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Publication Open Access Achieving transfer from mathematics learning(MDPI, 2023) Orón, José Víctor; Lizasoain Iriso, María Inmaculada; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2The question of transfer is a special challenge in mathematics teaching because the wide range and fragmentation of the curricula have in many cases fostered an instrumental understanding, which makes transfer difficult for the students. Although promoting a relational learning has been a huge step forward in achieving transfer, understanding usually remains at the technical level of learning. Fostering critical thinking and metacognition raises learning to the psychological level, as students are encouraged to analyse their own thinking. Despite this, our hypothesis is that transfer will only be achieved when students are helped to reach a personal dimension, being encouraged to discover their own way of approaching the global reality of their lives beyond the subject. Learning, for instance, the greatest common divisor should be an opportunity to discover that, as numbers can be presented by their prime factors, people can be recognised by their features and interests. As such, looking for the greatest common divisor should not differ from discovering common interests with friends. Integrating specific and general learning will make transfer no longer unattainable. Personalising learning means discovering how one specific learning impacts on the personal way of understanding reality (oneself, others, and world), thus making transfer natural.Publication Open Access Addendum to "uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces"(Springer, 2022) Albiac Alesanco, Fernando José; Ansorena, José L.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaAfter [Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces, Positivity 26 (2022), Paper no. 35] was published, we realized that Theorem 4.2 therein, when combined with work of Casazza and Kalton (Israel J. Math. 103:141-175, 1998) , solves the long-standing problem whether there exists a quasi-Banach space with a unique unconditional basis whose Banach envelope does not have a unique unconditional basis. Here we give examples to prove that the answer is positive. We also use auxiliary results in the aforementioned paper to give a negative answer to the question of Bourgain et al. (Mem Am Math Soc 54:iv+111, 1985)*Problem 1.11 whether the infinite direct sum l(1)(X) of a Banach space X has a unique unconditional basis whenever X does.Publication Open Access Aggregation of individual rankings through fusion functions: criticism and optimality analysis(IEEE, 2020) Bustince Sola, Humberto; Bedregal, Benjamin; Campión Arrastia, María Jesús; Silva, Ivanoska da; Fernández Fernández, Francisco Javier; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Santiago, Regivan; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasThroughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice where well-known impossibility results as the Arrovian ones are encountered and the decision-making approaches where the necessity of fusing rankings is unavoidable. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings IEEE.Publication Open Access Alleviating confounding in spatio-temporal areal models with an application on crimes against women in India(SAGE Publications, 2021) Adin Urtasun, Aritz; Goicoa Mangado, Tomás; Hodges, James S.; Schnell, Patrick M.; Ugarte Martínez, María Dolores; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasAssessing associations between a response of interest and a set of covariates in spatial areal models is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects can mask or even bias estimates of such associations due to confounding effects if they are not carefully handled. Though potentially harmful, confounding issues have often been ignored in practice leading to wrong conclusions about the underlying associations between the response and the covariates. In spatio-temporal areal models, the temporal dimension may emerge as a new source of confounding, and the problem may be even worse. In this work, we propose two approaches to deal with confounding of fixed effects by spatial and temporal random effects, while obtaining good model predictions. In particular, restricted regression and an apparently—though in fact not—equivalent procedure using constraints are proposed within both fully Bayes and empirical Bayes approaches. The methods are compared in terms of fixed-effect estimates and model selection criteria. The techniques are used to assess the association between dowry deaths and certain socio-demographic covariates in the districts of Uttar Pradesh, India.Publication Open Access Analysis and application of an overlapped FEM-BEM for wave propagation in unbounded and heterogeneous media(Elsevier, 2022) Domínguez Baguena, Víctor; Ganesh, M.