Primal-dual subgradient methods for minimizing uniformly convex functions

We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are adaptive with respect to the parameters of strong or uniform convexity of the objective: in the case when the total number of iterations $N$ is fixed, their accuracy coincides, up to a logarithmic in $N$ factor with the accuracy of optimal algorithms

Deterministic and stochastic primal-dual subgradient algorithms for uniformly convex minimization

International audienceWe discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are adaptive with respect to the parameters of strong or uniform convexity of the objective: in the case when the total number of iterations N is fixed, their accuracy coincides, up to a logarithmic in N factor with the accuracy of optimal algorithms

Primal-dual stochastic subgradient methods for uniformly convex minimization

International audienceWe discuss non-Euclidean stochastic approximation algorithms for optimization problems with strongly and uniformly convex objectives. These algorithms are adaptive with respect to the parameters regularity and of strong or uniform convexity of the objective: in the case when the total number of iterations N is fixed, their accuracy coincides, up to a logarithmic in N factor with the accuracy of optimal algorithms

Modeling the operation of mining shovel-truck systems

Load and haul operations at open-pit mines are performed by shovel-truck systems (STSs). One of the main problems of STS is the low level of its operation quality. A means of improving the STS operation quality is its optimization, based on a systems approach, according to which the operation of system components is studied by analyzing the operation of the STS as a whole. The issues of optimal design of open-pit mining machines were being addressed. They all consider separate machines. Interpretations for mining STSs, however, have not been made. With regard to the optimization of the STS performance indicators, the systems approach consists in their optimal coordination with each other, provided that they meet the requirements for the STS operation. The optimization of the STS performance indicators is carried out according to its mathematical model, which includes the objective function and restrictions, represented in the form of linear regression analysis equations, directly linking the corresponding output performance indicators with the parameters being optimized. It is proposed to use generalized estimates as an optimization criterion, and single indicators of the STS operation quality as the parameters being optimized. This simplifies optimization and increases its accuracy, as well as provides the best degree of consistency of the parameters being optimized between themselves and the external environment

Development of a Hybrid Biomimetic Enamel-Biocomposite Interface and a Study of Its Molecular Features Using Synchrotron Submicron ATR-FTIR Microspectroscopy and Multivariate Analysis Techniques

Using a biomimetic strategy and bioinspired materials, our work proposed a new technological approach to create a hybrid transitional layer between enamel and dental biocomposite. For this purpose, an amino acid booster conditioner based on a set of polar amino acids (lysine, arginine, hyaluronic acid), calcium alkali, and a modified adhesive based on BisGMA and nanocrystalline carbonate-substituted hydroxyapatite are used during dental enamel restoration. The molecular properties of the hybrid interface formed using the proposed strategy were understood using methods of multivariate statistical analysis of spectral information collected using the technique of synchrotron infrared microspectroscopy. The results obtained indicate the possibility of forming a bonding that mimics the properties of natural tissue with controlled molecular properties in the hybrid layer. The diffusion of the amino acid booster conditioner component, the calcium alkali, and the modified adhesive with nanocrystalline carbonate-substituted hydroxyapatite in the hybrid interface region creates a structure that should stabilize the reconstituted crystalline enamel layer. The developed technology can form the basis for an individualized, personalized approach to dental enamel restorations

A Study of the Effects of Medical Dental Laser and Diamond Drill on Dentin Tissue during Dental Restoration Based on Spectral Imaging and Multivariate Analysis of Synchrotron FTIR Microspectroscopy Data

In our work, the effect of a dental Er:YAG pulsed laser and a diamond cylindrical drill with a turbine handpiece on dentin tissue was studied using spectral imaging. The combination of spectral imaging of FTIR microspectroscopy data and subsequent multivariate analysis (hierarchical cluster analysis (HCA) and principal component analysis (PCA)) was shown to unambiguously detect visually indistinguishable structural changes occurring in the hard dental tissue (dentin) depending on the method used for their pre-processing, and to classify and differentiate the identified features at the submicron level with high spatial resolution. The detectable spectral transformations indicate that the preparation of dental tissue with a dental laser leads to significant changes in the organic components of dentin, which may affect adhesion. The use of a diamond cylindrical drill with a turbine handpiece is characterized by a larger area (depth) of the altered hard tissue than in the case of a dental laser for dental cavity preparation. The observed redistribution of the phase composition of the inorganic component in the tissue is associated with the emergence of additional phases of weak calcium phosphates, and changes in the organic component with transformations in the secondary structure of proteins. Active use of the proposed integrated approach in the future will clarify the areas of its applicability to the analysis of biological tissues and pathologies in them, which will help in the clinical setting to choose the optimal personalized approach for patients