Fitting Lorenz curves

This paper presents a functional form, linear in the parameters, to deal with income distribution and Lorenz curves. The function is fitted to the Brazilian income distribution. Data standard deviations were estimated from year-to-year variation of the income share. (C) 2010 Elsevier B.V. All rights reserved.

FAST, PARALLEL AND SECURE CRYPTOGRAPHY ALGORITHM USING LORENZ`S ATTRACTOR

A novel cryptography method based on the Lorenz`s attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction among the password, message and a chaotic system. It ensures that the algorithm yields a secure codification, even if the nature of the chaotic system is known. The algorithm has been implemented in two versions: one sequential and slow and the other, parallel and fast. Our algorithm assures the integrity of the ciphertext (we know if it has been altered, which is not assured by traditional algorithms) and consequently its authenticity. Numerical experiments are presented, discussed and show the behavior of the method in terms of security and performance. The fast version of the algorithm has a performance comparable to AES, a popular cryptography program used commercially nowadays, but it is more secure, which makes it immediately suitable for general purpose cryptography applications. An internet page has been set up, which enables the readers to test the algorithm and also to try to break into the cipher.

The energy cycle and structural evolution of cyclones over southeastern South America in three case studies

In this paper, the Lorenz energy cycle over a limited area was applied for three cyclones with different origins and evolutions, where each of them was formed in an important cyclogenetic region near southeastern South America. The synoptic conditions and energetics were analyzed during each system`s life cycle and showed important relationships between their energy cycle and the evolution of their vertical structure. In the case of the weak baroclinic cyclone which formed on Brazil`s south-southeastern coast, the analysis showed that it originated through a midlevel cutoff low with contribution from barotropic instability. Its evolution would indicate potential transition to a hybrid system if the convective activity were stronger. The system that occurred in the La Plata River mouth had features of an oceanic bomb-type cyclogenesis and showed an important contribution from the available potential energy generation term through the latent heat release by the convection. Meanwhile, the system of the southern Argentina coast presented a classical baroclinic development of extratropical cyclogenesis in the energy cycle, from the wave amplification up to the final occlusion of the associated frontal system. These analyses revealed that the development of some cyclones that occur in eastern South America can present different mechanisms that are not related to the classical extratropical cyclogenesis.

An analysis of the environmental energetics associated with the transition of the first South Atlantic hurricane

This study presents the first analysis of the energetics associated with a hybrid cyclone`s transition in the Southern Hemisphere, Hurricane Catarina ( March 2004). Catarina has earned a place in history as the first documented South Atlantic hurricane, but its unusual tropical transition is still poorly understood. Here we show that Catarina`s transition was preceded by marked environmental changes in the Lorenz energy cycle, with an abrupt shift from a baroclinic to a predominantly barotropic state. Such changes help to explain the unusual vortex`s growth until its transition was completed. Although the vortex`s energy flux is not explicitly calculated, a likely mechanism linking the environmental energetics with Catarina is the extraction of eddy kinetic energy from horizontal momentum and heat transfers within the through component of the blocking. The results advance the understanding of this rare event and suggest that the technique has a great potential to study transitioning systems in general.

Multivariate analysis of the energy cycle of the South American rainy season

The South American (SA) rainy season is studied in this paper through the application of a multivariate Empirical Orthogonal Function (EOF) analysis to a SA gridded precipitation analysis and to the components of Lorenz Energy Cycle (LEC) derived from the National Centers for Environmental Prediction (NCEP) reanalysis. The EOF analysis leads to the identification of patterns of the rainy season and the associated mechanisms in terms of their energetics. The first combined EOF represents the northwest-southeast dipole of the precipitation between South and Central America, the South American Monsoon System (SAMS). The second combined EOF represents a synoptic pattern associated with the SACZ (South Atlantic convergence zone) and the third EOF is in spatial quadrature to the second EOF. The phase relationship of the EOFs, as computed from the principal components (PCs), suggests a nonlinear transition from the SACZ to the fully developed SAMS mode by November and between both components describing the SACZ by September-October (the rainy season onset). According to the LEC, the first mode is dominated by the eddy generation term at its maximum, the second by both baroclinic and eddy generation terms and the third by barotropic instability previous to the connection to the second mode by September-October. The predominance of the different LEC components at each phase of the SAMS can be used as an indicator of the onset of the rainy season in terms of physical processes, while the existence of the outstanding spectral peaks in the time dependence of the EOFs at the intraseasonal time scale could be used for monitoring purposes. Copyright (C) 2009 Royal Meteorological Society

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.

UNIFORM DISSIPATIVENESS, ROBUST SYNCHRONIZATION AND LOCATION OF THE ATTRACTOR OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS

In this series of papers, we study issues related to the synchronization of two coupled chaotic discrete systems arising from secured communication. The first part deals with uniform dissipativeness with respect to parameter variation via the Liapunov direct method. We obtain uniform estimates of the global attractor for a general discrete nonautonomous system, that yields a uniform invariance principle in the autonomous case. The Liapunov function is allowed to have positive derivative along solutions of the system inside a bounded set, and this reduces substantially the difficulty of constructing a Liapunov function for a given system. In particular, we develop an approach that incorporates the classical Lagrange multiplier into the Liapunov function method to naturally extend those Liapunov functions from continuous dynamical system to their discretizations, so that the corresponding uniform dispativeness results are valid when the step size of the discretization is small. Applications to the discretized Lorenz system and the discretization of a time-periodic chaotic system are given to illustrate the general results. We also show how to obtain uniform estimation of attractors for parametrized linear stable systems with nonlinear perturbation.