№ 1 (2024)

The article explores an approach to constructing a fuzzy measure on p-adic balls that does not require the direct specification of the measure density. The relationships necessary for determining this measure for an arbitrary subset of a bounded numerical set, represented as a set of p-adic balls, are proven. Uniform and non-uniform fuzzy measures are considered. An algorithm for determining the fuzzy measure on p-adic balls is proposed. Examples of calculating this measure are provided.

Modern graphics accelerators (GPUs) can signi cantly speed up the execution of numerical tasks. However, porting programs to graphics accelerators is not an easy task, sometimes requiring their almost complete rewriting. CUDA graphics accelerators, thanks to technology developed by NVIDIA, allow you to have a single source code for both conventional processors (CPUs) and CUDA. However, in this single source code, you need to somehow tell the compiler which parts of this code to parallelize on shared memory. The use of the functional programming library developed by the authors allows you to hide the use of one or another parallelization mechanism on shared memory within the library and make the user source code completely independent of the computing device used (CPU or CUDA). This article shows how this can be done. 

Wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zhegalkin operators with multipliers of three variables is presented. The algorithm is implemented in Python.

The paper presents an algorithm and a description of its software implementation for detecting lineaments (ground erosions or cracks) in aerial photography images of open-pits. The proposed approach is based on the apparatus of convolutional neural networks based on the semantic classification of binarized images of objects (lineaments), as well as graph theory for determining the geometric location of linearized objects, followed by determining their lengths and areas. Three-channel RGB images of high-resolution aerial photography (pixel 10x10 cm) were used as initial data. The software unit of the model is logically divided into three layers: pre-processing, detection and post-processing. The first level includes preprocessing of input data to form a training sample based on successive transformations of an RGB image into a binary one using the OpenCV library. A neural network of the U-Net type, which includes blocks of the convolutional (Encoder) and scanning parts (Decoder), represents the second level of the information model. At this level, automatic lineament detection (washouts) is implemented. The third level of the model is responsible for calculating the areas and lengths of lineaments. The result of the work of the convolutional neural network is transferred to the input. Lineament area is calculated by summing the total number of points multiplied by the pixel size. The length of the lineaments is computed by linearizing a plane object into a line segmental object with nodal points and then calculating the lengths between them, also relying on the resolution of the original image. The software module can work with input images, with their subsequent resulting merging to the size of the original image.

The KIAM Astrodynamics Toolbox, a new software library for designing spacecraft orbital motion, is introduced. The toolbox is developed at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences using Fortran and Python languages, thus combining the computational speed and the flexibility of program design. The library can be useful for space flight mechanics specialists, as well as for students in relevant educational programs.

One of the basic aspects of information flow control in applications is security policy language. Such language should allow to define security policies for evaluation environment elements in coherence with higher level access control rules. So the language is expected to be flexible because there may be different access control paradigms implemented on the system level: mandatory, role-based etc. An application may also have its own specific restrictions. Finally it is also desirable that the language support declassification (controlled release of information) during the computation. One of such languages is Paralocks. The research is devoted to the logical semantics of modified version of Paralocks realized in TLA+. Paralocks represents a language basis for the perspective information flow control platform PLIF which is being developed for the analysis of PL/SQL program blocks with author’s participation. It includes the proofs of the partial order and lattice defined on the set of security policy expressions.

While modern rendering systems are effective at modeling complex light paths in complex environments, rendering refractive caustics still takes a long time. Caustics are light patterns that occur when light is refracted and reflected from a surface. Due to the sharp density distribution of these mirror events, rendering algorithms mainly rely on direct sampling of the bidirectional scattering distribution function on these surfaces to plot trajectories. This requires many calculations. Photonic maps are also used. However, there are problems limiting the applicability of caustic maps. Since each photon in the photon buffer must be processed, therefore, one has to choose between a strongly underestimated caustic sampling and a large decrease in speed in order to use a sufficient number of photons for caustics in order to obtain high-quality images. Complex mirror interactions cause oversampling in bright focal areas, while other areas of the caustic map remain under-selected and noisy. At the same time, speed takes precedence over realism in most interactive applications. However, the desire to improve the quality of graphics prompted the development of various fast approximations for realistic lighting.

This paper presents a combined method for visualizing refraction of light and caustics using reverse integration for illumination and direct integration for viewing rays. An approach is used for simultaneous propagation of light and for tracking rays in volume and, therefore, it does not require storing data of an intermediate volume of illumination. In the implementation of the method, the distance between the light planes is set to one voxel, which provides at least one sample per voxel for all orientations. The method does not use preliminary calculations; all rendering parameters can be changed interactively.

As a result, using the proposed method, it is possible to create plausible approximations of complex phenomena such as refractions and caustics. The effect of refraction on the shadow is shown. Complex light patterns are demonstrated due to the curved geometry of the objects. The visualization results show the importance of refraction for the appearance of transparent objects. For example, distortions caused by refraction and refraction at the interface between media. The difference in refractive indices between individual media causes a complex interaction between light and shadow areas. It is shown how refraction and caustics improve the visualization of functionally defined objects by providing additional information about shape and location.