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

Endocrine disrupters, microRNAs, and primordial germ cells: a dangerous cocktail

29 p.-2 fig.Endocrine-disrupting chemicals (EDCs) are environmental pollutants that may change the homeostasis of the endocrine system, altering the differentiation of germ cells with consequences for reproduction. In mammals, germ cell differentiation begins with primordial germ cells (PGCs) during embryogenesis. Primordial germ cell development and gametogenesis are genetically regulated processes, in which the posttranscriptional gene regulation could be mediated by small noncoding RNAs (sncRNAs) such as microRNAs (miRNAs). Here, we review the deleterious effects of exposure during fetal life to EDCs mediated by deregulation of ncRNAs, and specifically miRNAs on PGC differentiation. Moreover, the environmental stress induced by exposure to some EDCs during the embryonic window of development could trigger reproductive dysfunctions transgenerationally transmitted by epigenetic mechanisms with the involvement of miRNAs expressed in germ line cells.Del Mazo lab was supported by a grant from MINECO (BFU2013-42164-R), Spain.Peer reviewe

MINERÍA Y DESARROLLO REGIONAL. COMPETENCIA POR LOS RECURSOS DEL TERRITORIO EN BAJA CALIFORNIA Y SONORA

El desarrollo en amplias zonas del norte y noroeste de México ha estado sustentado históricamente en la minería. Baja California y Sonora comparten un pasado minero, aunque han experimentado los procesos en contextos y ritmos diferentes. En la actualidad, enfrentan el resurgimiento de esta actividad, que involucra procesos de producción con magnos impactos ecológicos y socio territoriales. Para controlar los efectos y los conflictos por usos de suelo que convergen en una región o territorio, en México existen instrumentos de política pública, como los ordenamientos ecológicos. Se trata de herramientas para conseguir el desarrollo, desde la perspectiva de la sustentabilidad y la resiliencia de las comunidades ante el cambio climático. El objetivo de la ponencia es proponer que el crecimiento actual de la minería en Baja California y Sonora implica conflictos que se expresan, a nivel territorial, en la incompatibilidad de usos de suelo entre las actividades extractivas de alto impacto y las acciones y propuestas de conservación. La metodología partió de la revisión de documentos oficiales y localización de las concesiones en la página del Sistema de Administración Minera (SIAM). Esta información se contrastó con la extensión y localización de las Áreas Naturales Protegidas (ANP) de la Comisión Nacional de Áreas Naturales Protegidas (CONANP) y las Regiones Terrestres Prioritarias (RTP), según la Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO). Se representan los conflictos por uso del suelo con la superposición de las representaciones cartográficas de cada actividad, a partir del Portal de GeoInformación de CONABIO

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

The extended halo of NGC 2682 (M 67) from Gaia DR2

Context: NGC 2682 is a nearby open cluster, approximately 3.5 Gyr old. Dynamically, most open clusters should dissolve on shorter timescales, of ~ 1 Gyr. Having survived until now, NGC 2682 was likely much more massive in the past, and is bound to have an interesting dynamical history. Aims: We investigate the spatial distribution of NGC 2682 stars to constrain its dynamical evolution, especially focusing on the marginally bound stars in the cluster outskirts. Methods: We use Gaia DR2 data to identify NGC 2682 members up to a distance of ~150 pc (10 degrees). Two methods (Clusterix and UPMASK) are applied to this end. We estimate distances to obtain three-dimensional stellar positions using a Bayesian approach to parallax inversion, with an appropriate prior for star clusters. We calculate the orbit of NGC 2682 using the GRAVPOT16 software. Results: The cluster extends up to 200 arcmin (50 pc) which implies that its size is at least twice as previously believed. This exceeds the cluster Hill sphere based on the Galactic potential at the distance of NGC 2682. Conclusions: The extra-tidal stars in NGC 2682 may originate from external perturbations such as disk shocking or dynamical evaporation from two-body relaxation. The former origin is plausible given the orbit of NGC 2682, which crossed the Galactic disk ~40 Myr ago.Comment: 9 pages, 5 figures, accepted for publication on A&

Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is characterized by their automorphisms. Thus, locally homogeneous multisymplectic manifolds extend the family of classical geometries possessing a similar property: symplectic, volume and contact. The proof of the first result relies on the characterization of invariant differential forms with respect to the graded Lie algebra of infinitesimal automorphisms, and on the study of the local properties of Hamiltonian vector fields on locally multisymplectic manifolds. In particular it is proved that the group of multisymplectic diffeomorphisms acts (strongly locally) transitively on the manifold. It is also shown that the graded Lie algebra of infinitesimal automorphisms of a locally homogeneous multisymplectic manifold characterizes their multisymplectic diffeomorphisms.Comment: 25 p.; LaTeX file. The paper has been partially rewritten. Some terminology has been changed. The proof of some theorems and lemmas have been revised. The title and the abstract are slightly modified. An appendix is added. The bibliography is update

Non-standard connections in classical mechanics

In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, which require the prior choice of a connection. Bearing these facts in mind, we analyze the situation in the jet-bundle description of time-dependent classical mechanics. So we prove that this connection-dependence also occurs in this case, although it is usually hidden by the use of the ``natural'' connection given by the trivial bundle structure of the phase spaces in consideration. However, we also prove that this dependence is dynamically irrelevant, except where the dynamical variation of the energy is concerned. In addition, the relationship between first integrals and connections is shown for a large enough class of lagrangians.Comment: 17 pages, Latex fil

Biomarkers in ocular chronic graft versus host disease: tear cytokine- and chemokine-based predictive model.

Producción CientíficaPurpose: To develop a tear molecule level-based predictive model based on a panel of tear cytokines and their correlation with clinical features in ocular chronic graft versus host disease (cGVHD). Methods: Twenty-two ocular cGVHD patients and 21 healthy subjects were evaluated in a controlled environmental research laboratory (CERLab). Clinical parameters were recorded, and tears were collected. Levels of 15 molecules (epidermal growth factor [EGF], IL receptor antagonist [IL-1Ra], IL-1β, IL-2, IL-6, IL-8/CXCL8, IL-10, IL-12p70, IL-17A, interferon inducible protein [IP]-10/CXCL10, IFN-γ, VEGF, TNF-α, eotaxin 1, and regulated on activation normal T cell expressed and secreted [RANTES]) were measured by multiplex-bead assay and correlated with clinical parameters. Logistic regression was used to develop a predictive model. Leave-one-out cross-validation was applied. Classification capacity was evaluated in a cohort of individuals with dry eye (DE) of other etiologies different from GVHD. Results: Epidermal growth factor and IP-10/CXCL10 levels were significantly decreased in ocular cGVHD, positively correlating with tear production and stability and negatively correlating with symptoms, hyperemia, and vital staining. Interleukin-1Ra, IL-8/CXCL8, and IL-10 were significantly increased in ocular cGVHD, and the first two correlated positively with symptoms, hyperemia, and ocular surface integrity while negatively correlating with tear production and stability. Predictive models were generated, and the best panel was based on IL-8/CXCL8 and IP-10/CXCL10 tear levels along with age and sex, with an area under the receiving operating curve of 0.9004, sensitivity of 86.36%, and specificity of 95.24%. Conclusions: A predictive model based on tear levels of IL-8/CXCL8 and IP-10/CXCL10 resulted in optimal sensitivity and specificity. These results add further knowledge to the search for potential biomarkers in this devastating ocular inflammatory disease.Ministry of Economy and Competitiveness, Madrid, Spain, SAF-2010 15631 (AES)

Classical field theory on Lie algebroids: Variational aspects

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.Comment: Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References adde

Tropical Grass Growth Functions Modeling by Using Nonlinear Mixed Models

Nonlinear Growth curves are used for modeling plant physiological variables. These models are preferable because the polynomial coefficients of the equations have a biological significance. The response variables of the curves occurs commonly with repeated measurements over time and measurements are on different environments. The traditional statistical analysis does not include a repeated measures approach, which can lead to improper estimation of the error terms. It is important to study the growth of tropical grass (Da Silva and Carvalho 2005)