Maass Spezialschar of level N

In this paper the image of the Saito-Kurokawa lift of level $N$ with Dirichlet character is studied. We give a new characterization of this so called Maass Spezialschar of level $N$ by symmetries involving Hecke operators related to $\Gamma_0(N)$. We finally obtain for all prime numbers $p$ local Maass relations. This generalizes known results for level $N=1$

Polynominals related to powers of the Dedekind eta function

The vanishing properties of Fourier coefficients of integral powers of the Dedekind eta function correspond to the existence of integral roots of integer-valued polynomials Pn(x) introduced by M. Newman. In this paper we study the derivatives of these polynomials. We obtain non-vanishing results at integral points. As an application we prove that integral roots are simple if the index n of the polynomial is equal to a prime power pm or to pm + 1. We obtain a formula for the derivative of Pn(x) involving the polynomials of lower degree

A reduced model for shock and detonation waves. II. The reactive case

We present a mesoscopic model for reactive shock waves, which extends a previous model proposed in [G. Stoltz, Europhys. Lett. 76 (2006), 849]. A complex molecule (or a group of molecules) is replaced by a single mesoparticle, evolving according to some Dissipative Particle Dynamics. Chemical reactions can be handled in a mean way by considering an additional variable per particle describing a rate of reaction. The evolution of this rate is governed by the kinetics of a reversible exothermic reaction. Numerical results give profiles in qualitative agreement with all-atom studies

Analysis of femtosecond pump-probe photoelectron-photoion coincidence measurements applying Bayesian probability theory

Ultrafast dynamical processes in photoexcited molecules can be observed with pump-probe measurements, in which information about the dynamics is obtained from the transient signal associated with the excited state. Background signals provoked by pump and/or probe pulses alone often obscure these excited state signals. Simple subtraction of pump-only and/or probe-only measurements from the pump-probe measurement, as commonly applied, results in a degradation of the signal-to-noise ratio and, in the case of coincidence detection, the danger of overrated background subtraction. Coincidence measurements additionally suffer from false coincidences. Here we present a probabilistic approach based on Bayesian probability theory that overcomes these problems. For a pump-probe experiment with photoelectron-photoion coincidence detection we reconstruct the interesting excited-state spectrum from pump-probe and pump-only measurements. This approach allows to treat background and false coincidences consistently and on the same footing. We demonstrate that the Bayesian formalism has the following advantages over simple signal subtraction: (i) the signal-to-noise ratio is significantly increased, (ii) the pump-only contribution is not overestimated, (iii) false coincidences are excluded, (iv) prior knowledge, such as positivity, is consistently incorporated, (v) confidence intervals are provided for the reconstructed spectrum, and (vi) it is applicable to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, the Bayesian approach allows to run experiments at higher ionization rates, resulting in a significant reduction of data acquisition times. The application to pump-probe coincidence measurements on acetone molecules enables novel quantitative interpretations about the molecular decay dynamics and fragmentation behavior

Effective affinities in microarray data

In the past couple of years several studies have shown that hybridization in Affymetrix DNA microarrays can be rather well understood on the basis of simple models of physical chemistry. In the majority of the cases a Langmuir isotherm was used to fit experimental data. Although there is a general consensus about this approach, some discrepancies between different studies are evident. For instance, some authors have fitted the hybridization affinities from the microarray fluorescent intensities, while others used affinities obtained from melting experiments in solution. The former approach yields fitted affinities that at first sight are only partially consistent with solution values. In this paper we show that this discrepancy exists only superficially: a sufficiently complete model provides effective affinities which are fully consistent with those fitted to experimental data. This link provides new insight on the relevant processes underlying the functioning of DNA microarrays.Comment: 8 pages, 6 figure