A Bayesian approach to the estimation of maps between riemannian manifolds

Let \Theta be a smooth compact oriented manifold without boundary, embedded in a euclidean space and let \gamma be a smooth map \Theta into a riemannian manifold \Lambda. An unknown state \theta \in \Theta is observed via X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of the map \gamma we derive a second-order asymptotic expansion for the related Bayesian risk. The calculation involves the geometry of the underlying spaces \Theta and \Lambda, in particular, the integration-by-parts formula. Using this result, a second-order minimax estimator of \gamma is found based on the modern theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s 31, 41, 4

Analysis of light scattering off photonic crystal slabs in terms of Feshbach resonances

Techniques to deal with Feshbach resonances are applied to describe resonant light scattering off one dimensional photonic crystal slabs. Accurate expressions for scattering amplitudes, free of any fitting parameter, are obtained for isolated as well as overlapping resonances. They relate the resonance properties to the properties of the optical structure and of the incident light. For the most common case of a piecewise constant dielectric function, the calculations can be carried out essentially analytically. After establishing the accuracy of this approach we demonstrate its potential in the analysis of the reflection coefficients for the diverse shapes of overlapping, interacting resonances.Comment: 12 pages, 5 figure

FPGA based data acquisition system for COMPASS experiment

This paper discusses the present data acquisition system (DAQ) of the COMPASS experiment at CERN and presents development of a new DAQ. The new DAQ must preserve present data format and be able to communicate with FPGA cards. Parts of the new DAQ are based on state machines and they are implemented in C++ with usage of the QT framework, the DIM library, and the IPBus technology. Prototype of the system is prepared and communication through DIM between parts was tested. An implementation of the IPBus technology was prepared and tested. The new DAQ proved to be able to fulfill requirements.Comment: 8 pages, CHEP 201

Semiclassical treatment of fusion processes in collisions of weakly bound nuclei

We describe a semiclassical treatment of nuclear fusion reactions involving weakly bound nuclei. In this treatment, the complete fusion probabilities are approximated by products of two factors: a tunneling probability and the probability that the system is in its ground state at the strong absorption radius. We investigate the validity of the method in a schematic two-channel application, where the channels in the continuum are represented by a single resonant state. Comparisons with full coupled-channels calculations are performed. The agreement between semiclassical and quantal calculations isquite good, suggesting that the procedure may be extended to more sophisticated discretizations of the continuum.Comment: 11 pages, 5 figure

Liquid-gas phase transition in finite nuclei

In a finite temperature Thomas-Fermi framework, we calculate density distributions of hot nuclei enclosed in a freeze-out volume of few times the normal nuclear volume and then construct the caloric curve, with and without inclusion of radial collective flow. In both cases, the calculated specific heats $C_v$ show a peaked structure signalling a liquid-gas phase transition. Without flow, the caloric curve indicates a continuous phase transition whereas with inclusion of flow, the transition is very sharp. In the latter case, the nucleus undergoes a shape change to a bubble from a diffuse sphere at the transition temperature.Comment: Proc. of 6th Int. Conf. on N-N Collisions (Gatlinburg); Nuclear Physics A (in press

On the active site of elastase: Partial mapping by means of specific peptide substrates

AbstractRNase-S peptide as well as some related octa- and hexapeptides were found to be highly, reactive substrates of porcine elastase (e.g. Ala4-Lys-Phe: Km = 4500 M−1, kcat = 32 sec−1, C = 1.4 × 105 M−1 sec−1). Comparison of the various peptides led to the conclusion that the active site of porcine elastase is composed of 6–7 subsites (c.f. [1]). Preliminary mapping shows that subsites S2, S′1 and S′2 have hydrophobic character. Occupation of subsite S4 by the substrate is important for efficient hydrolysis. Binding at this subsite was found to be stereospecific

Instantons and radial excitations in attractive Bose-Einstein condensates

Imaginary- and real-time versions of an equation for the condensate density are presented which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean field appraoch. We obtain quantized energies of collective finite amplitude radial oscillations and exact numerical instanton solutions which describe quantum tunneling from both the metastable and radially excited states of the BEC of 7Li atoms. The mass parameter for the radial motion is found different from the gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form slightly compressed harmonic spectrum, n=4 state lying lower than the second Bogolyubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter than true lifetime of the metastable state. By scaling arguments, results extend to other attractive BEC-s.Comment: 6 pages, 3 figure

Limitation of energy deposition in classical N body dynamics

Energy transfers in collisions between classical clusters are studied with Classical N Body Dynamics calculations for different entrance channels. It is shown that the energy per particle transferred to thermalised classical clusters does not exceed the energy of the least bound particle in the cluster in its ``ground state''. This limitation is observed during the whole time of the collision, except for the heaviest system.Comment: 13 pages, 15 figures, 1 tabl