Dulac-Cherkas functions for generalized Liénard systems

Dulac-Cherkas functions can be used to derive an upper bound for the number of limit cycles of planar autonomous differential systems including criteria for the non-existence of limit cycles, at the same time they provide information about their stability and hyperbolicity. In this paper, we present a method to construct  a special class of Dulac-Cherkas functions for  generalized Liénard systems of the type $\frac{dx}{dt} = y, \quad  \frac{dy}{dt} = \sum_{j=0}^l h_j(x) y^j$ with $l \ge 1$. In case $1 \le l \le 3$,  linear differential equations play a key role in this process, for $l \ge 4$, we have to solve a system of linear differential and algebraic equations, where the number of equations is larger than the number of unknowns. Finally,  we show that Dulac-Cherkas functions can be used to construct generalized Liénard systems with any $l$ possessing limit cycles

On the approximation of the limit cycles function

We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x)$, which is based on the Newton scheme applied to the Poincar'e function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Li'enard system. The obtained result supports a conjecture by Lins, de Melo and Pugh

Laser in the axial electric field as a tool to search for P-, T- invariance violation

We consider rotation of polarization plane of the laser light when a gas laser is placed in a longitudinal electric field (10~kV/cm). It is shown that residual anisotropy of the laser cavity 10^{-6} and the sensitivity to the angle of polarization plane rotation about 10^{-11} -10^{-12} rad allows one to measure an electron EDM with the sensitivity about 10^{-30} e cm.Comment: 12 page

An inhomogeneous toy-model of the quantum gravity with explicitly evolvable observables

An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt equation and the "particle on a sphere" type of the gauge condition is suggested. In the quantization scheme considered, the "problem of time" is solved by building of the quasi-Heisenberg operators acting in a space of solutions of the Wheeler-DeWitt equation and the normalization of the wave function corresponds to the Klein-Gordon type. To analyze the physical consequences of the scheme, a (1+1)-dimensional background space is considered for which a classical solution is found and quantized. The obtained estimations show the way to solution of the cosmological constant problem, which consists in compensation of the zero-point oscillations of the matter fields by the quantum oscillations of the scale factor. Along with such a compensation, a slow global evolution of a background corresponding to an universe expansion exists.Comment: 18 page

Testing of CP, CPT and causality violation with the light propagation in vacuum in presence of the uniform electric and magnetic fields

We have considered the structure of the fundamental symmetry violating part of the photon refractive index in vacuum in the presence of constant electric and magnetic fields. This part of the refractive index can, in principle, contain CPT symmetry breaking terms. Some of the terms violate Lorentz invariance, whereas the others violate locality and causality. Estimates of these effects, using laser experiments are considered.Comment: 12 page

Is telomere length socially patterned? Evidence from the West of Scotland Twenty-07 study

Lower socioeconomic status (SES) is strongly associated with an increased risk of morbidity and premature mortality, but it is not known if the same is true for telomere length, a marker often used to assess biological ageing. The West of Scotland Twenty-07 Study was used to investigate this and consists of three cohorts aged approximately 35 (N = 775), 55 (N = 866) and 75 years (N = 544) at the time of telomere length measurement. Four sets of measurements of SES were investigated: those collected contemporaneously with telomere length assessment, educational markers, SES in childhood and SES over the preceding twenty years. We found mixed evidence for an association between SES and telomere length. In 35-year-olds, many of the education and childhood SES measures were associated with telomere length, i.e. those in poorer circumstances had shorter telomeres, as was intergenerational social mobility, but not accumulated disadvantage. A crude estimate showed that, at the same chronological age, social renters, for example, were nine years (biologically) older than home owners. No consistent associations were apparent in those aged 55 or 75. There is evidence of an association between SES and telomere length, but only in younger adults and most strongly using education and childhood SES measures. These results may reflect that childhood is a sensitive period for telomere attrition. The cohort differences are possibly the result of survival bias suppressing the SES-telomere association; cohort effects with regard different experiences of SES; or telomere possibly being a less effective marker of biological ageing at older ages

Serotonin 5-HT4 receptor boosts functional maturation of dendritic spines via RhoA-dependent control of F-actin

Activity-dependent remodeling of excitatory connections underpins memory formation in the brain. Serotonin receptors are known to contribute to such remodeling, yet the underlying molecular machinery remains poorly understood. Here, we employ high-resolution time-lapse FRET imaging in neuroblastoma cells and neuronal dendrites to establish that activation of serotonin receptor 5-HT4 (5-HT4R) rapidly triggers spatially-restricted RhoA activity and G13-mediated phosphorylation of cofilin, thus locally boosting the filamentous actin fraction. In neuroblastoma cells, this leads to cell rounding and neurite retraction. In hippocampal neurons in situ, 5-HT4R-mediated RhoA activation triggers maturation of dendritic spines. This is paralleled by RhoA-dependent, transient alterations in cell excitability, as reflected by increased spontaneous synaptic activity, apparent shunting of evoked synaptic responses, and enhanced long-term potentiation of excitatory transmission. The 5-HT4R/G13/RhoA signaling thus emerges as a previously unrecognized molecular pathway underpinning use-dependent functional remodeling of excitatory synaptic connections

Genome-wide association scan meta-analysis identifies three Loci influencing adiposity and fat distribution.

To identify genetic loci influencing central obesity and fat distribution, we performed a meta-analysis of 16 genome-wide association studies (GWAS, N = 38,580) informative for adult waist circumference (WC) and waist-hip ratio (WHR). We selected 26 SNPs for follow-up, for which the evidence of association with measures of central adiposity (WC and/or WHR) was strong and disproportionate to that for overall adiposity or height. Follow-up studies in a maximum of 70,689 individuals identified two loci strongly associated with measures of central adiposity; these map near TFAP2B (WC, P = 1.9x10(-11)) and MSRA (WC, P = 8.9x10(-9)). A third locus, near LYPLAL1, was associated with WHR in women only (P = 2.6x10(-8)). The variants near TFAP2B appear to influence central adiposity through an effect on overall obesity/fat-mass, whereas LYPLAL1 displays a strong female-only association with fat distribution. By focusing on anthropometric measures of central obesity and fat distribution, we have identified three loci implicated in the regulation of human adiposity