Bernstein polynomials in element-free Galerkin method

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves,can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

Differential resultant formulas for linear od-polynomials.

Ponencia

Tunable Fano resonance in symmetric multilayered gold nanoshells

Fano resonances (FRs) are produced when a discrete state is coupled with a continuum. In addition to fundamental scientific interests, FRs in plasmonic systems give rise to the so-called plasmon-induced transparency. In this work we have studied the evolution of dipole-dipole all-plasmonic FRs in symmetric multilayered nanoshells as the function of their geometrical parameters. We demonstrate that symmetry breaking is not mandatory for controlling the Fano resonance in such multilayered nanoshells. Generation of FRs in these symmetric nanostructures presents clear advantages over their asymmetric counterparts, as they are easier to fabricate and can be used in a wider range of technological applications.

Design of spherical symmetric gradient index lenses

Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.

Tunable Fano resonance in symmetric multilayered gold nanoshells

We have studied the evolution of dipole–dipole all-plasmonic Fano resonances (FRs) in symmetric multilayered nanoshells as a function of their geometrical parameters. We demonstrate that symmetry breaking is not mandatory for controlling the Fano resonance in such multilayer structures. By carefully selecting the geometrical parameters, the position of the FR can be tuned between 600 and 950 nm and its intensity can be increased up to four fold with respect to the non-optimized structures. Generation of FRs in such symmetric nanostructures presents clear advantages over their asymmetric counterparts, as they are easier to fabricate and can be used in a wider range of technological applications.

Differential resultants of super essential systems of linear OD-polynomials

The sparse differential resultant dres(P) of an overdetermined system P of generic nonhomogeneous ordinary differential polynomials, was formally defined recently by Li, Gao and Yuan (2011). In this note, a differential resultant formula dfres(P) is defined and proved to be nonzero for linear "super essential" systems. In the linear case, dres(P) is proved to be equal, up to a nonzero constant, to dfres(P*) for the supper essential subsystem P* of P.

Preliminary design of symmetric arch-gravity dams

In this paper, a set of design parameters, such as the slopes of upstream and downstream faces of the dam, radius of the upper arch, width of the dam at the top level and height of the vertical upper part of the dam, are given as function of the valley characteristics when the dam is situated, such as its geometry and its geotechnical properties. These tables have been obtained using a regression of the design parameters of an arch-gravity dam with a minimum concrete volume, placed in a large number of valleys with different characteristics and properties. Elasticites for these design parameters are also discussed.

Learning Bayesian networks from data by the incremental compilation of new network polynomials

Probabilistic graphical models are a huge research field in artificial intelligence nowadays. The scope of this work is the study of directed graphical models for the representation of discrete distributions. Two of the main research topics related to this area focus on performing inference over graphical models and on learning graphical models from data. Traditionally, the inference process and the learning process have been treated separately, but given that the learned models structure marks the inference complexity, this kind of strategies will sometimes produce very inefficient models. With the purpose of learning thinner models, in this master thesis we propose a new model for the representation of network polynomials, which we call polynomial trees. Polynomial trees are a complementary representation for Bayesian networks that allows an efficient evaluation of the inference complexity and provides a framework for exact inference. We also propose a set of methods for the incremental compilation of polynomial trees and an algorithm for learning polynomial trees from data using a greedy score+search method that includes the inference complexity as a penalization in the scoring function.

Conditional density approximations with mixtures of polynomials

Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.

Inelastic torsional seismic response of nominally symmetric reinforced concrete frame structures: shaking table tests

This paper discusses the torsional response of a scaled reinforced concrete frame structure subjected to several uniaxial shaking table tests. The tested structure is nominally symmetric in the direction of shaking and exhibits torsion attributable to non-uniform yielding of structural components and uncertainties in the building process. Asymmetric behavior is analyzed in terms of displacement, strain in reinforcing bars, energy dissipated at plastic hinges, and damage at section and frame levels. The results show that for low levels of seismic hazard, for which the structure is expected to perform basically within the elastic range, the accidental eccentricity is not a concern for the health of the structure, but it significantly increases the lateral displacement demand in the frames (about 30%) and this might cause significant damage to non-structural components. For high levels of seismic hazard the effects of accidental torsion become less important. These results underline the need to consider accidental eccentricity in evaluating the performance of a structure for very frequent or frequent earthquakes, and suggest that consideration of torsion may be neglected for performance levels associated with rare or very rare earthquakes.

