The universality theorem for neighborly polytopes

In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of an even-dimensional neighborly polytope. This in particular provides the final step for Mn\"ev's proof of the universality theorem for simplicial polytopes.Comment: 5 pages, 1 figure. Small change

Universality theorems for inscribed polytopes and Delaunay triangulations

We prove that every primary basic semialgebraic set is homotopy equivalent to the set of inscribed realizations (up to M\"obius transformation) of a polytope. If the semialgebraic set is moreover open, then, in addition, we prove that (up to homotopy) it is a retract of the realization space of some inscribed neighborly (and simplicial) polytope. We also show that all algebraic extensions of $\mathbb{Q}$ are needed to coordinatize inscribed polytopes. These statements show that inscribed polytopes exhibit the Mn\"ev universality phenomenon. Via stereographic projections, these theorems have a direct translation to universality theorems for Delaunay subdivisions. In particular, our results imply that the realizability problem for Delaunay triangulations is polynomially equivalent to the existential theory of the reals.Comment: 15 pages, 2 figure

Non-circular rotating beams and CMB experiments

This paper is concerned with small angular scale experiments for the observation of cosmic microwave background anisotropies. In the absence of beam, the effects of partial coverage and pixelisation are disentangled and analyzed (using simulations). Then, appropriate maps involving the CMB signal plus the synchrotron and dust emissions from the Milky Way are simulated, and an asymmetric beam --which turns following different strategies-- is used to smooth the simulated maps. An associated circular beam is defined to estimate the deviations in the angular power spectrum produced by beam asymmetry without rotation and, afterwards, the deviations due to beam rotation are calculated. For a certain large coverage, the deviations due to pure asymmetry and asymmetry plus rotation appear to be very systematic (very similar in each simulation). Possible applications of the main results of this paper to data analysis in large coverage experiments --as PLANCK-- are outlined.Comment: 13 pages, 9 figures, to appear in A&

Determination of Compton profiles at solid surfaces from first-principles calculations

Projected momentum distributions of electrons, i.e. Compton profiles above the topmost atomic layer have recently become experimentally accessible by kinetic electron emission in grazing-incidence scattering of atoms at atomically flat single crystal metal surfaces. Sub-threshold emission by slow projectiles was shown to be sensitive to high-momentum components of the local Compton profile near the surface. We present a method to extract momentum distribution, Compton profiles, and Wigner and Husimi phase space distributions from ab-initio density-functional calculations of electronic structure. An application for such distributions to scattering experiments is discussed.Comment: 13 pages, 5 figures, submitted to PR

Self-consistent Green's functions calculation of the nucleon mean-free path

The extension of Green's functions techniques to the complex energy plane provides access to fully dressed quasi-particle properties from a microscopic perspective. Using self-consistent ladder self-energies, we find both spectra and lifetimes of such quasi-particles in nuclear matter. With a consistent choice of the group velocity, the nucleon mean-free path can be computed. Our results indicate that, for energies above 50 MeV at densities close to saturation, a nucleon has a mean-free path of 4 to 5 femtometers.Comment: 5 pages, 4 figures. Minor changes, bibliography corrected. Accepted version in Phys. Rev. Let

El eco de la fotografía de Barthes. La nueva cámara lúcida: Notas sobre el cine digital

Hace treinta años Roland Barthes buscaba un tercer nivel de lectura de imágenes que se alejaba de la rígida lectura informativa y simbólica para dejar que fuese el significante quien hablara. Sus análisis llegaron a su mayor notoriedad en el estudio de la fotografía La chambre claire. El artículo siguiente parte de que la hipótesis que Barthes dejó en sus notas sobre el medio fotográfico resuena hoy por un lado en la miniaturización de los recursos y la instantaneidad del soporte de la cámara de vídeo digital y por otro lado, en el principio de modularidad y accesibilidad de los nuevos medios. En una segunda parte, el texto ahonda en la idea de la memoria barthesiana y en el paralelismo que toma junto con las reflexiones que Jean-Luc Godard concedió a través de la imagen electrónica. La aparente arbitrariedad en la selección de las imágenes que integran el estudio sigue el análisis de Barthes, por ello, responde a un criterio de confianza en la espontaneidad y en la memoria del autor

Implantation of 3D-Printed Patient-Specific Aneurysm Models into Cadaveric Specimens: A New Training Paradigm to Allow for Improvements in Cerebrovascular Surgery and Research.

AimTo evaluate the feasibility of implanting 3D-printed brain aneurysm model in human cadavers and to assess their utility in neurosurgical research, complex case management/planning, and operative training.MethodsTwo 3D-printed aneurysm models, basilar apex and middle cerebral artery, were generated and implanted in four cadaveric specimens. The aneurysms were implanted at the same anatomical region as the modeled patient. Pterional and orbitozygomatic approaches were done on each specimen. The aneurysm implant, manipulation capabilities, and surgical clipping were evaluated.ResultsThe 3D aneurysm models were successfully implanted to the cadaveric specimens' arterial circulation in all cases. The features of the neck in terms of flexibility and its relationship with other arterial branches allowed for the practice of surgical maneuvering characteristic to aneurysm clipping. Furthermore, the relationship of the aneurysm dome with the surrounding structures allowed for better understanding of the aneurysmal local mass effect. Noticeably, all of these observations were done in a realistic environment provided by our customized embalming model for neurosurgical simulation.Conclusion3D aneurysms models implanted in cadaveric specimens may represent an untapped training method for replicating clip technique; for practicing certain approaches to aneurysms specific to a particular patient; and for improving neurosurgical research

Absolute Maximal Entanglement and Quantum Secret Sharing

We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a novel parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties. This equivalence implies the existence of AME states for an arbitrary number of parties based on known results about the existence of quantum secret sharing schemes.Comment: 5 pages, 2 figure

Spin wave excitations in low dimensional systems with large magnetic anisotropy

The low energy excitation spectrum of a two-dimensional ferromagnetic material is dominated by single-magnon excitations that show a gapless parabolic dispersion relation with the spin wave vector. This occurs as long as magnetic anisotropy and anisotropic exchange are negligible compared to isotropic exchange. However, to maintain magnetic order at finite temperatures, it is necessary to have sizable anisotropy to open a gap in the spin wave excitation spectrum. We consider four real two-dimensional systems for which ferromagnetic order at finite temperature has been observed or predicted. Density functional theory calculations of the total energy differences for different spin configurations permit us to extract the relevant parameters and connect them with a spin Hamiltonian. The corresponding values of the Curie temperature are estimated using a simple model and found to be mostly determined by the value of the isotropic exchange. The exchange and anisotropy parameters are used in a toy model of finite-size periodic chains to study the low-energy excitation spectrum, including single-magnon and two-magnon excitations. At low energies we find that single-magnon excitations appear in the spectrum together with two-magnon excitations. These excitations present a gap that grows particularly for large values of the magnetic anisotropy or anisotropic exchange, relative to the isotropic exchange.Comment: 11 pages, 3 figures, 2 table