Vol 30, No 3 (2019)

A ridge detection algorithm is proposed for tracing blood vessels on images of the ocular fundus. Multiscale non-maximum suppression is applied to the image Laplacian. The multiscale algorithm exploits the pyramidal fine structure similarly to the SIFT method. Anisotropic diffusion is used in preprocessing, which makes it possible to boost the value of the convolution of the Laplacian with the Gaussian on ridge structures. The proposed algorithm has been tested on the ophthalmological image database DRIVE. The proposed preprocessing has substantially improved the ridge detection quality.

Many constructions of cubic splines are described in the literature. Most of the methods focus on cubic splines of defect 1, i.e., cubic splines that are continuous together with their first and second derivative. However, many applications do not require continuity of the second derivative. The Hermitian cubic spline is used for such problems. For the construction of a Hermitian spline we have to assume that both the values of the interpolant function and the values of its derivative on the grid are known. The derivative values are not always observable in practice, and they are accordingly replaced with difference derivatives, and so on. In the present article, we construct a C¹ cubic spline so that its derivative has a minimum norm in L₂ . The evaluation of the first derivative on a grid thus reduces to the minimization of the first-derivative norm over the sought values.

We consider a model of nonlinear interaction of femtosecond pulses with a Kerr nonlinear medium, allowing for first and second order dispersion, nonlinear response dispersion, and mixed time and space derivatives. The invariants are constructed by a transformation of the generalized nonlinear Schrodinger equation that involves changing to new functions and reduces the original equation to a form without the nonlinear response derivatives and the mixed derivatives. Appropriate conservation laws are established for the transformed equation. The invariants derived in this article lead to conservative difference schemes and allow control of computer simulation results.

In this study, turbulence of the flow field as well as the flow free surface in a U-shaped channel located along a side weir under supercritical flow conditions are simulated using the RNG k-ε turbulence model and VOF scheme. Comparison of the numerical and laboratory results shows that the numerical model simulates the free surface and characteristics of the flow field with acceptable accuracy. Then, the effects of the upstream Froude number of the side weir on the flow pattern of the main channel are investigated. For all Froude numbers, in the vicinity of the inner bank a free surface drop occurs at the beginning of the side weir upstream, and a surface jump is formed at the final quarter of the side weir length. Across the surface jump, the kinematic energy of water increases and the potential energy decreases. The dividing stream surface and the stagnation zone dimensions increase as the Froude number increases.

We consider the sale of k securities in n trades, with not more than one security per trade. The sale results are assessed using the competitive ratio of the sum of k highest security prices to the total sale revenue. Lorenz constructed the solution of the game for 2k ≤ n. In this article, the solution is obtained in the general case both for the competitive ratio and for the Savage regret criterion.

Methods for the separation of a mixture of three-parameter lognormal distributions are investigated theoretically and empirically in the context of modeling message transmission delays in a computer cluster communication environment. Delay modeling based on mixtures of three-parameter lognormal distributions is proposed and parameter estimation methods for such models are investigated. Identifiability of the given family of distributions is proved, which is a necessary condition for the mixture separation problem to be well-posed. The proposed problem-oriented modifications of the standard algorithms are shown to be superior to the traditional methods.

We examine a new method for the calculation of the traveling wave characteristic in a layered medium. The seismic impedance tensor method is improved by introducing the notion of a potential function and new iterative relationships are obtained for isotropic layered media. Comparison of the dispersion equation roots between the generalized reflection-transmission coefficient method (GR/TC) and the seismic impedance tensor method (SIT) has detected some roots that do not exist in SIT. To check the accuracy of the roots in both methods, we have compared the experimental results between the classical transition matrix method (Thomson-Haskell) and our new method (SIT) for the same layered medium model. The experimental results show that the roots obtained by the impedance method coincide with the classical transition matrix method. This also shows that some roots obtained from the dispersion equation in GR/TC cannot be accurately determined.

The article constructs simultaneous (simultaneous) confidence intervals for the mean of repeated observations in a multiple linear normal regression. A numerical method is described and applied for the adjustment of point confidence intervals of the mean of repeated observations. A more accurate result is obtained by a numerical method that computes the critical value that determines the simultaneous confidence interval of a given level. We conduct numerical simulation and carry out a comparative analysis of the simultaneous confidence interval with the point confidence interval for the mean of repeated observations and for an individual observation.