The article is an overview. We carry out the comparison of actual machine learning libraries that can be used the neural networks development. The first part of the article gives a brief description of TensorFlow, PyTorch, Theano, Keras, SciKit Learn libraries, SciPy library stack. An overview of the scope of these libraries and the main technical characteristics, such as performance, supported programming languages, the current state of development is given. In the second part of the article, a comparison of five libraries is carried out on the example of a multilayer perceptron, which is applied to the problem of handwritten digits recognizing. This problem is well known and well suited for testing different types of neural networks. The study time is compared depending on the number of epochs and the accuracy of the classifier. The results of the comparison are presented in the form of graphs of training time and accuracy depending on the number of epochs and in tabular form.

When modeling such phenomena as population dynamics, controllable flows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we propose to derive new...

The problems of synthesis and analysis of multidimensional controlled models of population dynamics are of both theoretical and applied interest. The need to solve numerical optimization problems for such a class of models is associated with the expansion of ecosystem control requirements. The need to solve the problem of stochastization is associated with the emergence of new problems in the study of ecological systems properties under the influence of random factors. The aim of the work is to develop a new approach to studying the properties of population dynamics systems using methods of numerical optimization, stochastization and machine learning. The synthesis problems of nonlinear three-dimensional models of interconnected species number dynamics, taking into account trophic chains and competition in prey populations, are studied. Theorems on the asymptotic stability of equilibrium states are proved. A qualitative and numerical study of the models is carried out. Using computational experiments, the results of an analytical stability and permanent coexistence study are verified. The search for equilibrium states belonging to the stability and permanent coexistence region is made using the developed intelligent algorithm and evolutionary calculations. The transition is made from the model specified by the vector ordinary differential equation to the corresponding stochastic model. A comparative analysis of deterministic and stochastic models with competition and trophic chains is carried out. New effects are revealed that are characteristic of three-dimensional models, taking into account the competition in populations of prey. The formulation of the optimal control problem for a model with competition and trophic chains is proposed. To find optimal trajectories, new generalized algorithms for numerical optimization are developed. A methods for the synthesis of controllers based on the use of artificial neural networks and machine learning are developed. The results on the search for optimal trajectories and generation of control functions are presented.The obtained results can be used in modeling problems of ecological, demographic, socio-economic and chemical kinetics systems.

In this article, we compare the support for SIMD instructions for Julia and Fortran. The comparison is carried out according to the methodology described in work of T. Kalibera, R. E. Jones. The first part of the article gives a brief description of this technique. We emphasize on the practical implementation using Python, NumPy and SciPy. The second part of the article briefly discusses the syntactic capabilities of Fortran and Julia to work with SIMD processor extensions. Specific code snippets are given. Next, the performance of Julia and Fortran is compared for arithmetic operations on arrays of small length. The results are presented in tabular and graphical form.

The models of peer to peer protocols are presented with the help of one-step processes. On the basis of this presentation and the method of randomization of one-step processes, it is described method for constructing models of peer to peer protocols. The models of FastTrack and Bittorrent protocols are studied by means of proposed method.