Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames 'without inequalities' from lattices to non-uniform sets.

Quimiometria II: planilhas eletrônicas para cálculos de planejamentos experimentais, um tutorial

This work describes, through examples, a simple way to carry out experimental design calculations applying an spreadsheets. The aim of this tutorial is to introduce an alternative to sophisticated commercial programs that normally are too complex in data input and output. An overview of the principal methods is also briefly presented. The spreadsheets are suitable to handle different types of computations such as screening procedures applying factorial design and the optimization procedure based on response surface methodology. Furthermore, the spreadsheets are sufficiently versatile to be adapted to specific experimental designs.

Image Segmentation Using Information Bottleneck Method

In image processing, segmentation algorithms constitute one of the main focuses of research. In this paper, new image segmentation algorithms based on a hard version of the information bottleneck method are presented. The objective of this method is to extract a compact representation of a variable, considered the input, with minimal loss of mutual information with respect to another variable, considered the output. First, we introduce a split-and-merge algorithm based on the definition of an information channel between a set of regions (input) of the image and the intensity histogram bins (output). From this channel, the maximization of the mutual information gain is used to optimize the image partitioning. Then, the merging process of the regions obtained in the previous phase is carried out by minimizing the loss of mutual information. From the inversion of the above channel, we also present a new histogram clustering algorithm based on the minimization of the mutual information loss, where now the input variable represents the histogram bins and the output is given by the set of regions obtained from the above split-and-merge algorithm. Finally, we introduce two new clustering algorithms which show how the information bottleneck method can be applied to the registration channel obtained when two multimodal images are correctly aligned. Different experiments on 2-D and 3-D images show the behavior of the proposed algorithms

A reação de ciclização de prins: uma estratégia eficiente para síntese estereosseletiva de anéis tetraidropirânicos substituídos

The Prins cyclization reaction has significantly advanced in the last years as demonstrated by a number of applications described in the literature. The objective of this report is to introduce this powerful synthetic methodology to the undergraduate and graduated student, since it is rarely presented in an organic synthesis formal course. This reaction is, in some cases, the methodology of choice for the preparation of natural products or drugs that present the tetrahydropyrane moiety in their structures. In this report we show some aspects of this reaction, including mechanism, scope and limitations.

Fourier-based registration for robust forward-looking sonar mosaicing in low-visibility underwater environments

Vehicle operations in underwater environments are often compromised by poor visibility conditions. For instance, the perception range of optical devices is heavily constrained in turbid waters, thus complicating navigation and mapping tasks in environments such as harbors, bays, or rivers. A new generation of high-definition forward-looking sonars providing acoustic imagery at high frame rates has recently emerged as a promising alternative for working under these challenging conditions. However, the characteristics of the sonar data introduce difficulties in image registration, a key step in mosaicing and motion estimation applications. In this work, we propose the use of a Fourier-based registration technique capable of handling the low resolution, noise, and artifacts associated with sonar image formation. When compared to a state-of-the art region-based technique, our approach shows superior performance in the alignment of both consecutive and nonconsecutive views as well as higher robustness in featureless environments. The method is used to compute pose constraints between sonar frames that, integrated inside a global alignment framework, enable the rendering of consistent acoustic mosaics with high detail and increased resolution. An extensive experimental section is reported showing results in relevant field applications, such as ship hull inspection and harbor mapping

Splat-based surface reconstruction from defect-laden point sets

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface - a low-degree surface approximation - is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement. The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure

New approximation to the third-order density : application to the calculation of correlated multicenter indices

In this work we present the formulas for the calculation of exact three-center electron sharing indices (3c-ESI) and introduce two new approximate expressions for correlated wave functions. The 3c-ESI uses the third-order density, the diagonal of the third-order reduced density matrix, but the approximations suggested in this work only involve natural orbitals and occupancies. In addition, the first calculations of 3c-ESI using Valdemoro's, Nakatsuji's and Mazziotti's approximation for the third-order reduced density matrix are also presented for comparison. Our results on a test set of molecules, including 32 3c-ESI values, prove that the new approximation based on the cubic root of natural occupancies performs the best, yielding absolute errors below 0.07 and an average absolute error of 0.015. Furthemore, this approximation seems to be rather insensitive to the amount of electron correlation present in the system. This newly developed methodology provides a computational inexpensive method to calculate 3c-ESI from correlated wave functions and opens new avenues to approximate high-order reduced density matrices in other contexts, such as the contracted Schrödinger equation and the anti-Hermitian contracted Schrödinger equation

Anàlisi de les claus criptogràfiques utilitzades en bitcoin

El present projecte realitza una anàlisi de les claus criptogràfiques utilitzades en bitcoin. El projecte introdueix les nocions bàsiques necessàries de les corbes el·líptiques, la criptografia de corbes el·líptiques i els bitcoins per a realitzar l’anàlisi. Aquesta anàlisi consisteix en explorar el codi de diferents wallets bitcoin i realitzar un estudi empíric de l’aleatorietat de les claus. Per últim, el projecte introdueix el concepte de wallet determinista, el seu funcionament i alguns dels problemes que presenta.

Description of diffusive and propagative behavior on fractals

The known properties of diffusion on fractals are reviewed in order to give a general outlook of these dynamic processes. After that, we propose a description developed in the context of the intrinsic metric of fractals, which leads us to a differential equation able to describe diffusion in real fractals in the asymptotic regime. We show that our approach has a stronger physical justification than previous works on this field. The most important result we present is the introduction of a dependence on time and space for the conductivity in fractals, which is deduced by scaling arguments and supported by computer simulations. Finally, the diffusion equation is used to introduce the possibility of reaction-diffusion processes on fractals and analyze their properties. Specifically, an analytic expression for the speed of the corresponding travelling fronts, which can be of great interest for application purposes, is derived

Effects of punishment in a mobile population playing the prisoner’s dilemma game

We deal with a system of prisoner’s dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation