Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators aX+(1-a)P and (XP+PX)/2 are presented.

A. C. de la Torre

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.

A. C. de la Torre D. Goyeneche

The quantization of the electromagnetic field in vacuum is presented without reference to lagrangean quantum field theory. The equal time commutators of the fields are calculated from basic principles. A physical discussion of the commutators suggest that the electromagnetic fields are macroscopic emergent properties of more fundamental physical system: the photons.

A. C. de la Torre

The free electromagnetic field, solution of Maxwell's equations and carrier of energy, momentum and spin, is construed as an emergent collective property of an ensemble of photons, and with this, the consistency of an interpretation that considers that the photons, and not the electromagnetic fields, are the primary ontology is established.

A. C. de la Torre

It is shown that the Fourier transformation that relates position and momentum representations of quantum mechanics can be understood as a consequence of a symmetry principle that establishes the equivalence of being and becoming in the description of reality. There are however other transformation compatible with the same principle that could lead to different formalisms of quantum mechanics.

Alberto C. de la Torre

It is shown that adopting the \emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.

Alberto C. de la Torre

A simple locus model for the space-time fabric is presented and is compared with quantum foam and random walk models. The induced indeterminacies in momentum are calculated and it is shown that these space-time fabric indeterminacies are, in most cases, negligible compared with the quantum mechanical indeterminacies. This result restricts the possibilities of an experimental observation of the space-time fabric.

Alberto C. de la Torre

In this paper, we get the sharpest known to date lower bounds for the minimal Green energy of the compact harmonic manifolds of any dimension.

Carlos Beltrán Víctor de la Torre Fátima Lizarte

Detecting vehicles in aerial images is difficult due to complex backgrounds, small object sizes, shadows, and occlusions. Although recent deep learning advancements have improved object detection, these models remain susceptible to adversarial attacks (AAs), challenging their reliability. Traditional AA strategies often ignore practical implementation constraints. Our work proposes realistic and practical constraints on texture (lowering resolution, limiting modified areas, and color ranges) and analyzes the impact of shape modifications on attack performance. We conducted extensive experiments with three object detector architectures, demonstrating the performance-practicality trade-off: more practical modifications tend to be less effective, and vice versa. We release both code and data to support reproducibility at https://github.com/humansensinglab/texture-shape-adversarial-attacks.

Mikael Yeghiazaryan Sai Abhishek Siddhartha Namburu Emily Kim Stanislav Panev Celso de Melo Fernando De la Torre Jessica K. Hodgins

We show that the set of F_q-rational points of either certain Fermat curves or certain F_q-Frobenius non-classical plane curves is a complete (k,d)-arc in P^2(F_q), where k and d are respectively the number of F_q-rational points and the degree of the underlying curve.

M. Giulietti F. Pambianco F. Torres E. Ughi