The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry

The Dirac theory of constraints has been widely studied and applied very successfully by physicists since the original works by Dirac and by Bergmann. From a mathematical standpoint, several aspects of the theory have been exposed rigorously afterwards by many authors. However, many questions related to, for instance, singular or infinite dimensional cases remain open. The work of Gotay and Nester presents a mathematical generalization in terms of presymplectic geometry, which introduces a dual point of view. We present a study of the Dirac theory of constraints emphasizing the duality between the Poisson-algebraic and the geometric points of view, related respectively to the work of Dirac and of Gotay and Nester, under strong regularity conditions. We deal with some questions insufficiently treated in the literature: a study of uniqueness of solution; avoiding almost completely the use of coordinates; the role of the Pontryagin bundle. We also show how one can globalize some results usually treated locally in the literature. For instance, we introduce the globalnotion of second class submanifoldas being tangent to a second class subbundle. A general study of global results for Dirac and Gotay-Nester theories remains an open question in this theory.La Teoría de ligaduras deDirac, lateoría de Gotay-Nester y geometría dePoissin. La teoría de Dirac ha sido ampliamente estudiada y aplicada muy exitosamente por los físicos desde los trabajos originales de Dirac y de Bergmann. Desde un punto de vista matemático, varios aspectos de la teoría han sido expuestos rigurosamente por varios autores. Sin embargo, aún quedan abiertas varias preguntas relacionadas, por ejemplo, con casos singulares o infinito-dimensionales. El trabajo de Gotay y Nester presenta una generalización matemática en términos de la geometría presimpléctica, lo cual introduce un punto de vista dual. Presentamos un estudio de la teoría de ligaduras de Dirac enfatizando la dualidad entre los puntos de vista de las álgebras de Poisson y de la geometría presimpléctica, relacionados respectivamente con los trabajos de Dirac y de Gotay-Nester, bajo condiciones de regularidad fuertes. Abordamos algunas cuestiones insuficientemente tratadas en la literatura: un estudio de la unicidad de solución; evitar casi completamente el uso de coordenadas; el rol del fibrado de Pontryagin. También mostramos cómo se pueden globalizar algunos resultados usualmente tratados localmente en la literatura. Por ejemplo, introducimos la noción globalde subvariedad de segunda clasecomo variedad tangente a un subfibrado de segunda clase. Un estudio general de resultados globales para las teorías de Dirac y de Gotay-Nester sigue siendo una pregunta abierta en esta teoría.Fil: Cendra, Hernan. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Etchechoury, María del Rosario. Universidad Nacional de La Plata; ArgentinaFil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

An extension of the dirac and gotay-nester theories of constraints for dirac dynamical systems

This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical systems are viewed as constrained systems where the constraint submanifolds are foliated. The cases considered usually in the literature correspond to a trivial foliation, with only one leaf. A Constraint Algorithm for Dirac dynamical systems (CAD), which extends the Gotay-Nester algorithm, is developed. Evolution equations are written using a Dirac bracket adapted to the foliations and an adapted total energy. The interesting example of LC circuits is developed in detail. The paper emphasizes the point of view that Dirac and Gotay-Nester theories are, in a certain sense, dual and that using a combination of results from both theories may have advantages in dealing with a given example, rather than using systematically one or the other.Laboratorio de Electrónica Industrial, Control e Instrumentació

Bioaccessible heavy metals-sediment particles from Reconquista River induce lung inflammation in mice

