Corrigendum to "Approximation by C^{p}-smooth, Lipschitz functions on Banach spaces" [J. Math. Anal. Appl., 315 (2006), 599-605]

In this erratum, we recover the results from an earlier paper of the author's which contained a gap. Specifically, we prove that if X is a Banach space with an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and Y is a convex subset of X, then any uniformly continuous function f: Y->R can be uniformly approximated by Lipschitz, C^{p}-smooth functions K:X->R. Also, if Z is any Banach space and f:X->Z is L-Lipschitz, then the approximates K:X->Z can be chosen CL-Lipschitz and C^{p}-smooth, for some constant C depending only on X

Numerical Solution of the Dynamic Programming Equation for the Optimal Control of Quantum Spin Systems

The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined on a Lie group. We employ recent extensions of the theory of viscosity solutions from Euclidean space to Riemannian manifolds to interpret possibly non-differentiable solutions to this equation. Results from differential topology on the triangulation of manifolds are then used to develop a finite difference approximation method, which is shown to converge using viscosity solution techniques. An example is provided to illustrate the method.Comment: 11 pages, 5 figure

Smooth extensions of functions on separable Banach spaces

Let $X$ be a Banach space with a separable dual $X^{*}$. Let $Y\subset X$ be a closed subspace, and $f:Y\to\mathbb{R}$ a $C^{1}$-smooth function. Then we show there is a $C^{1}$ extension of $f$ to $X$.Comment: 19 pages. This version fixes a gap in the previous proof of Theorem 1 by providing a sharp version of Lemma

Combined homogeneous and heterogeneous hydrogenation to yield catalyst-free solutions of parahydrogen-hyperpolarized [1-13C]succinate

We show that catalyst-free aqueous solutions of hyperpolarized [1-13C]succinate can be produced using parahydrogen-induced polarization (PHIP) and a combination of homogeneous and heterogeneous catalytic hydrogenation reactions. We generate hyperpolarized [1-13C]fumarate via PHIP using para-enriched hydrogen gas with a homogeneous ruthenium catalyst, and subsequently remove the toxic catalyst and reaction side products via a purification procedure. Following this, we perform a second hydrogenation reaction using normal hydrogen gas to convert the fumarate into succinate using a solid Pd/Al2O3 catalyst. This inexpensive polarization protocol has a turnover time of a few minutes, and represents a major advance for in vivo applications of [1-13C]succinate as a hyperpolarized contrast agent

The impact of the COVID-19 lockdown on depression sufferers: a qualitative study from the province of Zaragoza, Spain

Background and purpose: The impact of COVID-19 and its control measures have exacerbated existing mental health conditions. Although the deleterious effects of mental health problems are well known, fewer studies have examined the links between the Social Determinants of Health (SDHs) and depression. This study provides insights into the relationship between SDHs and depression during the first strict lockdown in Spain, which lasted for a period of 7 weeks. Methods: Fifty-two structured interviews were conducted with people diagnosed with depression during June 2020 in the province of Zaragoza (Spain). Interviews were conducted by telephone due to lockdown constraints. Inductive thematic content analysis was used to explore, develop, and define emergent categories of analysis, which were mapped against the SDH framework. Results: Listening to people’s experiences of living with depression during lockdown provided insights into their concerns and coping strategies, which are greatly influenced by the conditions in which they live, their job and their age. Examples of these factors include access to and quality of physical spaces, including housing conditions and public spaces for socialising, social support, adverse working conditions which include caring responsibilities, and access to digital technologies and healthcare services. Conclusion: SDHs have played a fundamental role in shaping people’s health and well-being during the COVID-19 pandemic, and this study has shown that they have a considerable effect on depression outcomes. Governments should consider implementing social welfare programs to tackle both psychosocial problems and material need during crisis situations

A benchmark for orientation control of a multirotor in a three degrees-of-freedom rotation structure