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasAn overlapped continuous model framework, for the Helmholtz wave propagation problem in unbounded regions comprising bounded heterogeneous media, was recently introduced and analyzed by the authors (2020) [10]. The continuous Helmholtz system incorporates a radiation condition (RC) and our equivalent hybrid framework facilitates application of widely used finite element methods (FEM) and boundary element methods (BEM), and the resulting discrete systems retain the RC exactly. The FEM and BEM discretizations, respectively, applied to the designed interior heterogeneous and exterior homogeneous media Helmholtz systems include the FEM and BEM solutions matching in artificial interface domains, and allow for computations of the exact ansatz based far-fields. In this article we present rigorous numerical analysis of a discrete two-dimensional FEM-BEM overlapped coupling implementation of the algorithm. We also demonstrate the efficiency of our discrete FEM-BEM framework and analysis using numerical experiments, including applications to non-convex heterogeneous multiple particle Janus configurations. Simulations of the far-field induced differential scattering cross sections (DSCS) of heterogeneous configurations and orientation-averaged (OA) counterparts are important for several applications, including inverse wave problems. Our robust FEM-BEM framework facilitates computations of such quantities of interest, without boundedness or homogeneity or shape restrictions on the wave propagation model. © 2021 IMACSPublication Open Access Analysis of bright bolides recorded between October and November 2022 by the Southwestern Europe Meteor Network(MeteorNews, 2023) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; San Segundo, A.; Ávila, D.; Tosar, B.; Gómez-Hernández, A.; Gómez-Martínez, Juan; García, Antonio; Aimee, A. I.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2We present in this work the analysis of some of the bright fireballs spotted in the framework of the Southwestern Europe Meteor Network (SWEMN) between October and November 2022. They have been observed from the Iberian Peninsula and had a maximum brightness ranging from mag. –7 to mag. –15. Most meteors included in this report were linked to the sporadic background and also to the Southern Taurids.Publication Open Access Analysis of remarkable bolides observed between June and July 2022 in the framework of the Southwestern EuropeMeteor Network(MeteorNews, 2022) Madiedo, J. M.; Ortiz, J. L.; Izquierdo, J.; Santos-Sanz, P.; Aceituno, J.; Guindos, E. de; Yanguas Sayas, Patricia; Palacián Subiela, Jesús Francisco; San Segundo, A.; Ávila, D.; Tosar, B.; Gómez-Hernández, A.; Gómez-Martínez, J.; García, A.; Aimee, A. I.; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2Some of the bright bolides spotted in the framework of the Southwestern Europe Meteor Network from June to July 2022 are discussed here. These were observed from Spain. Their absolute magnitude ranges from –6 to –11. Fireballs included in this work were generated by different sources: the sporadic background, major meteoroid streams, and poorly known streams.Publication Open Access Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions(University of Szeged (Hungría), 2020) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasWe consider the second-order linear differential equation (x2 − 1)y'' + f (x)y′ + g(x)y = h(x) in the interval (−1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed Dirichlet–Neumann). The functions f, g and h are analytic in a Cassini disk Dr with foci at x = ±1 containing the interval [−1, 1]. Then, the two end points of the interval may be regular singular points of the differential equation. The two-point Taylor expansion of the solution y(x) at the end points ±1 is used to study the space of analytic solutions in Dr of the differential equation, and to give a criterion for the existence and uniqueness of analytic solutions of the boundary value problem. This method is constructive and provides the two-point Taylor appro-ximation of the analytic solutions when they exist.Publication Open Access An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions(Springer, 2022) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three variables x, y or z (with the other two fixed). We proceed by considering a more general parametric integral from which RD(x,y,z) is a particular case. It turns out that this parametric integral is an integral representation of the Appell function F1(a;b,c;a+1;x,y). Therefore, as a byproduct, we deduce convergent expansions of F1(a;b,c;a+1;x,y). We also compute error bounds at any order of the approximation. Some numerical examples show the accuracy of the expansions and their uniform