A new multisymplectic unified formalism for second-order classical field theories

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincar\'e-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.Comment: 52 pp. Revision of our previous paper. Minor corrections on the statement of some results. A new example is added (Section 6.1). Conclusions and bibliography have been enlarged, and some comments on the higher-order case have been adde

Geometrical structures of higher-order dynamical systems and field theories

In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian counterpart. These geometric frameworks are used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.Comment: Ph.D. Thesis at Universitat Polit\`{e}cnica de Catalunya - BarcelonaTech. 256 pages. Acknowledgments have been removed with respect to the original version. Qualification: Excellent Cum Laud

Unified formalism for the generalized kth-order Hamilton-Jacobi problem

The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.Comment: 9pp. Revised version: Minor corrections done. Second part of our previous work arXiv:1309.2166. arXiv admin note: substantial text overlap with arXiv:1309.216

Variational principles and symmetries on fibered multisymplectic manifolds

summary:The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics

Unified formalism for higher-order non-autonomous dynamical systems

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition

Validation of a simple method for the interpretation of uterine cytology in cows

One of the main drawbacks of using endometrial cytology in cows is the time required for sample collection and interpretation. It is recommended to count a large number of polymorphonuclear neutrophils (PMN) and to calculate their overall percentage. However, since counting a large number of cells is a laborious method, it would be preferable to simplify the analysis by counting the number of PMN in few microscopic fields. Therefore, the aim of this study was to assess whether a simple test, based on calculating the average number of PMN in 10 fields at 1000×, could be a reliable technique for the diagnosis of endometritis. Two hundred and sixty endometrial samples were taken from Holstein cows at different postpartum stages using an adapted cytobrush. Smears obtained were air-dried for fixing and stained with a Romanowsky-type procedure. To evaluate the counting method, the percentage of PMN in 150 cells was calculated as well as the average number of PMN in 10 fields at 1000×. Receiver operating characteristic (ROC) curves was constructed to evaluate both methods, the percentage of PMN (used as reference) and the average number of PMN. It was observed that the area under the curve is (regardless of cut-off used) higher than 0.99 and the correspondence between both methods were 1.58 PMN/field for the cut-off value of 15% and 2.40 PMN/field for the cut-off value of 20%. These results show that this simple method could be used to determine the percentage of PMN in endometrial cytological samples and to diagnose endometritis in cowsSupported by the Xunta de Galicia (Galician Plan for Research and Technological Development; Grant No. PGIDIT07MRU002E) and the Friesian Federation of Galician, A Coruna, SpainS

Modulation of folic acid bioaccessibility by encapsulation in pH-responsive gated mesoporous silica particles

[EN] A study on the controlled release of folic acid (FA) from pH-responsive gated mesoporous silica particles (MSP) is reported. The MCM-41 support was synthesized using tetraethyl orthosilicate (TEOS) as hydrolytic inorganic precursor and the surfactant hexadecyltrimethylammonium bromide (CTAB) as porogen species. Calcination of the mesostructured phase resulted in the starting solid. This solid was loaded with FA to obtain the initial support S0. Moreover, this FA-loaded material was further functionalized with 3-[2-(2-aminoethylamino)ethylamino]propyltrimethoxysilane (N3) in order to obtain the gated polyamine-functionalised material S1. Solids S0 and S1 were characterized using standard solid state procedures. It was found that the functionalization process and the inclusion of FA on the pores did not modify the mesoporous structure of the starting material. FA delivery studies in water with solids S0 and S1 were carried out in water at pH 2 and 7.5. S0 was not able to completely inhibit FA delivery at acidic pH yet a rapid FA release at neutral pH was observed in few minutes. In contrast, S1 was tightly capped at pH 2 and displayed a sustained delivery of FA when the pH was switched to 7.5. In the second part of the study, FA loading and functionalization of S1-like supports was optimized. In particular, solids loaded with FA in phosphate buffered saline (PBS) and capped with N3 in acetate buffer at pH 2 exhibited a delivery capacity up to 95 μg FA/mg solid. Finally, FA release from the selected optimized supports was studied following an in vitro digestion procedure. The results showed that amine-capped MSP were not only able to hinder the release of the vitamin in gastric fluids (pH 2), but were also capable of deliver progressively the FA in presence of a simulated intestinal juice (pH 7.5) offering a suitable mechanism to control the bioaccessibility of the vitaminAuthors gratefully acknowledge the financial support from the Ministerio de Economia y Competitividad (Projects AGL201239597-C02 and MAT2012-38429-004-01) and the Generalitat Valenciana (project PROMETEO/2009/016). E.P. is grateful to the Ministerio de Ciencia e Innovacion for his Grant (AP2008-00620). C.C. thanks the Generalitat Valenciana for her post-doctoral contract VALi+D.Pérez-Esteve, É.; Fuentes López, A.; Coll Merino, MC.; Acosta, C.; Bernardos Bau, A.; Amoros Del Toro, PJ.; Marcos Martínez, MD.... (2015). Modulation of folic acid bioaccessibility by encapsulation in pH-responsive gated mesoporous silica particles. Microporous and Mesoporous Materials. 202:124-132. https://doi.org/10.1016/j.micromeso.2014.09.049S12413220

