Heuristic search of (semi-)bent functions based on cellular automata

An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter

Hard x-ray spectroscopy in NaxCoO2 and superconducting NaxCoO2 - yH2O: A view on the bulk Co electronic properties

The electronic properties of Co in bulk Na0.7CoO2 and the superconducting hydrated compound Na0.35CoO2 - y H2O have been investigated by x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray scattering (RIXS) using hard x-rays. The XAS spectra at the Co K-edge were measured in both compounds with two different polarization directions. The changes in the XAS spectra upon hydration and their polarization dependence are well accounted for by linear muffin- tin orbital calculations in the local density approximation. The underlying electronic structure indicates the strong hybridization between the Co 3d and O 2p states in both compounds, while the electron localization is enhanced in the hydrated compound due to the increase of the Co-Co interplanar distance. The Co K pre-edge further highlights the splitting of the d band as a result of the crystal field effect and demonstrates the Co valency increase when Na0.7CoO2 is hydrated. The RIXS spectra measured at the Co K-edge show an energy loss feature around 10 eV in both compounds in fair agreement with the calculated dynamical structure factor. The RIXS feature is associated to a damped plasmon excitation.Comment: 8 page

A Deoxyribonucleic Acid Decoy Trapping DUX4 for the Treatment of Facioscapulohumeral Muscular Dystrophy

Facioscapulohumeral dystrophy (FSHD) is characterized by a loss of repressive epigenetic marks leading to the aberrant expression of the DUX4 transcription factor. In muscle, DUX4 acts as a poison protein though the induction of multiple downstream genes. So far, there is no therapeutic solution for FSHD. Because DUX4 is a transcription factor, we developed an original therapeutic approach, based on a DNA decoy trapping the DUX4 protein, preventing its binding to genomic DNA and thereby blocking the aberrant activation of DUX4’s transcriptional network. In vitro, transfection of a DUX4 decoy into FSHD myotubes reduced the expression of the DUX4 network genes. In vivo, both double-stand DNA DUX4 decoys and adeno-associated viruses (AAVs) carrying DUX4 binding sites reduced transcriptional activation of genes downstream of DUX4 in a DUX4-expressing mouse model. Our study demonstrates, both in vitro and in vivo, the feasibility of the decoy strategy and opens new avenues of research

Soft-x-ray resonant scattering from V/Fe (001) magnetic superlattices

The magnetic properties of Fe and V in (n ML V / 5 ML Fe) (001) superlattices (n = 1, 2, and 5 ML) have been investigated by measuring the magnetization dependent scattering of elliptically polarized soft x rays at various scattering angles and for photon energies across the 2p x-ray-absorption edges of both Fe and V. A quantitative estimate of the magnetic moment induced on vanadium is obtained from the analysis of the resonant scattering data. [S0163-1829(99)50842-4]

General approach to the study of vacuum space-times with an isometry

In vacuum space-times the exterior derivative of a Killing vector field is a 2-form (named here as the Papapetrou field) that satisfies Maxwell's equations without electromagnetic sources. In this paper, using the algebraic structure of the Papapetrou field, we will set up a new formalism for the study of vacuum space-times with an isometry, which is suitable to investigate the connections between the isometry and the Petrov type of the space-time. This approach has some advantages, among them, it leads to a new classification of these space-times and the integrability conditions provide expressions that determine completely the Weyl curvature. These facts make the formalism useful for application to any problem or situation with an isometry and requiring the knowledge of the curvature.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum Gravit

Spinor classification of the Weyl tensor in five dimensions

We investigate the spinor classification of the Weyl tensor in five dimensions due to De Smet. We show that a previously overlooked reality condition reduces the number of possible types in the classification. We classify all vacuum solutions belonging to the most special algebraic type. The connection between this spinor and the tensor classification due to Coley, Milson, Pravda and Pravdov\'a is investigated and the relation between most of the types in each of the classifications is given. We show that the black ring is algebraically general in the spinor classification.Comment: 40 page

On the Papapetrou field in vacuum

In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum space-times (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as well as for the search, characterization, and study of exact solutions of Einstein's equations. The first part of this paper is devoted to an algebraic study in which we give an explicit and covariant procedure to construct the principal null directions of a Papapetrou field. In the second part, we focus on the main differential properties of the principal directions, studying when they are geodesic, and in that case we compute their associated optical scalars. With this information we get the conditions that a principal direction of the Papapetrou field must satisfy in order to be aligned with a multiple principal direction of the Weyl tensor in the case of algebraically special vacuum space-times. Finally, we illustrate this study using the Kerr, Kasner and pp waves space-times.Comment: 24 pages, LaTeX2e, IOP style. To appear in Classical and Quantum Gravit

Consequences of a Killing symmetry in spacetime's local structure

In this paper we discuss the consequences of a Killing symmetry on the local geometrical structure of four-dimensional spacetimes. We have adopted the point of view introduced in recent works where the exterior derivative of the Killing plays a fundamental role. Then, we study some issues related with this approach and clarify why in many circumstances its use has advantages with respect to other approaches. We also extend the formalism developed in the case of vacuum spacetimes to the general case of an arbitrary energy-momentum content. Finally, we illustrate our framework with the case of spacetimes with a gravitating electromagnetic field.Comment: 20 pages, LaTeX2e, IOP style. Revised version accepted for publication in Classical and Quantum Gravit

Observation of magnetic circular dichroism in Fe L_{2,3} x-ray-fluorescence spectra

We report experiments demonstrating circular dichroism in the x-ray-fluorescence spectra of magnetic systems, as predicted by a recent theory. The data, on the L_{2,3} edges of ferromagnetic iron, are compared with fully relativistic local spin density functional calculations, and the relationship between the dichroic spectra and the spin-resolved local density of occupied states is discussed