The Beneficial Role of Random Strategies in Social and Financial Systems

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.     

On Pythagoras Theorem for Products of Spectral Triples

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes’ distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Three-dimensional image fusion by use of multiwavelength digital holography

We present three-dimensional (3D) image fusion by use of digital holography. We demonstrate experimentally that, through the image fusion technique with multiresolution wavelet decomposition, it is possible to increase the details and contrast of 3D reconstructed images obtained by multiwavelength digital holography. Although there is substantial activity in the fields of image fusion and holography, to the best of our knowledge, this is the first report of 3D image fusion by use of digital holography.     

Structural and magnetic characteristics of Co1−xNix/2Srx/2Fe2O4 nanoparticles

Co_1−xNi_x/2Sr_x/2Fe₂O₄ (x=0–0.5 in steps of 0.1) ferrite nanoparticles have been synthesized at room temperature, without calcination, using a reverse micelle process. The site preference was determined by Mössbauer spectroscopy at 300 K. The hyperfine parameters were obtained, for the whole series of solid solutions. For the X≤0.20 samples, the spectra were fitted with two discrete sextets and for the X>0.20 samples, a magnetic hyperfine field distribution and a doublet were also imposed in the fit procedure. Hysteresis loops were measured using a superconducting quantum interference device magnetometer at 2 K and 300 K. The results indicate that the relative decrease in saturation magnetization of nanoparticles compared to the submicron particles could be attributed to a surface spin termination and disorder. Magnetic dynamics of the nanoparticles was studied by the measurement of ac magnetic susceptibility versus temperature at different frequencies and it is found that the results are well described by the Vogel–Fulcher model.     

Quantum interference induced by initial system–environment correlations

We investigate the quantum interference induced by a relative phase in the correlated initial state of a system which consists in a two-level atom interacting with a damped mode of the radiation field. We show that the initial relative phase has significant effects on both the evolution of the atomic excited-state population and the information flow between the atom and the reservoir, as quantified by the trace distance. Furthermore, by considering two two-level atoms interacting with a common damped mode of the radiation field, we highlight how initial relative phases can affect the subsequent entanglement dynamics.     

Simultaneous near field imaging of electric and magnetic field in photonic crystal nanocavities

The insertion of a metal-coated tip on the surface of a photonic crystal microcavity is used for simultaneous near field imaging of electric and magnetic fields in photonic crystal nanocavities, via the radiative emission of embedded semiconductor quantum dots (QD). The photoluminescence intensity map directly gives the electric field distribution, to which the electric dipole of the QD is coupled. The magnetic field generates, via Faraday's law, a circular current in the apex of the metallized probe that can be schematized as a ring. The resulting magnetic perturbation of the photonic modes induces a blue shift, which can be used to map the magnetic field, within a single near-field scan.