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

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

Loop Groups, Kaluza-Klein Reduction and M-Theory

We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain generalized characteristic classes of the loop group bundle encode the Bianchi identities of the antisymmetric tensor fields of IIA supergravity. We further show that the low dimensional characteristic classes of the central extension of the loop group encode the Bianchi identities of massive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde

Near-UV and optical observations of the transiting exoplanet TrES-3b

We observed nine primary transits of the hot Jupiter TrES-3b in several optical and near-UV photometric bands from 2009 June to 2012 April in an attempt to detect its magnetic field. Vidotto, Jardine and Helling suggest that the magnetic field of TrES-3b can be constrained if its near-UV light curve shows an early ingress compared to its optical light curve, while its egress remains unaffected. Predicted magnetic field strengths of Jupiter-like planets should range between 8 G and 30 G. Using these magnetic field values and an assumed B_star of 100 G, the Vidotto et al. method predicts a timing difference of 5-11 min. We did not detect an early ingress in our three nights of near-UV observations, despite an average cadence of 68 s and an average photometric precision of 3.7 mmag. However, we determined an upper limit of TrES-3b's magnetic field strength to range between 0.013 and 1.3 G (for a 1-100 G magnetic field strength range for the host star, TrES-3) using a timing difference of 138 s derived from the Nyquist-Shannon sampling theorem. To verify our results of an abnormally small magnetic field strength for TrES-3b and to further constrain the techniques of Vidotto et al., we propose future observations of TrES-3b with other platforms capable of achieving a shorter near-UV cadence. We also present a refinement of the physical parameters of TrES-3b, an updated ephemeris and its first published near-UV light curve. We find that the near-UV planetary radius of Rp = 1.386+0.248-0.144 RJup is consistent with the planet's optical radius.Comment: Accepted for Publication in Monthly Notices of the Royal Astronomical Society (2012 September 21). 13 pages, 5 figure

Group elastic symmetries common to continuum and discrete defective crystals

The Lie group structure of crystals which have uniform continuous distributions of dislocations allows one to construct associated discrete structures—these are discrete subgroups of the corresponding Lie group, just as the perfect lattices of crystallography are discrete subgroups of R 3 , with addition as group operation. We consider whether or not the symmetries of these discrete subgroups extend to symmetries of (particular) ambient Lie groups. It turns out that those symmetries which correspond to automorphisms of the discrete structures do extend to (continuous) symmetries of the ambient Lie group (just as the symmetries of a perfect lattice may be embedded in ‘homogeneous elastic’ deformations). Other types of symmetry must be regarded as ‘inelastic’. We show, following Kamber and Tondeur, that the corresponding continuous automorphisms preserve the Cartan torsion, and we characterize the discrete automorphisms by a commutativity condition, (6.14), that relates (via the matrix exponential) to the dislocation density tensor. This shows that periodicity properties of corresponding energy densities are determined by the dislocation density

Origin of ocean island basalts: A new model based on lead and helium isotope systematics

Free to read at publisher's site. Current models of ocean island basalt (OIB) Pb isotope systematics based on longterm isolation of recycled oceanic crust (with pr without sediment) are not supported by solutions to both terrestrial Pb paradoxes. St follows that the linear arrays of OIB data in Pb isotope diagrams are mixing lines and have no age significance. A new model is presented that takes into account current solutions to both terrestrial Pb paradoxes and that explains combined Pb and He isotope evidence in terms of binary mixing. The key feature of this model is a two-stage evolution: first, long-term separation of depleted mantle from undepleted lowermost lower mantle. Mixing between these two reservoirs results in the wide spread in Pb-207/(204)Pbti` and generally high (but variable) He-3/He-4 ratios that typify enriched mantle 1 (EM1) OIBs. The second stage involves metasomatism of depleted upper mantle by EM1 type, lowermost mantle-derived melts. Evolution in the metasomatized environment is characterized by variable but generally high (Th+U)/(Pb+He) ratio that leads to a rapid increase in Pb-208/Pb-204 and Pb-206/Pb-204 ratios and decrease in He-3/He-4. Mixing between depleted mantle and melts from metasomatized mantle portions reproduces the characteristics of high mu (HIMU) OIBs. The Sr versus Nd isotope array is compatible with binary mixing between depleted mantle and near-chondritic lowermost mantle because of the large variation in Sr/Nd ratios observed in EMI and HIMU OIBs. OIBs contaminated by subcontinental lithospheric mantle (EM2) exhibit more complex isotope systematics that mask their primary geochemical evolution

CCPG1 Is a Non-canonical Autophagy Cargo Receptor Essential for ER-Phagy and Pancreatic ER Proteostasis

Mechanisms of selective autophagy of the ER, known as ER-phagy, require molecular delineation, particularly in vivo. It is unclear how these events control ER proteostasis and cellular health. Here, we identify cell-cycle progression gene 1 (CCPG1), an ER-resident protein with no known physiological role, as a non-canonical cargo receptor that directly binds to core autophagy proteins via an LIR motif to mammalian ATG8 proteins and, independently and via a discrete motif, to FIP200. These interactions facilitate ER-phagy. The CCPG1 gene is inducible by the unfolded protein response and thus directly links ER stress to ER-phagy. In vivo, CCPG1 protects against ER luminal protein aggregation and consequent unfolded protein response hyperactivation and tissue injury of the exocrine pancreas. Thus, via identification of this autophagy protein, we describe an unexpected molecular mechanism of ER-phagy and provide evidence that this may be physiologically relevant in ER luminal proteostasis

Risk of acute kidney injury and survival in patients treated with Metformin:an observational cohort study

Background: Whether metformin precipitates lactic acidosis in patients with chronic kidney disease (CKD) remains under debate. We examined whether metformin use was associated with an increased risk of acute kidney injury (AKI) as a proxy for lactic acidosis and whether survival among those with AKI varied by metformin exposure. Methods: All individuals with type 2 diabetes and available prescribing data between 2004 and 2013 in Tayside, Scotland were included. The electronic health record for diabetes which includes issued prescriptions was linked to laboratory biochemistry, hospital admission, death register and Scottish Renal Registry data. AKI events were defined using the Kidney Disease Improving Global Outcomes criteria with a rise in serum creatinine of at least 26.5 μmol/l or a rise of greater than 150% from baseline for all hospital admissions. Cox Regression Analyses were used to examine whether person-time periods in which current metformin exposure occurred were associated with an increased rate of first AKI compared to unexposed periods. Cox regression was also used to compare 28 day survival rates following first AKI events in those exposed to metformin versus those not exposed. Results: Twenty-five thousand one-hundred fourty-eight patients were included with a total person-time of 126,904 person years. 4944 (19.7%) people had at least one episode of AKI during the study period. There were 32.4 cases of first AKI/1000pyrs in current metformin exposed person-time periods compared to 44.9 cases/1000pyrs in unexposed periods. After adjustment for age, sex, diabetes duration, calendar time, number of diabetes drugs and baseline renal function, current metformin use was not associated with AKI incidence, HR 0.94 (95% CI 0.87, 1.02, p = 0.15). Among those with incident AKI, being on metformin at admission was associated with a higher rate of survival at 28 days (HR 0.81, 95% CI 0.69, 0.94, p = 0.006) even after adjustment for age, sex, pre-admission eGFR, HbA1c and diabetes duration. Conclusions: Contrary to common perceptions, we found no evidence that metformin increases incidence of AKI and was associated with higher 28 day survival following incident AKI