Improving the Hough Transform gathering process for affine transformations

In this paper, we show that significant wrong evidence can be generated when the Hough Transform (HT) is used to extract arbitrary shapes under rigid transformations. In order to reduce the amount of wrong evidence, we consider two types of constraints. First, we define constraints by considering invariant features. Secondly, we consider constraints defined via gradient direction information. Our results show that these constraints can significantly improve the gathering strategy, leading to identification of the correct parameters. The presented formulation is valid for any rigid transformations represented by affine mappings

Compact approach to the positivity of Brown-York mass]{Compact approach to the positivity of Brown-York mass and rigidity of manifolds with mean-convex boundaries in flat and spherical contexts

In this article we develope a spinorial proof of the Shi-Tam theorem for the positivity of the Brown-York mass without necessity of building non smooth infinite asymptotically flat hypersurfaces in the Euclidean space and use the positivity of the ADM mass proved by Schoen-Yau and Witten. This same compact approach provides an optimal lower bound \cite{HMZ} for the first non null eigenvalue of the Dirac operator of a mean convex boundary for a compact spin manifold with non negative scalar curvature, an a rigidity result for mean-convex bodies in flat spaces. The same machinery provides analogous, but new, results of this type, as far as we know, in spherical contexts, including a version of Min-Oo's conjecture

Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap phase of cuprate superconductors in the context of an emergent SU(2)-symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful we exhibit three solutions of the spin-fermion model at the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys. $\bf{9}$, 1745 (2013)].The CDW is sensitive to the shape of the Fermi surface in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.Comment: 15 pages, 15 figures, final version + typo corrected in Eq. (12

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with the special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic (AF) quantum critical point (QCP) in two dimensions, in which preemptive orders in the charge and superconducting (SC) sectors emerged, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SU(2) pairing fluctuations are dominant and argue that they are unstable towards the formation of a Resonant Peierls Excitonic (RPE) state at the pseudogap (PG) temperature $T^{*}$. We discuss the implications of this scenario for a few key experiments.Comment: 16 pages, 17 figure

η\eta collective mode as A1g_{1g} Raman resonance in cuprate superconductors

We discuss the possible existence a spin singlet excitation with charge $\pm2$ ($\eta$-mode) originating the $A_{1g}$ Raman resonance in cuprate superconductors. This $\eta$-mode relates the $d$-wave superconducting singlet pairing channel to a $d$-wave charge channel. We show that the $\eta$ boson forms a particle-particle bound state below the $2\Delta$ threshold of the particle-hole continuum where $\Delta$ is the maximum $d$-wave gap. Within a generalized random phase approximation and Bethe-Salpether approximation study, we find that this mode has energies similar to the resonance observed by Inelastic Neutron Scattering (INS) below the superconducting (SC) coherent peak at $2\Delta$ in various SC cuprates compounds. We show that it is a very good candidate for the resonance observed in Raman scattering below the $2\Delta$ peak in the $A_{1g}$ symmetry. Since the $\eta$-mode sits in the $S=0$ channel, it may be observable via Raman, X -ray or Electron Energy Loss Spectroscopy probes

Strong competition between ΘII\Theta_{II}-loop-current order and dd-wave charge order along the diagonal direction in a two-dimensional hot spot model

We study the fate of the so-called $\Theta_{II}$-loop-current order that breaks both time-reversal and parity symmetries in a two-dimensional hot spot model with antiferromagnetically mediated interactions, using Fermi surfaces relevant to the phenomenology of the cuprate superconductors. We start from a three-band Emery model describing the hopping of holes in the CuO$_{2}$ plane that includes two hopping parameters $t_{pp}$ and $t_{pd}$, local on-site Coulomb interactions $U_{d}$ and $U_{p}$ and nearest-neighbor $V_{pd}$ couplings between the fermions in the copper [Cu$(3d_{x^{2}-y^{2}})$] and oxygen [O$(2p_{x})$ and O$(2p_{y})$] orbitals. By focusing on the lowest-energy band, we proceed to decouple the local interaction $U_{d}$ of the Cu orbital in the spin channel using a Hubbard-Stratonovich transformation to arrive at the interacting part of the so-called spin-fermion model. We also decouple the nearest-neighbor interaction $V_{pd}$ to introduce the order parameter of the $\Theta_{II}$-loop-current order. In this way, we are able to construct a consistent mean-field theory that describes the strong competition between the composite order parameter made of a quadrupole-density-wave and $d$-wave pairing fluctuations proposed in Efetov \emph{et al.} [Nat. Phys. \textbf{9}, 442 (2013)] with the $\Theta_{II}$-loop-current order parameter that is argued to be relevant for explaining important aspects of the physics of the pseudogap phase displayed in the underdoped cuprates.Comment: 16 pages, 5 figures. v2: minor revisions, references added. The magnetic moment per unit-cell associated with the $\Theta_{II}$-loop-current-phase is calculated and compared with experimental results. Accepted for publication in Physical Review

Construyendo la noción de función trigonométrica: estrategias de aprendizaje

La enseñanza contemporánea se ve modificada, considerablemente, a causa de los resultados recientes de la investigación en matemática educativa tanto al nivel nacional como al de las diferentes regiones y escuelas de pensamiento en el mundo de hoy; estos resultados plantean, por ejemplo, que los asuntos del aprendizaje ligados al papel de la representación, la visualización y la utilización de tecnologías de la información juegan un papel prioritario en el diseño de secuencias didácticas novedosas para la escuela y la universidad. En el marco de este curso, dimos cuenta del estudio de las condiciones de construcción social de las funciones trigonométricas y lo presentamos a la luz de propuestas didácticas para favorecer los aprendizajes de los alumnos

Design of a controller for wheeled mobile robots based on automatic movement sequencing

There are many kinds of robots and among them the wheeled mobile robots (WMR) stand out, because they are relatively cheap and easy to build. These features make WMRs the test prototypes for control strategies or motion generation. In general, the controllers developed are based on sensory schemes that give an WMR the ability to travel through flat or obstructed environments. However, these strategies are highly reactive, i.e. they are based on the control-action scheme and are not adaptive; or, they are motion schemes built from simulations that assume the environmental conditions to determine the robot's path. In both cases, WMRs do not adapt perfectly to the change of environment, since the controller does not find appropriate movements for the  robot to move from one point to another. Therefore, this article proposesapartial solution to this problem, with a controller that generates sets of adaptive movements for an WMR to travel around its environment from the sensory perception information