Global Minimum Depth In Edwards-Anderson Model

In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit $N\to\infty$. We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.Comment: 10 pages, 4 figures, 2 tables, submitted to conference on Engineering Applications of Neural Networks (EANN 2019

Surface photometry of 50 dwarf galaxies in the Local Volume

Results of surface photometry of 50 galaxies in the Local Volume based on archived images obtained with the Hubble Space Telescope are presented. Integrated magnitudes in the V and I bands are introduced for the sample galaxies, along with brightness and color profiles. The obtained photometric parameters are compared with the measurements of other authors.Comment: 12 pages, 1 figure, 1 tabl

Generation of entangled coherent states via cross phase modulation in a double electromagnetically induced transparency regime

The generation of an entangled coherent state is one of the most important ingredients of quantum information processing using coherent states. Recently, numerous schemes to achieve this task have been proposed. In order to generate travelling-wave entangled coherent states, cross phase modulation, optimized by optical Kerr effect enhancement in a dense medium in an electromagnetically induced transparency (EIT) regime, seems to be very promising. In this scenario, we propose a fully quantized model of a double-EIT scheme recently proposed [D. Petrosyan and G. Kurizki, {\sl Phys. Rev. A} {\bf 65}, 33833 (2002)]: the quantization step is performed adopting a fully Hamiltonian approach. This allows us to write effective equations of motion for two interacting quantum fields of light that show how the dynamics of one field depends on the photon-number operator of the other. The preparation of a Schr\"odinger cat state, which is a superposition of two distinct coherent states, is briefly exposed. This is based on non-linear interaction via double-EIT of two light fields (initially prepared in coherent states) and on a detection step performed using a $50:50$ beam splitter and two photodetectors. In order to show the entanglement of a generated entangled coherent state, we suggest to measure the joint quadrature variance of the field. We show that the entangled coherent states satisfy the sufficient condition for entanglement based on quadrature variance measurement. We also show how robust our scheme is against a low detection efficiency of homodyne detectors.Comment: 15 pages, 9 figures; extensively revised version; added Section

NONPARAMETRIC METHOD OF RECONSTRUCTING PROBABILITY DENSITY ACCORDING TO THE OBSERVATIONS OF A RANDOM VARIABLE

When investigating the statistical characteristics of a field formed by locally inhomogeneous regions, the problem of reconstructing the probability density function with several vertices on the basis of the results of experimental observations arises. In this case, it is very difficult to apply parametric methods for reconstructing the probability density. Therefore, to restore the probability density, it makes sense to use non-parametric methods of recovery. The Rosenblatt-Parzen method usually used for these purposes has low accuracy and convergence rate. The method proposed in the work of Chentsov N.N. has higher accuracy and convergence rate. However, for multi-vertex distributions its convergence rate is also low. Similar conclusions can be drawn regarding the method proposed in the work of Vapnik V.N. Thus, the problem of developing a technique for reconstructing the multi-vertex probability density on the basis of the results of experimental observations becomes very urgent. The article suggests a nonparametric method of reconstructing probability density according to the observations of a random variable. The method is regular in the sense of Tikhonov regularization and, as the analysis and solution of test problems show, it has sufficiently high accuracy and convergence rate