Person: Gómez Ullate, David
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David
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Gómez Ullate
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IE University
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IE School of Science & Technology
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Applied Mathematics
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Publication Effectiveness of Non-pharmaceutical Interventions in Nine Fields of Activity to Decrease SARS-CoV-2 Transmission(Frontiers, 2023-04-12) Gómez Ullate, David; Barbeito, Inés; Precioso, Daniel; Sierra, María José; Vegas Azcárate, Susana; Fernández Balbuena, Sonia; Vitoriano, Begoña; Cao, Ricardo; Monge, Susana; Ozayr Mahomed; University of KwaZulu-Natal; South Africa; https://ror.org/02jjdwm75Background: We estimated the association between the level of restriction in nine different fields of activity and SARS-CoV-2 transmissibility in Spain, from 15 September 2020 to 9 May 2021. Methods: A stringency index (0-1) was created for each Spanish province (n = 50) daily. A hierarchical multiplicative model was fitted. The median of coefficients across provinces (95% bootstrap confidence intervals) quantified the effect of increasing one standard deviation in the stringency index over the logarithmic return of the weekly percentage variation of the 7-days SARS-CoV-2 cumulative incidence, lagged 12 days. Results: Overall, increasing restrictions reduced SARS-CoV-2 transmission by 22% (RR = 0.78; one-sided 95%CI: 0, 0.82) in 1 week, with highest effects for culture and leisure 14% (0.86; 0, 0.98), social distancing 13% (0.87; 0, 0.95), indoor restaurants 10% (0.90; 0, 0.95) and indoor sports 6% (0.94; 0, 0.98). In a reduced model with seven fields, culture and leisure no longer had a significant effect while ceremonies decreased transmission by 5% (0.95; 0, 0.96). Models R 2 was around 70%. Conclusion: Increased restrictions decreased COVID-19 transmission. Limitations include remaining collinearity between fields, and somewhat artificial quantification of qualitative restrictions, so the exact attribution of the effect to specific areas must be done with caution.Publication Thresholding methods in non-intrusive load monitoring(Springer Nature Link, 2023-04-01) Gómez Ullate, David; Precioso, Daniel; https://ror.org/02jjdwm75Non-intrusive load monitoring (NILM) is the problem of predicting the status or consumption of individual domestic appliances only from the knowledge of the aggregated power load. NILM is often formulated as a classification (ON/OFF) problem for each device. However, the training datasets gathered by smart meters do not contain these labels, but only the electric consumption at every time interval. This paper addresses a fundamental methodological problem in how a NILM problem is posed, namely how the different possible thresholding methods lead to different classification problems. Standard datasets and NILM deep learning models are used to illustrate how the choice of thresholding method affects the output results. Some criteria that should be considered for the choice of such methods are also proposed. Finally, we propose a slight modification to current deep learning models for multi-tasking, i.e. tackling the classification and regression problems simultaneously. Transfer learning between both problems might improve performance on each of them.Publication Corrigendum on the proof of completeness for exceptional Hermite polynomials(Science Direct, 2020-05) Gómez Ullate, David; Grandati, Yves; Milson, Robert; Ministry of Economy, Industry and Competitiveness; Federación Española de Enfermedades Raras; https://ror.org/02jjdwm75Exceptional orthogonal polynomials are complete families of orthogonal polynomials that arise as eigenfunctions of a Sturm Liouville problem. Antonio Durán discovered a gap in the original proof of completeness for exceptional Hermite polynomials, that has propagated to analogous results for other exceptional families. In this paper we provide an alternative proof that follows essentially the same arguments, but provides a direct proof of the key lemma on which the completeness proof is based. This direct proof makes use of the theory of trivial monodromy potentials developed by Duistermaat and Grünbaum and OblomkovPublication Cyclic Maya diagrams and rational solutions of higher order Painlevé systems(Wiley, 2020-01-22) Gómez Ullate, David; Clarkson, Peter; Grandati, Yves; Milson, Robert; https://ror.org/02jjdwm75This paper focuses on the construction of rational solutions for the A2n-Painlev´e system, also called the Noumi-Yamada system, which are considered the higher order generalizations of PIV. In this even case, we introduce a method to construct the rational solutions based on cyclic dressing chains of Schr¨odinger operators with potentials in the class of rational extensions of the harmonic oscillator. Each potential in the chain can be indexed by a single Maya diagram and expressed in terms of a Wronskian determinant whose entries are Hermite polynomials. We introduce the notion of cyclic Maya diagrams and we characterize them for any possible period, using the concepts of genus and interlacing. The resulting classes of solutions can be expressed in terms of special polynomials that generalize the families of generalized Hermite, generalized Okamoto and Umemura polynomials, showing that they are particular cases of a larger family.Publication Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials(Cornell University, 2018-02-15) Gómez Ullate, David; Grandati, Yves; Milson, Robert; https://ror.org/02jjdwm75In a previous paper we derived equivalence relations for pseudo-Wronskian determinants of Hermite polynomials. In this paper we obtain the analogous result for Laguerre and Jacobi polynomials. The equivalence formulas are richer in this case since rational Darboux transformations can be defined for four families of seed functions, as opposed to only two families in the Hermite case. The pseudo-Wronskian determinants of Laguerre and Jacobi type will thus depend on two Maya diagrams, while Hermite pseudo-Wronskians depend on just one Maya diagram. We show that these equivalence relations can be interpreted as the general transcription of shape invariance and specific discrete symmetries acting on the parameters of the isotonic oscillator and Darboux-P¨oschl-Teller potential.