Vector measure orthogonal sequences in spaces of square integrable functions

This doctoral thesis is devoted to the analysis of orthogonal sequences in subspaces of spaces L2(m) of square integrable functions with respect to a Banach space valued countably additive measure m. The motivation of our work is to generalize the geometric arguments that provide the classical approximation procedures in Hilbert spaces. The notion of orthogonality lies in the center of the Hilbert space theory, and it allows to develop the theory of convergence of sequences in these spaces. Almost everywhere convergence, norm convergence and weak convergence are nowadays well known topics in the Hilbert space function theory. The Banach function spaces L2(m) of a vector measure m represent a broad class of Banach lattices: each 2-convex order continuous Banach lattice with a weak unit can be represented (by means of an order isomorphism) as a space L2(m) for an adequate vector measure m. The integral structure that the vector measure integration provides in these spaces allows to generalize the orthogonality arguments of the Hilbert space theory, although the spaces L2(m) are far from being Hilbert spaces. The first chapter of this memoir is devoted to introduce some fundamental concepts on Banach function spaces, vector measure integration and other topics that will be necessary in the rest of the work. Some results on convergence of sequences in Banach function spaces and Banach spaces are explained, and the general framework is established. Some orthogonality arguments are already introduced, both for sequences in L2(m) and for the integrals of these sequences when the vector measure m is Hilbert space valued. Unconditional convergence for sequences from the abstract point of view of the function spaces of integrable functions is analyzed, and a version of the Kadec and Pelczynsky method for finding disjoint sequences for the vector measure setting is given. In the second chapter three notions of orthogonality of a sequence with respect to a vector measure are formally introduced, and the main characterizations of these sequences are given. Weak m-orthogonal sequences, (natural) m-orthogonal sequences and strongly m-orthogonal sequences are de ned and studied, providing also examples that show the relation with some classical problems in analysis. The geometry of these sets of sequences are also studied. In Chapter 3 we analyze almost everywhere convergence of weakm-orthogonal sequences. Our main result is a general vector measure version of the Mencho - Rademacher Theorem. A particular case involving c0-sums of Hilbert spaces is also intensively studied in order to show the properties of the convergence. Finally, Chapter 4 is devoted to show a concrete application. We develop an approximation method with respect to a parametric measure based on our ideas. A Bochner integrable function and an weak m-orthonormal sequence are the main elements of our procedure, that allows to nd the Fourier coefficients -that are in this case measurable functions- for a given function in the space L2(m). Some applications for signal approximation for data coming from experimental acoustics are also shown.Jiménez Fernández, E. (2011). Vector measure orthogonal sequences in spaces of square integrable functions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/13832Palanci

Index spaces and standard indices in metric modelling

This research was partially supported by the grant PID2019-105708RB funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe". The second, third and fourth authors gratefully acknowledge the support of the Catedra de Transparencia y Gestion de Datos, Universitat Politecnica de Valencia, Generalitat Valenciana.We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented.MCIN/AEI PID2019-105708RBERDF A way of making EuropeCatedra de Transparencia y Gestion de Datos, Universitat Politecnica de Valencia, Generalitat Valencian

European Union Cohesion Policy: Socio‑Economic Vulnerability of the Regions and the COVID‑19 Shock

The European Union Cohesion Policy for the period 2021–2027 focuses on five goals to make the European Union smarter, greener, more connected, more social and closer to citizens. However, a macroeconomic index is proposed as the predominant criterion for allocating the Structural Funds among regions. In this paper, we hypothesise that it is possible to take into account new, complementary criteria that better reflect citizens’ quality of life. To that end, we build a composite index of socio-economic vulnerability for the 233 regions. The results show that following our multidimensional approach for allocating the Structural Funds, there are remarkable differences in the maps of priority regions. In addition, the COVID- 19 pandemic represents a threat to well-being. Are all regions equally exposed to COVID-19 in terms of their socio-economic vulnerability? To address this issue, we estimate multilevel models which indicate that country characteristics interact with regions’ characteristics to alter patterns of vulnerability. More specifically, increases in government expenditures in education and an improvement in political stability would reduce the regional vulnerability or foster the capacity for resilience, whereas increases in poverty would be associated with greater vulnerability. Likewise, more vulnerable regions would be the most exposed to the negative socio-economic effects of COVID-19. However, it is remarkable that several regions of Sweden and Finland would be among the group of regions whose socio-economic vulnerability would be the most negatively affected.Universidad de Granada/CBUAproject ERDF-University of Granada B-SEJ-242.UGR2

Comparative analysis and predictors of biopsychosocial functioning in various health conditions: multiple sclerosis and organ transplantation

