypes are extremely high (>0.98), indicating a strong co-regulation of the entire expression network. Further correlation analyses reveal genome-wide response is biphasic, i) acute-stochastic mode consisting of small number of sharply induced immune-related genes and ii) collective mode consisting of majority of weakly induced genes of diverse cellular processes which collectively adjust their expression level. Notably, temporal correlations of a small number of randomly selected genes from collective mode show scalability. Furthermore, in collective mode, the transition from large scatter in expression distributions for single ORFs to smooth linear lines emerges as an organizing principle when grouping of 50 ORFs and above. With this emergent behavior, the role of MyD88, TRIF and novel MyD88, TRIF-independent processes for gene induction can be linearly superposed to decipher quantitative whole genome differential control of transcriptional and mRNA decay machineries. Our work demonstrates genome-wide co-regulated responses subsequent to specific innate immune stimulus which have been largely neglected