Parameter Estimation of Gaussian Stationary Processes using the Generalized Method of Moments

We consider the class of all stationary Gaussian process with explicit parametric spectral density. Under some conditions on the autocovariance function, we defined a GMM estimator that satisfies consistency and asymptotic normality, using the Breuer-Major theorem and previous results on ergodicity. This result is applied to the joint estimation of the three parameters of a stationary Ornstein-Uhlenbeck (fOU) process driven by a fractional Brownian motion. The asymptotic normality of its GMM estimator applies for any H in (0,1) and under some restrictions on the remaining parameters. A numerical study is performed in the fOU case, to illustrate the estimator's practical performance when the number of datapoints is moderate

Strong Ramsey Games in Unbounded Time

For two graphs $B$ and $H$ the strong Ramsey game $\mathcal{R}(B,H)$ on the board $B$ and with target $H$ is played as follows. Two players alternately claim edges of $B$. The first player to build a copy of $H$ wins. If none of the players win, the game is declared a draw. A notorious open question of Beck asks whether the first player has a winning strategy in $\mathcal{R}(K_n,K_k)$ in bounded time as $n\rightarrow\infty$. Surprisingly, in a recent paper Hefetz et al. constructed a $5$-uniform hypergraph $\mathcal{H}$ for which they proved that the first player does not have a winning strategy in $\mathcal{R}(K_n^{(5)},\mathcal{H})$ in bounded time. They naturally ask whether the same result holds for graphs. In this paper we make further progress in decreasing the rank. In our first result, we construct a graph $G$ (in fact $G=K_6\setminus K_4$) and prove that the first player does not have a winning strategy in $\mathcal{R}(K_n \sqcup K_n,G)$ in bounded time. As an application of this result we deduce our second result in which we construct a $4$-uniform hypergraph $G'$ and prove that the first player does not have a winning strategy in $\mathcal{R}(K_n^{(4)},G')$ in bounded time. This improves the result in the paper above. An equivalent formulation of our first result is that the game $\mathcal{R}(K_\omega\sqcup K_\omega,G)$ is a draw. Another reason for interest on the board $K_\omega\sqcup K_\omega$ is a folklore result that the disjoint union of two finite positional games both of which are first player wins is also a first player win. An amusing corollary of our first result is that at least one of the following two natural statements is false: (1) for every graph $H$, $\mathcal{R}(K_\omega,H)$ is a first player win; (2) for every graph $H$ if $\mathcal{R}(K_\omega,H)$ is a first player win, then $\mathcal{R}(K_\omega\sqcup K_\omega,H)$ is also a first player win.Comment: 18 pages, 46 figures; changes: fully reworked presentatio

Analysis of body differences for the design of children's clothing

This paper discusses anthropometric data obtained through 3D body scanner technology, aiming the dimensioning of Portuguese children's measurements for the design of clothing. The study comprises boys and girls from the Northern Region of Portugal aged between two and ten years old. The main objective of this part of the study was to evaluate the possibility of grouping children with six and seven years old in a same garment size, proposing the same body measurements in the final standard measurements table. In addition to the children's anthropometric measurements, it was checked the body conformation of the children and the possibility of identifying the main biotypes. As a preliminary result, through cluster analysis it was found that it is possible to combine these children in the same group in the proposed standard measurements table.POFC - Programa Operacional Temático Factores de Competitividade(UID/CTM/000264

Affine arithmetic-based methodology for energy hub operation-scheduling in the presence of data uncertainty

In this study, the role of self-validated computing for solving the energy hub-scheduling problem in the presence of multiple and heterogeneous sources of data uncertainties is explored and a new solution paradigm based on affine arithmetic is conceptualised. The benefits deriving from the application of this methodology are analysed in details, and several numerical results are presented and discussed

Interactions of accessible solitons with interfaces in anisotropic media: the case of uniaxial nematic liquid crystals

We investigate, both theoretically and experimentally, spatial soliton interaction with dielectric interfaces in a strongly anisotropic medium with non-locality, such as nematic liquid crystals. We throw light on the role of refractive index gradients as well as optic axis variations in both voltage- and self-driven angular steering of non-local solitons. We specifically address and then employ in experiments a suitably designed electrode geometry in a liquid crystalline cell in order to define and tune a graded dielectric interface by exploiting the electro-optic response of the material through the in-plane reorientation of the optic axis in two distinct regions. We study both refraction and total internal reflection as well as voltage controlled steering of spatial solitons