De Bruijn Structured Illumination Studying Within The Task Of Restoring Hands Relief

In the course of studies on the problem of restoring hands relief, using the de Bruijn structured illumination, methods of solving this problem are proposed. This is a method of simple quantitative detection of Hough segments on the skin of the hand, a method of qualitative visual evaluation of the effectiveness of the color palette using the dominant color, and a method of the weight coefficients of the components of the color palette.The proposed methods make it possible to quantitatively determine the optimal choice of the color scheme for generating the de Bruijn bands when illumination of the hand, to restore its relief.The work describes the stages of this study, led from visual observation to a full quantitative calculation of the quality of calibration illuminations, with the possibility of their optimal choice.In the course of experiments and observations, the requirements for the technical support of research were developed to achieve the best quality of the images of the hands. Also, the paper presents a high-speed de Bruijn sequence generating algorithm using Lyndon's words, which excludes the search for Euler chains or Hamiltonian cycles, for various kinds of de Bruijn graphs. With its help, the generation of structured light patterns with various color schemes was carried out, with the purpose of further analysis of their use in 3D reconstruction systems of hands

Reentrant stability of BEC standing wave patterns

We describe standing wave patterns induced by an attractive finite-ranged external potential inside a large Bose-Einstein Condensate (BEC). As the potential depth increases, the time independent Gross-Pitaevskii equation develops pairs of solutions that have nodes in their wavefunction. We elucidate the nature of these states and study their dynamical stability. Although we study the problem in a two-dimensional BEC subject to a cylindrically symmetric square-well potential of a radius that is comparable to the coherence length of the BEC, our analysis reveals general trends, valid in two and three dimensions, independent of the symmetry of the localized potential well, and suggestive of the behavior in general, short- and large-range potentials. One set of nodal BEC wavefunctions resembles the single particle n node bound state wavefunction of the potential well, the other wavefunctions resemble the n-1 node bound-state wavefunction with a kink state pinned by the potential. The second state, though corresponding to the lower free energy value of the pair of n node BEC states, is always unstable, whereas the first can be dynamically stable in intervals of the potential well depth, implying that the standing wave BEC can evolve from a dynamically unstable to stable, and back to unstable status as the potential well is adiabatically deepened, a phenomenon that we refer to as "reentrant dynamical stability".Comment: 13 pages, 9 figures; revised discussion in Sec.

Influence of Coulomb interaction on the Aharonov-Bohm effect in an electronic Fabry-Perot interferometer

We study the role of Coulomb interaction in an electronic Fabry-Perot interferometer (FPI) realized with chiral edge states in the integer quantum Hall regime in the limit of weak backscattering. Assuming that a compressible Coulomb island in a bulk region of the FPI is formed, we develop a capacitance model which explains the plethora of experimental data on the flux and gate periodicity of conductance oscillations. It is also shown that a suppression of finite-bias visibility stems from a combination of weak Coulomb blockade and a nonequilibrium dephasing by the quantum shot noise

Online Learning of Power Transmission Dynamics

We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of convex estimators that adapt to the structure of the problem depending on the available prior information. The proposed method is fully data-driven and does not assume any knowledge of system parameters. It can be implemented in near real-time and requires a small amount of data. Our learning algorithms can be used for model validation and calibration, and can also be applied to related problems of system stability, detection of forced oscillations, generation re-dispatch, as well as to the estimation of the system state.Comment: 7 pages, 4 figure

Nonlinear stationary states in PT-symmetric lattices

In the present work we examine both the linear and nonlinear properties of two related PT-symmetric systems of the discrete nonlinear Schrodinger (dNLS) type. First, we examine the parameter range for which the finite PT-dNLS chains have real eigenvalues and PT-symmetric linear eigenstates. We develop a systematic way of analyzing the nonlinear stationary states with the implicit function theorem at an analogue of the anti-continuum limit for the dNLS equation. Secondly, we consider the case when a finite PT-dNLS chain is embedded as a defect in the infinite dNLS lattice. We show that the stability intervals of the infinite PT-dNLS lattice are wider than in the case of a finite PT-dNLS chain. We also prove existence of localized stationary states (discrete solitons) in the analogue of the anti-continuum limit for the dNLS equation. Numerical computations illustrate the existence of nonlinear stationary states, as well as the stability and saddle-center bifurcations of discrete solitons.Comment: 28 page