Recovering S1S^1-invariant metrics on S2S^2 from the equivariant spectrum

We prove an inverse spectral result for $S^1$-invariant metrics on $S^2$ based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the $S^1$ action on the eigenspaces. Our result generalizes an inverse spectral result of the first and last named authors, together with Victor Guillemin, concerning $S^1$-invariant metrics on $S^2$ which are invariant under the antipodal map. We use higher order terms in the asymptotic expansion of a natural spectral measure associated with the Laplacian and the $S^1$ action.Comment: 16 pages; minor revisions throughout following comments from referee

Hearing Delzant polytopes from the equivariant spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.Comment: 23 pages, 9 figures; v2 is published versio

Ect2/Pbl Acts via Rho and Polarity Proteins to Direct the Assembly of an Isotropic Actomyosin Cortex upon Mitotic Entry.

Entry into mitosis is accompanied by profound changes in cortical actomyosin organization. Here, we delineate a pathway downstream of the RhoGEF Pbl/Ect2 that directs this process in a model epithelium. Our data suggest that the release of Pbl/Ect2 from the nucleus at mitotic entry drives Rho-dependent activation of Myosin-II and, in parallel, induces a switch from Arp2/3 to Diaphanous-mediated cortical actin nucleation that depends on Cdc42, aPKC, and Par6. At the same time, the mitotic relocalization of these apical protein complexes to more lateral cell surfaces enables Cdc42/aPKC/Par6 to take on a mitosis-specific function-aiding the assembly of a relatively isotropic metaphase cortex. Together, these data reveal how the repolarization and remodeling of the actomyosin cortex are coordinated upon entry into mitosis to provide cells with the isotropic and rigid form they need to undergo faithful chromosome segregation and division in a crowded tissue environment

Increasing U.S. Hard Red Winter Wheat Competitiveness in Latin American Markets

The United States wheat sector leadership in world markets is facing serious challenges. Canada, Australia, Argentina, the European Union (EU), and the Former Soviet Union (FSU) are growing contenders for international wheat markets. Wheat buyers´ concerns about quality specifications and its consistency have intensified without precedents in the last years. The study focuses on identifying the attributes that wheat buyers most value at the moment of purchase. The study will be done in two stages. The first stage will focus in estimating preferences from actual wheat transactions from different grain-sheds in the HRW growing area. The second stage will focus on the demand from Latin American millers and will estimate their attribute preference and elicit willingness to pay. The second stage will start with Mexican millers, given their importance for the HRW exports. A hedonic price model will be used for the first stage. The second part of the study will attempt to elicit miller´s preferences by using a self explicated approach. Expected results are that the "easy-to-measure attributes": test weight, and protein levels; and all functionality characteristics such as bake absorption, farinograph peak time, farinograph stability, alveograph p/l ratio will be the most valued by the wheat customers. We hypothesize that millers will be willing to pay a premium if those attributes are present in desirable levels. The information should provide insight into the efforts being made by wheat marketing agencies and the U.S. Wheat Associates to promote quality-based marketing of wheat to domestic and foreign millers. Discussion may also include the impacts of quality-based marketing on U.S. share of the world wheat market.International Relations/Trade,

Effect of Publicly Released Quality Information for US Hard Red Winter Wheat on Mexican Millers' Welfare

Entities have been providing quality related information to overseas wheat buyers as a response to the increased requests for this information. This study measures the value of information to Mexican millers. The value to Mexican millers is measured by the difference of the flour mill surplus and compensating variation.Agribusiness, Research and Development/Tech Change/Emerging Technologies,

Ultralight boson cloud depletion in binary systems

Ultralight scalars can extract rotational energy from astrophysical black holes through superradiant instabilities, forming macroscopic boson clouds. This process is most efficient when the Compton wavelength of the boson is comparable to the size of the black hole horizon, i.e. when the "gravitational fine structure constant" $\alpha\equiv G \mu M/\hbar c\sim 1$. If the black hole/cloud system is in a binary, tidal perturbations from the companion can produce resonant transitions between the energy levels of the cloud, depleting it by an amount that depends on the nature of the transition and on the parameters of the binary. Previous cloud depletion estimates considered binaries in circular orbit and made the approximation $\alpha\ll 1$. Here we use black hole perturbation theory to compute instability rates and decay widths for generic values of $\alpha$, and we show that this leads to much larger cloud depletion estimates when $\alpha \gtrsim 0.1$. We also study eccentric binary orbits. We show that in this case resonances can occur at all harmonics of the orbital frequency, significantly extending the range of frequencies where cloud depletion may be observable with gravitational wave interferometers.Comment: 12 pages, 6 figures. v2: references added, matches published versio

Massive vector fields on the Schwarzschild spacetime: quasinormal modes and bound states

We study the propagation of a massive vector or Proca field on the Schwarzschild spacetime. The field equations are reduced to a one-dimensional wave equation for the odd-parity part of the field and two coupled equations for the even-parity part of the field. We use numerical techniques based on solving (scalar or matrix-valued) three-term recurrence relations to compute the spectra of both quasi-normal modes and quasi-bound states, which have no massless analogue, complemented in the latter case by a forward-integration method. We study the radial equations analytically in both the near-horizon and far-field regions and use a matching procedure to compute the associated spectra in the small-mass limit. Finally, we comment on extending our results to the Kerr geometry and its phenomenological relevance for hidden photons arising e.g. in string theory compactifications.Comment: 15 pages, 8 figures; minor corrections, to be published in Phys. Rev.

Electric properties of granitic rocks

The objective of this work is to clarify the role of water content on the charge trans- port mechanisms of different granitic rocks. The mineralogical content of the rocks will also be taken into account. From the electrical point of view these materials are rather insulating porous media where charge injection creates different phenomena like build-up charges, space charge limited currents, surface effects and other behav- iors that resemble much a variety of oxides, like AlO

Photon Self-Induced Spin to Orbital Conversion in TGG crystal at high laser power

In this paper, we present experimental evidence of a newly discovered third-order nonlinear optical process Self-Induced Spin-to-Orbital Conversion (SISTOC) of the photon angular momentum. This effect is the physical mechanism at the origin of the depolarization of very intense laser beams propagating in isotropic materials. The SISTOC process, like self-focusing, is triggered by laser heating leading to a radial temperature gradient in the medium. In this work we tested the occurrence of SISTOC in a terbium gallium garnet (TGG) rod for an impinging laser power of about 100~W. To study the SISTOC process we used different techniques: polarization analysis, interferometry and tomography of the photon orbital angular momentum. Our results confirm, in particular, that the apparent depolarization of the beam is due to the occurrence of maximal entanglement between the spin and orbital angular momentum of the photons undergoing the SISTOC process. This explanation of the true nature of the depolarization mechanism could be of some help in finding novel methods to reduce or to compensate for this usually unwanted depolarization effect in all cases where very high laser power and good beam quality are required.Comment: 6 pages, 10 figures, submitte