On the number of two-dimensional threshold functions

A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such functions only asymptotic bounds are known. We give an exact formula for the number of two-dimensional threshold functions and derive more accurate asymptotics.Comment: 17 pages, 2 figure

Oxygen non-stoichiometry and defect structure of LaMn1-zCuzO3+δ

The quantitative model analysis of the defect structure of copper doped lanthanum manganites LaMn1-zCuzO3+δ (z = 0.05 and 0.1) was performed. In the framework of the model, the independent course of the three reactions of defect formation, including the electronic exchange between manganese and copper, completion of a lattice by the absorption of oxygen and the disproportionation of manganese was considered. It is shown that the increase in the dopant content leads to a change in the dominant electronic process. This is reflected in the lock and disproportionation and leads to the increase in the concentration of holes and decrease the concentration of electrons localized on the manganese atoms

The influrence of an optical receiving system on statistical characteristics of a lidar signal

The effects connected with correlation of direct and backward waves propagating through the same randomly inhomogeneous media can be observed along the path with refection in a turbulent atmosphere. In particular, the mean intensity of the reflected wave can increase in comparison with the wave propagating in the forward direction at a doubled distance; the intensity fluctuations can become stronger. These effects depend on the strength of optical turbulence, as well as on the diffraction sizes of the exit apertures of the source and the reflector. However, the focusing of radiation reflected with a receiving telescope leads, in some cases, to the fact that the dependence of amplification effects on the parameters becomes essentially different. This should be taken into account when alayzing the lidar signals. The effect of backscattering amplification and amplification of the intensity fluctuations is discussed

Gaussian process hyper-parameter estimation using parallel asymptotically independent Markov sampling

Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator. Due to computational cost, such training set is bound to be limited and quantifying the resulting uncertainty in the hyper-parameters of the emulator by uni-modal distributions is likely to induce bias. In order to quantify this uncertainty, this paper proposes a computationally efficient sampler based on an extension of Asymptotically Independent Markov Sampling, a recently developed algorithm for Bayesian inference. Structural uncertainty of the emulator is obtained as a by-product of the Bayesian treatment of the hyper-parameters. Additionally, the user can choose to perform stochastic optimisation to sample from a neighbourhood of the Maximum a Posteriori estimate, even in the presence of multimodality. Model uncertainty is also acknowledged through numerical stabilisation measures by including a nugget term in the formulation of the probability model. The efficiency of the proposed sampler is illustrated in examples where multi-modal distributions are encountered. For the purpose of reproducibility, further development, and use in other applications the code used to generate the examples is freely available for download at https://github.com/agarbuno/paims_codesComment: Computational Statistics \& Data Analysis, Volume 103, November 201

A combined Raman lidar for low tropospheric studies

One of the main goals of laser sensing of the atmosphere was the development of techniques and facilities for remote determination of atmospheric meteorological and optical parameters. Of lidar techniques known at present the Raman-lidar technique occupies a specific place. On the one hand Raman lidar returns due to scattering on different molecular species are very simple for interpretation and for extracting the information on the atmospheric parameters sought, but, on the other hand, the performance of these techniques in a lidar facility is overburdened with some serious technical difficulties due to extremely low cross sections of Raman effect. Some results of investigations into this problem is presented which enables the construction of a combined Raman lidar capable of acquiring simultaneously the profiles of atmospheric temperature, humidity, and some optical characteristics in the ground atmospheric layer up to 1 km height. The operation of this system is briefly discussed

Optical models of the molecular atmosphere

The use of optical and laser methods for performing atmospheric investigations has stimulated the development of the optical models of the atmosphere. The principles of constructing the optical models of molecular atmosphere for radiation with different spectral composition (wideband, narrowband, and monochromatic) are considered in the case of linear and nonlinear absorptions. The example of the development of a system which provides for the modeling of the processes of optical-wave energy transfer in the atmosphere is presented. Its physical foundations, structure, programming software, and functioning were considered

The influence of scattering particles morphology on the characteristics of lidar signals

The characteristics of light scattering by a separate spherical particle are used as a priori information when interpreting the data on laser sounding of atmospheric aerosols. Analogously, it is necessary to have a priori information on the characteristics of light scattering by a single crystals in order to restitute the microstructure of crystal formation in the atmosphere. In contrast to the aerosol particles the crystals are of different shapes. On the one hand, this complicates the solution of electrodynamic problems on light scattering by such crystals. On the other hand, if obtaining such a solution is possible, one can determine the morphology of scattering particles accoring to the sounding data and this enables additonal information to be obtained on such meteorological parameters as temperature, pressure, and humidity. Using the geometric-wave approach the problem of scattering of plane electromagnetic wave on convex polyhedrons of arbitrary form was solved. As a result, the expressions were obtained for electric field components of perpendicular and parallel polarizations scattered in any given direction