Search results for "Jacobi"

Jacobi Fields, Conjugate Points

2001

Let us go back to the action principle as realized by Jacobi, i.e., time is eliminated, so we are dealing with the space trajectory of a particle. In particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space.

New Types of Jacobian-Free Approximate Riemann Solvers for Hyperbolic Systems

2017

We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Moreover, they can be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems with complex Jacobians, as the relativistic magnetohydrodynamics (RMHD) equations. The proposed solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method. Som…

Mappings of finite distortion: Reverse inequalities for the Jacobian

2007

Let f be a nonconstant mapping of finite distortion. We establish integrability results on 1/Jf by studying weights that satisfy a weak reverse Holder inequality where the associated constant can depend on the ball in question. Here Jf is the Jacobian determinant of f.

Computing variations of entropy and redundancy under nonlinear mappings not preserving the signal dimension: quantifying the efficiency of V1 cortex

2021

In computational neuroscience, the Efficient Coding Hypothesis argues that the neural organization comes from the optimization of information-theoretic goals [Barlow Proc.Nat.Phys.Lab.59]. A way to confirm this requires the analysis of the statistical performance of biological systems that have not been statistically optimized [Renart et al. Science10, Malo&Laparra Neur.Comp.10, Foster JOSA18, Gomez-Villa&Malo J.Neurophysiol.19]. However, when analyzing the information-theoretic performance, cortical magnification in the retina-cortex pathway poses a theoretical problem. Cortical magnification stands for the increase the signal dimensionality [Cowey&Rolls Exp. Brain Res.74]. Conventional mo…

Säätöteoria ja Hamilton-Jacobi-yhtälöt

2008

Política, virtud y terror en el jacobinismo

2010

La Revolución francesa de 1789 fue el escenario donde se libró una lucha abierta entre dos concepciones de la libertad y sus respectivas repercusiones en la concepción del poder político: la libertad particular que el individuo reclama para sí al margen del Estado, e incluso contra él, y la libertad del ciudadano, entendida como la libertad de obedecer a la voluntad general. El objetivo de este ensayo es perfilar, en líneas generales, la posición que adoptó el jacobinismo con respecto a la relación entre sociedad civil y Estado, en confrontación con el enfoque liberal que, siguiendo los modelos americano e inglés, propugnaron los sectores moderados de la Revolución.