Instituto de Telecomunicações

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Publications

Computing the exact number of periodic orbits for planar flows

Publication . Graça, Daniel; Zhong, Ning

In this paper, we consider the problem of determining the exact number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the problem is noncomputable on the one hand and, on the other hand, computable uniformly on the set of all structurally stable systems defined on the unit disk. We also prove that there is a family of polynomial planar systems which does not have a computable sharp upper bound on the number of its periodic orbits.

2022Journal article

Open access

The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable

Publication . Graça, Daniel; Zhong, Ning

In this note, we construct an algorithm that, on input of a description of a structurally stable planar dynamical flow $f$ defined on the closed unit disk, outputs the exact number of the (hyperbolic) equilibrium points and their locations with arbitrary accuracy. By arbitrary accuracy it is meant that any accuracy required by the input can be achieved. The algorithm can be further extended to a root-finding algorithm that computes the exact number of zeros as well the location of each zero of a continuously differentiable function $f$ defined on the closed unit ball of $\mathbb{R}^{d}$, provided that the Jacobian of $f$ is invertible at each zero of $f$; moreover, the computation is uniform in $f$.

2021Journal article

Restricted access

A continuous characterization of PSPACE using polynomial ordinary differential equations

Publication . Bournez, Olivier; Gozzi, Riccardo; Graça, Daniel; Pouly, Amaury

In this paper we provide a characterization of the complexity class PSPACE by using a purely continuous model defined with polynomial ordinary differential equations.

2023-08Journal article

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The Synergy between artificial intelligence, remote sensing, and archaeological fieldwork validation

Publication . Canedo, Daniel; Hipólito, João; Fonte, João; Dias, Rita; Pereiro, Tiago do; Georgieva, Petia; Gonçalves-Seco, Luís; Vázquez, Marta; Pires, Nelson; Fábrega-Álvarez, Pastor; Menéndez-Marsh, Fernando; Neves, António J. R.

The increasing relevance of remote sensing and artificial intelligence (AI) for archaeological research and cultural heritage management is undeniable. However, there is a critical gap in this field. Many studies conclude with identifying hundreds or even thousands of potential sites, but very few follow through with crucial fieldwork validation to confirm their existence. This research addresses this gap by proposing and implementing a fieldwork validation pipeline. In northern Portugal's Alto Minho region, we employed this pipeline to verify 237 potential burial mounds identified by an AI-powered algorithm. Fieldwork provided valuable information on the optimal conditions for burial mounds and the specific factors that led the algorithm to err. Based on these insights, we implemented two key improvements to the algorithm. First, we incorporated a slope map derived from LiDAR-generated terrain models to eliminate potential burial mound inferences in areas with high slopes. Second, we trained a Vision Transformer model using digital orthophotos of both confirmed burial mounds and previously identified False Positives. This further refines the algorithm's ability to distinguish genuine sites.

2024-05-28Journal article

Open access

Electrical impedance spectroscopy for potassium content analysis and botanical origin identification of honey

Publication . Elamine, Youssef; INÁCIO, PEDRO; Miguel, Maria da Graça; Carlier, Jorge; Costa, Maria Clara; Estevinho, Leticia M.; Gomes, Henrique L.

Minerals are reported to dominate the electrical properties of honey and indicate its botanical and geographical origins. In this study, Electrochemical Impedance Spectroscopy (EIS) was used to assess the relation between mineral elements, electrical properties and botanical origin using three honey varieties - Citrus sp., Eucalyptus sp., and Erica sp. These varieties are identified through pollen analysis and market labelling. Flame atomic absorption and emission spectroscopies were used to quantify the concentrations of eight elements (potassium, sodium, calcium, magnesium, manganese, zinc, copper, and iron). Among all the mineral elements, potassium showed a consistent correlation with impedance. The potassium estimation in honey and standard solutions (calibration curve) had similar sensitivities of 153.43 nF/mM and 132.68 nF/mM, respectively. Additionally, the analysis revealed that potassium dominates the mineral composition, with the other species present in minimal quantities. The EIS technique showed high sensitivity to potassium and other ionisable species, making it possible to classify the botanical origin of these three honey types. The EIS technique proved to be both time and cost effective, yielding a classification rate higher than that achieved by analysing mineral composition.

2024-09Journal article

Restricted access