Central limit theorems for the real eigenvalues of large Gaussian random matrices

Let G be an N×N real matrix whose entries are independent identically distributed standard normal random variables Gij∼N(0,1). The eigenvalues of such matrices are known to form a two-component system consisting of purely real and complex conjugated points. The purpose of this paper is to show that by appropriately adapting the methods of [E. Kanzieper, M. Poplavskyi, C. Timm, R. Tribe and O. Zaboronski, Annals of Applied Probability 26(5) (2016) 2733–2753], we can prove a central limit theorem of the following form: if λ1,…,λNR are the real eigenvalues of G, then for any even polynomial function P(x) and even N=2n, we have the convergence in distribution to a normal random variable 1E(NR)−−−−−√⎛⎝∑j=1NRP(λj/2n−−√)−E∑j=1NRP(λj/2n−−√)⎞⎠→N(0,σ2(P)) as n→∞, where σ2(P)=2−2√2∫1−1P(x)2dx

Correlation induced switching of local spatial charge distribution in two-level system

We present theoretical investigation of spatial charge distribution in the two-level system with strong Coulomb correlations by means of Heisenberg equations analysis for localized states total electron filling numbers taking into account pair correlations of local electron density. It was found that tunneling current through nanometer scale structure with strongly coupled localized states causes Coulomb correlations induced spatial redistribution of localized charges. Conditions for inverse occupation of two-level system in particular range of applied bias caused by Coulomb correlations have been revealed. We also discuss possibility of charge manipulation in the proposed system.Comment: 6 pages, 4 figures Submitted to JETP Letter

Correlations between zeros of a random polynomial

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval $(-1,1)$ are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random polynomial.Comment: 31 pages, 2 figures; a revised version of the J. Stat. Phys. pape

Behavioral Impact of the Regulation of the Brain 2-Oxoglutarate Dehydrogenase Complex by Synthetic Phosphonate Analog of 2-Oxoglutarate: Implications into the Role of the Complex in Neurodegenerative Diseases

Decreased activity of the mitochondrial 2-oxoglutarate dehydrogenase complex (OGDHC) in brain accompanies neurodegenerative diseases. To reveal molecular mechanisms of this association, we treated rats with a specific inhibitor of OGDHC, succinyl phosphonate, or exposed them to hypoxic stress. In males treated with succinyl phosphonate and in pregnancy-sensitized females experiencing acute hypobaric hypoxia, we revealed upregulation of brain OGDHC (within 24 hours), with the activity increase presumably representing the compensatory response of brain to the OGDHC inhibition. This up-regulation of brain OGDHC was accompanied by an increase in exploratory activity and a decrease in anxiety of the experimental animals. Remarkably, the hypoxia-induced elevation of brain OGDHC and most of the associated behavioral changes were abrogated by succinyl phosphonate. The antagonistic action of hypoxia and succinyl phosphonate demonstrates potential therapeutic significance of the OGDHC regulation by the phosphonate analogs of 2-oxoglutarate

Scanning tunneling microscopy and spectroscopy at low temperatures of the (110) surface of Te doped GaAs single crystals

We have performed voltage dependent imaging and spatially resolved spectroscopy on the (110) surface of Te doped GaAs single crystals with a low temperature scanning tunneling microscope (STM). A large fraction of the observed defects are identified as Te dopant atoms which can be observed down to the fifth subsurface layer. For negative sample voltages, the dopant atoms are surrounded by Friedel charge density oscillations. Spatially resolved spectroscopy above the dopant atoms and above defect free areas of the GaAs (110) surface reveals the presence of conductance peaks inside the semiconductor band gap. The appearance of the peaks can be linked to charges residing on states which are localized within the tunnel junction area. We show that these localized states can be present on the doped GaAs surface as well as at the STM tip apex.Comment: 8 pages, 8 figures, accepted for publication in PR

Study of Convergence and Divergence of EAEU Integration Processes Based on the Gini Index

Regionalization and participation at the integration associations represent a typical way of national economic development. To be inside an integration process allows member states to address better their socio-economic problems and political coordination. The stability and resilience of integration associations are critical to their success. In this optic the integration associations may be subjects convergence and divergence. These phenomena may be envisaged in the income inequality of the participating countries.Aim. To study the features and prospects of the socio-economic convergence within the EEU member states, the EEU strategic contour and within the main trends of integration processes in Eurasia.Task. The tasks are following. The first one is to study the sustainability of the EEU and within its strategic contours formed by agreements on free trade zones through the convergent and divergent trends assessment. The second task is to conduct a comparative analysis of Eurasian integration to the European Union and ASEAN development.Methods. Assess the level and dynamics of income inequality among the EEU states and samples of states with which the EEU has agreements on free trade zones, which are the CIS, Serbia, Vietnam, Iran and Singapore, as well as states with which such agreements are planned to be concluded in the near future. This list of the EEU’s prospect partners includes Egypt, Israel and India, based on the Gini index, using the European Union and ASEAN as reference parameters. Use calculations to interpret the processes of convergence and divergence of various types of integration processes.Results. The estimates showed, in general, a significant interpretive potential of the interstate Gini index. The study particular results demonstrated that the EEU has a level of convergence comparable to the level of the EU before the accession of a large array of states in 2004. The level of convergence of the CIS, estimated using the Gini index, is comparable to the current level of the European Union. It was also revealed that both in the EU and in the CIS, the reduction in inequality over the selected analysis interval does not have a clear prospect. Calculations also showed the convergence of states within the EEU and its strategic contours to be sensitive to external shocks, while the convergence of ASEAN states is more directed.Conclusions. The approach used by the authors to assess the convergence of integration processes based on the calculation of the interstate Gini index explains with sufficient completeness the reasons for the successful development of the EEU and its sustainability. At the same time, the use of the interstate Gini index for the analysis of convergence and divergence of integration processes made it possible to conclude that the integration models of the states of the Global North and the Global South are diverse

