Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes

A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear Inverse Modeling (LIM), under the common principle of relative entropy minimization. The power of the new method is demonstrated on a stochastic approximation of the El Nino phenomenon studied in climate research

Numerical Tests of Rotational Mixing in Massive Stars with the new Population Synthesis Code BONNFIRES

We use our new population synthesis code BONNFIRES to test how surface abundances predicted by rotating stellar models depend on the numerical treatment of rotational mixing, such as spatial resolution, temporal resolution and computation of mean molecular weight gradients. We find that even with identical numerical prescriptions for calculating the rotational mixing coefficients in the diffusion equation, different timesteps lead to a deviation of the coefficients and hence surface abundances. We find the surface abundances vary by 10-100% between the model sequences with short timestep of 0.001Myr to model sequences with longer timesteps. Model sequences with stronger surface nitrogen enrichment also have longer main-sequence lifetimes because more hydrogen is mixed to the burning cores. The deviations in main-sequence lifetimes can be as large as 20%. Mathematically speaking, no numerical scheme can give a perfect solution unless infinitesimally small timesteps are used. However, we find that the surface abundances eventually converge within 10% between modelling sequences with sufficiently small timesteps below 0.1Myr. The efficiency of rotational mixing depends on the implemented numerical scheme and critically on the computation of the mean molecular weight gradient. A smoothing function for the mean molecular weight gradient results in stronger rotational mixing. If the discretization scheme or the computational recipe for calculating the mean molecular weight gradient is altered, re-calibration of mixing parameters may be required to fit observations. If we are to properly understand the fundamental physics of rotation in stars, it is crucial that we minimize the uncertainty introduced into stellar evolution models when numerically approximating rotational mixing processes.Comment: 8 pages, 6 figures, accepted by A&

Thermodes and Theories

This brief outline reviews some of the important studies done with various types of thermodes employed for heating or cooling loci in the brain and discusses some sources of the findings relevant to our understanding of temperature regulation in mammals

MUNICIPAL CORPORATIONS-ZONING-RIGHT OF GRANTEE TO ACT ON VARIANCE ISSUED TO HIS GRANTOR

A zoning ordinance prohibited the erection of private garages within twenty feet of the street line. Because of the peculiar shape of the lot in question, a variance was granted to the then owner permitting the building of a garage closer to the street line. However, before the garage was built, the land was sold to the present owner who obtained a building permit and began construction. Plaintiffs, owners of the adjoining lot, objected to the granting of the permit and appealed to the zoning board of review which denied their appeal. On certiorari, held, present owner might act on the variance granted to his predecessor. Mastrati v. Strauss, (R.I. 1949) 67 A. (2d) 29