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.

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

Resonance Raman and FTIR spectroscopic characterization of the closed and open states of channelrhodopsin-1.

Channelrhodopsin-1 from Chlamydomonas augustae (CaChR1) is a light-activated cation channel, which is a promising optogenetic tool. We show by resonance Raman spectroscopy and retinal extraction followed by high pressure liquid chromatography (HPLC) that the isomeric ratio of all-trans to 13-cis of solubilized channelrhodopsin-1 is with 70:30 identical to channelrhodopsin-2 from Chlamydomonas reinhardtii (CrChR2). Critical frequency shifts in the retinal vibrations are identified in the Raman spectrum upon transition to the open (conductive P2(380)) state. Fourier transform infrared spectroscopy (FTIR) spectra indicate different structures of the open states in the two channelrhodopsins as reflected by the amide I bands and the protonation pattern of acidic amino acids

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

Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

Measuring the vertical age structure of the Galactic disc using asteroseismology and SAGA

The existence of a vertical age gradient in the Milky Way disc has been indirectly known for long. Here, we measure it directly for the first time with seismic ages, using red giants observed by Kepler. We use Stroemgren photometry to gauge the selection function of asteroseismic targets, and derive colour and magnitude limits where giants with measured oscillations are representative of the underlying population in the field. Limits in the 2MASS system are also derived. We lay out a method to assess and correct for target selection effects independent of Galaxy models. We find that low mass, i.e. old red giants dominate at increasing Galactic heights, whereas closer to the Galactic plane they exhibit a wide range of ages and metallicities. Parametrizing this as a vertical gradient returns approximately 4 Gyr/kpc for the disc we probe, although with a large dispersion of ages at all heights. The ages of stars show a smooth distribution over the last 10 Gyr, consistent with a mostly quiescent evolution for the Milky Way disc since a redshift of about 2. We also find a flat age-metallicity relation for disc stars. Finally, we show how to use secondary clump stars to estimate the present-day intrinsic metallicity spread, and suggest using their number count as a new proxy for tracing the ageing of the disc. This work highlights the power of asteroseismology for Galactic studies; however, we also emphasize the need for better constraints on stellar mass-loss, which is a major source of systematic age uncertainties in red giant stars.Comment: MNRAS, accepted. SAGA website and data at http://www.mso.anu.edu.au/saga/data_access.htm

A Vertex Correction in the Gap Equation for the High Temperature Superconductors

We show that the Migdal theorem is obviously violated in the high Tc cuprates and the vertex correction should be included, in particular, in the gap equation, in order to be consistent with the anomalously strong inelastic scattering in the ``hot spots'', which is observed from the various normal state experiments. The vertex correction is obtained by utilizing the generalized Ward identity, which is shown to hold in the important scattering channel for the pairing interaction in the high Tc cuprates. As a result, we find a strong enhancement of Tc from the vertex correction despite of the strong pair breaking effect due to the inelastic scattering.Comment: 5 pages, 2 figure

Elastic properties of FeSi

Measurements of the sound velocities in a single crystal of FeSi were performed in the temperature range 4-300 K. Elastic constants $C_{12}$ and $C_{44}$ deviate from a quasiharmonic behavior at high temperature; whereas, $C_{12}$ increases anomalously in the entire range of temperature, indicating a change in the electron structure of this materia

The Kondo Dynamics of YbIn(1-x)AgxCu4

We present an infrared/optical study of the dynamics of the strongly correlated electron system YbIn(1-x)AgxCu4 as a function of doping and temperature for x ranging from 0 to 1, and T between 20 and 300 K. This study reveals information about the unusual phase transition as well as the phases themselves. Scaling relations emerge from the data and are investigated in detail using a periodic Anderson model based calculation. We also provide a picture in which to view both the low and high-energy x-dependent features of the infrared data, including identification of high energy, temperature dependent features.Comment: 12 pages, 11 figures, submitted Phys. Rev.