The paper presents an overview of methods for solving an ill-posed problem of constrained convex quadratic minimization based on the Fejér-type iterative methods, which widely use the ideas and ...approaches developed in the works of I. I. Eremin, the founder of the Ural research school of mathematical programming. Along with a problem statement of general form, we consider variants of the original problem with constraints in the form of systems of equalities and inequalities, which have numerous applications. In addition, particular formulations of the problem are investigated, including the problem of finding a metric projection and solving a linear program, which are of independent interest. A distinctive feature of these methods is that not only convergence but also stability with respect to errors in the input data are established for them; i.e., the methods generate regularizing algorithms in contrast to the direct methods, which do not have this property.
t An ill-posed problem in the form of a linear operator equation is considered. It is assumed that the solution to the equation in the one-dimensional case can be represented in the form of a sum of ...three components: the first component contains discontinuities, the second contains discontinuities in the derivative, and the third is continuous. To construct a stable approximate solution, the three-component Tikhonov method is used. In this case, the stabilizer is the sum of three functionals: BVp-norm of the first component, BVp-norm of the derivative for the second component and the norm of the Sobolev space for the third component, and each functional depends on only one component. The convergence of the sum of regularized components to the solution of the original equation is proved. In addition, piecewise uniform convergence of approximate solutions is established. The results of numerical experiments on reconstructing a three-component model solution for the Fredholm equation of the first kind are presented.
Membrane potential is a fundamental property of biological cells. Changes in membrane potential characterize a vast number of vital biological processes, such as the activity of neurons and ...cardiomyocytes, tumorogenesis, cell-cycle progression, etc. A common strategy to record membrane potential changes that occur in the process of interest is to utilize organic dyes or genetically-encoded voltage indicators with voltage-dependent fluorescence. Sensors are introduced into target cells, and alterations of fluorescence intensity are recorded with optical methods. Techniques that allow recording relative changes of membrane potential and do not take into account fluorescence alterations due to factors other than membrane voltage are already widely used in modern biological and biomedical studies. Such techniques have been reviewed previously in many works. However, in order to investigate a number of processes, especially long-term processes, the measured signal must be corrected to exclude the contribution from voltage-independent factors or even absolute values of cell membrane potential have to be evaluated. Techniques that enable such measurements are the subject of this review.
A brief survey is given concerning iterative processes of Fejér type for basic statements of ill-posed problems, including constrained quadratic and convex minimization problems, variational ...inequalities, and linear and nonlinear operator equations in Hilbert spaces. By applying the method of successive approximations and its modification using correction factors, all these statements reduce to the problem of finding fixed points of nonexpansive Fejér operators. Material is also presented related to a two-stage method of constructing a regularizing algorithm for nonlinear ill-posed problems with monotone operators. An economic way is described by which the algorithm takes into account additional a priori information on the solution using Fejér maps.
Graphene oxide (GO) films were formed by drop-casting method and were studied by FTIR spectroscopy, micro-Raman spectroscopy (mRS), X-ray photoelectron spectroscopy (XPS), four-points probe method, ...atomic force microscopy (AFM), and scanning Kelvin probe force (SKPFM) microscopy after low-temperature annealing at ambient conditions. It was shown that in temperature range from 50 to 250 °C the electrical resistivity of the GO films decreases by seven orders of magnitude and is governed by two processes with activation energies of 6.22 and 1.65 eV, respectively. It was shown that the first process is mainly associated with water and OH groups desorption reducing the thickness of the film by 35% and causing the resistivity decrease by five orders of magnitude. The corresponding activation energy is the effective value determined by desorption and electrical connection of GO flakes from different layers. The second process is mainly associated with desorption of oxygen epoxy and alkoxy groups connected with carbon located in the basal plane of GO. AFM and SKPFM methods showed that during the second process, first, the surface of GO plane is destroyed forming nanostructured surface with low work function and then at higher temperature a flat carbon plane is formed that results in an increase of the work function of reduced GO.
The implementation of RNAi technology into the clinical practice has been significantly postponing due to the issues regarding to the delivery of naked siRNA predominantly to target cells. Here we ...report the approach to enhance the efficiency of siRNA delivery by encapsulating the siRNA into new carrier systems which are obtained via the combination of widely used layer-by-layer technique and in situ modification by sol-gel chemistry. We used three types of siRNAs (NP-717, NP-1155 and NP-1496) in encapsulated form as new therapeutic agents against H1N1 influenza virus infection. By employing the hybrid microcontainers for the siRNA encapsulation we demonstrate the reduction of viral nucleoprotein (NP) level and inhibition of influenza virus production in infected cell lines (MDCK and A549). The obtained hybrid carriers based on assembled biodegradable polyelectrolytes and sol-gel coating possess several advantages such as a high cell uptake efficiency, low toxicity, efficient intracellular delivery of siRNAs and the protection of siRNAs from premature degradation before reaching the target cells. These findings underpin a great potential of versatile microencapsulation technology for the development of anti-viral RNAi delivery systems against influenza virus infection.
Fluorescence of the vast majority of natural opsin-based photoactive proteins is extremely low, in accordance with their functions that depend on efficient transduction of absorbed light energy. ...However, several recently proposed classes of engineered rhodopsins with enhanced fluorescence, along with the discovery of a new natural highly fluorescent rhodopsin, NeoR, opened a way to exploit these transmembrane proteins as fluorescent sensors and draw more attention to studies on this untypical rhodopsin property. Here, we review the available data on the fluorescence of the retinal chromophore in microbial and animal rhodopsins and their photocycle intermediates, as well as different isomers of the protonated retinal Schiff base in various solvents and the gas phase.
In this review, we analyze the epidemiological and ecological features of influenza B, one of the most common and severe respiratory infections. The review presents various strategies for ...cross-protective influenza B vaccine development, including recombinant viruses, virus-like particles, and recombinant proteins. We provide an overview of viral proteins as cross-protective vaccine targets, along with other updated broadly protective vaccine strategies. The importance of developing such vaccines lies not only in influenza B prevention, but also in the very attractive prospect of eradicating the influenza B virus in the human population.
A typical feature of proteins from the rhodopsin family is the sensitivity of their absorption band maximum to protein amino acid composition. For this reason, studies of these proteins often require ...methodologies that determine spectral shift caused by amino acid substitutions. Generally, quantum mechanics/molecular mechanics models allow for the calculation of a substitution-induced spectral shift with high accuracy, but their application is not always easy and requires special knowledge. In the present study, we propose simple models that allow us to estimate the direct effect of a charged or polar residue substitution without extensive calculations using only rhodopsin three-dimensional structure and plots or tables that are provided in this article. The models are based on absorption maximum values calculated at the SORCI+Q level of theory for cis- and trans-forms of retinal protonated Schiff base in an external electrostatic field of charges and dipoles. Each value corresponds to a certain position of a charged or polar residue relative to the retinal chromophore. The proposed approach was evaluated against an example set consisting of twelve bovine rhodopsin and sodium pumping rhodopsin mutants. The limits of the applicability of the models are also discussed. The results of our study can be useful for the interpretation of experimental data and for the rational design of rhodopsins with required spectral properties.
We consider the problem on constructing a stable approximate solution of an inverse problem formulated as a nonlinear irregular equation with a monotone operator. We suggest a two-stage method based ...on Lavrentiev’s regularization scheme and iterative approximation with the use of either modified Newton’s method or a regularized κ-process. We prove that the iterative processes converge and the iterations possess the Fejér property. We show that our method generates a regularization algorithm under a certain adjustment of control parameters. On the set of source-like representable solutions, we find an optimal-order error estimate for the algorithm.
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