On recent SFR calibrations and the constant SFR approximation

Star Formation Rate (SFR) inferences are based in the so-called constant SFR approximation, where synthesis models are require to provide a calibration; we aims to study the key points of such approximation to produce accurate SFR inferences. We use the intrinsic algebra used in synthesis models, and we explore how SFR can be inferred from the integrated light without any assumption about the underling Star Formation history (SFH). We show that the constant SFR approximation is actually a simplified expression of more deeper characteristics of synthesis models: It is a characterization of the evolution of single stellar populations (SSPs), acting the SSPs as sensitivity curve over different measures of the SFH can be obtained. As results, we find that (1) the best age to calibrate SFR indices is the age of the observed system (i.e. about 13Gyr for z=0 systems); (2) constant SFR and steady-state luminosities are not requirements to calibrate the SFR; (3) it is not possible to define a SFR single time scale over which the recent SFH is averaged, and we suggest to use typical SFR indices (ionizing flux, UV fluxes) together with no typical ones (optical/IR fluxes) to correct the SFR from the contribution of the old component of the SFH, we show how to use galaxy colors to quote age ranges where the recent component of the SFH is stronger/softer than the older component. Particular values of SFR calibrations are (almost) not affect by this work, but the meaning of what is obtained by SFR inferences does. In our framework, results as the correlation of SFR time scales with galaxy colors, or the sensitivity of different SFR indices to sort and long scale variations in the SFH, fit naturally. In addition, the present framework provides a theoretical guide-line to optimize the available information from data/numerical experiments to improve the accuracy of SFR inferences.Comment: A&A accepted, 13 pages, 4 Figure

Non-Kramers Freezing and Unfreezing of Tunneling in the Biaxial Spin Model

The ground state tunnel splitting for the biaxial spin model in the magnetic field, H = -D S_{x}^2 + E S_{z}^2 - g \mu_B S_z H_z, has been investigated using an instanton approach. We find a new type of spin instanton and a new quantum interference phenomenon associated with it: at a certain field, H_2 = 2SE^{1/2}(D+E)^{1/2}/(g \mu_B), the dependence of the tunneling splitting on the field switches from oscillations to a monotonic growth. The predictions of the theory can be tested in Fe_8 molecular nanomagnets.Comment: 7 pages, minor changes, published in EP

Entropy production for coarse-grained dynamics

Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We show that the corresponding coarse-grained entropy production contains information on microscopic currents that are not captured by the Fokker-Planck equation and thus cannot be deduced from it. We study a discrete-state and a continuous-state system, deriving in both the cases an analytical expression for the coarse-graining corrections to the entropy production. This result elucidates the limits in which there is no loss of information in passing from a Master Equation to a Fokker-Planck equation describing the same system. Our results are amenable of experimental verification, which could help to infer some information about the underlying microscopic processes

Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory

We show that it is possible to adapt to nonparametric disturbance auto-correlation in time series regression in the presence of long memory in both regressors and disturbances by using a smoothed nonparametric spectrum estimate in frequency-domain generalized least squares. When the collective memory in regressors and disturbances is sufficiently strong, ordinary least squares is not only asymptotically inefficient but asymptotically non-normal and has a slow rate of convergence, whereas generalized least squares is asymptotically normal and Gauss-Markov efficient with standard convergence rate. Despite the anomalous behaviour of nonparametric spectrum estimates near a spectral pole, we are able to justify a standard construction of frequency-domain generalized least squares, earlier considered in case of short memory disturbances. A small Monte Carlo study of finite sample performance is included.Time series regression, long memory, adaptive estimation.