Modeling of the Integral Index of Investment and Innovation Security

The study is devoted to solving the theoretical and applied problem of assessment of the investment and innovation security status of Ukraine based on the modeling of the Integral index of investment and innovation security and on identifying the interrelationships between different indicators characterizing innovation and investment spheres of Ukraine. The Integral (composite) index model was tested based on actual data from Ukraine for the period 2014–2022 using methods of data normalization and determination of characteristic values of the factor variables based on international experience and analysis of national regulatory restrictions for relevant indicators. Integration of factor variables into the Integral index estimates was carried out based on weighting coefficients calculated both based on expert evaluation method and alternative statistical methods: correlation analysis, pairwise correlation between GDP growth rates and every factor variable, as well as the principal component method. It has been proven that when identifying weak associations between indicators of innovative development and GDP dynamics, determining the weights of indicators based on their correlation with GDP growth rates leads to an overestimation of the Integral index of investment and innovation security. The proposed statistical methods for calculating the weighting coefficients of the variables in the model do not lead to distortion of trends in investment and innovation security, and therefore ensure obtaining consistent and, in contrast to the expert evaluation method, unbiased estimates of the status of investment and innovation security of the country. The results obtained are important in the context of solving strategic problems to prevent risks for the investment and innovation security of Ukraine and forming an innovative foundation for the revival of Ukraine’s economy

Local heterogeneity analysis of crystallographic and cryo-EM maps using shell-approximation

In X-ray crystallography and cryo-EM, experimental maps can be heterogeneous, showing different level of details in different regions. In this work we interpret heterogeneity in terms of two parameters, assigned individually for each atom, combining the conventional atomic displacement parameter with the resolution of the atomic image in the map. We propose a local real-space procedure to estimate the values of these heterogeneity parameters, assuming that a fragment of the density map and atomic positions are given. The procedure is based on an analytic representation of the atomic image, as a function of the inhomogeneity parameters and atomic coordinates. In this article, we report the results of the tests both with maps simulated and those derived from experimental data. For simulated maps containing regions with different resolutions, the method determines the local map resolution around the atomic centers and the values of the displacement parameter with reasonable accuracy. For experimental maps, obtained as a Fourier synthesis of a given global resolution, estimated values of the local resolution are close to the global one, and the values of the estimated displacement parameters are close to the respective values of the closest atoms in the refined model. Shown successful applications of the proposed method to experimental crystallographic and cryo-EM maps can be seen as a practical proof of method

Ab initio phasing based on topological restraints: automated determination of the space group and the number of molecules in the unit cell

International audienceThe connectivity-based phasing method has been demonstrated to be capable of finding molecular packing and envelopes even for difficult cases of structure determination, as well as of identifying, in favorable cases, secondary-structure elements of protein molecules in the crystal. This method uses a single set of structure factor magnitudes and general topological features of a crystallographic image of the macromolecule under study. This information is expressed through a number of parameters. Most of these parameters are easy to estimate, and the results of phasing are practically independent of these parameters when they are chosen within reasonable limits. By contrast, the correct choice for such parameters as the expected number of connected regions in the unit cell is sometimes ambiguous. To study these dependencies, numerous tests were performed with simulated data, experimental data and mixed data sets, where several reflections missed in the experiment were completed by computed data. This paper demonstrates that the procedure is able to control this choice automatically and helps in difficult cases to identify the correct number of molecules in the asymmetric unit. In addition, the procedure behaves abnormally if the space group is defined incorrectly and therefore may distinguish between the rotation and screw axes even when high-resolution data are not available