features.Publication Open Access Association of intrinsic capacity with incidence and mortality of cardiovascular disease: prospective study in UK Biobank(Wiley, 2023) Ramírez Vélez, Robinson; Iriarte-Fernández, María; Santafé Rodrigo, Guzmán; Malanda Trigueros, Armando; Beard, John R.; García Hermoso, Antonio; Izquierdo Redín, Mikel; Ciencias de la Salud; Estadística, Informática y Matemáticas; Ingeniería Eléctrica, Electrónica y de Comunicación; Institute for Advanced Materials and Mathematics - INAMAT2; Osasun Zientziak; Estatistika, Informatika eta Matematika; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaBackground: The World Health Organization proposed the concept of intrinsic capacity (IC; the composite of all the physical and mental capacities of the individual) as central for healthy ageing. However, little research has investigated the interaction and joint associations of IC with cardiovascular disease (CVD) incidence and CVD mortality in middle- and older-aged adults. Methods: Using data from 443 130 UK Biobank participants, we analysed seven biomarkers capturing the level of functioning of five domains of IC to calculate a total IC score (ranging from 0 [better IC] to +4 points [poor IC]). Associations between IC score and incidence of six long-term CVD conditions (hypertension, stroke/transient ischaemic attack stroke, peripheral vascular disease, atrial fibrillation/flutter, coronary artery disease and heart failure), and grouped mortality from these conditions were estimated using Cox proportional models, with a 1-year landmark analysis to triangulate the findings. Results: Over 10.6 years of follow-up, CVD morbidity grouped (n = 384 380 participants for the final analytic sample) was associated with IC scores (0 to +4): mean hazard ratio (HR) [95% confidence interval, CI] 1.11 [1.08–1.14], 1.20 [1.16–1.24], 1.29 [1.23–1.36] and 1.56 [1.45–1.59] in men (C-index = 0.68), and 1.17 [1.13–1.20], 1.30 [1.26–1.36], 1.52 [1.45–1.59] and 1.78 [1.67–1.89] in women (C-index = 0.70). In regard to mortality, our results indicated that the higher IC score (+4 points) was associated with a significant increase in subsequent CVD mortality (mean HR [95% CI]: 2.10 [1.81–2.43] in men [C-index = 0.75] and 2.29 [1.85–2.84] in women [C-index = 0.78]). Results of all sensitivity analyses by full sample, sex and age categories were largely consistent independent of major confounding factors (P < 0.001). Conclusions: IC deficit score is a powerful predictor of functional trajectories and vulnerabilities of the individual in relation to CVD incidence and premature death. Monitoring an individual's IC score may provide an early-warning system to initiate preventive efforts.Publication Open Access Association of intrinsic capacity with respiratory disease mortality(Elsevier, 2023) Ramírez Vélez, Robinson; Iriarte-Fernández, María; Santafé Rodrigo, Guzmán; Malanda Trigueros, Armando; Beard, John R.; García Hermoso, Antonio; Izquierdo Redín, Mikel; Ciencias de la Salud; Estadística, Informática y Matemáticas; Ingeniería Eléctrica, Electrónica y de Comunicación; Institute for Advanced Materials and Mathematics - INAMAT2; Osasun Zientziak; Estatistika, Informatika eta Matematika; Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio IngeniaritzarenThe World Health Organization (WHO) introduced a framework for healthy aging in 2015 that emphasizes functional ability instead of absence of disease. Healthy ageing is defined as “the process of building and maintaining the functional ability that enables well-being”. This framework considers an individual’s intrinsic capacity (IC), environment, and the interaction between them to determine functional ability. In this prospective cohort study, we investigated the link between mortality and various respiratory diseases in almost half a million adults who are part of the UK Biobank. We derived an IC score using measures from 4 of the 5 domains: two for psychological capacity, two for sensory capacity, two for vitality and one for locomotor capacity. The exposure variable in the study was the number of reported factors, which was summed and categorized into IC scores of zero, one, two, three, or at least four. The outcome was respiratory disease-related mortality, which was linked to national mortality records. The follow-up period started from participants’ inclusion in the UK Biobank study (2006–2010) and ended on December 31, 2021, or the participant’s death was censored. The average follow-up was 10.6 years (IQR 10.0; 11.3). During a median follow-up period of 10.6 years, 27,251 deaths were recorded. Out of these, 7.5% (2059) were primarily attributed to respiratory disease. The results showed that a higher IC score (+4 points) was associated with a significantly increased risk of respiratory disease mortality, with HRs of 3.34 [2.64 to 4.23] for men (C-index = 0.83) and 3.87 [2.86 to 5.23] for women (C-index = 0.84), independent of major confounding factors (P < 0.001). Our study provides evidence that lower levels of the WHO’s IC construct are associated with increased risk of mortality and various adverse health outcomes. The IC construct, which is easily and inexpensively measured, holds great promise for transforming geriatric care worldwide, including in regions without established geriatric medicine.Publication Open Access Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals(Wiley, 2023) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe consider the highly oscillatory integral 𝐹(𝑤) ∶= ∫ ∞ −∞ 𝑒𝑖𝑤(𝑡𝐾+2+𝑒𝑖𝜃𝑡𝑝) 𝑔(𝑡)𝑑𝑡 for large positive values of 𝑤, −𝜋 < 𝜃 ≤ 𝜋, 𝐾 and 𝑝 positive integers with 1 ≤ 𝑝 ≤ 𝐾, and 𝑔(𝑡) an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when 𝑤 → +∞ for general values of 𝐾 and 𝑝 in terms of elementary functions, and determine the Stokes lines. For 𝑝 ≠ 1, the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters 𝐾 and 𝑝; the special case 𝑝=1 requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals Ψ𝐾(𝑥1, 𝑥2,…,𝑥𝐾) for large values of one of its variables, say 𝑥𝑝, and bounded values of the remaining ones. This family of integrals may be written in the form 𝐹(𝑤) for appropriate values of the parameters 𝑤, 𝜃 and the function 𝑔(𝑡). Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large |𝑥𝑝|. The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al.Publication Open Access An asymptotic expansion of the hyberbolic umbilic catastrophe integral(Springer, 2022) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe obtain an asymptotic expansion of the hyperbolic umbilic catastrophe integral Ψ(H) (x,y,z) := ∫∞−∞∫∞−∞exp(i(s3+t3+zst +yt+xs))ds dt for large values of |x| and bounded values of |y| and |z|. The expansion is given in terms of Airy functions and inverse powers of x. There is only one Stokes ray at argx=π . We use the modified saddle point method introduced in (López et al. J Math Anal Appl 354(1):347–359, 2009). The accuracy and the asymptotic character of the approximations are illustrated with numerical experiments.Publication Open Access Asymptotic expansions for Moench's integral transform of hydrology(MDPI, 2023) López García, José Luis; Pagola Martínez, Pedro Jesús; Pérez Sinusía, Ester; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PRO-UPNA (6158) 2022Theis' theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of the pumping function g that depends on the time t and the relative position r to the pumping point as well as on other physical parameters. Several analytic approximations of H[g](r,t) have been investigated in the literature that are valid and accurate in certain regions of r, t and the mentioned physical parameters. In this paper, the analysis of possible analytic approximations of H[g](r,t) is completed by investigating asymptotic expansions of H[g](r,t) in a region of the parameters that is of interest in practical situations, but that has not yet been investigated. Explicit and/or recursive algorithms for the computation of the coefficients of the expansions and estimates for the remainders are provided. Some numerical examples based on an actual physical experiment conducted by Layne-Western Company in 1953 illustrate the accuracy of the approximations.Publication Open Access Asymptotic greediness of the Haar system in the spaces Lp[0 , 1] , 1< p< ∞(Springer, 2019) Albiac Alesanco, Fernando José; Ansorena, José L.; Berná, Pablo M.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasOur aim in this paper is to attain a sharp asymptotic estimate for the greedy constant Cg[H(p), Lp] of the (normalized) Haar system H(p) in Lp[0 , 1] for 1 < p < ∞. We will show that the super-democracy constant of H(p) in Lp[0 , 1] grows as p∗= max { p, p/ (p- 1) } as p∗ goes to ∞. Thus, since the unconditionality constant of H(p) in Lp[0 , 1] is p∗- 1 , the well-known general estimates for the greedy constant of a greedy basis obtained from the intrinsic features of greediness (namely, democracy and unconditionality) yield that p∗≲Cg[H(p),Lp]≲(p∗)2. Going further, we develop techniques that allow us to close the gap between those two bounds, establishing that, in fact, Cg[H(p), Lp] ≈ p∗. Our work answers a question that was raised by Hytonen (2015).Publication Open Access An axiomatic approach to finite means(Elsevier, 2018) Campión Arrastia, María Jesús; Candeal, Juan Carlos; García Catalán, Olga Raquel; Giarlotta, Alfio; Induráin Eraso, Esteban; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasIn this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications.Publication Open Access Bayesian inference in multivariate spatio-temporal areal models using INLA: analysis of gender-based violence in small areas(Springer, 2020) Vicente Fuenzalida, Gonzalo; Goicoa Mangado, Tomás; Ugarte