Tesis descargada de TESEOIn the present Ph.D. dissertation, four empirical and pioneering works have been carried out addressing the biopsychosocial functioning of patients diagnosed with multiple sclerosis (MS) and of transplant recipients (hepatic and renal). The level of analysis of this group of pieces of research will range from a general level (all quality-of-life dimensions) in the first two papers, to specific domains of the biopsychosocial functioning (difficulties in affective processing and pain) in the third and fourth studies. Particularly, the first two works aimed to compare the quality of life of patients diagnosed with MS and of transplant recipients (hepatic and renal) in order to determine the relative impact that these medical conditions have on the biopsychosocial functioning of the affected people. The SF-36 Health Survey was administered to the following participant samples: a) with respect to the first work, 31 patients with MS and 31 liver transplant recipients, both groups matched for gender; b) regarding the second study, 30 patients with MS and 30 renal transplant recipients, both groups matched for gender and homogenized according to age and working status. Analysis of Covariance was conducted in both studies, controlling for time since diagnosis of multiple sclerosis/time since transplantation surgery until assessment (first work), and controlling for age (in the second study) as covariates. The comparative framework underlying both works is very suitable from a clinical point of view, as both populations share immunotherapy as a pharmacologic first-line treatment, thereby being exposed to similar stressors. Likewise, these two studies presented complementary study designs, cross-sectional (the first one) and longitudinal (the second one), so that the trajectory of the differences between groups could even be determined at six months from baseline. Finally, all these results were analyzed in terms of clinical significance, using two representative samples of the general Spanish population according to the specific age interval of the participant sample involved in each study. In all domains in which statistically significant differences between both clinical conditions were found, neurological patients showed worse quality-of-life levels. These differences belonged to the physical domain when the comparison with liver transplant recipients was carried out, whereas the differences were broader, both in physical and psychosocial facets, when the contrast involved renal transplant recipients. Moreover, while patients diagnosed with multiple sclerosis showed a clinically relevant deterioration in all dimensions of quality of life in both works and measurement points, transplant recipients, and especially liver transplant recipients, also showed clinically significant impairment in several domains of the biopsychosocial functioning. Therefore, it becomes clear that both these neurological patients and transplant recipients are medical populations that require special health care. The third work included in this Ph.D. dissertation was also pioneering from a scientific standpoint, by being the first work that studied the factor structure of the Toronto Alexithymia Scale (TAS-20) in patients diagnosed with multiple sclerosis, as well as the first work that addressed alexithymia in these neurological patients in Spain. Furthermore, in this study, an improved version of the Spanish adaptation of this instrument was proposed (named the TAS-20-S), with respect to those ones already available in our language. This work, which involved 221 patients, supported the traditional three-factor structure of the TAS-20 using confirmatory factor analysis, and showed appropriate reliability levels for the total scale and for each of its subscales. Therefore, these findings justify conducting future empirical research in order to assess the differential predictive value of each of the dimensions of alexithymia as measured by the TAS-20. In line with this, the fourth study aimed to determine the relative importance of the various subscales of the TAS-20-S with respect to other variables of an affective (anxious-depressive symptomatology measured by the Mental health subscale of the SF-36 Health Survey) and sociodemographic nature (age, gender and educational level), to predict various parameters of pain (intensity and functional interference using the Brief Pain Inventory, and the Bodily pain subscale of the SF-36 Health Survey) in patients with MS. Using a longitudinal design (baseline -211 patients-, at 6 months -200 patients- and at 18 months -201 patients), a new statistical method based on relative weights was used to perform a more realistic analysis of the contribution of each predictor, taking into account the actual correlation between variables and the measurement error of each predictor. All predictors belonged to the baseline of the study. Anxious-depressive symptomatology significantly predicted the various parameters of pain in all models, except for one. In turn, the subscale of the TAS-20-S, Difficulty Identifying Feelings, statistically predicted the SF-36 Bodily pain subscale and functional interference due to pain, both parameters belonging to the third measurement point of the study -18 months after baseline. Interestingly, in the latter two models where Difficulty Identifying Feelings was a significant predictor, no statistically significant differences were found between this alexithymic dimension and anxious-depressive symptomatology in predicting the above-mentioned facets of pain (SF-36 Bodily pain subscale and functional interference due to pain). These results indicate that psychological interventions to treat pain in patients with MS should address negative affect and alexithymic difficulty identifying feelings as well as differentiating between feelings and the somatic sensations associated with affective arousal.Premio Extraordinario de Doctorado U

Approximation of integration maps of vector measures and limit representations of Banach function spaces

[EN] We study whether or not the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon¿Nikodým derivatives. The positive cases are obtained by using the circle of ideas related to the approximation property for Banach spaces. The negative ones are given by means of an appropriate use of the Daugavet property. As an application, we analyse when the norm in a space L 1 (m) of integrable functions can be computed as a limit of the norms of the spaces of integrable functions with respect to the Radon¿Nikodým derivatives of m.E. Jiménez Fernández was supported by Junta de Andalucía and FEDER (grant no. P09-FQM-4911 (Spain)) and by Ministerio de Economía, Industria y Competitividad (grant no. MTM2012-36740-C02- 02 (Spain)). E. A. Sánchez Pérez was supported by Ministerio de Economía, Industria y Competitividad (grant no. MTM2016-77054-C2-1-P (Spain)).Jiménez Fernández, E.; Sánchez Pérez, EA.; Werner, D. (2017). Approximation of integration maps of vector measures and limit representations of Banach function spaces. Annales Polonici Mathematici. 120(1):63-81. https://doi.org/10.4064/ap170407-21-9S6381120

What drives interdependence of FDI among host countries? The role of geographic proximity and similarity in public debt

We investigate the drivers of interdependence between flows of foreign direct investment (FDI), focusing on two potential channels: interdependence between geographically close FDI destination countries, and between destination countries with similar levels of public debt. Using data on bilateral FDI flows between the 27 EU member countries in 2007, we find that in addition to geographic proximity, similarity in public debt levels drives cross-country correlation in FDI inflows. The public debt threshold of 60% of GDP prescribed by the Maastricht Treaty is a crucial driver of interdependence between FDI inflows. FDI inflows are correlated within the group of compliant countries as well as within the group of non-compliers. This is consistent with the fact that foreign investors distinguish between countries which violate this Maastricht criterion and those that do not

Index spaces and standard indices in metric modelling

We analyze the basic structure of certain metric models, which are constituted by an index I acting on a metric space (D; d) representing a relevant property of the elements of D. We call such a structure (D; d; I) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented