Minkowski superspaces and superstrings as almost real-complex supermanifolds

In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the collection of subspaces of the tangent space, and in every subspace a complex structure is given. An almost complex structure on a real supermanifold can be given by an even or odd operator; it is complex (without "always") if the suitable superization of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we define the circumcised analog of the Nijenhuis tensor. We compute it for the Minkowski superspaces and superstrings. The space of values of the circumcised Nijenhuis tensor splits into (indecomposable, generally) components whose irreducible constituents are similar to those of Riemann or Penrose tensors. The Nijenhuis tensor vanishes identically only on superstrings of superdimension 1|1 and, besides, the superstring is endowed with a contact structure. We also prove that all real forms of complex Grassmann algebras are isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to related recent work by Witten is adde

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Topology Change in Canonical Quantum Cosmology

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.Comment: 23 pages, LaTex file. We added in the conclusion some comments about path integral formalism and corrected litle misprinting

Advanced Three Level Approximation for Numerical Treatment of Cosmological Recombination

New public numerical code for fast calculations of the cosmological recombination of primordial hydrogen-helium plasma is presented. The code is based on the three-level approximation (TLA) model of recombination and allows us to take into account some fine physical effects of cosmological recombination simultaneously with using fudge factors. The code can be found at http://www.ioffe.ru/astro/QC/CMBR/atlant/atlant.htmlComment: 10 pages, 7 figures, 1 table, to be submitted to MNRA

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

Immunological Mechanisms Mediating Hantavirus Persistence in Rodent Reservoirs

Hantaviruses, similar to several emerging zoonotic viruses, persistently infect their natural reservoir hosts, without causing overt signs of disease. Spillover to incidental human hosts results in morbidity and mortality mediated by excessive proinflammatory and cellular immune responses. The mechanisms mediating the persistence of hantaviruses and the absence of clinical symptoms in rodent reservoirs are only starting to be uncovered. Recent studies indicate that during hantavirus infection, proinflammatory and antiviral responses are reduced and regulatory responses are elevated at sites of increased virus replication in rodents. The recent discovery of structural and non-structural proteins that suppress type I interferon responses in humans suggests that immune responses in rodent hosts could be mediated directly by the virus. Alternatively, several host factors, including sex steroids, glucocorticoids, and genetic factors, are reported to alter host susceptibility and may contribute to persistence of hantaviruses in rodents. Humans and reservoir hosts differ in infection outcomes and in immune responses to hantavirus infection; thus, understanding the mechanisms mediating viral persistence and the absence of disease in rodents may provide insight into the prevention and treatment of disease in humans. Consideration of the coevolutionary mechanisms mediating hantaviral persistence and rodent host survival is providing insight into the mechanisms by which zoonotic viruses have remained in the environment for millions of years and continue to be transmitted to humans

Li@C60 as a multi-state molecular switch

R.S. acknowledges financial support from the Scottish Funding Council through SRD-Grant (HR07003). E.E.B.C. gratefully acknowledges Idea International Inc., Sendai, for providing samples of [Li@C60]+(PF6)–. H.J.C. and M.S. acknowledge financial support of EPSRC DTG studentships (EP/M508214/1 and EP/N509644/1, respectively).The field of molecular electronics aims at advancing the miniaturization of electronic devices, by exploiting single molecules to perform the function of individual components. A molecular switch is defined as a molecule that displays stability in two or more states (e.g. “on” and “off” involving conductance, conformation etc.) and upon application of a controlled external perturbation, electric or otherwise, undergoes a reversible change such that the molecule is altered. Previous work has shown multi-state molecular switches with up to four and six distinct states. Using low temperature scanning tunnelling microscopy and spectroscopy, we report on a multi-state single molecule switch using the endohedral fullerene Li@C60 that displays 14 molecular states which can be statistically accessed. We suggest a switching mechanism that relies on resonant tunnelling via the superatom molecular orbitals (SAMOs) of the fullerene cage as a means of Li activation, thereby bypassing the typical vibronic excitation of the carbon cage that is known to cause molecular decomposition.Publisher PDFPeer reviewe