New membership determination and proper motions of NGC 1817. Parametric and non-parametric approach

We have calculated proper motions and re-evaluated the membership probabilities of 810 stars in the area of two NGC objects, NGC 1817 and NGC 1807. We have obtained absolute proper motions from 25 plates in the reference system of the Tycho-2 Catalogue. The plates have a maximum epoch difference of 81 years; and they were taken with the double astrograph at Zo-Se station of Shanghai Observatory, which has an aperture of 40 cm and a plate scale of 30 arcsec/mm. The average proper motion precision is 1.55 mas/yr. These proper motions are used to determine the membership probabilities of stars in the region, based on there being only one very extended physical cluster: NGC 1817. With that aim, we have applied and compared parametric and non-parametric approaches to cluster/field segregation. We have obtained a list of 169 probable member stars.Comment: 11 pages, 8 figures, A&A in pres

Beyond the Hype: RPA Horizon for Robot-Human Interaction

Medium and big organizations have embraced RPA in the last years bringing to light the high maturity of the technology. Current trends are towards including “human-in-the-loop” which promotes efficient ways for robot-human interaction. This is especially relevant since most real RPA projects require a collaboration between the human and the robot leading to hybrids approaches. The challenges that arise from this line can be addressed by both asynchronous (i.e., landing area or task queues where robots and humans share information) and synchronous solutions (i.e., human digital augmentation where robots provide immediate support). This paper goes in deep elaborating in these two alternatives by setting the benefits, requirements, and future research lines which are envisioned through industrial experiences. In addition, this work exposes the role of process mining in this journey since it allows for the necessary efficiency in the process analysis, time-to-market reduction, and continuous improvement that this robot-human collaboration requires.Ministerio de Economía y Competitividad TIN2016-76956-C3-2-RJunta de Andalucía CEI-12-TIC02

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

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

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

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

Higher-order Mechanics: Variational Principles and other topics

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.Comment: New version of the paper "Variational principles for higher-order dynamical systems", which was presented in the "III Iberoamerican Meeting on Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A detailed review is added. Sections containing results about variational principles are enlarged with additional comments, diagrams and summarizing results. Bibliography is update

Cohesin Removal along the Chromosome Arms during the First Meiotic Division Depends on a NEK1-PP1γ-WAPL Axis in the Mouse

SummaryMammalian NIMA-like kinase-1 (NEK1) is a dual-specificity kinase highly expressed in mouse germ cells during prophase I of meiosis. Loss of NEK1 induces retention of cohesin on chromosomes at meiotic prophase I. Timely deposition and removal of cohesin is essential for accurate chromosome segregation. Two processes regulate cohesin removal: a non-proteolytic mechanism involving WAPL, sororin, and PDS5B and direct cleavage by separase. Here, we demonstrate a role for NEK1 in the regulation of WAPL loading during meiotic prophase I, via an interaction between NEK1 and PDS5B. This regulation of WAPL by NEK1-PDS5B is mediated by protein phosphatase 1 gamma (PP1γ), which both interacts with and is a phosphotarget of NEK1. Taken together, our results reveal that NEK1 phosphorylates PP1γ, leading to the dephosphorylation of WAPL, which, in turn, results in its retention on chromosome cores to promote loss of cohesion at the end of prophase I in mammals

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

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