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Browsing Research Articles by Department "Applied Mathematics"
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Publication Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation(Cornell University, 2021-11-15) Ballester, Rafael; Usvyatsov, Mikhail; Makarova, Anastasia; Rakhuba, Maxim; Krause, Andreas; Schindler, Konrad; https://ror.org/02jjdwm75We propose an end-to-end trainable framework that processes large-scale visual data tensors by looking at a fraction of their entries only. Our method combines a neural network encoder with a tensor train decomposition to learn a low-rank latent encoding, coupled with cross-approximation (CA) to learn the representation through a subset of the original samples. CA is an adaptive sampling algorithm that is native to tensor decompositions and avoids working with the full high-resolution data explicitly. Instead, it actively selects local representative samples that we fetch out-of-core and on-demand. The required number of samples grows only logarithmically with the size of the input. Our implicit representation of the tensor in the network enables processing large grids that could not be otherwise tractable in their uncompressed form. The proposed approach is particularly useful for large-scale multidimensional grid data (e.g., 3D tomography), and for tasks that require context over a large receptive field (e.g., predicting the medical condition of entire organs).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 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 Quantitative probability estimation of light-induced inactivation of SARS-CoV-2(Nature Research, 2024) Quintana, Jaime; Alda, Irene; Alda, Javier; Universidad Complutense de Madrid; Comunidad de Madrid; https://ror.org/02jjdwm75During the COVID pandemic caused by the SARS-CoV-2 virus,studies have shown the efficiency of deactivating this virus via ultraviolet light. The damage mechanism is well understood: UV light disturbs the integrity of the RNA chain at those locations where specific nucleotide neighbors occur. In this contribution,we present a model to address certain gaps in the description of the interaction between UV photons and the RNA sequence for virus inactivation. We begin by exploiting the available information on the pathogen’s morphology,physical,and genomic characteristics,enabling us to estimate the average number of UV photons required to photochemically damage the virus’s RNA. To generalize our results,we have numerically generated random RNA sequences and checked that the distribution of pairs of nucleotides susceptible of damage for the SARS-CoV-2 is within the expected values for a random-generated RNA chain. After determining the average number of photons reaching the RNA for a preset level of fluence (or photon density),we applied the binomial probability distribution to evaluate the damage of nucleotide pairs in the RNA chain due to UV radiation. Our results describe this interaction in terms of the probability of damaging a single pair of nucleotides,and the number of available photons. The cumulative probability exhibits a steep sigmoidal shape,implying that a relatively small change in the number of affected pairs may trigger the inactivation of the virus. Our light-RNA interaction model quantitatively describes how the fraction of affected pairs of nucleotides in the RNA sequence depends on the probability of damaging a single pair and the number of photons impinging on it. A better understanding of the underlying inactivation mechanism would help in the design of optimum experiments and UV sanitization methods. Although this paper focuses on SARS-CoV-2,these results can be adapted for any other type of pathogen susceptible of UV damage. © The Author(s) 2024.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.Publication The social base and career development of Spanish mayors(Asociacion Espanola de Ciencia Politica y de la Administracion, 2018) Navarro, Carmen; Sanz, Alberto; Ministerio de Economía y Competitividad; https://ror.org/02jjdwm75The growing corpus of studies about political elites in Spain has tended to focus on national and regional parliaments and executives,rather than on the municipal level of government. And yet,it is in these local settings that politicians acquire skills and political experience,develop their notions of democracy,and often start their political careers. Exploring patterns of political recruitment in Spanish local democracies allows us to look at some of the literature findings on this topic and check whether they also apply at the municipal level in Spain,enhancing in this way our understanding of who governs our cities,too. This article analyzes Spanish mayors' social profiles,their patterns of professionalization and their political ambitions,trying to address questions such as: do municipal leaders share a common background? Are they amateurs or professionals in politics? Is the municipal level the first stage of an identifiable political career of Spanish representatives? In responding to these questions,this paper draws on survey data from a representative sample of 303 mayors in municipalities with populations larger than 10 000 inhabitants. The analysis confirms that Spanish mayors follow to a great extent the patterns found in studies of political elites and particularly those of local executives in other countries in Europe,but with some distinctive singularities. © Revista Española de Ciencia Política,2018.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 Tntorch: Tensor Network Learning with PyTorch(JMLR, 2022) Ballester, Rafael; Usvyatsov, Mikhail; Schindler, Konrad; https://ror.org/02jjdwm75We present tntorch, a tensor learning framework that supports multiple decompositions (including Candecomp/Parafac, Tucker, and Tensor Train) under a unified interface. With our library, the user can learn and handle low-rank tensors with automatic differentiation, seamless GPU support, and the convenience of PyTorch’s API. Besides decomposition algorithms, tntorch implements differentiable tensor algebra, rank truncation, crossapproximation, batch processing, comprehensive tensor arithmetics, and more.