Superconducting Quantum Interference in Fractal Percolation Films. Problem of 1/f Noise

An oscillatory magnetic field dependence of the DC voltage is observed when a low-frequency current flows through superconducting Sn-Ge thin-film composites near the percolation threshold. The paper also studies the experimental realisations of temporal voltage fluctuations in these films. Both the structure of the voltage oscillations against the magnetic field and the time series of the electric "noise" possess a fractal pattern. With the help of the fractal analysis procedure, the fluctuations observed have been shown to be neither a noise with a large number of degrees of freedom, nor the realisations of a well defined dynamic system. On the contrary the model of voltage oscillations induced by the weak fluctuations of a magnetic field of arbitrary nature gives the most appropriate description of the phenomenon observed. The imaging function of such a transformation possesses a fractal nature, thus leading to power-law spectra of voltage fluctuations even for the simplest types of magnetic fluctuations including the monochromatic ones. Thus, the paper suggests a new universal mechanism of a "1/f noise" origin. It consists in a passive transformation of any natural fluctuations with a fractal-type transformation function.Comment: 17 pages, 13 eps-figures, Latex; title page and figures include

Пределы и риски цифровой трансформации

Currently, the process of digital transformation is actively going on in the economy, science, education, and society as a whole. This process has a number of restrictions and risks we consider. The mathematical theory of complexity reveals a large class of the restrictions. The exact solution of a number of simple-looking problems with a small amount of input data requires resources many times greater than the capabilities of all available computers.On the "border" between natural and artificial intelligence lies the "cognitive barrier". This, as a rule, makes it impossible to use the results of a number of artificial intelligence systems to adjust our strategies. We and computers "think" differently. They have to be considered as "black boxes". It is very likely that the tester of artificial intelligence systems will become one of the mass professions in the close future.We give examples to show that the "translation" from "continuous" to "discrete" language can lead to qualitatively different behavior of mathematical models. In a number of problems associated with a computational experiment this can be quite significant.Great risks arise when passing to the "fast world", approaching the "Lem's barrier". It happens when artificial intelligence systems are assigned strategically important tasks that they must solve at a speed inaccessible to humans.The analysis shows that managing the risks of digital transformation and its limitations requires the attention of the scientific and expert community, as well as active participants in this process.В настоящее время процесс цифровой трансформации активно идет в экономике, науке, образовании и в обществе в целом. С ним связан ряд ограничений и рисков, рассматриваемых в статье. Большой класс ограничений позволяет выявить математическая теория сложности. Точное решение ряда простых по виду проблем с небольшим объемом входных данных требует ресурсов, многократно превышающих возможности всех доступных компьютеров.На «границе» между естественным и искусственным интеллектом имеет место «когнитивный барьер». Это приводит к тому, что мы, как правило, не можем воспользоваться результатами работы ряда систем с искусственным интеллектом, чтобы скорректировать свои стратегии. Мы и машины «думаем» по-разному. Их приходится рассматривать как «черные ящики». Весьма вероятно, что тестер систем искусственного интеллекта станет одной из массовых профессий уже в недалеком будущем.Приведены примеры, показывающие, что «перевод» с «непрерывного» на «дискретный» язык может приводить к качественно различному поведению математических моделей. В ряде задач, связанных с вычислительным экспериментом, это может быть весьма существенно.Большие риски возникают при переходе в «быстрый мир», при приближении к «барьеру Лема». Это происходит, когда системам искусственного интеллекта препоручаются стратегически важные задачи, которые они должны решать в темпе, недоступном для человека.Проведенный анализ показывает, что управление рисками цифровой трансформации и её ограничений требует внимания научного и экспертного сообщества, а также активных участников этого процесса

Structures and waves in a nonlinear heat-conducting medium

The paper is an overview of the main contributions of a Bulgarian team of researchers to the problem of finding the possible structures and waves in the open nonlinear heat conducting medium, described by a reaction-diffusion equation. Being posed and actively worked out by the Russian school of A. A. Samarskii and S.P. Kurdyumov since the seventies of the last century, this problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer Proceedings in Mathematics and Statistics, Numerical Methods for PDEs: Theory, Algorithms and their Application

Limits and Risks of Digital Transformation

Currently, the process of digital transformation is actively going on in the economy, science, education, and society as a whole. This process has a number of restrictions and risks we consider. The mathematical theory of complexity reveals a large class of the restrictions. The exact solution of a number of simple-looking problems with a small amount of input data requires resources many times greater than the capabilities of all available computers.On the "border" between natural and artificial intelligence lies the "cognitive barrier". This, as a rule, makes it impossible to use the results of a number of artificial intelligence systems to adjust our strategies. We and computers "think" differently. They have to be considered as "black boxes". It is very likely that the tester of artificial intelligence systems will become one of the mass professions in the close future.We give examples to show that the "translation" from "continuous" to "discrete" language can lead to qualitatively different behavior of mathematical models. In a number of problems associated with a computational experiment this can be quite significant.Great risks arise when passing to the "fast world", approaching the "Lem's barrier". It happens when artificial intelligence systems are assigned strategically important tasks that they must solve at a speed inaccessible to humans.The analysis shows that managing the risks of digital transformation and its limitations requires the attention of the scientific and expert community, as well as active participants in this process