On the Rate of Quantum Ergodicity on hyperbolic Surfaces and Billiards

The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g=2 and of two triangular billiards on a surface of constant negative curvature are investigated. One of the triangular billiards belongs to the class of arithmetic systems. There are no peculiarities observed in the arithmetic system concerning the rate of quantum ergodicity. This contrasts to the peculiar behaviour with respect to the statistical properties of the quantal levels. It is demonstrated that the rate of quantum ergodicity in the three considered systems fits well with the known upper and lower bounds. Furthermore, Sarnak's conjecture about quantum unique ergodicity for hyperbolic surfaces is confirmed numerically in these three systems.Comment: 19 pages, Latex, This file contains no figures. A postscript file with all figures is available at http://www.physik.uni-ulm.de/theo/qc/ (Delay is expected to 23.7.97 since our Web master is on vacation.

Extension of CART using multiple splits under order restrictions

CART was introduced by Breiman et al. (1984) as a classification tool. It divides the whole sample recursively in two subpopulations by finding the best possible split with respect to a optimisation criterion. This method, restricted up to date to binary splits, is extended in this paper for allowing also multiple splits. The main problem with this extension is related to the optimal number of splits and the location of the corresponding cutpoints. In order to reduce the computational effort and enhance parsimony, the reduced isotonic regression was used in order to solve this problem. The extended CART method was tested in a simulation study and was compared with the classical approach in an epidemiological study. In both studies the extended CART turned out to be a useful and reliable alternative

On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds

Guaranteed funds with crediting rates for fixed periods determined by a Pension Provider or Insurance Company are common features of accumulation annuity contracts. Policyholders can transfer money back and forth between these accounts and Money Market accounts which give them features similar to demand deposits and yet they frequently credit a higher rate than the Money Market. Transfer restrictions are commonly employed to prevent arbitrage. In this paper, we model the interaction between company and policyholder as a multiperiod game in which the company maximizes risk-neutral expected present value of profits and the policyholder maximizes his expected discounted utility. We find that the optimal strategy on the part of the company is to credit a rate higher than money market rate in the first period to entice the policyholder to invest in the guaranteed fund. The company then credits the floor in the remaining periods as the policyholder transfers out the maximum amount. This does better for the policyholder in low interest rate environments and worse in high interest rate environments and acts as a type of “interest rate insurance” for the policyholder

Light-regulated interactions with SPA proteins underlie cryptochrome-mediated gene expression.

Cryptochromes are a class of photosensory receptors that control important processes in animals and plants primarily by regulating gene expression. How photon absorption by cryptochromes leads to changes in gene expression has remained largely elusive. Three recent studies, including Lian and colleagues (pp. 1023-1028) and Liu and colleagues (pp. 1029-1034) in this issue of Genes & Development, demonstrate that the interaction of light-activated Arabidopsis cryptochromes with a class of regulatory components of E3 ubiquitin ligase complexes leads to environmentally controlled abundance of transcriptional regulators

Numerical computation of Maass waveforms and an application to cosmology

We compute numerically eigenvalues and eigenfunctions of the Laplacian in a three-dimensional hyperbolic space. Applying the results to cosmology, we demonstrate that the methods learned in quantum chaos can be used in other fields of research.Comment: A version of the paper with high resolution figures is available at http://www.physik.uni-ulm.de/theo/qc/publications.htm

Heat exchanger test experimental apparatus. Section I - Helium heater. Section II - Helium circulator Summary report

Molybdenum heater tube for heating helium to operating temperature of high temperature heat exchanger facility - performance of helium circulato

The Effect of Labor Income and Health Uncertainty on the Valuation of Guaranteed Minimum Death Benefits

We examine the effect of labor income and health uncertainty on the optimal choices of policyholders with Guaranteed Minimum Death Benefits embedded in Variable Annuities. These choices are determined in the context of a utility-based life cycle model including bequest motives and optimal term life purchases. We then determine risk-neutral prices from the perspective of the issuing financial institutions. In contrast to previous studies which do not include income and health uncertainty, we find that very risk-averse policyholders in weak job markets would be willing to pay the risk-neutral price in order to receive these benefits. This occurs because an unemployed individual with a low account balance would be unwilling to pay for term insurance, but has precommitted to pay the now small GMDB fees in exchange for the death benefits

