A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page

Indices y referencia en Peirce.

Sin resume

Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty

We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the application of Dirac's quantization rule to the various symplectic structures recently reported for this classical system. It is pointed out that that these quantum theories are inequivalent in the sense that the mean values for the operators (observables) associated with the same physical classical observable do not agree with each other. The inequivalence does not arise from ambiguities in the ordering of operators but from the fact of having several symplectic structures defined with respect to the same set of coordinates. It is also shown that the uncertainty relations between the fundamental observables depend on the particular quantum theory chosen. It is important to emphasize that these (somehow paradoxical) results emerge from the combination of two paradigms: Dirac's quantization rule and the usual Copenhagen interpretation of quantum mechanics.Comment: 8 pages, LaTex file, no figures. Accepted for publication in Phys. Rev.

Contextualizing The Higher Education In A Post-Pandemic Era: A Trisectoral Perception

The sudden shift towards remote learning two years ago to curb the spread of the pandemic caught educational institutions off-guard. It specifically proved to be a struggle in the Philippine context because as noted by Mineo (2020), not all learners were prepared for the shift in learning modalities. However, even with the current easing of restrictions nationwide, the Commission on Education chair Prospero de Vera III implied that as far as the higher education is concerned, flexible learning is now here to stay. As such, this study aimed to explore the perceptions of students, faculty members, and university administrators on hybrid flexible (HyFlex) instruction. The study utilized a mixed method research design. To interpret the results, frequency distributions and mean values were presented. Findings revealed that. While the students moderately agree that like the flexibility that hybrid flexible courses may offer, they were still undecided whether they can study at home as much as I can when attending face-to-face classes. On the other hand, faculty members and the university administrators mostly have positive perspectives on hybrid flexible (HyFlex) learning design which may be related to the fact that most of them already participated in trainings related to the designing and implementation of a hybrid flexible classroom. Accordingly, the following recommendations were formulated: for the students to continuously participate and engage in research studies that aims to devise teaching and learning continuity plan in the context of post-pandemic education; for faculty members to regularly attend capacity-building trainings; for the university administration in general to consider the hybrid flexible learning design as an option since both the students and faculty members were found to have positive perceptions on it; lastly, for future researchers to assess other organizational considerations related to the implementation of HyFlex courses

Charged particle dynamics in the presence of non-Gaussian L\'evy electrostatic fluctuations

Full orbit dynamics of charged particles in a $3$-dimensional helical magnetic field in the presence of $\alpha$-stable L\'evy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The L\'evy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of L\'evy fluctuations. The absolute value of the power law decay exponents are linearly proportional to the L\'evy index $\alpha$. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian L\'evy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.Comment: 5 pages, 5 figures. Accepted as a letter in Physics of Plasma

A Study of the N-D-K Scalability Problem in Large-Scale Image Classification

Image classification is a extensively studied problem that lies at the heart of computer vision. However, the challenge remains to develop a system that can identify and classify thousands of objects like the human visual system. The accumulation of massive image data sets has permitted the study of this problem at a big-data scale. However current algorithms have been shown to fall short of being practical and accurate at scale. To further understand how these algorithms scale, we developed a library of functions to explore the scalability of the support vector machine (SVM) linear classification algorithm when applied to problems of image classification. Our study provides valuable insights into not only how the SVM algorithm scales up and where it falls short, but also into how to create smarter and more efficient image classifiers that are fine- tuned for the large scale image classification challenge