Evolution of the use of corticosteroids for the treatment of hospitalised COVID-19 patients in Spain between March and November 2020: SEMI-COVID national registry

Objectives: Since the results of the RECOVERY trial, WHO recommendations about the use of corticosteroids (CTs) in COVID-19 have changed. The aim of the study is to analyse the evolutive use of CTs in Spain during the pandemic to assess the potential influence of new recommendations. Material and methods: A retrospective, descriptive, and observational study was conducted on adults hospitalised due to COVID-19 in Spain who were included in the SEMI-COVID- 19 Registry from March to November 2020. Results: CTs were used in 6053 (36.21%) of the included patients. The patients were older (mean (SD)) (69.6 (14.6) vs. 66.0 (16.8) years; p < 0.001), with hypertension (57.0% vs. 47.7%; p < 0.001), obesity (26.4% vs. 19.3%; p < 0.0001), and multimorbidity prevalence (20.6% vs. 16.1%; p < 0.001). These patients had higher values (mean (95% CI)) of C-reactive protein (CRP) (86 (32.7-160) vs. 49.3 (16-109) mg/dL; p < 0.001), ferritin (791 (393-1534) vs. 470 (236- 996) µg/dL; p < 0.001), D dimer (750 (430-1400) vs. 617 (345-1180) µg/dL; p < 0.001), and lower Sp02/Fi02 (266 (91.1) vs. 301 (101); p < 0.001). Since June 2020, there was an increment in the use of CTs (March vs. September; p < 0.001). Overall, 20% did not receive steroids, and 40% received less than 200 mg accumulated prednisone equivalent dose (APED). Severe patients are treated with higher doses. The mortality benefit was observed in patients with oxygen saturation </=90%. Conclusions: Patients with greater comorbidity, severity, and inflammatory markers were those treated with CTs. In severe patients, there is a trend towards the use of higher doses. The mortality benefit was observed in patients with oxygen saturation </=90%

The evolution of the ventilatory ratio is a prognostic factor in mechanically ventilated COVID-19 ARDS patients

Background: Mortality due to COVID-19 is high, especially in patients requiring mechanical ventilation. The purpose of the study is to investigate associations between mortality and variables measured during the first three days of mechanical ventilation in patients with COVID-19 intubated at ICU admission. Methods: Multicenter, observational, cohort study includes consecutive patients with COVID-19 admitted to 44 Spanish ICUs between February 25 and July 31, 2020, who required intubation at ICU admission and mechanical ventilation for more than three days. We collected demographic and clinical data prior to admission; information about clinical evolution at days 1 and 3 of mechanical ventilation; and outcomes. Results: Of the 2,095 patients with COVID-19 admitted to the ICU, 1,118 (53.3%) were intubated at day 1 and remained under mechanical ventilation at day three. From days 1 to 3, PaO2/FiO2 increased from 115.6 [80.0-171.2] to 180.0 [135.4-227.9] mmHg and the ventilatory ratio from 1.73 [1.33-2.25] to 1.96 [1.61-2.40]. In-hospital mortality was 38.7%. A higher increase between ICU admission and day 3 in the ventilatory ratio (OR 1.04 [CI 1.01-1.07], p = 0.030) and creatinine levels (OR 1.05 [CI 1.01-1.09], p = 0.005) and a lower increase in platelet counts (OR 0.96 [CI 0.93-1.00], p = 0.037) were independently associated with a higher risk of death. No association between mortality and the PaO2/FiO2 variation was observed (OR 0.99 [CI 0.95 to 1.02], p = 0.47). Conclusions: Higher ventilatory ratio and its increase at day 3 is associated with mortality in patients with COVID-19 receiving mechanical ventilation at ICU admission. No association was found in the PaO2/FiO2 variation