Dispersal Dynamics of the Bivalve Gemma Gemma in a Patchy Environment

The purpose of this study was to analyze the dispersal dynamics of the ovoviviparous bivalve Gemma gemma (hereafter referred to as Gemma) in an environment disturbed by the pit-digging activities of horseshoe crabs, Limulus polyphemus. Gemma broods its young and has no planktonic larval stage, so all dispersal is the result of juvenile and adult movement. Animal movement was measured using natural crab pits, hand-dug simulated crab pits, and cylindrical bottom traps in the intertidal zone at Tom\u27s Cove, Virginia, USA. This study demonstrated that horseshoe crabs create localized patches with reduced densities of Gemma, that all sizes and ages of Gemma quickly disperse into these low density patches, and that the mechanism of dispersal is passive bedload and suspended load transport. Freshly excavated natural pits had significantly lower Gemma densities than did undisturbed background sediment, but there were no significant differences in total density of other species, number of species, and species diversity (H\u27). Equitability (J\u27) was greater in pits than in controls because of the reduced abundance of Gemma, the numerically dominant species. Newly dug simulated crab pits also had significantly lower Gemma densities than controls and returned to control levels by the next day. Density recovery trajectories for individually marked pits showed consistent responses in summer and fall, but not in winter when low Gemma abundance resulted in greater variability among pits. Significant positive correlations between the volume of sediment and the number of Gemma collected per bottom trap support the hypothesis that Gemma dispersal is a passive transport phenomenon. Assuming no active, density-dependent movement, the product of the Gemma density frequency distribution in undisturbed background sediment and the frequency distribution of sediment volume collected per trap created a predicted Gemma frequency distribution in traps that matched the actual distribution. Absolute dispersal rates and relative dispersal rates (absolute dispersal rate divided by background density in undisturbed sediment) into pits and traps were greater in summer than winter. Dispersal rate results suggest that increased horseshoe crab disturbance in summer may cause an increase in Gemma transport. Because Gemma individuals are dispersed by hydrodynamic action, it was expected that small, young individuals would be most easily transported in the bedload. There was, however, little evidence that movement into pits and traps was size- or age-selective. Most recent benthic dispersal research has focused on the large-scale movement and settlement patterns of invertebrate larvae. The results from this study illustrate that dispersal of bottom-dwelling juveniles and adults plays an important role in regulating the local distribution and abundance of Gemma. Previous workers have shown that young Gemma live in dense aggregations and that growth and fecundity are reduced at such high densities, leading to population crashes. This study demonstrated a mechanism by which Gemma disperses into low-density patches where intraspecific competition may be mitigated, possibly resulting in enhanced individual reproductive success and population fitness

UVR8-mediated inhibition of shade avoidance involves HFR1 stabilization in Arabidopsis.

Sun-loving plants perceive the proximity of potential light-competing neighboring plants as a reduction in the red:far-red ratio (R:FR), which elicits a suite of responses called the "shade avoidance syndrome" (SAS). Changes in R:FR are primarily perceived by phytochrome B (phyB), whereas UV-B perceived by UV RESISTANCE LOCUS 8 (UVR8) elicits opposing responses to provide a counterbalance to SAS, including reduced shade-induced hypocotyl and petiole elongation. Here we show at the genome-wide level that UVR8 broadly suppresses shade-induced gene expression. A subset of this gene regulation is dependent on the UVR8-stabilized atypical bHLH transcription regulator LONG HYPOCOTYL IN FAR-RED 1 (HFR1), which functions in part redundantly with PHYTOCHROME INTERACTING FACTOR 3-LIKE 1 (PIL1). In parallel, UVR8 signaling decreases protein levels of the key positive regulators of SAS, namely the bHLH transcription factors PHYTOCHROME INTERACTING FACTOR 4 (PIF4) and PIF5, in a COP1-dependent but HFR1-independent manner. We propose that UV-B antagonizes SAS via two mechanisms: degradation of PIF4 and PIF5, and HFR1- and PIL1-mediated inhibition of PIF4 and PIF5 function. This work highlights the importance of typical and atypical bHLH transcription regulators for the integration of light signals from different photoreceptors and provides further mechanistic insight into the crosstalk of UVR8 signaling and SAS