An Innovative University Course for Cooperating Teachers

The transformation of a course for certifying cooperating teachers in Puerto Rico is described. The course was transformed to strengthen the teaching of science and mathematics and to make the course more congruent with the educational principles of constructivism promoted by the CETP projects at the national level, including Puerto Rico. The 45-hour requirement was distributed over nine days. The Open Space strategy was modified to include multiple active teaching-learning and assessment techniques, which promoted a learning environment based on trust, dedication, and the commitment of all participants to learn and help each other learn. Even more relevant was the fact that more content was covered and in more depth. The modified version of the course was offered to secondary level science and mathematics teachers, especially to teachers who work at the practicum centers that are part of the PR-CETP

Propagation of mesons in asymmetric nuclear matter in a density dependent coupling model

We study the propagation of the light mesons sigma, omega, rho, and a0(980) in dense hadronic matter in an extended derivative scalar coupling model. Within the scheme proposed it is possible to unambiguously define effective density-dependent couplings at the Lagrangian level. We first apply the model to study asymmetric nuclear matter with fixed isospin asymmetry, and then we pay particular attention to hypermatter in beta-equilibrium. The equation of state and the potential contribution to the symmetry coefficient arising from the mean field approximation are investigated.Comment: 17 pages, 15 PostScript figure

Observability and Synchronization of Neuron Models

Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. In the case of networks composed of neuron models, the observability of the network depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, a study of observability is conducted using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, a multivariate singular spectrum analysis (M-SSA) is performed to detect phase synchronization in networks composed by neuron models. This tool, to the best of the authors' knowledge has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization i)~without having to measure all the state variables, but only one from each node, and ii)~without having to estimate the phase

Measuring the properties of extragalactic dust and implications for the Hubble diagram

Scattering and absorption of light by a homogeneous distribution of intergalactic large dust grains has been proposed as an alternative, non-cosmological explanation for the faintness of Type Ia supernovae at z\s im 0.5. We investigate the differential extinction for high-redshift sources caused by extragalactic dust along the line of sight. Future observations of Type Ia supernovae up to $z\sim 2$, e.g. by the proposed SNAP satellite, will allow the measurement of the properties of dust over cosmological distances. We show that 1% {\em relative} spectrophotometric accuracy (or broadband photometry) in the wavelength interval 0.7--1.5 $\mu$m is required to measure the extinction caused by ``grey'' dust down to $\delta m=0.02$ magnitudes. We also argue that the presence of grey dust is not necessarily inconsistent with the recent measurement of the brightness of a supernova at $z=1.7$ (SN 1997ff), in the absence of accurate spectrophotometric information of the supernova.Comment: Accepted by A&

Testing Asteroseismic Radii of Dwarfs and Subgiants with Kepler and Gaia

We test asteroseismic radii of Kepler main-sequence and subgiant stars by deriving their parallaxes which are compared with those of the first Gaia data release. We compute radii based on the asteroseismic scaling relations as well as by fitting observed oscillation frequencies to stellar models for a subset of the sample, and test the impact of using effective temperatures from either spectroscopy or the infrared flux method. An offset of 3%, showing no dependency on any stellar parameters, is found between seismic parallaxes derived from frequency modelling and those from Gaia. For parallaxes based on radii from the scaling relations, a smaller offset is found on average; however, the offset becomes temperature dependent which we interpret as problems with the scaling relations at high stellar temperatures. Using the hotter infrared flux method temperature scale, there is no indication that radii from the scaling relations are inaccurate by more than about 5%. Taking the radii and masses from the modelling of individual frequencies as reference values, we seek to correct the scaling relations for the observed temperature trend. This analysis indicates that the scaling relations systematically overestimate radii and masses at high temperatures, and that they are accurate to within 5% in radius and 13% in mass for main-sequence stars with temperatures below 6400 K. However, further analysis is required to test the validity of the corrections on a star-by-star basis and for more evolved stars.Comment: 12 pages, 9 figures. Accepted for publication in MNRA

Grassmanian and Bosonic Thirring Models with Jump Defects

In this paper we discuss the Lax formulation of the Grassmanian and Bosonic Thirring models in the presence of jump defects. For the Grassmanian case, the defect is described by B\"acklund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the B\"acklund transformation for the Bosonic Thirring model which is verified by some B\"acklund transitions like Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and Two solitons - Two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model.Comment: Latex 21 page