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

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

Properties of Multisymplectic Manifolds

This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical models, and other relevant kinds of multisymplectic manifolds, such as those where the existence of Darboux-type coordinates is assured. The Hamiltonian structures that can be defined in these manifolds are also studied, as well as other important properties, such as their invariant forms and the characterization by automorphisms.Comment: 10 pp. Changes in Sections 5 and 7 (where brief guides to the proofs of theorems have been added). Lecture given at the workshop on {\sl Classical and Quantum Physics: Geometry, Dynamics and Control. (60 Years Alberto Ibort Fest), Instituto de Ciencias Matem\'aticas (ICMAT)}, Madrid (Spain), 5--9 March 201

Competencias necesarias en el ejercicio de la profesión de ingeniería informática: Experimento sobre la percepción de los estudiantes

Congreso Universitario de Innovación Educativa En las Enseñanzas Técnicas, CUIEET (26º. 2018. Gijón

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

A Unified Model Representation of Machine Learning Knowledge

Nowadays, Machine Learning (ML) algorithms are being widely applied in virtually all possible scenarios. However, developing a ML project entails the effort of many ML experts who have to select and configure the appropriate algorithm to process the data to learn from, between other things. Since there exist thousands of algorithms, it becomes a time-consuming and challenging task. To this end, recently, AutoML emerged to provide mechanisms to automate parts of this process. However, most of the efforts focus on applying brute force procedures to try different algorithms or configuration and select the one which gives better results. To make a smarter and more efficient selection, a repository of knowledge is necessary. To this end, this paper proposes (1) an approach towards a common language to consolidate the current distributed knowledge sources related the algorithm selection in ML, and (2) a method to join the knowledge gathered through this language in a unified store that can be exploited later on, and (3) a traceability links maintenance. The preliminary evaluations of this approach allow to create a unified store collecting the knowledge of 13 different sources and to identify a bunch of research lines to conduct.2019-2

Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model

ABSTRACT Background: The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM). Method: The model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (TGF − β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM. Results: The results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time “τ ”, the maximal growth rate of tumor “r” and the maximal efficiency of tumor cytotoxic cells rate “aT” are the most sensitive model parameters. Conclusion: By using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to obtain a good approximation of the biological trials data. It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results

Síntesis y caracterización fisicoquímica de circonia promovida con ácido tungstofosfórico y ácido bórico utilizada como catalizador en la isomerización de n-pentano

En este trabajo se muestra la preparación, caracterización y evaluación de la actividad catalítica de materiales del tipo ZrO2 promovida con ácido tungstofosfórico y ácido bórico. El Zr(OH)4 se sintetizó por el método sol-gel utilizando como precursores al n-butóxido de circonio y 1-butanol, manteniendo un pH = 8 durante la síntesis. El Zr(OH)4 se impregnó con un 15% en pesodel agente ácido, calcinado a 600 ºC e impregnado  posteriormente con 0,5% en peso de platino. Se observó que los iones [PW12O40]3– y [BO3]3– permanecen fuertementeenlazados a la superficie de la ZrO2 inhibiendo el crecimiento de la partícula, retardando la sinterización del material y la aparición de la fase monoclínica.Además, con la incorporación de estos dopantes se incrementó la acidez total del material, específicamente la población de sitios ácidos fuertes, siendo este tipo de sitios los predominantes en las muestras acidificadas.La acidez desarrollada por los materiales fue la adecuada para lograr catalizar la reacción de isomerización de n-pentano con conversiones superiores al 20% y selectividades hacia el isopentano que fluctuaron alrededor del 90%

Enhanced transport protocols

The book presents mechanisms, protocols, and system architectures to achieve end-to-end Quality-of-Service (QoS) over heterogeneous wired/wireless networks in the Internet. Particular focus is on measurement techniques, traffic engineering mechanisms and protocols, signalling protocols as well as transport protocol extensions to support fairness and QoS. It shows how those mechanisms and protocols can be combined into a comprehensive end-to-end QoS architecture to support QoS in the Internet over heterogeneous wired/wireless access networks. Finally, techniques for evaluation of QoS mechanisms such as simulation and emulation are presented. The book is aimed at graduate and post-graduate students in Computer Science or Electrical Engineering with focus in data communications and networking as well as for professionals working in this area