Mario Zacarés

A relevance feedback CBIR algorithm based on fuzzy sets

CBIR (content-based image retrieval) systems attempt to allow users to perform searches in large picture repositories. In most existing CBIR systems, images are represented by vectors of low level features. Searches in these systems are usually based on distance measurements defined in terms of weighted combinations of the low level features. This paper presents a novel approach to combining features when using multi-image queries consisting of positive and negative selections. A fuzzy set is defined so that the degree of membership of each image in the repository to this fuzzy set is related to the users interest in that image. Positive and negative selections are then used to determine the degree of membership of each picture to this set. The system attempts to capture the meaning of a selection by modifying a series of parameters at each iteration to imitate user behavior, becoming more selective as the search progresses. The algorithm has been evaluated against four other representative relevance feedback approaches. Both the performance and usability of the five CBIR systems have been studied. The algorithm presented is easy to use and yields the highest performance in terms of the average number of iterations required to find a specific image. However, it is computationally more expensive and requires more memory than two of the other techniques.

Angular Pseudomomentum Theory for the Generalized Nonlinear Schrodinger Equation in Discrete Rotational Symmetry Media

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schrodinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schrodinger equation with a nonlinearity depending on the modulus of the eld. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classied according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the re- lationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.

Topological charge selection rule for phase singularities

We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.

A group-theory method to find stationary states in nonlinear discrete symmetry systems

In the field of nonlinear optics, the self-consistency method has been applied to searching optical solitons in different media. In this paper, we generalize this method to other systems, adapting it to discrete symmetry systems by using group theory arguments. The result is a new technique that incorporates symmetry concepts into the iterative procedure of the self-consistency method, that helps the search of symmetric stationary solutions. An efficient implementation of this technique is also presented, which restricts the computational work to a reduced section of the entire domain and is able to find different types of solutions by specifying their symmetry properties. As a practical application, we develop an efficient algorithm for solving the nonlinear Schrodinger equation with a discrete symmetry potential.

Self-Trapped localized modes in photonic crystal fibers

We demonstrate the existence of self-trapped localized modes in photonic crystal fibers. We analyze these solutions in terms of the parameters of the photonic crystal cladding and the nonlinear coupling.

Photonic Nambu-Goldstone bosons

We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chess board pattern, with a difference of

Soliplasmon Excitations at Metal/Dielectric/Kerr Structures

\pi

A Topological Charge Selection Rule for Phase Singularities

between neighboring sites. We show that the lowest lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the intensity of the light that, because of the nonlinearity, affects the dynamics of the phase fluctuations. We interpret the results using methods of condensed matter physics, based on an effective description of the optical system. This interpretation sheds new light on the phenomena, facilitating the understanding of individual systems and leading to a framework for relating different problems with the same symmetry. In this context, we show that the perturbative excitations of the phase are Nambu-Goldstone bosons of a spontaneously broken

Photonic systems acting as magnetic solids

U(1)

Spatial effects in nonlinear photonic crystal fibers

symmetry.