On the Suitability of Genetic-Based Algorithms for Data Mining

Data mining has as goal to extract knowledge from large databases. A database may be considered as a search space consisting of an enormous number of elements, and a mining algorithm as a search strategy. In general, an exhaustive search of the space is infeasible. Therefore, efficient search strategies are of vital importance. Search strategies on genetic-based algorithms have been applied successfully in a wide range of applications. We focus on the suitability of genetic-based algorithms for data mining. We discuss the design and implementation of a genetic-based algorithm for data mining and illustrate its potentials

A Universal Bound on Excitations of Heavy Fields during Inflation

We discuss a universal bound on any excitation of heavy fields during inflation: the ratio of the heavy field's energy density to the one driving inflation must be less than the maximally allowed relative amplitude of oscillations in the power-spectrum (less than one percent according to PLANCK). This bound can be traced back to the sudden change of the equation of state parameter across the excitation event. We employ a sudden transition approximation at the perturbed level, which has been used before in different settings; we check its validity by comparison to the full multi-field result in a concrete case study involving a sudden mass change of an inflaton.Comment: 31 pages, 9 figures; v2: reference added, minor typos corrected, conclusions unchange

Universal Aspects of U(1)U(1) Gauge Field Localization on Branes in DD-dimensions

In this work, we study the general properties of the $D$-vector field localization on $(D-d-1)$-brane with co-dimension $d$. We consider a conformally flat metric with the warp factor depending only on the transverse extra dimensions. We employ the geometrical coupling mechanism and find an analytical solution for the $U(1)$ gauge field valid for any warp factor. Using this solution we find that the only condition necessary for localization is that the bulk geometry is asymptotically AdS. Therefore, our solution has an universal validity for any warp factor and is independent of the particular model considered. We also show that the model has no tachyonic modes. Finally, we study the scalar components of the $D$-vector field. As a general result, we show that if we consider the coupling with the tensor and the Ricci scalar in higher co-dimensions, there is an indication that both sectors will be localized. As a concrete example, the above techniques are applied for the intersecting brane model. We obtain that the branes introduce boundary conditions that fix all parameters of the model in such a way that both sectors, gauge and scalar fields, are confined.Comment: 26 pages, 5 figures, Accepted version for publication in JHE

Polytropic equation of state and primordial quantum fluctuations

We study the primordial Universe in a cosmological model where inflation is driven by a fluid with a polytropic equation of state $p = \alpha\rho + k\rho^{1 + 1/n}$. We calculate the dynamics of the scalar factor and build a Universe with constant density at the origin. We also find the equivalent scalar field that could create such equation of state and calculate the corresponding slow-roll parameters. We calculate the scalar perturbations, the scalar power spectrum and the spectral index.Comment: 16 pages, 4 figure

On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

Bounds and extremal domains for Robin eigenvalues with negative boundary parameter

We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter case the disk maximises the first eigenvalue for all values of the parameter. This is in contrast with what happens in the constant area problem, where the disk is the maximiser only for small values of the boundary parameter. We also present sharp upper and lower bounds for the first eigenvalue of the ball and spherical shells. These results are complemented by the numerical optimisation of the first four and two eigenvalues in 2 and 3 dimensions, respectively, and an evaluation of the quality of the upper bounds obtained. We also study the bifurcations from the ball as the boundary parameter becomes large (negative).Comment: 26 pages, 20 figure

Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian

We consider the problem of minimising the $n^{th}-$eigenvalue of the Robin Laplacian in $\mathbb{R}^{N}$. Although for $n=1,2$ and a positive boundary parameter $\alpha$ it is known that the minimisers do not depend on $\alpha$, we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on $\alpha$. We derive a Wolf-Keller type result for this problem and show that optimal eigenvalues grow at most with $n^{1/N}$, which is in sharp contrast with the Weyl asymptotics for a fixed domain. We further show that the gap between consecutive eigenvalues does go to zero as $n$ goes to infinity. Numerical results then support the conjecture that for each $n$ there exists a positive value of $\alpha_{n}$ such that the $n^{\rm th}$ eigenvalue is minimised by $n$ disks for all $0<\alpha<\alpha_{n}$ and, combined with analytic estimates, that this value is expected to grow with $n^{1/N}$