Vol 26, No 10 (2020)

This paper presents the ways to identify systems described by models with errors in recording of input and output variables. It is considered that in the absence of information on the error parameters in the case of their large values, it is impossible to obtain acceptable estimates of all the required parameters of the model without additional, in comparison with the regression analysis, assumptions. The determination of the regression parameters in the presence of errors in the input and output variables is important for solving many tasks related to data processing. In all existing approaches, either the assumptions regarding the noise in the form of e.g. given relations between the noises dispersions are made, or the method of successive approximations is applied. To determine the parameters of the linear function, it is proposed to use the condition of the symmetry of the joint probability density of the observed input and output variables in the oblique coordinates. For the case of normality of the noise, the article gives a formula for determining the parameter of the relationship via the estimates of the fourth-order semi-invariants.

Modular representations of numerical quantities in the form of residue vectors by prime modules from a finite set can be considered as a set of modular vectors. The set of modular vectors is considered as a linear subspace in a vector space containing vectors with components of limited size; its ring structure is not taken into account. The properties of a linear modular subspace, methods for determining new scalar products are analyzed, which allows us to introduce new metrics. The introduced algebraic constructions are designed to analyze the convergence of multi-bit parallel computing processes in large computer ranges that operate with numerical values in the modular representation. The introduced numerical vector representations are oriented for application in modular reconfigurable computing systems of SIMD architecture.

There is considered the problem of increasing the performance of the public kley-agreement schemes based on the computational complexity of the hidden discrete logarithm problem defined in finite non-commutative associative algebras of various types. To increase the rate of cryptoschemes of the said type, it is proposed to use algebras as their algebraic support, in which the associative multiplication operation is specified using sparse multiplication tables of basis vectors. In framework of this method the rate increase is achieved by a significant reduction in the number of multiplications in the finite field, over which the algebra is specified, which are necessary to perform one multiplication operation in the algebra. The principal realizability of this method has been demonstrated for cases of four-dimensional and six-dimensional algebras, for which the sparse tables are given that specify the associative multiplication operation and providing two-times reduction of the number of multiplications in the field. Another proposed way to increase the rate is to specify the procedure for generating permutable key elements in the form of a computational procedure performed according to specially derived mathematical formulas, free from the operation of exponentiation to a large-size integer power. The second method is based on the idea of defining a set of mutually permutable vectors of a finite non-commutative associative algebra, described by a fairly compact mathematical formula. Moreover, the latter defines a procedure for calculating a random vector from the indicated set of vectors, which has significantly lower computational complexity compared to the exponentiation operation used in well-known cryptoschemes of the considered type to generate random pairs of permutable vectors. The potential feasibility of the second method is demonstrated by the derivation of the indicated formula for a four-dimensional algebra given by sparse multiplication tables of basis vectors. Specific public key-agreement cryptoschemes have been developed that implement the developed methods for increasing performance, which are of interest for practical use as post-quantum public key-agreement schemes. To further increase the performance of cryptoschemes of the considered type, it is proposed to use the algebras set over finite extensions of a binary field.

In this paper we consider the task of user preferences analysis for recommender engines based on a gallery of his or her mobile device. In particular, we propose the novel three-phase method for simultaneous image-based detection and recognition of particular objects. Conventional object detection techniques cannot be applied if there are many categories of the same object (pet breeds, car models, etc.) and there is a lack of large dataset with known bounding boxes for each object category. In order to deal with this issue, we estimate the borders of base objects (dogs, cats, cars, etc.) by using such existing neural network architectures as high precision Faster R-CNN or fast single-shot detectors. Secondly, the visual features (embeddings) of each object are extracted by using a multi-task convolutional neural network model with several outputs — one for each type of object. Finally, these embeddings are used to predict the concrete categories and group different photos of the same object by using cluster analysis techniques. The proposed approach is implemented in a special mobile application for Android. Experimental results for recognizing dog and cat breeds are presented. It is demonstrated that our method makes it possible to improve the accuracy of dog detection and recognition when compared to the known single-task neural nets. Moreover, we gather a special dataset of real photos with pets to estimate the clustering quality. It is shown that the L1-normed features extracted by our multi-task model may be grouped rather accurately if hierarchical agglomerative clustering or HDBSCAN method are used.

Results of the software tool which implements the Digital Twin concept for the PV module are presented. The possibility of transition from the time series of the measured PV module parameters to the vector of internal electrical parameters obtained by creating its digital twin is demonstrated. The possibility of fault detection automation for PV modules is presented. The influence and interconnection of PV module fault types on the digital twin accuracy are analyzed.