Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

Emotions associated with the first sexual relationship in gays and lesbians

El objetivo del presente trabajo fue evaluar en una muestra de gays y lesbianas, las emociones que experimentaron en su primera relación sexual, así como la relación con el uso de condón, planeación, concenso y edad del debut sexual. Participaron 336 hombres y mujeres, quienes respondieron en línea el cuestionario de Emociones, Estrés y Afrontamiento y algunas preguntas adicionales sobre su primera relación sexual. Se encontraron diferencias significativas en las emociones que experimentan hombres y mujeres, y entre aquellos que usaron condón, planearon y consensuaron su primera relación sexual. Los resultados se discuten en términos de cómo las emociones pueden afectar la vida sexual de gays y lesbianas.The objective of the present work was to evaluate in a sample of gays and lesbians, the emotions they experienced in their first sexual relationship, as well as the relationship with condom use, planning, consensus and age of sexual debut. 336 men and women participated, who responded online the Emotions, Stress and Coping questionnaire and some additional questions about their first sexual relationship. Significant differences were found in the emotions experienced by men and women, and among those who used a condom, they planned and agreed on their first sexual relationship. The results are discussed in terms of how emotions can affect the sex life of gays and lesbians

Staging Parkinson’s Disease Combining Motor and Nonmotor Symptoms Correlates with Disability and Quality of Life

Malaltia de Parkinson; Qualitat de vidaEnfermedad de Parkinson; Calidad de vidaParkinson's Disease; Quality of LifeIntroduction. In a degenerative disorder such as Parkinson’s disease (PD), it is important to establish clinical stages that allow to know the course of the disease. Our aim was to analyze whether a scale combining Hoehn and Yahr’s motor stage (H&Y) and the nonmotor symptoms burden (NMSB) (assessed by the nonmotor symptoms scale (NMSS)) provides information about the disability and the patient’s quality of life (QoL) with regard to a defined clinical stage. Materials and Methods. Cross-sectional study in which 603 PD patients from the COPPADIS cohort were classified according to H&Y (1, stage I; 2, stage II; 3, stage III; 4, stage IV/V) and NMSB (A: NMSS = 0–20; B: NMSS = 21–40; C: NMSS = 41–70; D: NMSS ≥ 71) in 16 stages (HY.NMSB, from 1A to 4D). QoL was assessed with the PDQ-39SI, PQ-10, and EUROHIS-QOL8 and disability with the Schwab&England ADL (Activities of Daily Living) scale. Results. A worse QoL and greater disability were observed at a higher stage of H&Y and NMSB (). Combining both (HY.NMSB), patients in stages 1C and 1D and 2C and 2D had significantly worse QoL and/or less autonomy for ADL than those in stages 2A and 2B and 3A and 3B, respectively (; e.g., PDQ-39SI in 1D [n = 15] vs 2A [n = 101]: 28.6 ± 17.1 vs 7.9 ± 5.8; ). Conclusion. The HY.NMSB scale is simple and reflects the degree of patient involvement more accurately than the H&Y. Patients with a lower H&Y stage may be more affected if they have a greater NMS burden

On some aspects of the geometry of differential equations in physics

In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular differential equations, and partial differential equations in field theories. The geometric structures underlying these systems are presented and commented. The main results concerning these structures are stated and discussed, as well as their influence on the study of the differential equations with which they are related. Furthermore, research to be developed in these areas is also commented.Comment: 21 page

Extended gamma-ray sources around pulsars constrain the origin of the positron flux at Earth

The unexpectedly high flux of cosmic ray positrons detected at Earth may originate from nearby astrophysical sources, dark matter, or unknown processes of cosmic-ray secondary production. We report the detection, using the HighAltitude Water Cherenkov Observatory (HAWC), of extended tera-electron volt gamma-ray emission coincident with the locations of two nearby middle-aged pulsars (Geminga and PSR B0656+14). The HAWC observations demonstrate that these pulsars are indeed local sources of accelerated leptons, but the measured tera-electron volt emission profile constrains the diffusion of particles away from these sources to be much slower than previously assumed. We demonstrate that the leptons emitted by these objects are therefore unlikely to be the origin of the excess positrons, which may have a more exotic origin.Comment: 16 pages (including supplementary material), 5 figure

Constraining the pˉ/p\bar{p}/p Ratio in TeV Cosmic Rays with Observations of the Moon Shadow by HAWC

