On distributive modules and rings

In this paper we study ω-distributive modules, where ω is a cardinal number. We extend a characterization of distributive modules to ω-distributive modules. In particular, the case in which ω = n is a finite cardinal is considered. We apply the results to the case n = 2, obtaining new characterizations for distributive modules and rings. Special attention is given to saturated submodules and ideals.     

From X- to O-shaped spatiotemporal spectra of light filaments in water

We show that the angle-wavelength spectra of light filaments excited by ultrashort pulses experience a transition from X- to O-like structures when their carrier wavelengths are switched from normal to anomalous dispersion. Calculations confirm that the O-shaped conical emission follows the elliptic geometry of the nonlinear Schr?dinger equation with anomalous dispersion.     

Phase-object analysis with a speckle interferometer

We describe the characteristics of a double-exposure specklegram obtained through a double-aperture system, by introduction of a wedge in front of one aperture in one exposure. It is assumed that a uniform displacement of the diffuser is produced between exposures. The average intensity distribution and visibility of the interferometric fringes in the Fourier plane are analyzed. An alternative interferometric technique for phase-object detection is proposed.     

Aberrations theory of a time dependent magnetic field lens

We analyze new forms of aberrations affecting a time dependent magnetic field lens recently proposed. The lens consist of an axially symmetric ellipsoidal solenoid producing a spatially uniform but time pulsating homogeneous field. The dynamics of electrons emitted by some object and injected into this coil shows that this system is capable of focusing a parallel beam or produce images free of geometrical aberrations. The cardinal elements of this lens change periodically in positions and therefore to obtain a stationary image it is necessary to employ a chopped electron beam. Two forms of aberrations originate from the finite duration of the electron pulse and the energy dispersion of the incoming beam (chromatic aberration). Their image degradation effects are quite similar and result from recording different axially displaced images at some fixed stationary plane. We show how, by adjusting the parameters characterizing the magnetic pulse and introducing small apertures that increase the depth of focus, their effects can be reduced or in some cases eliminated. Other forms of instrumental aberrations characteristic of this time dependent magnetic field lens are briefly discussed.     

Quantum optical predictions inQ representation for Bell's type experiments

Using the Q representation, we study the disagreement between quantum optical formalism and local realism and we show that the phenomenon of enhancement, first revealed by the local realist analysis, could receive a simple explanation if we use this particular version of the quantum formalism. Nevertheless, some fundamental difficulties remain.     

Toward a Comparison of Classical and New Privacy Mechanism

In the last decades, the development of interconnectivity, pervasive systems, citizen sensors, and Big Data technologies allowed us to gather many data from different sources worldwide. This phenomenon has raised privacy concerns around the globe, compelling states to enforce data protection laws. In parallel, privacy-enhancing techniques have emerged to meet regulation requirements allowing companies and researchers to exploit individual data in a privacy-aware way. Thus, data curators need to find the most suitable algorithms to meet a required trade-off between utility and privacy. This crucial task could take a lot of time since there is a lack of benchmarks on privacy techniques. To fill this gap, we compare classical approaches of privacy techniques like Statistical Disclosure Control and Differential Privacy techniques to more recent techniques such as Generative Adversarial Networks and Machine Learning Copies using an entire commercial database in the current effort. The obtained results allow us to show the evolution of privacy techniques and depict new uses of the privacy-aware Machine Learning techniques.     

Selecting an Effective Entropy Estimator for Short Sequences of Bits and Bytes with Maximum Entropy

Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.