Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model

For estimating the parameters of models for financial market data, the use of robust techniques is of particular interest. Conditional forecasts, based on the capital asset pricing model, and a factor model are considered. It is proposed to consider least median of squares estimators as one possible alternative to ordinary least squares. Given the complexity of the objective function for the least median of squares estimator, the estimates are obtained by means of optimization heuristics. The performance of two heuristics is compared, namely differential evolution and threshold accepting. It is shown that these methods are well suited to obtain least median of squares estimators for real world problems. Furthermore, it is analyzed to what extent parameter estimates and conditional forecasts differ between the two estimators. The empirical analysis considers daily and monthly data on some stocks from the Dow Jones Industrial Average Index.     

Self-trapping of interacting electrons in crystalline nonlinear chains

Considering the nonlinearity arising from the interaction between electrons and latticevibrations, an effective electronic model with a self-interaction cubic term is employedto study the interplay between electron-electron and electron-phonon interactions. Basedon numerical solutions of the time-dependent nonlinear Schroedinger equation for aninitially localized two-electron singlet state, we show that the magnitude of theelectron-phonon coupling χ necessary to promote the self-trapping of theelectronic wave packet decreases as a function of the electron-electron interactionU. We show that such dependence is directly linked to the narrowing ofthe band of bounded two-electron states as U increases. We obtain thetransition line in the χ × U parameter space separatingthe phases of self-trapped and delocalized electronic wave packets. The present resultsindicates that nonlinear contributions plays a relevant role in the electronic wave packetdynamics, particularly in the regime of strongly correlated electrons.     

Suppressed transmission in aperiodically modulated multilayered dielectric structures

We investigate the transmission of electromagnetic plane waves through 1D binary dielectric multilayered structures that exhibit aperiodic incommensurated sequences of refractive indices. The aperiodicity is introduced by considering the sequence of refractive indices to follow a sinusoidal function whose phase varies as a power-law of the layer index, ∝i^ν. For ν>1, the resulting sequence is effectively uncorrelated leading to the Anderson localization of most of the electromagnetic modes, except at the Bragg resonances. The crossover from a uniform structure at ν=0 to a quasi-periodic structure at ν=1 is signaled by a minimum at the spectrally averaged transmission. We perform a spectral analysis of the refractive index sequence to show its close connection to the main features exhibited by the averaged optical transmittance. Our results suggest that aperiodically modulated dielectric structures can potentially be used in the development of wide-band filters.     

Neubegründung der reinen Infinitesimalgeometrie

Ohne Zusammenfassung     

Study of the Performance of an All-Optical Half-Adder Based on Three-Core Non-Linear Directional Fiber Coupler Under Delayed and Instantaneous Non-Linear Kerr Responses

Abstract

Recently, much attention has been given to the influence of the relaxation process of the non-linear response, because the usual assumption of instantaneous non-linear response fails for ultra-short pulses, and additional contributions coming from non-linear dispersion and delayed non-linearity have to be taken into account. This article presents a numerical analysis of the symmetric planar and asymmetric planar three-core non-linear directional fiber couplers operating with a soliton pulse, where effects of both delayed and instantaneous non-linear Kerr responses are analyzed for implementation of an all-optical half-adder. To implement this all-optical half-adder, eight configurations were analyzed for the non-linear directional fiber coupler, with two symmetric and six asymmetric configurations. The half-adder is the key building block for many digital processing functions, such as shift register, binary counter, and serial parallel data converters. The optical coupler is an important component for applications in optical-fiber telecommunication systems and all integrated optical circuit because of its very high switching speeds. In this numerical simulation, the symmetric/asymmetric planar presents a structure with three cores in a parallel equidistant arrangement, three logical inputs, and two output energy. To prove the effectiveness of the theoretical model for generation of the all-optical half-adder, the best phase to be applied to the control pulse was sought, and a study was done of the extinction ratio level as a function of the Δ > parameter, the normalized time duration, and the Sum and Carry outputs of the (symmetric planar/asymmetric planar) non-linear directional fiber coupler. In this article, the interest is in transmission characteristics, extinction ratio level, normalized time duration, and pulse evolution along the non-linear directional fiber coupler. To compare the performance of the all-optical half-adders, the figure of merit of the logic gates was used. All results were obtained numerically, considering a simple model for generation of an all-optical half-adder.     

Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential

We study the dynamics of an electron wave-packet in a two-dimensional square lattice with an aperiodic site potential in the presence of an external uniform electric field. The aperiodicity is described by at lattice sites (mx,my), with πα being a rational number, and νx and νy tunable parameters, controlling the aperiodicity. Using an exact diagonalization procedure and a finite-size scaling analysis, we show that in the weakly aperiodic regime (νx,νy<1), a phase of extended states emerges in the center of the band at zero field giving support to a macroscopic conductivity in the thermodynamic limit. Turning on the field gives rise to Bloch oscillations of the electron wave-packet. The spectral density of these oscillations may display a double peak structure signaling the spatial anisotropy of the potential landscape. The frequency of the oscillations can be understood using a semi-classical approach.     

Determination of Na, K, Ca and Mg in biodiesel samples by flame atomic absorption spectrometry (F AAS) using microemulsion as sample preparation

This study proposes a procedure for determining sodium, potassium, calcium and magnesium in biodiesel samples by flame atomic absorption spectrometry (F AAS). The sample was prepared as a microemulsion without surfactant. The optimized composition of the microemulsion was 10% (w/v) biodiesel, 75% (v/v) n-propanol, 1% (v/v) concentrated nitric acid and 14% (v/v) of aqueous solution formed by 0.2% (v/v) of nitric acid and 0.5% (v/v) of ionization suppressor. Analyte signals in the samples as microemulsion were found to be stable for a period of 15 days. Analytical curves were obtained using organometallic standard solutions. The limits of detection (LOD) found for the proposed procedure were 0.1 µg g^− 1, 0.01 µg g^− 1, 0.04 µg g^− 1, and 0.004 µg g^− 1 for Na, K, Ca and Mg, respectively. The reference method established by ABNT (Brazilian Association of Technical Norms) NBR 15556:2008 was used to verify the accuracy of the proposed procedure. No significant statistical difference was found between the results obtained with the proposed and the chosen reference procedure. The proposed procedure showed no matrix influence when recovery tests were performed (89%-103%). The results found in this study show that the proposed procedure is a good alternative for determining Na, K, Ca, and Mg by F AAS in biodiesel samples.