The Reconquista River (RR), one of the most polluted watercourses in Argentina, receives effluent discharges from heavily industrialized and highly populated settlements. During winter and summer, the floodplain remains dry, producing the oxidation of sulfide and organic matter present in the sediment, making heavy metals more bioaccessible. Dispersion of this sediment occurs, and thus harmful effects on the pulmonary health of residents and workers inhabiting the RR bank may take place. The authors characterized the sediment particles of the RR (RR-PM) morphologically by scanning electron microscopy and its elemental composition by energy dispersive X-ray spectroscopy (EDX) and Community Bureau of Reference (BCR) sequential extraction. Furthermore, the authors evaluated its biological impact on the respiratory system of BALB/c mice, generating four groups: control healthy, sensibilized with ovalbumin, exposed to particles, and sensibilized and exposed to particles. Sediment particles of the Reconquista River contained fine particulate matter, with a high concentration of bioaccessible Cu and Zn. The authors found that animal exposure to RR-PM caused polymorphonuclear cell lung infiltration, augmentation of O2-, increase of proinflammatory cytokines (tumor necrosis factor alpha [TNFα], interleukin-6 [IL-6]) and apoptosis. This adverse response was more dramatic in the sensibilized and exposed to particles group. Even more, they proved the bioaccessible fraction present in the RR-PM to be responsible for these harmful effects. The authors conclude that RR-PM produces an adverse biological impact on the airways of healthy animals, which is largely aggravated in previously sensibilized animals.Fil: Ferraro, Sebastián Ariel. Universidad Nacional de San Martín. Instituto de Investigación e Ingeniería Ambiental. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación e Ingeniería Ambiental; ArgentinaFil: Curutchet, Gustavo Andres. Universidad Nacional de San Martín. Instituto de Investigación e Ingeniería Ambiental. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación e Ingeniería Ambiental; ArgentinaFil: Tasat, Deborah Ruth. Universidad de Buenos Aires. Facultad de Odontología. Cátedra de Histología y Embriología; Argentin

The Dirac theory of constraints, the Gotay-Nester theory and Poisson geometry

The Dirac theory of constraints has been widely studied and applied very successfully by physicists since the original works by Dirac and by Bergmann. From a mathematical standpoint, several aspects of the theory have been exposed rigorously afterwards by many authors. However, many questions related to, for instance, singular or infinite dimensional cases remain open. The work of Gotay and Nester presents a mathematical generalization in terms of presymplectic geometry, which introduces a dual point of view. We present a study of the Dirac theory of constraints emphasizing the duality between the Poisson-algebraic and the geometric points of view, related respectively to the work of Dirac and of Gotay and Nester, under strong regularity conditions. We deal with some questions insufficiently treated in the literature: a study of uniqueness of solution; avoiding almost completely the use of coordinates; the role of the Pontryagin bundle. We also show how one can globalize some results usually treated locally in the literature. For instance, we introduce the globalnotion of second class submanifoldas being tangent to a second class subbundle. A general study of global results for Dirac and Gotay-Nester theories remains an open question in this theory.La teoría de Dirac ha sido ampliamente estudiada y aplicada muy exitosamente por los físicos desde los trabajos originales de Dirac y de Bergmann. Desde un punto de vista matemático, varios aspectos de la teoría han sido expuestos rigurosamente por varios autores. Sin embargo, aún quedan abiertas varias preguntas relacionadas, por ejemplo, con casos singulares o infinito-dimensionales. El trabajo de Gotay y Nester presenta una generalización matemática en términos de la geometría presimpléctica, lo cual introduce un punto de vista dual. Presentamos un estudio de la teoría de ligaduras de Dirac enfatizando la dualidad entre los puntos de vista de las álgebras de Poisson y de la geometría presimpléctica, relacionados respectivamente con los trabajos de Dirac y de Gotay-Nester, bajo condiciones de regularidad fuertes. Abordamos algunas cuestiones insuficientemente tratadas en la literatura: un estudio de la unicidad de solución; evitar casi completamente el uso de coordenadas; el rol del fibrado de Pontryagin. También mostramos cómo se pueden globalizar algunos resultados usualmente tratados localmente en la literatura. Por ejemplo, introducimos la noción globalde subvariedad de segunda clasecomo variedad tangente a un subfibrado de segunda clase. Un estudio general de resultados globales para las teorías de Dirac y de Gotay-Nester sigue siendo una pregunta abierta en esta teoría.Instituto de Investigaciones en Electrónica, Control y Procesamiento de SeñalesFacultad de Ciencias Exacta

An Integrated Ecological-Social Simulation Model of Farmer Decisions and Cropping System Performance in the Rolling Pampas (Argentina)

Changes in agricultural systems are a multi-causal process involving climate change, globalization and technological change. These complex interactions regulate the landscape transformation process by imposing land use and cover change (LUCC) dynamics. In order to better understand and forecast the LUCC process we developed a spatially explicit agent-based model in the form of a Cellular Automata: the AgroDEVS model. The model was designed to project viable LUCC dynamics along with their associated economic and environmental changes. AgroDEVS is structured with behavioral rules and functions representing a) crop yields, b) weather conditions, c) economic profits, d) farmer preferences, e) adoption of technology levels and f) natural resource consumption based on embodied energy accounting. Using data from a typical location of the Pampa region (Argentina) for the period 1988-2015, simulation exercises showed that economic goals were achieved, on average, each 6 out of 10 years, but environmental thresholds were only achieved in 1.9 out of 10 years. In a set of 50-years simulations, LUCC patterns converge quickly towards the most profitable crop sequences, with no noticeable trade-off between economic and environmental conditions.Fil: Pessah, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Ferraro, Diego Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura; ArgentinaFil: Blanco, Daniela. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Castro, Rodrigo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentin

Geometric Integrators for Higher-Order Variational Systems and Their Application to Optimal Control

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for higher-order Lagrangian systems. Given a regular higher-order Lagrangian L: T( k )Q→ R with k≥ 1 , the resulting discrete equations define a generally implicit numerical integrator algorithm on T( k - 1 )Q× T( k - 1 )Q that approximates the flow of the higher-order Euler–Lagrange equations for L. The algorithm equations are called higher-order discrete Euler–Lagrange equations and constitute a variational integrator for higher-order mechanical systems. The general idea for those variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the invariants of the original system, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. We construct an exact discrete Lagrangian Lde using the locally unique solution of the higher-order Euler–Lagrange equations for L with boundary conditions. By taking the discrete Lagrangian as an approximation of Lde, we obtain variational integrators for higher-order mechanical systems. We apply our techniques to optimal control problems since, given a cost function, the optimal control problem is understood as a second-order variational problem.Fil: Colombo, Leonardo Jesus. University of Michigan; Estados UnidosFil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Martin de Diego, David. Instituto de Ciencias Matemáticas; España. Consejo Superior de Investigaciones Científicas; Españ

Particulate matter cytotoxicity in cultured SH-SY5Y cells is modulated by simvastatin: Toxicological assessment for oxidative damage

Epidemiological studies have shown a positive correlation between environmental particulate matter and adverse health effects. In particular, residual oil fly ash (ROFA) induces inflammation and reactive oxygen species (ROS), exerting not only local, but also systemic adverse effects. Previously, in an experimental animal model, we found that simvastatin (Sv) pretreatment was effective in preventing ROFA induced lung inflammation. Herein, using the human neuroblastoma SH-SY5Y cell line as a neurotoxicity in vitro model, we studied the potential Sv protective effect on ROFA cytotoxicity. We evaluated cell viability by the MTT assay, superoxide anion generation by NBT test, Nrf2 activation by immunofluorescence, apoptosis by cleaved-PARP and active-caspase 3 expressions, and senescence by b-galactosidase activity. SH-SY5Y cells exposed to ROFA (10 and 50mg/ml) for 24 h showed decreased cell viability, increased superoxide anion generation, apoptosis and senescence. Pretreatment with Sv (1mM) for 6 days, restored cell viability to basal levels, reduced ROFA-induced O2 generation as well as the number of apoptotic and senescent cells. Sv pretreatment stimulated the basal and ROFA-induced levels of Nrf2 nuclear translocation suggesting that activation of the cellular antioxidant defense system prevented particle-induced oxidative stress. In parallel, rescue experiments with mevalonate did not modify the effects of SV pretreatment in any of the parameters evaluated in this study. We conclude that simvastatin may provide neuroprotection against air particulate matter-induced neurotoxicity independently of its ability to inhibit cholesterol synthesis.Fil: Ferraro, Sebastián Ariel. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología. Centro de Estudios en Salud y Medio Ambiente; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Astort, Francisco. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología. Centro de Estudios en Salud y Medio Ambiente; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Yakisich, Juan Sebastian. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología. Centro de Estudios en Salud y Medio Ambiente; ArgentinaFil: Tasat, Deborah Ruth. Universidad Nacional de San Martín. Escuela de Ciencia y Tecnología. Centro de Estudios en Salud y Medio Ambiente; Argentina. Universidad de Buenos Aires. Facultad de Odontología. Cátedra de Histología y Embriología; Argentin

Un paquete para cálculos en reticulados

En este trabajo presentamos un paquete que hemos desarrollado para manejar y visualizar reticulados y álgebras de Łukasiewicz finitos. Este provee al investigador matemático herramientas para realizar en forma sencilla cálculos que normalmente conllevan un arduo trabajo. El paquete ha sido probado con numerosos ejemplos por miembros de un grupo de investigación en lógica algebraica de nuestra universidad. Su diseño orientado a objetos prevé su expansión futura.Eje: I - Workshop de Ingeniería de Software y Base de DatosRed de Universidades con Carreras en Informática (RedUNCI