Martínez, María Dolores; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasMultivariate models for spatial count data are currently receiving attention in disease mapping to model two or more diseases jointly. They have been thoroughly studied from a theoretical point of view, but their use in practice is still limited because they are computationally expensive and, in general, they are not implemented in standard software to be used routinely. Here, a new multivariate proposal, based on the recently derived M models for spatial data, is developed for spatio-temporal areal data. The model takes account of the correlation between the spatial and temporal patterns of the phenomena being studied, and it also includes spatio-temporal interactions. Though multivariate models have been traditionally fitted using Markov chain Monte Carlo techniques, here we propose to adopt integrated nested Laplace approximations to speed up computations as results obtained using both fitting techniques were nearly identical. The techniques are used to analyse two forms of crimes against women in India. In particular, we focus on the joint analysis of rapes and dowry deaths in Uttar Pradesh, the most populated Indian state, during the years 2001-2014.Publication Open Access Bayesian modeling approach in Big Data contexts: an application in spatial epidemiology(IEEE, 2020) Orozco Acosta, Erick; Adin Urtasun, Aritz; Ugarte Martínez, María Dolores; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasIn this work we propose a novel scalable Bayesian modeling approach to smooth mortality risks borrowing information from neighbouring regions in high-dimensional spatial disease mapping contexts. The method is based on the well-known divide and conquer approach, so that the spatial domain is divided into D subregions where local spatial models can be fitted simultaneously. Model fitting and inference has been carried out using the integrated nested Laplace approximation (INLA) technique. Male colorectal cancer mortality data in the municipalities of continental Spain have been analyzed using the new model proposals. Results show that the new modeling approach is very competitive in terms of model fitting criteria when compared with a global spatial model, and it is computationally much more efficient.Publication Open Access Bidemocratic bases and their connections with other greedy-type bases(Springer, 2023) Albiac Alesanco, Fernando José; Ansorena, José L.; Berasategui, Miguel; Berná, Pablo M.; Lassalle, Silvia; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaIn nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this article we shift the viewpoint and study them for their own sake, just as we would with any other kind of greedy-type bases. In particular we show that bidemocratic bases need not be quasi-greedy, despite the fact that they retain a strong unconditionality flavor which brings them very close to being quasi-greedy. Our constructive approach gives that for each 1 < p < infinity the space L-p has a bidemocratic basis which is not quasi-greedy. We also present a novel method for constructing conditional quasi-greedy bases which are bidemocratic, and provide a characterization of bidemocratic bases in terms of the new concepts of truncation quasi-greediness and partially demo-cratic bases.Publication Open Access Big problems in spatio-temporal disease mapping: methods and software(Elsevier, 2023) Orozco Acosta, Erick; Adin Urtasun, Aritz; Ugarte Martínez, María Dolores; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, PJUPNA20001Background and objective: Fitting spatio-temporal models for areal data is crucial in many fields such as cancer epidemiology. However, when data sets are very large, many issues arise. The main objective of this paper is to propose a general procedure to analyze high-dimensional spatio-temporal areal data, with special emphasis on mortality/incidence relative risk estimation. Methods: We present a pragmatic and simple idea that permits hierarchical spatio-temporal models to be fitted when the number of small areas is very large. Model fitting is carried out using integrated nested Laplace approximations over a partition of the spatial domain. We also use parallel and distributed strategies to speed up computations in a setting where Bayesian model fitting is generally prohibitively time-consuming or even unfeasible. Results: Using simulated and real data, we show that our method outperforms classical global models. We implement the methods and algorithms that we develop in the open-source R package bigDM where specific vignettes have been included to facilitate the use of the methodology for non-expert users. Conclusions: Our scalable methodology proposal provides reliable risk estimates when fitting Bayesian hierarchical spatio-temporal models for high-dimensional data.