On the Rabinowitz Floer homology of twisted cotangent bundles

Consider the cotangent bundle of a Riemannian manifold $(M,g)$ of dimension 2 or more, endowed with a twisted symplectic structure defined by a closed weakly exact 2-form $\sigma$ on $M$ whose lift to the universal cover of $M$ admits a bounded primitive. We compute the Rabinowitz Floer homology of energy hypersurfaces $\Sigma_{k}=H^{-1}(k)$ of mechanical (kinetic energy + potential) Hamiltonians $H$ for the case when the energy value k is greater than the Mane critical value c. Under the stronger condition that k>c_{0}, where c_{0} denotes the strict Mane critical value, Abbondandolo and Schwarz recently computed the Rabinowitz Floer homology of such hypersurfaces, by means of a short exact sequence of chain complexes involving the Rabinowitz Floer chain complex and the Morse (co)chain complex associated to the free time action functional. We extend their results to the weaker case k>c, thus covering cases where $\sigma$ is not exact. As a consequence, we deduce that the hypersurface corresponding to the energy level k is never displaceable for any k>c. Moreover, we prove that if dim M > 1, the homology of the free loop space of $M$ is infinite dimensional, and if the metric is chosen generically, a generic Hamiltonian diffeomorphism has infinitely many leaf-wise intersection points in $\Sigma_{k}$.Comment: V4 - final version, accepted for publication in CVPD

Commercial potential of remote sensing data from the Earth observing system

The purpose was to assess the market potential of remote sensing value-added products from the Earth Observing System (EOS) platform. Sensors on the EOS platform were evaluated to determine which qualities and capabilities could be useful to the commercial user. The approach was to investigate past and future satellite data distribution programs. A questionnaire was developed for use in a telephone survey. Based on the results of the survey of companies that add value to remotely sensed data, conversations with the principal investigators in charge of each EOS sensor, a study of past commercial satellite data ventures, and reading from the commercial remote sensing industry literature, three recommendations were developed: develop a strategic plan for commercialization of EOS data, define a procedure for commercial users within the EOS data stream, and develop an Earth Observations Commercial Applications Program-like demonstration program within NASA using EOS simulated data

Floer homology for magnetic fields with at most linear growth on the universal cover

The Floer homology of a cotangent bundle is isomorphic to loop space homology of the underlying manifold, as proved by Abbondandolo-Schwarz, Salamon-Weber, and Viterbo. In this paper we show that in the presence of a Dirac magnetic monopole which admits a primitive with sublinear growth on the universal cover, the Floer homology in atoroidal free homotopy classes is again isomorphic to loop space homology. As a consequence we prove that for any atoroidal free homotopy class and any sufficiently small T>0, any magnetic flow associated to the Dirac magnetic monopole has a closed orbit of period T belonging to the given free homotopy class. In the case where the Dirac magnetic monopole admits a bounded primitive on the universal cover we also prove the Conley conjecture for Hamiltonians that are quadratic at infinity, i.e., we show that such Hamiltonians have infinitely many periodic orbits.Comment: 24 pages, V2 - minor corrections, final version to appear in JF

Impaired Nuclear Export of Polyglutamine-Expanded Androgen Receptor in Spinal and Bulbar Muscular Atrophy.

Spinal and bulbar muscular atrophy (SBMA) is a neuromuscular disease caused by polyglutamine (polyQ) expansion in the androgen receptor (AR). Prior studies have highlighted the importance of AR nuclear localization in SBMA pathogenesis; therefore, in this study, we sought to determine the role of AR nuclear export in the pathological manifestations of SBMA. We demonstrate here that the nuclear export of polyQ-expanded AR is impaired, even prior to the formation of intranuclear inclusions of aggregated AR. Additionally, we find that promoting AR export with an exogenous nuclear export signal substantially reduces its aggregation and blocks hormone-induced toxicity. Moreover, we show that these protective effects are conferred by destabilization of the mutant protein due to an increase in proteasomal degradation of the cytoplasmic AR. Despite a growing body of evidence that global disruption of nucleo/cytoplasmic transport occurs in ALS and HD, our data suggest that no such global disruption occurs in models of SBMA; rather, AR-specific mechanisms, including reduced phosphorylation at Serine 650, are likely responsible for the impaired nuclear export of polyQ-expanded AR

Closed orbits of a charge in a weakly exact magnetic field

We prove that for a weakly exact magnetic system on a closed connected Riemannian manifold, almost all energy levels contain a closed orbit. More precisely, we prove the following stronger statements. Let $(M,g)$ denote a closed connected Riemannian manifold and $\sigma$ a weakly exact 2-form. Let $\phi_{t}$ denote the magnetic flow determined by $\sigma$, and let $c$ denote the Mane critical value of the pair $(g,\sigma)$. We prove that if $k>c$, then for every non-trivial free homotopy class of loops on $M$ there exists a closed orbit with energy $k$ whose projection to $M$ belongs to that free homotopy class. We also prove that for almost all $k<c$ there exists a closed orbit with energy $k$ whose projection to $M$ is contractible. In particular, when $c=\infty$ this implies that almost every energy level has a contractible closed orbit. As a corollary we deduce that if $\sigma$ is not exact and $M$ has an amenable fundamental group (which implies $c=\infty$) then there exist contractible closed orbits on almost every energy level.Comment: 25 pages. v3 - minor corrections, this version to appear in PJ

FEDERAL ESTATE AND GIFT TAX: CONCEPT OF A TRANSFER

The first of the modern federal death tax laws, enacted in 1916 imposed upon the transfer of the net estate of every decedent a tax measured essentially by the net value of certain property interests at the time of his death. The tax was upheld as an indirect tax or excise upon the privilege of transmitting property at death and its fundamental nature has never been changed. There has been, however, an almost continuous controversy as to the property interests which may and should be included in the basic measure of the tax-the gross estate--and the present law embodies numerous amendments in this respect. The property interests included may be classified as (1) interests passing by will or the laws of succession and (2) interests of which the decedent for no valuable consideration made a transfer inter vivos related in some manner to his death. The latter type of interests, included in the gross estate in an effort to prevent tax avoidance, have precipitated most of the Supreme Court decisions in the estate tax field, and as to the inclusion of these interests there has been painfully developed a concept of a transfer which is unique