An indirect measurement of the antiproton flux in cosmic rays is possible as the particles undergo deflection by the geomagnetic field. This effect can be measured by studying the deficit in the flux, or shadow, created by the Moon as it absorbs cosmic rays that are headed towards the Earth. The shadow is displaced from the actual position of the Moon due to geomagnetic deflection, which is a function of the energy and charge of the cosmic rays. The displacement provides a natural tool for momentum/charge discrimination that can be used to study the composition of cosmic rays. Using 33 months of data comprising more than 80 billion cosmic rays measured by the High Altitude Water Cherenkov (HAWC) observatory, we have analyzed the Moon shadow to search for TeV antiprotons in cosmic rays. We present our first upper limits on the $\bar{p}/p$ fraction, which in the absence of any direct measurements, provide the tightest available constraints of $\sim1\%$ on the antiproton fraction for energies between 1 and 10 TeV.Comment: 10 pages, 5 figures. Accepted by Physical Review

Sleep Problems Are Related to a Worse Quality of Life and a Greater Non-Motor Symptoms Burden in Parkinson’s Disease

COPPADIS Study Group.[Introduction] The aim of the present study was to examine the frequency of self-reported sleep problems and their associated factors in a large cohort of PD patients.[Methods] PD patients and controls, recruited from 35 centers of Spain from the COPPADIS cohort were included in this cross-sectional study. Sleep problems were assessed by the Spanish version of the Parkinson’s disease Sleep Scale version 1 (PDSS-1). An overall score below 82 or a score below 5 on at least 1 item was defined as sleep problems.[Results] The frequency of sleep problems was nearly double in PD patients compared to controls: 65.8% (448/681) vs 33.5% (65/206) (p < 0.0001). Mean total PDSS score was lower in PD patients than controls: 114.9 ± 28.8 vs 132.8 ± 16.3 (p < 0.0001). Quality of life (QoL) was worse in PD patients with sleep problems compared to those without: PDQ-39SI, 19.3 ± 14 vs 13 ± 11.6 (p < 0.0001); EUROHIS-QoL8, 3.7 ± 0.5 vs 3.9 ± 0.5 (p < 0.0001). Non-motor symptoms burden (NMSS; OR = 1.029; 95%CI 1.015–1.043; p < 0.0001) and impulse control behaviors (QUIP-RS; OR = 1.054; 95%CI 1.009–1.101; p = 0.018) were associated with sleep problems after adjustment for age, gender, disease duration, daily equivalent levodopa dose, H&Y, UPDRS-III, UPDRS-IV, PD-CRS, BDI-II, NPI, VAS-Pain, VAFS, FOGQ, and total number of non-antiparkinsonian treatments.[Conclusion] Sleep problems were frequent in PD patients and were related to both a worse QoL and a greater non-motor symptoms burden in PD. These findings call for increased awareness of sleep problems in PD patients.Peer reviewe

Fire and brief human occupations in Iberia during MIS 4: Evidence from Abric del Pastor (Alcoy, Spain)

There is a relatively low amount of Middle Paleolithic sites in Europe dating to MIS 4. Of the few that exist, several of them lack evidence for anthropogenic fire, raising the question of how this period of global cooling may have affected the Neanderthal population. The Iberian Peninsula is a key area to explore this issue, as it has been considered as a glacial refugium during critical periods of the Neanderthal timeline and might therefore yield archaeological contexts in which we can explore possible changes in the behaviour and settlement patterns of Neanderthal groups during MIS 4. Here we report recent data from Abric del Pastor, a small rock shelter in Alcoy (Alicante, Spain) with a stratified deposit containing Middle Palaeolithic remains. We present absolute dates that frame the sequence within MIS 4 and multi-proxy geoarchaeological evidence of in situ anthropogenic fire, including microscopic evidence of in situ combustion residues and thermally altered sediment. We also present archaeostratigraphic evidence of recurrent, functionally diverse, brief human occupation of the rock shelter. Our results suggest that Neanderthals occupied the Central Mediterranean coast of the Iberian Peninsula during MIS 4, that these Neanderthals were not undergoing climatic stress and they were habitual fire users.This research was funded by a Leakey Foundation General Grant, Spanish Ministry of Science, Innovation and Universities Projects HAR2008-06117/HIST and HAR2015-68321-P, Junta de Castilla y León-FEDER Project BU235P18, the LabEx Sciences Archéologiques de Bordeaux (LaScArBx ANR-10-LABX-52) and ERC Consolidator Grant ERC-CoG-2014. Archaeological excavations at Abric del Pastor are supported by the Archaeological Museum of Alcoy and the Government of Valencia Cultural Heritage Department