The transverse index theorem for proper cocompact actions of Lie groupoids

Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples the meaning of the index pairing and our index formula.Comment: 29 page

The index of geometric operators on Lie groupoids

We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formulae for Lie groupoid analogues of the familiar geometric operators on manifolds such as the signature and Dirac operator expressed in terms of the usual characteristic classes in Lie algebroid cohomology.Comment: 15 page

Quantization of Whitney functions

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization of Whitney functions over a closed subset of a symplectic manifold. Under the assumption that the underlying symplectic manifold is analytic and the singular subset subanalytic, we determine that the Hochschild and cyclic homology of the deformed algebra of Whitney functions over the subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page

Polyelectrolyte Condensation Induced by Linear Cations

We examine the role of the condensing agent in the formation of polyelectrolyte bundles, via grand-canonical Monte Carlo simulations. Following recent experiments we use linear, rigid divalent cations of various lengths to induce condensation. Our results clarify and explain the experimental results for short cations. For longer cations we observe novel condensation behavior owing to alignment of the cations. We also study the role of the polyelectrolyte surface charge density, and find a nonmonotonic variation in bundle stability. This nonmonotonicity captures two trends that have been observed in separate experiments.Comment: To appear in Physical Review Letter

Generalized linear isotherm regularity equation of state applied to metals

A three-parameter equation of state (EOS) without physically incorrect oscillations is proposed based on the generalized Lennard-Jones (GLJ) potential and the approach in developing linear isotherm regularity (LIR) EOS of Parsafar and Mason [J. Phys. Chem., 1994, 49, 3049]. The proposed (GLIR) EOS can include the LIR EOS therein as a special case. The three-parameter GLIR, Parsafar and Mason (PM) [Phys. Rev. B, 1994, 49, 3049], Shanker, Singh and Kushwah (SSK) [Physica B, 1997, 229, 419], Parsafar, Spohr and Patey (PSP) [J. Phys. Chem. B, 2009, 113, 11980], and reformulated PM and SSK EOSs are applied to 30 metallic solids within wide pressure ranges. It is shown that the PM, PMR and PSP EOSs for most solids, and the SSK and SSKR EOSs for several solids, have physically incorrect turning points, and pressure becomes negative at high enough pressure. The GLIR EOS is capable not only of overcoming the problem existing in other five EOSs where the pressure becomes negative at high pressure, but also gives results superior to other EOSs.Comment: 9 pages, 3 figure

Calcium-Sensing Receptor Regulates Cytosolic [Ca 2+ ] and Plays a Major Role in the Development of Pulmonary Hypertension.

Pulmonary arterial hypertension (PAH) is a progressive disease characterized by elevated pulmonary vascular resistance (PVR) leading to right heart failure and premature death. The increased PVR results in part from pulmonary vascular remodeling and sustained pulmonary vasoconstriction. Excessive pulmonary vascular remodeling stems from increased pulmonary arterial smooth muscle cell (PASMC) proliferation and decreased PASMC apoptosis. A rise in cytosolic free Ca2+ concentration ([Ca2+]cyt) in PASMC is a major trigger for pulmonary vasoconstriction and a key stimulus for PASMC proliferation and migration, both contributing to the development of pulmonary vascular remodeling. PASMC from patients with idiopathic PAH (IPAH) have increased resting [Ca2+]cyt and enhanced Ca2+ influx. Enhanced Ca2+ entry into PASMC due to upregulation of membrane receptors and/or Ca2+ channels may contribute to PASMC contraction and proliferation and to pulmonary vasoconstriction and pulmonary vascular remodeling. We have shown that the extracellular Ca2+-sensing receptor (CaSR), which is a member of G protein-coupled receptor (GPCR) subfamily C, is upregulated, and the extracellular Ca2+-induced increase in [Ca2+]cyt is enhanced in PASMC from patients with IPAH in comparison to PASMC from normal subjects. Pharmacologically blockade of CaSR significantly attenuate the development and progression of experimental pulmonary hypertension in animals. Additionally, we have demonstrated that dihydropyridine Ca2+ channel blockers (e.g., nifedipine), which are used to treat PAH patients but are only effective in 15-20% of patients, activate CaSR resulting in an increase in [Ca2+]cyt in IPAH-PASMC, but not normal PASMC. Our data indicate that CaSR functionally couples with transient receptor potential canonical (TRPC) channels to mediate extracellular Ca2+-induced Ca2+ influx and increase in [Ca2+]cyt in IPAH-PASMC. Upregulated CaSR is necessary for the enhanced extracellular Ca2+-induced increase in [Ca2+]cyt and the augmented proliferation of PASMC in patients with IPAH. This review will highlight the pathogenic role of CaSR in the development and progression of PAH