[EN] A fully equipped quadrotor is attached to a structure that allows free rotation without translation. Additionally, a set of MATLAB-Simulink® tools execute the flight controller programming and manage the real-time transmission of commands and flight states for the remote pilot. For this test bench a simulator is offered. It faithfully reproduces the behaviour of the real system in order to propose a benchmark on Control Engineering. This aims to control the quadrotor orientation described using the Euler angles. Thus the three control actions that attack the propulsion system must be generated taking into account the rotation speeds and angles that are estimated by the navigation system and the angle set points. During the performance tests, a modifiable supply voltage replaces the battery charge level and a control action emulates the height control, resulting in dierent operating points of the system as in a real flight. The simulator allows free setup of closed and open loop experiments for model identification tasks or analysing the control performance for dierent inputs and operating points. The final objective is to incorporate a control law that improves the behaviour given as a reference for a certain experiment. After a simulation, an evaluation function quantifies the dierences in tracking error and control action between the current control and the reference control for each degree of freedom. The main challenge is a narrow control bandwidth to govern a complex three-variable system.[ES] Un cuatrirrotor con todo el equipamiento de vuelo se encuentra fijado a una estructura que permite la rotación en el espacio sin desplazamiento. Además, un conjunto de herramientas software desarrolladas con MATLAB-Simulink® ejecutan la programación de su controladora y gestionan la transmisión en tiempo real de consignas y estados del vuelo pilotado remotamente. Para este banco de pruebas se ofrece un simulador que reproduce fielmente el comportamiento del sistema real con el fin de plantear un benchmark de Ingeniería de Control. El problema propuesto es controlar la orientación del mutirrotor definida por los ángulos de Euler. Para ello, deben generarse las tres acciones de control que atacan al sistema de propulsión, considerando las velocidades y ángulos que estima el sistema de navegacion y las consignas angulares. Para lograr un mayor realismo, en las pruebas de comportamiento se pueden modificar la tensión de alimentación, que simula el nivel de carga de la batería, y una acción de control que emula el control de la altura, lo que da lugar a diferentes puntos de operación. El simulador permite configurar experimentos en lazo abierto o cerrado, para tareas de identificación o para analizar el comportamiento de los controladores en diferentes puntos de operación y ante diferentes entradas. El objetivo final es incorporar una ley de control que mejore el comportamiento dado como referencia para cierto experimento. Tras una simulación, una función de evaluación cuantifica las diferencias en el error de seguimiento y en la acción de control entre el control actual y el de referencia para cada grado de libertad. El principal desafío es optimizar el reducido ancho de banda disponible para controlar un sistema dinámico complejo.Los autores agradecen la ayuda prestada por el Gobierno de La Rioja a través del proyecto de I+D ADER 2017-I-IDD00035, y por la Universidad de La Rioja a través de la Ayuda para la realización de Proyectos de Innovación Docente 2020 PID Nº 36 y la Ayuda a Grupos de Investigación REGI2020 /23.Rico-Azagra, J.; Gil-Martínez, M.; Rico, R.; Nájera, S.; Elvira, C. (2021). Benchmark de control de la orientación de un multirrotor en una estructura de rotación con tres grados de libertad. Revista Iberoamericana de Automática e Informática industrial. 18(3):265-276. https://doi.org/10.4995/riai.2021.14356OJS265276183Bejarano, G., Alfaya, J., Rodriguez, D., Ortega, M., Morilla, F., 2019. Control de un sistema de refrigeración. Visitado 27.03.2021. URL: http://www.dia.uned.es/∼fmorilla/CIC2019/Bigazzi, L., Gherardini, S., Innocenti, G., Basso, M., 2021. Development of non expensive technologies for precise maneuvering of completely autonomous unmanned aerial vehicles. Sensors (Switzerland) 21 (2), 1-24. https://doi.org/10.3390/s21020391Blasco, X., García-Nieto, S., Reynoso-Meza, G., 2012. Control autónomo del seguimiento de trayectorias de un vehículo cuatrirrotor. Simulación y evaluación de propuestas. Revista Iberoamericana de Automática e Informática Industrial 9 (2), 194-199. https://doi.org/10.1016/j.riai.2012.01.001Bo, G., Xin, L., Hui, Z., Ling, W., 2016. Quadrotor helicopter attitude control using cascade PID. 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Teaching tool for a control systems laboratory using a quadrotor as a plant in MATLAB. IEEE Transactions on Education 60 (4), 249-256. https://doi.org/10.1109/TE.2017.2653762Lim, H., Park, J., Lee, D., Kim, H., 2012. Build your own quadrotor: Opensource projects on unmanned aerial vehicles. IEEE Robotics and Automation Magazine 19 (3), 33-45. https://doi.org/10.1109/MRA.2012.2205629Lotufo, M., Colangelo, L., Perez-Montenegro, C., Canuto, E., Novara, C., 2019. UAV quadrotor attitude control: An ADRC-EMC combined approach. Control Engineering Practice 84, 13-22. https://doi.org/10.1016/j.conengprac.2018.11.002Madridano, A., Campos, S., Al-Kaff, A., García, F., Martín, D., Escalera, A., 2020. Vehículo aéreo no tripulado para vigilancia y monitorización de incendios. Revista Iberoamericana de Automática e Informática industrial 17 (3), 254-263. https://doi.org/10.4995/riai.2020.11806Mercader, P., Cánovas, C. D., Baños, A., 2019. Control PID multivariable de una caldera de vapor. Revista Iberoamericana de Automática e Informática Industrial 16 (1), 15-25. https://doi.org/10.4995/riai.2018.9034Morilla, F., Rodríguez, C., 2017. Control de una caldera de vapor. Visitado 27.03.2021. URL: http://www.dia.uned.es/∼fmorilla/CIC2017/Nájera, S., Rico-Azagra, J., Elvira, C., Gil-Martínez, M., 2019. Plataforma giroscópica realizada mediante impresión 3D para el control de actitud y orientación de UAVs multi-rotor. In: Actas de las XL Jornadas de Automática, Comité Español de Automática de la IFAC. pp. 317-323. https://doi.org/10.17979/spudc.9788497497169.317Nascimento, T. P., Saska, M., 2019. Position and attitude control of multi-rotor aerial vehicles: A survey. Annual Reviews in Control 48, 129-146. https://doi.org/10.1016/j.arcontrol.2019.08.004Rico, R., Maisterra, P., Gil-Martínez, M., Rico-Azagra, J., S., N., 2015. Identificación experimental de los parámetros de un cuatrirrotor. In: Actas de las XXXVI Jornadas de Automática, Comité Español de Automática de la 'IFAC. pp. 973-982.Rico-Azagra, J., Gil-Martínez, M., Rico, R., Maisterra, P., 2016a. Plataforma didáctica de bajo coste para el control de actitud y orientación de UAVs multi-rotor. In: Actas de las XXXVII Jornadas de Automática, Comité Español de Automática de la IFAC. pp. 989-997.Rico-Azagra, J., Gil-Martínez, M., Rico-Azagra, R., Maisterra, P., 2016b. Low-cost attitude estimation for a ground vehicle. Advances in Intelligent Systems and Computing 417, 121-132. https://doi.org/10.1007/978-3-319-27146-0Rico-Azagra, J., Rico, R., Maisterra, P., Gil-Martínez, M., 2015. Comparación de algoritmos de estimación de actitud. In: Actas de las XXXVI Jornadas de Automática, Comité Español de Automática de la IFAC. pp. 911-920.Romero, J. A., Sanchis, R., 2011. Benchmark para la evaluación de algoritmos de auto-ajuste de controladores PID. 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Fracture experience among participants from the FROCAT study: what thresholding is appropriate using the FRAX tool?

