The trace of the heat kernel on a compact hyperbolic 3-orbifold

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the discrete group \Ga contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.Comment: 11 page

Generalized second Bargmann transforms associated with the hyperbolic Landau levels on the Poincar\'e disk

We deal with a family of generalized coherent states associated to the hyperbolic Landau levels of the Schr\"odinger operator with uniform magnetic field on the Poincar\'e disk. Their associated coherent state transforms constitute a class of generalized second Bargmann transforms.Comment: 7 page

Trace formulae for three-dimensional hyperbolic lattices and application to a strongly chaotic tetrahedral billiard

This paper is devoted to the quantum chaology of three-dimensional systems. A trace formula is derived for compact polyhedral billiards which tessellate the three-dimensional hyperbolic space of constant negative curvature. The exact trace formula is compared with Gutzwiller's semiclassical periodic-orbit theory in three dimensions, and applied to a tetrahedral billiard being strongly chaotic. Geometric properties as well as the conjugacy classes of the defining group are discussed. The length spectrum and the quantal level spectrum are numerically computed allowing the evaluation of the trace formula as is demonstrated in the case of the spectral staircase N(E), which in turn is successfully applied in a quantization condition.Comment: 32 pages, compressed with gzip / uuencod

START in a five-dimensional conformal domain

In this paper we give a brief review of the pseudo-Riemannian geometry of the five-dimensional homogeneous space for the conformal group O(4,2). Its topology is described and its relation to the conformally compactified Minkowski space is described. Its metric is calculated using a generalized half-space representation. Compactification via Lie-sphere geometry is outlined. Possible applications to Jaime Keller's START theory may follow by using its predecessor - the 5-optics of Yu. B. Rumer. The point of view of Rumer is given extensively in the last section of the paper. Keywords. Kaluza,Klein, Rumer, conformal symmetry, hyperbolic space, START, fifth dimension, action coordinate, 5-opticsComment: Latex, 13 pages, 3 figures, added sections 3.2. Christoffel symbols and geodesics and 3.3. {\Sigma}- as the space of hyperboloids; accepted for publication in the special volume of AACA in memory of Prof. Jaime Kelle

Differences in zinc status and the leptin axis in anorexic and recovered adolescents and young adults: a pilot study

Evidence from animal studies suggests that leptin metabolism is associated with zinc (Zn) status. However, research investigating this relationship in adolescents and young adults with anorexia nervosa (AN) is scarce; the present study aims to fill that gap.Serum concentrations of leptin, the soluble leptin receptor (sOB-R) and the free leptin index (FLI) were obtained in healthy control subjects (n=19), acutely ill individuals (n=14) and recovered patients with AN (n=15). Serum Zn concentrations noted in previous research data were also incorporated for all groups.Leptin, FLI and Zn concentrations were higher in recovered subjects with AN when compared with acutely ill AN patients. Remitted patients showed higher sOB-R concentrations but no difference in FLI compared with the control group. Leptin and FLI were lower in the acutely ill patients compared with the control subjects, who showed no differences in Zn concentrations. Zn concentrations were not correlated with leptin, sOB-R or FLI concentrations in any of the three investigated subgroups.The present investigation does not entirely support an association between Zn, Leptin and FLI concentrations in subjects with AN, possibly due to limited statistical power. Further research and replication of the present findings related to the interaction between leptin and Zn is warranted. However, with respect to serum leptin levels the data of the present investigation indicate that acutely ill and remitted patients with AN differ as regards serum leptin concentrations and FLI, which is in line with previous research

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

Hyperthermic Isolated Limb Perfusion with TNF α and Cisplatin in the Treatment of Osteosarcoma of the Extremities: A Feasibility Study in Healthy Dogs

Purpose. The feasibility of hyperthermic isolated limb perfusion (HILP) with tumor necrosis factor-α (TNFα ) and cisplatin for the management of osteosarcoma was studied in the canine model

The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

Exon expression arrays as a tool to identify new cancer genes

Background: Identification of genes that are causally implicated in oncogenesis is a major goal in cancer research. An estimated 10-20% of cancer-related gene mutations result in skipping of one or more exons in the encoded transcripts. Here we report on a strategy to screen in a global fashion for such exon-skipping events using PAttern based Correlation (PAC). The PAC algorithm has been used previously to identify differentially expressed splice variants between two predefined subgroups. As genetic changes in cancer are sample specific, we tested the ability of PAC to identify aberrantly expressed exons in single samples. Principal Findings: As a proof-of-principle, we tested the PAC strategy on human cancer samples of which the complete coding sequence of eight cancer genes had been screened for mutations. PAC detected all seven exon-skipping mutants among 12 cancer cell lines. PAC also identified exon-skipping mutants in clinical cancer specimens although detection was compromised due to heterogeneous (wild-type) transcript expression. PAC reduced the number candidate genes/exons for subsequent mutational analysis by two to three orders of magnitude and had a substantial true positive rate. Importantly, of 112 randomly selected outlier exons, sequence analysis identified two novel exon skipping events, two novel base changes and 21 previously reported base changes (SNPs). Conclusions: The ability of PAC to enrich for mutated transcripts and to identify known and novel genetic changes confirms its suitability as a strategy to identify candidate cancer genes