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This paper formulates and solves a practical problem of data recovery regarding the distribution of languages on regional level in context of China. The necessity of this recovery is related to the problem of the determination of the linguistic diversity indices, which, in turn, are used to analyze empirically and to predict sources of social and economic development as well as to indicate potential conflicts at regional level. We use Ethnologue database and China census as the initial data sources. For every language spoken in China, the data contains (a) an estimate of China residents who claim this language to be their mother tongue, and (b) indicators of the presence of such residents in China provinces. For each pair language/province, we aim to estimate the number of the province inhabitants that claim the language to be their mother tongue. This base problem is reduced to solving an undetermined system of algebraic equations. Given additional restriction that Ethnologue database introduces data collected at different time moments because of gaps in Ethnologue language surveys and accompanying data collection expenses, we relate those data to a single time moment, that turns the initial task to an ’ill-posed’ system of algebraic equations with imprecisely determined right hand side. Therefore, we are looking for an approximate solution characterized by a minimal discrepancy of the system. Since some languages are much less distributed than the others, we minimize the weighted discrepancy, introducing weights that are inverse to the right hand side elements of the equations. This definition of discrepancy allows to recover the required variables. More than 92% of the recovered variables are robust to probabilistic modelling procedure for potential errors in initial data.

Analysis and practical aspects of implementing developed in the control theory robust control methods in studying economic systems is carried out. The main emphasis is placed on studying results obtained for dynamical systems with structured uncertainty. Practical aspects of implementing such results in control of economic systems on the basis of dynamical models with uncertain parameters and perturbations (stabilization of price on the oil market and inflation in macroeconomic systems) are discussed. With the help of specially constructed aggregate model of oil price dynamics studied the problem of finding control which provides minimal deviation of price from desired levels over middle range period. The second real problem considered in the article consists in determination of stabilizing control providing minimal deviation of inflation from desired levels (on the basis of constructed aggregate macroeconomic model of the USA over middle range period).

Upper levels of parameters uncertainty and control laws guaranteeing stabilizability of the real considered economic systems have been found using the robust method of control with structured uncertainty. At the same time we have come to the conclusion that received estimates of parameters uncertainty upper levels are conservative. Monte-Carlo experiments carried out for the article made it possible to analyze dynamics of oil price and inflation under received limit levels of models parameters uncertainty and under implementing found robust control laws for the worst and the best scenarios. Results of these experiments show that received robust control laws may be successfully used under less stringent uncertainty constraints than it is guaranteed by sufficient conditions of stabilization.

The aim of the paper is to obtain a numerical solution for linear and higher-order delay differential equations (DDEs) using the coded differential transform method (CDTM). The CDTM is developed and applied to delay problems to show the efficiency of the proposed method. The coded differential transform method is a combination of the differential transform method and Mathematica software. We construct recursive relations for a few delay problems, which results in simultaneous equations, and solve them to obtain various series solution terms using the coded differential transform method. The numerical solution obtained by CDTM is compared with an exact solution. Numerical results and error analysis are presented for delay differential equations to show that the proposed method is suitable for solving delay differential equations. It is established that the delay differential equations under discussion are solvable in a specific domain. The error between the CDTM solution and the exact solution becomes very small if more terms are included in the series solution. The coded differential transform method reduces complex calculations, avoids discretization, linearization, and saves calculation time. In addition, it is easy to implement and robust. Error analysis shows that CDTM is consistent and converges fast. We obtain more accurate results using the coded differential transform method as compared to other methods.

Industrial robots have made it possible for robotics to become a worldwide discipline both in economy and in science. However, their capabilities are limited, especially regarding contact tasks where it is required to regulate or at least limit contact forces. At one point, it was noticed that elasticity in the joint transmission, which was treated as a drawback previously, is actually helpful in this regard. This observation led to the introduction of elastic joint robots that are well-suited to contact tasks and cooperative behavior in particular, so they become more and more widespread nowadays. Many researchers try to implement such devices not with trivial series elastic actuators (SEA) but with more sophisticated variable stiffness actuators (VSA) that can regulate their own mechanical stiffness. All elastic actuators demonstrate shock robustness and safe interaction with external objects to some extent, but when stiffness may be varied, it provides additional benefits, e. g., in terms of energy efficiency and task adaptability. Here, we present a novel variable stiffness actuator with a magnetic coupler as an elastic element. Magnetic transmission is contactless and thus advantageous in terms of robustness to misalignment. In addition, the friction model of the transmission becomes less complex. It also has milder stiffness characteristic than typical mechanical nonlinear springs, moreover, the stiffness curve has a maximum after which it descends. Therefore, when this maximum torque is achieved, the coupler slips, and a new pair of poles defines the equilibrium position. As a result, the risk of damage is smaller for this design solution. The design of the joint is thoroughly described, along with its mathematical model. Finally, the control system is also proposed, and simulation tests confirm the design ideas.

