Finsler geodesics in the presence of a convex function and their applications

We obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.Comment: 16 pages, AMSLaTex. v2 is a minor revision: title changed, references updated, typos fixed; it matches the published version. This preprint and arXiv:math/0702323v3 [math.DG] substitute arXiv:math/0702323v2 [math.DG

Topological classification of black Hole: Generic Maxwell set and crease set of horizon

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat's principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structure of the Maxwell sets and the generic topologies of the spatial section of the horizon.Comment: 22 pages, 6 figure

GeneLink: a database to facilitate genetic studies of complex traits

BACKGROUND: In contrast to gene-mapping studies of simple Mendelian disorders, genetic analyses of complex traits are far more challenging, and high quality data management systems are often critical to the success of these projects. To minimize the difficulties inherent in complex trait studies, we have developed GeneLink, a Web-accessible, password-protected Sybase database. RESULTS: GeneLink is a powerful tool for complex trait mapping, enabling genotypic data to be easily merged with pedigree and extensive phenotypic data. Specifically designed to facilitate large-scale (multi-center) genetic linkage or association studies, GeneLink securely and efficiently handles large amounts of data and provides additional features to facilitate data analysis by existing software packages and quality control. These include the ability to download chromosome-specific data files containing marker data in map order in various formats appropriate for downstream analyses (e.g., GAS and LINKAGE). Furthermore, an unlimited number of phenotypes (either qualitative or quantitative) can be stored and analyzed. Finally, GeneLink generates several quality assurance reports, including genotyping success rates of specified DNA samples or success and heterozygosity rates for specified markers. CONCLUSIONS: GeneLink has already proven an invaluable tool for complex trait mapping studies and is discussed primarily in the context of our large, multi-center study of hereditary prostate cancer (HPC). GeneLink is freely available at

Time-dependent quantum many-body theory of identical bosons in a double well: Early time ballistic interferences of fragmented and number entangled states

A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states.Comment: 16 pages, 5 figure

Multiconfigurational Hartree-Fock theory for identical bosons in a double well

Multiconfigurational Hartree-Fock theory is presented and implemented in an investigation of the fragmentation of a Bose-Einstein condensate made of identical bosonic atoms in a double well potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized many-body states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and Hylleraas-Undheim theorems to find the optimal ground and excited states of the interacting system. The resulting energy spectrum and associated eigenstates are presented as a function of double well barrier height. Delocalized and localized single configurational states are found in the extreme limits of the simple and fragmented condensate ground states, while multiconfigurational states and macroscopic quantum superposition states are revealed throughout the full extent of barrier heights. Comparison is made to existing theories that either neglect mean field or correlation effects and it is found that contributions from both interactions are essential in order to obtain a robust microscopic understanding of the condensate's atomic structure throughout the fragmentation process.Comment: 21 pages, 13 figure

Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal

In Schwarzschild spacetime the value $r=3m$ of the radius coordinate is characterized by three different properties: (a) there is a ``light sphere'', (b) there is ``centrifugal force reversal'', (c) it is the upper limiting radius for a non-transparent Schwarschild source to act as a gravitational lens that produces infinitely many images. In this paper we prove a theorem to the effect that these three properties are intimately related in {\em any} spherically symmetric static spacetime. We illustrate the general results with some examples including black-hole spacetimes and Morris-Thorne wormholes.Comment: 18 pages, 3 eps-figure

Spectrally resolved observations of atmospheric emitted radiance in the H2O rotation band

This paper presents the project Earth Cooling by Water Vapor Radiation, an observational programme, which aims at developing a database of spectrally resolved far infrared observations, in atmospheric dry conditions, in order to validate radiative transfer models and test the quality of water vapor continuum and line parameters. The project provides the very first set of far-infrared spectral downwelling radiance measurements, in dry atmospheric conditions, which are complemented with Raman Lidar-derived temperature and water vapor profiles

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Macroscopic superposition states of ultracold bosons in a double-well potential

We present a thorough description of the physical regimes for ultracold bosons in double wells, with special attention paid to macroscopic superpositions (MSs). We use a generalization of the Lipkin-Meshkov-Glick Hamiltonian of up to eight single particle modes to study these MSs, solving the Hamiltonian with a combination of numerical exact diagonalization and high-order perturbation theory. The MS is between left and right potential wells; the extreme case with all atoms simultaneously located in both wells and in only two modes is the famous NOON state, but our approach encompasses much more general MSs. Use of more single particle modes brings dimensionality into the problem, allows us to set hard limits on the use of the original two-mode LMG model commonly treated in the literature, and also introduces a new mixed Josephson-Fock regime. Higher modes introduce angular degrees of freedom and MS states with different angular properties.Comment: 15 pages, 8 figures, 1 table. Mini-review prepared for the special issue of Frontiers of Physics "Recent Progresses on Quantum Dynamics of Ultracold Atoms and Future Quantum Technologies", edited by Profs. Lee, Ueda, and Drummon

WNT signaling regulates self-renewal and differentiation of prostate cancer cells with stem cell characteristics

Prostate cancer cells with stem cell characteristics were identified in human prostate cancer cell lines by their ability to form from single cells self-renewing prostaspheres in non-adherent cultures. Prostaspheres exhibited heterogeneous expression of proliferation, differentiation and stem cell-associated makers CD44, ABCG2 and CD133. Treatment with WNT inhibitors reduced both prostasphere size and self-renewal. In contrast, addition of Wnt3a caused increased prostasphere size and self-renewal, which was associated with a significant increase in nuclear Β-catenin, keratin 18, CD133 and CD44 expression. As a high proportion of LNCaP and C4-2B cancer cells express androgen receptor we determined the effect of the androgen receptor antagonist bicalutamide. Androgen receptor inhibition reduced prostasphere size and expression of PSA, but did not inhibit prostasphere formation. These effects are consistent with the androgen-independent self-renewal of cells with stem cell characteristics and the androgen-dependent proliferation of transit amplifying cells. As the canonical WNT signaling effector Β-catenin can also associate with the androgen receptor, we propose a model for tumour propagation involving a balance between WNT and androgen receptor activity. That would affect the self-renewal of a cancer cell with stem cell characteristics and drive transit amplifying cell proliferation and differentiation. In conclusion, we provide evidence that WNT activity regulates the self-renewal of prostate cancer cells with stem cell characteristics independently of androgen receptor activity. Inhibition of WNT signaling therefore has the potential to reduce the self-renewal of prostate cancer cells with stem cell characteristics and improve the therapeutic outcome.Peer reviewe