Geometric phase for nonlinear oscillators from perturbative renormalization group

We formulate a renormalization group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous models with time-independent parameters, as well as nonautonomous models with slowly varying parameters. We show that the renormalization group equations for the nonautonomous case can be used to determine the geometric phase acquired by the oscillator during the change of its parameters. We illustrate the obtained results by applying them to the Van der Pol, and Van der Pol-Duffing models.Comment: 12 pages, 2 figure

Stage-Specific Germ-Cell Marker Genes Are Expressed in All Mouse Pluripotent Cell Types and Emerge Early during Induced Pluripotency

Embryonic stem cells (ESCs) generated from the in-vitro culture of blastocyst stage embryos are known as equivalent to blastocyst inner cell mass (ICM) in-vivo. Though several reports have shown the expression of germ cell/pre-meiotic (GC/PrM) markers in ESCs, their functional relevance for the pluripotency and germ line commitment are largely unknown. In the present study, we used mouse as a model system and systematically analyzed the RNA and protein expression of GC/PrM markers in ESCs and found them to be comparable to the expression of cultured pluripotent cells originated from the germ line. Further, siRNA knockdown experiments have demonstrated the parallel maintenance and independence of pluripotent and GC/PrM networks in ESCs. Through chromatin immunoprecipitation experiments, we observed that pluripotent cells exhibit active chromatin states at GC marker genes and a bivalent chromatin structure at PrM marker genes. Moreover, gene expression analysis during the time course of iPS cells generation revealed that the expression of GC markers precedes pluripotency markers. Collectively, through our observations we hypothesize that the chromatin state and the expression of GC/PrM markers might indicate molecular parallels between in-vivo germ cell specification and pluripotent stem cell generation

Statistical Derivation of Basic Equations of Diffusional Kinetics in Alloys with Application to the Description of Diffusion of Carbon in Austenite

Basic equations of diffusional kinetics in alloys are statistically derived using the master equation approach. To describe diffusional transformations in substitution alloys, we derive the "quasi-equilibrium" kinetic equation which generalizes its earlier versions by taking into account possible "interaction renormalization" effects. For the interstitial alloys Me-X, we derive the explicit expression for the diffusivity D of an interstitial atom X which notably differs from those used in previous phenomenological treatments. This microscopic expression for D is applied to describe the diffusion of carbon in austenite basing on some simple models of carbon-carbon interaction. The results obtained enable us to make certain conclusions about the real form of these interactions, and about the scale of the "transition state entropy" for diffusion of carbon in austenite.Comment: 26 pages, 5 postscript figures, LaTe

First Measurement of Coherent Elastic Neutrino-Nucleus Scattering on Argon

We report the first measurement of coherent elastic neutrino-nucleus scattering (\cevns) on argon using a liquid argon detector at the Oak Ridge National Laboratory Spallation Neutron Source. Two independent analyses prefer \cevns over the background-only null hypothesis with greater than $3\sigma$ significance. The measured cross section, averaged over the incident neutrino flux, is (2.2 $\pm$ 0.7) $\times$10$^{-39}$ cm$^2$ -- consistent with the standard model prediction. The neutron-number dependence of this result, together with that from our previous measurement on CsI, confirms the existence of the \cevns process and provides improved constraints on non-standard neutrino interactions.Comment: 8 pages, 5 figures with 2 pages, 6 figures supplementary material V3: fixes to figs 3,4 V4: fix typo in table 1, V5: replaced missing appendix, V6: fix Eq 1, new fig 3, V7 final version, updated with final revision

Gender differences in the structure of the cerebrospinal fluid system of pre-school children

Relevance Investigation of the cerebrospinal fluid system of children of different ages, especially pre-school and school periods of childhood, becomes essential, since the further development of the brain and its proper functioning depends on the way it functions. Considering the MRI indications of the elements of the cerebrospinal fluid system of children is important for the development of neurology and neurosurgery, it is necessary to consider gender differences in the brain size and structure.Objective To study the sex differences in the structure of the cerebrospinal fluid system in seven-year-old children.Material and Methods For the study, archival data on the sizes of the lateral ventricles of the brain of 120 children aged 7 (60 boys and 60 girls) were involved, in particular: 1) the length of the anterior horn; 2) the width of the anterior horn; 3) the length of the central part; 4) the width of the central part; 5) the length of the posterior horn; 6) the width of the posterior horn; 7) the length of the lower horn; 8) the anteroposterior size; 9) the distance between the anterior horns; 10) the distance between the posterior horns; 11) the length of the third ventricle; 12) the height of the third ventricle; 13) the length of the aqueduct; 14) the length of the fourth ventricle; 15) the height of the fourth ventricle. The studies were carried out using the method of magnetic resonance imaging. Quantitative indicators were assessed for compliance with the normal distribution using the KolmogorovSmirnov test. The accumulation, correction, systematization of the initial information were carried out in Microsoft Excel 2016. Statistical analysis was carried out using the Statistica 10.0 software (StatSoft Inc., USA). The results were considered statistically significant at p < 0.05.Results The data obtained in the study of the cerebrospinal fluid system in children during their pre-school period of childhood are indicators of the norm and can be used for diagnostic studies in the departments of radiation diagnostics. The bilateral asymmetry of the lateral ventricles of the brain in pre-school children, discovered during the work, is of crucial clinical significance. The morphometric indicators of the elements of the cerebrospinal fluid system should be considered by specialists in the study of brain neuroplasticity.Conclusion Analysis of the obtained in vivo encephalometric data indicates the presence of sexual variability of the brain and parameters of the structures of the cerebrospinal fluid