In the paper three characteristic scales of a biological system are proposed: microscopic (gene's size), mesoscopic (cell’s size) and macroscopic level (organism’s size). For each case the approach to modeling of circadian rhythms is discussed on the base of a time-delay model. At gene’s scale the stochastic description has been used. The robustness of rhythms mechanism to the fluctuations has been demonstrated. At the mesoscopic scale we propose the deterministic description within the spatially extended model. It was found the effect of collective synchronization of rhythms in cells. Macroscopic effects have been studied within the discrete model describing the collective behaviour of large amount of cells. The problem of cross-linking of results obtained at different scales is discussed. The comparison with experimental data is given.

This work is devoted to the analysis of conformational changes in tubulin dimers and tetramers, in particular, the assessment of the bending of microtubule protofilaments. Three recently exploited approaches for estimating the bend of tubulin protofilaments are reviewed: (1) measurement of the angle between the vector passing through the H7 helices in $\alpha$ and $\beta$ tubulin monomers in the straight structure and the same vector in the curved structure of tubulin; (2) measurement of the angle between the vector, connecting the centers of mass of the subunit and the associated GTP nucleotide, and the vector, connecting the centers of mass of the same nucleotide and the adjacent tubulin subunit; (3) measurement of the three rotation angles of the bent tubulin subunit relative to the straight subunit. Quantitative estimates of the angles calculated at the intra- and inter-dimer interfaces of tubulin in published crystal structures, calculated in accordance with the three metrics, are presented. Intra-dimer angles of tubulin in one structure, measured by the method (3), as well as measurements by this method of the intra-dimer angles in different structures, were more similar, which indicates a lower sensitivity of the method to local changes in tubulin conformation and characterizes the method as more robust. Measuring the angle of curvature between H7-helices (method 1) produces somewhat underestimated values of the curvature per dimer. Method (2), while at first glance generating the bending angle values, consistent the with estimates of curved protofilaments from cryoelectron microscopy, significantly overestimates the angles in the straight structures. For the structures of tubulin tetramers in complex with the stathmin protein, the bending angles calculated with all three metrics varied quite significantly for the first and second dimers (up to 20% or more), which indicates the sensitivity of all metrics to slight variations in the conformation of tubulin dimers within these complexes. A detailed description of the procedures for measuring the bending of tubulin protofilaments, as well as identifying the advantages and disadvantages of various metrics, will increase the reproducibility and clarity of the analysis of tubulin structures in the future, as well as it will hopefully make it easier to compare the results obtained by various scientific groups.

Location-based models — one of areas of CAMA (computer-assisted mass apriasal) building. When taking into account the location of the object using spatial autoregressive models structure of models (type of spatial autocorrelation, choice of “nearest neighbors”) cannot always be determined before its construction. Moreover, in practice there are situations where more efficient methods are taking into account different rates depending on the type of the object from its location. In this regard there are important issues in spatial methods area:

– fields of methods efficacy;

– sensitivity of the methods on the choice of the type of spatial model and on the selected number of nearest neighbors.

This article presents a methodology for assessing the effectiveness of computer evaluation of real estate objects. There are results of approbation on methods based on location information of the objects.

Data hiding in digital images is a promising direction of cybersecurity. Digital steganography methods provide imperceptible transmission of secret data over an open communication channel. The information embedding efficiency depends on the embedding imperceptibility, capacity, and robustness. These quality criteria are mutually inverse, and the improvement of one indicator usually leads to the deterioration of the others. A balance between them can be achieved using metaheuristic optimization. Metaheuristics are a class of optimization algorithms that find an optimal, or close to an optimal solution for a variety of problems, including those that are difficult to formalize, by simulating various natural processes, for example, the evolution of species or the behavior of animals. In this study, we propose an approach to data hiding in the hybrid spatial-frequency domain of digital images based on metaheuristic optimization. Changing a block of image pixels according to some change matrix is considered as an embedding operation. We select the change matrix adaptively for each block using metaheuristic optimization algorithms. In this study, we compare the performance of three metaheuristics such as genetic algorithm, particle swarm optimization, and differential evolution to find the best change matrix. Experimental results showed that the proposed approach provides high imperceptibility of embedding, high capacity, and error-free extraction of embedded information. At the same time, storage of change matrices for each block is not required for further data extraction. This improves user experience and reduces the chance of an attacker discovering the steganographic attachment. Metaheuristics provided an increase in imperceptibility indicator, estimated by the PSNR metric, and the capacity of the previous algorithm for embedding information into the coefficients of the discrete cosine transform using the QIM method [Evsutin, Melman, Meshcheryakov, 2021] by 26.02% and 30.18%, respectively, for the genetic algorithm, 26.01% and 19.39% for particle swarm optimization, 27.30% and 28.73% for differential evolution.