ObjectiveTo perform an external validation of FRAX algorithm thresholds for reporting level of risk of fracture in Spanish women (low <5%; intermediate ?5% and <7.5%; high ?7.5%) taken from a prospective cohort “FRIDEX”.MethodsA retrospective study of 1090 women aged ?40 and ?90 years old obtained from the general population (FROCAT cohort). FRAX was calculated with data registered in 2002. All fractures were validated in 2012. Sensitivity analysis was performed.ResultsWhen analyzing the cohort (884) excluding current or past anti osteoporotic medication (AOM), using our nominated thresholds, among the 621 (70.2%) women at low risk of fracture, 5.2% [CI95%: 3.4–7.6] sustained a fragility fracture; among the 99 at intermediate risk, 12.1% [6.4–20.2]; and among the 164 defined as high risk, 15.9% [10.6–24.2]. Sensitivity analysis against model risk stratification FRIDEX of FRAX Spain shows no significant difference. By including 206 women with AOM, the sensitivity analysis shows no difference in the group of intermediate and high risk and minimal differences in the low risk group.ConclusionsOur findings support and validate the use of FRIDEX thresholds of FRAX when discussing the risk of fracture and the initiation of therapy with patients

Measuring health-related quality of life in men with osteoporosis or osteoporotic fracture

<p>Abstract</p> <p>Background</p> <p>Osteoporosis is a serious health problem that worsens the quality of life and the survival rate of individuals with this disease on account the osteoporotic fractures. Studies have long focused on women, and its presence in men has been underestimated. While many studies conducted in different countries mainly assess health-related quality of life and identify fracture risks factors in women, few data are available on a Spanish male population.</p> <p>Methods/Design</p> <p>Observational study.</p> <p>Study population</p> <p>Men ≥ 40 years of age with/without diagnosed osteoporosis and with/without osteoporotic fracture included by their family doctor.</p> <p>Measurements</p> <p>The relationship between customary clinical risk factors for osteoporotic fracture and health-related quality of life in a Spanish male population. A telephone questionnaire on health-related quality of life is made.</p> <p>Statistical analysis</p> <p>The association between qualitative variables will be assessed by the Chi-square test. The distribution of quantitative variables by Student's t-test. If the conditions for using this test are not met, the non-parametric Mann-Whitney's U test will be used.</p> <p>The validation of the results obtained by the FRAX™ tool will be performed by way of the Hosmer-Lemeshow test and by calculating the area under the Receiver Operating Characteristic (ROC) curve (AUC). All tests will be performed with a confidence intervals set at 95%.</p> <p>Discussion</p> <p>The applicability and usefulness of Health-related quality of life (HRQOL) studies are well documented in many countries. These studies allow implementing cost-effective measures in cases of a given disease and reducing the costly consequences derived therefrom. This study attempts to provide objective data on how quality of life is affected by the clinical aspects involved in osteoporosis in a Spanish male population and can be useful as well in cost utility analyses conducted by health authorities.</p> <p>The sample selected is not based on a high fracture risk group. Rather, it is composed of men in the general population, and accordingly comparisons should not lead to erroneous interpretations.</p> <p>A possible bias correction will be ensured by checking reported fractures against healthcare reports and X-rays, or by consulting health care centers as applicable.</p