ОТСУТСТВИЕ УЗКИХ ГОРЛОВИН В АРХИТЕКТУРЕ НЕЙРОННОЙ СЕТИ ОПРЕДЕЛЯЕТ ЕЕ СВОЙСТВА КАК ФУНКЦИИ ОБЩЕГО ПОЛОЖЕНИЯ
It is proved that an artificial neural network with smooth activation functions and without bottlenecks
is a Morse function for almost all, with respect to the Lebesgue measure, sets of weights.
We consider the space $X_h$ of Hermitian matrices having staircase form and the given simple spectrum. There is a natural action of a compact torus on this space. Using generalized Toda flow, we show that $X_h$ is a smooth manifold and its smooth type is independent of the spectrum. Morse theory is then used to show the vanishing of odd degree cohomology, so that $X_h$ is an equivariantly formal manifold. The equivariant and ordinary cohomology rings of $X_h$ are described using GKM-theory. The main goal of this paper is to show the connection between the manifolds $X_h$ and regular semisimple Hessenberg varieties well known in algebraic geometry. Both spaces $X_h$ and Hessenberg varieties form wonderful families of submanifolds in the complete flag variety. There is a certain symmetry between these families which can be generalized to other submanifolds of the flag variety.
The article is based on the annual Perm All-Russian scientific and practical conference "Artificial intelligence in solving urgent social and economic problems of the XXI century" (http://www.permai.ru/files/26.05.2018.pdf). It is also a brief overview of the results of the Perm branch of the Scientific Council of the Russian Academy of Sciences on the methodology of artificial intelli- gence, as well as several departments of the Perm state University, Perm state humanitarian pedagogi- cal University, National research University Higher school of Economics, Perm state medical University. The review covers the works that develop and apply the methods of artificial intelligence in the classical sense, i.e., those methods that simulate human intellectual activity by simulating natural mechanisms.
These are expert systems, genetic algorithms, neural networks, fuzzy mathematics. The scientific priori- ty of Perm scientists in the development of theoretical foundations and practical applications of artificial intelligence is emphasized.
Keywords: Artificial intelligence, neural network, expert system, genetic algorithm, theory, prac- tice, modeling, forecasting, optimization, recognition, data processing, knowledge extraction.
In today’s era, most of the people are suffering with chronic diseases because of their lifestyle, food habits and reduction in physical activities. Diabetes is one of the most common chronic diseases which has affected to the people of all ages. Diabetes complication arises in human body due to increase of blood glucose (sugar) level than the normal level. Type-2 diabetes is considered as one of the most prevalent endocrine disorders. In this circumstance, we have tried to apply Machine learning algorithm to create the statistical prediction based model that people having diabetes can be aware of their prevalence. The aim of this paper is to detect the prevalence of diabetes relevant complications among patients with Type-2 diabetes mellitus. The processing and statistical analysis we used are Scikit-Learn, and Pandas for Python. We also have used unsupervised Machine Learning approaches known as Artificial Neural Network (ANN) and K-means Clustering for developing classification system based prediction model to judge Type-2 diabetes mellitus chronic diseases.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.