Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients

We consider deformations of $2\times2$ and $3\times3$ matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don't satisfy the well-known system of Schlesinger equations (or its natural generalization). Some general statements concerning reducibility of such deformations for $2\times2$ ODEs are proved. An explicit example of the general non-Schlesinger deformation of $2\times2$-matrix ODE of the Fuchsian type with 4 singular points is constructed and application of such deformations to the construction of special solutions of the corresponding Schlesinger systems is discussed. Some examples of isomonodromy and non-isomonodromy deformations of $3\times3$ matrix ODEs are considered. The latter arise as the compatibility conditions with linear ODEs with non-singlevalued coefficients.Comment: 15 pages, to appear in J. Phys.

Prospects for the Characterization and Confirmation of Transiting Exoplanets via the Rossiter-McLaughlin Effect

The Rossiter-McLaughlin (RM) effect is the distortion of stellar spectral lines that occurs during eclipses or transits, due to stellar rotation. We assess the future prospects for using the RM effect to measure the alignment of planetary orbits with the spin axes of their parent stars, and to confirm exoplanetary transits. We compute the achievable accuracy for the parameters of interest, in general and for the 5 known cases of transiting exoplanets with bright host stars. We determine the requirements for detecting the effects of differential rotation. For transiting planets with small masses or long periods (as will be detected by forthcoming satellite missions), the velocity anomaly produced by the RM effect can be much larger than the orbital velocity of the star. For a terrestrial planet in the habitable zone of a Sun-like star found by the Kepler mission, it will be difficult to use the RM effect to confirm transits with current instruments, but it still may be easier than measuring the spectroscopic orbit.Comment: 18 pages, 8 figures, one table. Minor changes. Accepted to ApJ, to appear in the Jan 20, 2007 issue (v655

The Rossiter-McLaughlin effect and analytic radial velocity curves for transiting extrasolar planetary systems

A transiting extrasolar planet sequentially blocks off the light coming from the different parts of the disk of the host star in a time dependent manner. Due to the spin of the star, this produces an asymmetric distortion in the line profiles of the stellar spectrum, leading to an apparent anomaly of the radial velocity curves, known as the Rossiter - McLaughlin effect. Here, we derive approximate but accurate analytic formulae for the anomaly of radial velocity curves taking account of the stellar limb darkening. The formulae are particularly useful in extracting information of the projected angle between the planetary orbit axis and the stellar spin axis, \lambda, and the projected stellar spin velocity, V sin I_s. We create mock samples for the radial curves for the transiting extrasolar system HD209458, and demonstrate that constraints on the spin parameters (V sin I_s, \lambda) may be significantly improved by combining our analytic template formulae and the precision velocity curves from high-resolution spectroscopic observations with 8-10 m class telescopes. Thus future observational exploration of transiting systems using the Rossiter - McLaughlin effect is one of the most important probes to better understanding of the origin of extrasolar planetary systems, especially the origin of their angular momentum.Comment: 39 pages, 16 figures, Accepted to ApJ. To match the published version (ApJ 623, April 10 issue

Semiclassical Solution of One Dimensional Model of Kondo Insulator

The model of Kondo chain with $M$-fold degenerate band of conduction electrons of spin 1/2 interacting with localized spins $S$ is studied for the case when the electronic band is half filled. It is shown that the spectrum of spin excitations in the continuous limit is described by the O(3) nonlinear sigma model with the topological term with $\theta = \pi(2S - M)$. For a case $|M - 2S| =$(even) the system is an insulator and single electron excitations at low energies are massive spin polarons. Otherwise the density of states has a pseudogap and vanishes only at the Fermi level. The relevance of this picture to higher dimensional Kondo insulators is discussed.Comment: 10 pages, LaTe

Optical investigation of the metal-insulator transition in FeSb2FeSb_2

We present a comprehensive optical study of the narrow gap $FeSb_2$ semiconductor. From the optical reflectivity, measured from the far infrared up to the ultraviolet spectral range, we extract the complete absorption spectrum, represented by the real part $\sigma_1(\omega)$ of the complex optical conductivity. With decreasing temperature below 80 K, we find a progressive depletion of $\sigma_1(\omega)$ below $E_g\sim 280$ cm$^{-1}$, the semiconducting optical gap. The suppressed (Drude) spectral weight within the gap is transferred at energies $\omega>E_g$ and also partially piles up over a continuum of excitations extending in the spectral range between zero and $E_g$. Moreover, the interaction of one phonon mode with this continuum leads to an asymmetric phonon shape. Even though several analogies between $FeSb_2$ and $FeSi$ were claimed and a Kondo-insulator scenario was also invoked for both systems, our data on $FeSb_2$ differ in several aspects from those of $FeSi$. The relevance of our findings with respect to the Kondo insulator description will be addressed.Comment: 17 pages, 5 figure

