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Calibration of parameters in Dynamic Energy Budget models using Direct-Search methods
Publication . Morais, J. V.; Custódio, A. L.; Marques, G. M.; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; Springer Science Business Media
Dynamic Energy Budget (DEB) theory aims to capture the quantitative aspects of metabolism at the individual level, for all species. The parametrization of a DEB model is based on information obtained through the observation of natural populations and experimental research. Currently the DEB toolbox estimates these parameters using the Nelder–Mead Simplex method, a derivative-free direct-search method. However, this procedure presents some limitations regarding convergence and how to address constraints. Framed in the calibration of parameters in DEB theory, this work presents a numerical comparison between the Nelder–Mead Simplex method and the SID-PSM algorithm, a Directional Direct-Search method for which convergence can be established both for unconstrained and constrained problems. A hybrid version of the two methods, named as Simplex Directional Direct-Search, provides a robust and efficient algorithm, able to solve the constrained optimization problems resulting from the parametrization of the biological models.
Monthly prediction of drought classes using log-linear models under the influence of NAO for early-warning of drought and water management
Publication . Moreira, Elsa; Russo, Ana; Trigo, Ricardo M.; CMA - Centro de Matemática e Aplicações; MDPI - Multidisciplinary Digital Publishing Institute
Drought class transitions over a sector of Eastern Europe were modeled using log-linear models. These drought class transitions were computed from time series of two widely used multiscale drought indices, the Standardized Preipitation Evapotranspiration Index (SPEI) and the Standardized Precipitation Index (SPI), with temporal scales of 6 and 12 months for 15 points selected from a grid over the Prut basin in Romania over a period of 112 years (1902-2014). The modeling also took into account the impact of North Atlantic Oscillation (NAO), exploring the potential influence of this large-scale atmospheric driver on the climate of the Prut region. To assess the probability of transition among different drought classes we computed their odds and the corresponding confidence intervals. To evaluate the predictive capabilities of the modeling, skill scores were computed and used for comparison against benchmark models, namely using persistence forecasts or modeling without the influence of the NAO index. The main results indicate that the log-linear modeling performs consistently better than the persistence forecast, and the highest improvements obtained in the skill scores with the introduction of the NAO predictor in the modeling are obtained when modeling the extended winter months of the SPEI6 and SPI12. The improvements are however not impressive, ranging between 4.7 and 6.8 for the SPEI6 and between 4.1 and 10.1 for the SPI12, in terms of the Heidke skill score.
Decision problems for word-hyperbolic semigroups
Publication . Cain, Alan J.; Pfeiffer, Markus; CMA - Centro de Matemática e Aplicações; Elsevier
This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan and Gilman. A fundamental investigation reveals that the natural definition of a ‘word-hyperbolic structure’ has to be strengthened slightly in order to define a unique semigroup up to isomorphism. (This does not alter the class of word-hyperbolic semigroups.) The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the situation for word-hyperbolic groups). It is proved that it is undecidable whether a word-hyperbolic semigroup is automatic, asynchronously automatic, biautomatic, or asynchronously biautomatic. (These properties do not hold in general for word-hyperbolic semigroups.) It is proved that the uniform word problem for word-hyperbolic semigroups is solvable in polynomial time (improving on the previous exponential-time algorithm). Algorithms are presented for deciding whether a word-hyperbolic semigroup is a monoid, a group, a completely simple semigroup, a Clifford semigroup, or a free semigroup.
On the linear combination of independent logistic random variables
Publication . Marques, Filipe J.; DM - Departamento de Matemática; International Academic Press
In this work the exact distribution of the linear combination of p independent logistic random variables is studied. It is shown that the exact distribution may be represented as a shifted infinite sum of independent random variables distributed as the difference of two independent Generalized Integer Gamma distributions. In addition, two near-exact approximations are developed for this distribution. Numerical studies are conducted to access the degree of precision and also the computational performance of these approximations. The developed methodology is used to derive near-exact approximations for the linear combination of independent generalized logistic random variables.
Deciding conjugacy in sylvester monoids and other homogeneous monoids
Publication . Cain, Alan J.; Malheiro, Antonio; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; World Scientific
We give a combinatorial characterization of conjugacy in the sylvester monoid, showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids.
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Fundação para a Ciência e a Tecnologia
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5876
Número da atribuição
UID/MAT/00297/2013