Analyzing size-symmetric vs. size-asymmetric and intra-vs. inter-specific competition in beech (Fagus sylvatica L.) mixed stands

In mixed stands, inter-specific competition can be lower than intra-specific competition when niche complementarity and/or facilitation between species prevail. These positive interactions can take place at belowground and/or aboveground levels. Belowground competition tends to be size symmetric while the aboveground competition is usually for light and almost always size-asymmetric. Interactions between forest tree species can be explored analyzing growth at tree level by comparing intra and inter-specific competition. At the same time, possible causes of niche complementarity can be inferred relating intra and inter-specific competition with the mode of competition, i.e. size-symmetric or sizeasymmetric. The aim of this paper is to further our understanding of the interactions between species and to detect possible causes of competition reduction in mixed stands of beech (Fagus sylvatica L.) with other species: pine?beech, oak?beech and fir?beech. To test whether species growth is better explained by size-symmetric and/or size-asymmetric competition, five different competition structures where included in basal area growth models fitted using data from the Spanish National Forest Inventory for the Pyrenees. These models considered either size-symmetry only (Reineke?s stand density index, SDI), size-asymmetry only (SDI of large trees or SDI of small trees), or both combined. In order to assess the influence of the admixture, these indices were introduced in two different ways, one of which was to consider that trees of all species compete in a similar way, and the other was to split the stand density indices into intra- and inter-specific competition components. The results showed that in pine?beech mixtures, there is a slightly negative effect of beech on pine basal area growth while beech benefitted from the admixture of Scots pine; this positive effect being greater as the proportion of pine trees in larger size classes increases. In oak?beech mixtures, beech growth was also positively influenced by the presence of oaks that were larger than the beech trees. The growth of oak, however, decreased when the proportion of beech in SDI increased, although the presence of beech in larger size classes promoted oak growth. Finally, in fir?beech mixtures, neither fir nor beech basal area growth were influenced by the presence of the other species. The results indicate that size-asymmetric is stronger than size-symmetric competition in these mixtures, highlighting the importance of light in competition. Positive species interactions in size-asymmetric competition involved a reduction of asymmetry in tree size-growth relationships.

A finite class of orthogonal functions generated by Routh-Romanovski polynomials

It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh-Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity.

Vector Boolean Functions: Applications in Symmetric Cryptography

Esta tesis establece los fundamentos teóricos y diseña una colección abierta de clases C++ denominada VBF (Vector Boolean Functions) para analizar funciones booleanas vectoriales (funciones que asocian un vector booleano a otro vector booleano) desde una perspectiva criptográfica. Esta nueva implementación emplea la librería NTL de Victor Shoup, incorporando nuevos módulos que complementan a las funciones de NTL, adecuándolas para el análisis criptográfico. La clase fundamental que representa una función booleana vectorial se puede inicializar de manera muy flexible mediante diferentes estructuras de datas tales como la Tabla de verdad, la Representación de traza y la Forma algebraica normal entre otras. De esta manera VBF permite evaluar los criterios criptográficos más relevantes de los algoritmos de cifra en bloque y de stream, así como funciones hash: por ejemplo, proporciona la no-linealidad, la distancia lineal, el grado algebraico, las estructuras lineales, la distribución de frecuencias de los valores absolutos del espectro Walsh o del espectro de autocorrelación, entre otros criterios. Adicionalmente, VBF puede llevar a cabo operaciones entre funciones booleanas vectoriales tales como la comprobación de igualdad, la composición, la inversión, la suma, la suma directa, el bricklayering (aplicación paralela de funciones booleanas vectoriales como la empleada en el algoritmo de cifra Rijndael), y la adición de funciones coordenada. La tesis también muestra el empleo de la librería VBF en dos aplicaciones prácticas. Por un lado, se han analizado las características más relevantes de los sistemas de cifra en bloque. Por otro lado, combinando VBF con algoritmos de optimización, se han diseñado funciones booleanas cuyas propiedades criptográficas son las mejores conocidas hasta la fecha. ABSTRACT This thesis develops the theoretical foundations and designs an open collection of C++ classes, called VBF, designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This new implementation uses the NTL library from Victor Shoup, adding new modules which complement the existing ones making VBF better suited for cryptography. The fundamental class representing a vector Boolean function can be initialized in a flexible way via several alternative types of data structures such as Truth Table, Trace Representation, Algebraic Normal Form (ANF) among others. This way, VBF allows the evaluation of the most relevant cryptographic criteria for block and stream ciphers as well as for hash functions: for instance, it provides the nonlinearity, the linearity distance, the algebraic degree, the linear structures, the frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, VBF can perform operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions. This thesis also illustrates the use of VBF in two practical applications. On the one hand, the most relevant properties of the existing block ciphers have been analysed. On the other hand, by combining VBF with optimization algorithms, new Boolean functions have been designed which have the best known cryptographic properties up-to-date.

Estimation of Symmetric Channels for Discrete Cosine Transform Type-I Multicarrier Systems: A Compressed Sensing Approach

The problem of channel estimation for multicarrier communications is addressed. We focus on systems employing the Discrete Cosine Transform Type-I (DCT1) even at both the transmitter and the receiver, presenting an algorithm which achieves an accurate estimation of symmetric channel filters using only a small number of training symbols. The solution is obtained by using either matrix inversion or compressed sensing algorithms. We provide the theoretical results which guarantee the validity of the proposed technique for the DCT1. Numerical simulations illustrate the good behaviour of the proposed algorithm.

Bivariate Krawtchouk polynomials: Inversion and connection problems with the NAVIMA algorithm

In this paper we present a recurrent procedure to solve an inversion problem for monic bivariate Krawtchouk polynomials written in vector column form, giving its solution explicitly. As a by-product, a general connection problem between two vector column of monic bivariate Krawtchouk families is also explicitly solved. Moreover, in the non monic case and also for Krawtchouk families, several expansion formulas are given, but for polynomials written in scalar form.