De novo DNA demethylation and non-coding transcription define active intergenic regulatory elements

Deep sequencing of mammalian DNA methylomes has uncovered a previously unpredicted number of discrete hypomethylated regions in intergenic space (iHMRs). Here, we combined whole genome bisulfite sequencing data with extensive gene-expression and chromatin-state data to define functional classes of iHMRs, and to reconstruct the dynamics of their establishment in a developmental setting. Comparing HMR profiles in embryonic stem and primary blood cells, we show that iHMRs mark an exclusive subset of active DNase hypersensitive sites (DHS), and that both developmentally constitutive and cell-type specific iHMRs display chromatin states typical of distinct regulatory elements. We also observe that iHMR changes are more predictive of nearby gene activity than the promoter HMR itself, and that expression of non-coding RNAs within the iHMR accompanies full activation and complete demethylation of mature B cell enhancers. Conserved sequence features corresponding to iHMR transcript start sites, including a discernable TATAA motif, suggest a conserved, functional role for transcription in these regions. Similarly, we explored both primate-specific and human-population variation at iHMRs, finding that while enhancer iHMRs are more variable in sequence and methylation status than any other functional class, conservation of the TATA box is highly predictive of iHMR maintenance, reflecting the impact of sequence plasticity and transcriptional signals on iHMR establishment. Overall, our analysis allowed us to construct a 3-step timeline in which 1) intergenic DHS are pre-established in the stem cell, 2) partial demethylation of blood specific intergenic DHSs occurs in blood progenitors, and 3) complete iHMR formation and transcription coincide with enhancer activation in lymphoid-specified cells

PO and ID BCG vaccination in humans induce distinct mucosal and systemic immune responses and CD4(+) T cell transcriptomal molecular signatures.

Protective efficacy of Bacillus Calmette-Guérin (BCG) may be affected by the methods and routes of vaccine administration. We have studied the safety and immunogenicity of oral (PO) and/or intradermal (ID) administration of BCG in healthy human subjects. No major safety concerns were detected in the 68 healthy adults vaccinated with PO and/or ID BCG. Although both PO and ID BCG could induce systemic Th1 responses capable of IFN-γ production, ID BCG more strongly induced systemic Th1 responses. In contrast, stronger mucosal responses (TB-specific secretory IgA and bronchoalveolar lavage T cells) were induced by PO BCG vaccination. To generate preliminary data comparing the early gene signatures induced by mucosal and systemic BCG vaccination, CD4(+) memory T cells were isolated from subsets of BCG vaccinated subjects pre- (Day 0) and post-vaccination (Days 7 and 56), rested or stimulated with BCG infected dendritic cells, and then studied by Illumina BeadArray transcriptomal analysis. Notably, distinct gene expression profiles were identified both on Day 7 and Day 56 comparing the PO and ID BCG vaccinated groups by GSEA analysis. Future correlation analyses between specific gene expression patterns and distinct mucosal and systemic immune responses induced will be highly informative for TB vaccine development.Mucosal Immunology advance online publication 30 August 2017; doi:10.1038/mi.2017.67

Non-Fermi liquid behavior of SrRuO_3 -- evidence from infrared conductivity

The reflectivity of the itinerant ferromagnet SrRuO_3 has been measured between 50 and 25,000 cm-1 at temperatures ranging from 40 to 300 K, and used to obtain conductivity, scattering rate, and effective mass as a function of frequency and temperature. We find that at low temperatures the conductivity falls unusually slowly as a function of frequency (proportional to \omega^{-1/2}), and at high temperatures it even appears to increase as a function of frequency in the far-infrared limit. The data suggest that the charge dynamics of SrRuO_3 are substantially different from those of Fermi-liquid metals.Comment: 4 pages, 3 postscript figure

Fractional differentiability of nowhere differentiable functions and dimensions

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the `critical order' 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/ local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals.Comment: minor changes, 19 pages, Late

The optical response of Ba_{1-x}K_xBiO_3: Evidence for an unusual coupling mechanism of superconductivity?

We have analysed optical reflectivity data for Ba_{1-x}K_xBiO_3 in the far-infrared region using Migdal-Eliashberg theory and found it inconsistent with standard electron-phonon coupling: Whereas the superconducting state data could be explained using moderate coupling, \lambda=0.7, the normal state properties indicate \lambda \le 0.2. We have found that such behaviour could be understood using a simple model consisting of weak standard electron-phonon coupling plus weak coupling to an unspecified high energy excitation near 0.4 eV. This model is found to be in general agreement with the reflectivity data, except for the predicted superconducting gap size. The additional high energy excitation suggests that the dominant coupling mechanism in Ba_{1-x}K_xBiO_3 is not standard electron-phonon.Comment: 5 pages REVTex, 5 figures, 32 refs, accepted for publication in Phys. Rev.