An innovative approach to the treatment of high-risk HPV patients using allokin-alpha

Introduction. In the research literature, there have been recorded instances of imbalance of interleukins and tumour necrosis factors in the cervix tissues, endocervical mucus, suggestive of the potential feasibility of the use of immunomodulatory therapy.Purpose of the study. To assess the effectiveness of the use of the domestic drug allokin-alpha in the treatment of high-risk HPV infection (HPV) in patients of reproductive age, without elimination of the virus within more than 6–12 months and planning pregnancy.Materials and methods. The study included 60 patients of reproductive age with chronic HPV carriage – BP infection. They are represented in the study by two groups: 1st: 30 people in whose therapy allokin-alpha was not used (control group); and 30 patients without HPV BPV elimination in terms of more than 6–12 months, planning pregnancy and taking the domestic cytokiton-like immunomodulator allokin-alpha.Results. Spontaneous pregnancy occurred in 2/30 (6.7%) in the group without immunomodulator and in 9/30 patients in the group with allokin-alpha (30%) cases (c² = 5.45; p = 0.02; OR = 6.0 [1.17–30.72])Conclusion. The sustained virological response that we have achieved indicates the advisability of the use of allokin-alpha, a domestic immunomodulator of natural origin, in patients with high-risk chronic HPV infection and reproductive planning

Real roots of Random Polynomials: Universality close to accumulation points

We identify the scaling region of a width O(n^{-1}) in the vicinity of the accumulation points $t=\pm 1$ of the real roots of a random Kac-like polynomial of large degree n. We argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent, identically distributed coefficients c_i, as long as the second moment \sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to the previously reported abrupt) and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled as \mu_n\sim n^{-1/2}.Comment: Some minor mistakes that crept through into publication have been removed. 10 pages, 12 eps figures. This version contains all updates, clearer pictures and some more thorough explanation

Results of a study on the stress-strain behavior of the cornea in polarized light under conditions of visual work

Background: Near visual work causes redistribution of internal stresses in the cornea, leading to a change in the shape and parameters of the interference patterns observed on the cornea in polarized light. Purpose: To assess the effect of various types of visual load on the extraocular muscles (EOM) in children and adolescents on the basis of characteristics of the interference patterns observed on the cornea in polarized light. Material and Methods: The interference patterns observed on the cornea in polarized light were studied in children and adolescents before and after they performed a visual load task which consisted in either working with texts printed on paper at different parameters of convenience for reading (97 individuals) or playing Tetris on a smartphone (58 adolescents). A symmetry coefficient K was calculated for the quantitative assessment of changes in interference pattern parameters induced by visual load. Results: Performing a visual load task which consisted in working with texts printed on paper resulted in a significant increase in asymmetry between the actions of the EOM in 60% to 73% of children; this was indicated by the values of a symmetry coefficient K which were twofold to six-fold higher than normal. Performing a visual load task which consisted in playing Tetris on a smartphone resulted in an increase in asymmetry between the actions of the EOM in 64% of adolescents. Conclusion: Our research confirmed that studies on the stress-strain behavior of the cornea in polarized light are promising for assessing the effect of various types of visual load on the function of EOM

Assessment of fire blight resistance in apple clonal rootstocks using molecular markers

Background. Clonal apple rootstocks are one of the main components of intensive gardening. The degree of rootstock damage by fire blight affects the resistance of the variety–rootstock combination. The paper presents a study on marking quantitative trait loci (QTL) of resistance to fire blight Erwinia amylovora in clonal apple rootstock.Materials and methods. A collection of 20 rootstock forms was analyzed. For the study, SCAR markers GE-8019, AE10-375 and microsatellite marker CH-F7-FB1 were used.Results. Polymorphism was observed for all three markers, and their various combinations in one genotype were revealed. It was previously noted that genotypes that carry all three markers were more resistant than those that lack them. The presence of all three markers was observed only in forms 62-396 (В10), 16-1 and 2-9-102. The other genotypes did not have the GE8019 marker. The AE10-375 marker was identified in eight clonal rootstocks. Microsatellite marker CH-F7-FB1 was present in all tested rootstocks. However, polymorphism was detected there. Most genotypes had a 174 bp fragment, but a 210 bp fragment was identified in two of the 20 forms. Clonal rootstock 70-20-21 proved heterozygous for this marker. The analyzed collection also included samples that had only the microsatellite marker: G16, Malysh Budagovskogo, Paradizka Budagovskogo (B9), 54-118 (В118), 57-491, 70-20-20 (В119), 70-20-21, 71-7-22, 76-3-6, 83-1-15, 87-7-12, and 2-12-10. The study of rootstock forms on the basis of resistance to metabolites of the fire blight pathogen was carried out under laboratory conditions using the E. amylovora culture filtrate in vitro on leaf explants. Most of the studied genotypes had different combinations of markers. However, the experiments showed that forms 62-396 and 14-1 with two out of three markers (AE10-375 and CH-F7-FB1) phenotypically manifested the trait of resistance to metabolites of E. amylovora