Dirac constraints in field theory and exterior differential systems

The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the jet variables. So it is natural to ask if there exists a formulation of this kind of field theories which avoids this problem, retaining the versatility of the known approach. The following paper deals with a family of variational problems, namely, the so called non standard variational problems, which intends to capture the data necessary to set up such a formulation for field theories; moreover, we will formulate a multisymplectic structure for the family of non standard variational problems, and we will relate this with the (pre)symplectic structure arising on the space of sections of the bundle of fields. In this setting the Dirac theory of constraints will be studied, obtaining among other things a novel characterization of the constraint manifold which arises in this theory, as generators of an exterior differential system associated to the equations of motion and the chosen slicing. Several examples of application of this formalism are discussed: Two of them motivated from the physical point of view, that is, electromagnetism and Poisson sigma models, and two examples of mathematical application. In the case of electromagnetism, it is shown that this formulation avoids the problems arising in the usual approach.Comment: 51 pages, aims; added examples and references, typos added, improved some content, to appear in "Journal of Geometric Mechanics"

The Transition to College Process in PR-CETP Scholars

This article describes a study about the experiences of a group of students during the transition from high school to college. The students are future teachers who evidenced a high level of academic achievement in high school and received merit scholarships from the Puerto Rico Collaborative for Excellence in Teacher Preparation (PR-CETP). Two groups of students were compared: those who sustained a high GPA during their freshman year, and those who did not and, therefore, no longer qualified for the scholarship. The study was carried out through focused interviews with eight students, from three universities, four of whom maintained the scholarship and four who did not. Findings indicate that the main problems encountered were academic and social, and that the students received support from their families during the entire process. Regarding formal support, they pointed out that they felt highly satisfied with the services provided by PR-CETP and the universities, but they also pointed out (particularly those who lost the scholarship) that they needed additional services from the universities. They suggested, for example, better tutoring, and social activities among the scholars. The interviewed students, in general, consider that they faced the transition successfully since most of them described their academic, emotional, and social status as satisfactory at the time of the interviews

Moral, Politics and Law. The discourse ethics and their contributions to democratic rule of law

El objetivo del artículo es explicitar la contribución que la ética del discurso de Apel puede realizar al mejoramiento de la calidad institucional del estado democrático de derecho. Se parte del concepto de estado de derecho que Habermas planteara en sus conferencias de las Tanner Lectures (1986), lo cual permite mostrar que el mismo resulta compatible con los presupuestos de esta teoría ética. A continuación se explicita que tal contribución puede justificarse a partir del sentido reconstructivo de la pragmática trascendental del lenguaje de la ética del discurso de Apel para la fundamentación racional de las normas morales.The object of this article is to make explicit the contribution that Apelian’s discourse ethics can make to the improving of the institutional quality of the democratic rule of law. The point of start is the Habermas's concept of rule of law that he established in the Tanner Lectures (1986), which allows to demonstrate that it is consistent with the assumptions of this ethical theory. This comment makes clear that such a contribution is justified bearing in mind the reconstruction sense of the language's transcendental pragmatic that Apel’s discourse ethics sets to the rational foundations of the moral norm

Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE, which is enough to solve the degeneracy in the NODDIDA model parameter estimation.Comment: 22 pages, 7 figure

The Impact of Invasive Plants on the Recreational Value of Florida's Coastal, Freshwater and Upland Natural Areas

This study examines the impact of invasive plants on recreational activities on Floridas coastal, freshwater and upland natural areas using a multi-attribute utility (MAU) model. Six MAU surveys were electronically distributed to Florida residents in early 2007. We specified a conditional Logit model to estimate the relative weights associated with a change in Fees, Invasive Species, Native Animal Species, Native Plant Species, and Facilities. Using Fees as a payment vehicle, we estimate the average Florida residents marginal willingness to pay for changes to attributes, including having fewer invasive plants and more positive attributes such as facilities and the presence of native animal and plant species. Florida residents have a marginal willingness to pay to reduce invasive plant species between $5.81 7.15, which is higher than their willingness to pay to improve park facilities or increase the abundance of native plants or animals.Resource /Energy Economics and Policy,