Note on the paper of Fu and Wong on strictly pseudoconvex domains with K\"ahler--Einstein Bergman metrics

It is shown that the Ramadanov conjecture implies the Cheng conjecture. In particular it follows that the Cheng conjecture holds in dimension two

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

The density of stationary points in a high-dimensional random energy landscape and the onset of glassy behaviour

We calculate the density of stationary points and minima of a $N\gg 1$ dimensional Gaussian energy landscape. We use it to show that the point of zero-temperature replica symmetry breaking in the equilibrium statistical mechanics of a particle placed in such a landscape in a spherical box of size $L=R\sqrt{N}$ corresponds to the onset of exponential in $N$ growth of the cumulative number of stationary points, but not necessarily the minima. For finite temperatures we construct a simple variational upper bound on the true free energy of the $R=\infty$ version of the problem and show that this approximation is able to recover the position of the whole de-Almeida-Thouless line.Comment: a revised and shortened version with a few typos corrected and references added. To appear in JETP Letter

On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page

Performance of ePix10K, a high dynamic range, gain auto-ranging pixel detector for FELs

ePix10K is a hybrid pixel detector developed at SLAC for demanding free-electron laser (FEL) applications, providing an ultrahigh dynamic range (245 eV to 88 MeV) through gain auto-ranging. It has three gain modes (high, medium and low) and two auto-ranging modes (high-to-low and medium-to-low). The first ePix10K cameras are built around modules consisting of a sensor flip-chip bonded to 4 ASICs, resulting in 352x384 pixels of 100 $\mu$m x 100 $\mu$m each. We present results from extensive testing of three ePix10K cameras with FEL beams at LCLS, resulting in a measured noise floor of 245 eV rms, or 67 e$^-$ equivalent noise charge (ENC), and a range of 11000 photons at 8 keV. We demonstrate the linearity of the response in various gain combinations: fixed high, fixed medium, fixed low, auto-ranging high to low, and auto-ranging medium-to-low, while maintaining a low noise (well within the counting statistics), a very low cross-talk, perfect saturation response at fluxes up to 900 times the maximum range, and acquisition rates of up to 480 Hz. Finally, we present examples of high dynamic range x-ray imaging spanning more than 4 orders of magnitude dynamic range (from a single photon to 11000 photons/pixel/pulse at 8 keV). Achieving this high performance with only one auto-ranging switch leads to relatively simple calibration and reconstruction procedures. The low noise levels allow usage with long integration times at non-FEL sources. ePix10K cameras leverage the advantages of hybrid pixel detectors with high production yield and good availability, minimize development complexity through sharing the hardware, software and DAQ development with all other versions of ePix cameras, while providing an upgrade path to 5 kHz, 25 kHz and 100 kHz in three steps over the next few years, matching the LCLS-II requirements.Comment: 9 pages, 5 figure

MicroRNA regulation of the paired-box transcription factor Pax3 confers robustness to developmental timing of myogenesis

Commitment of progenitors in the dermomyotome to myoblast fate is the first step in establishing the body musculature. Pax3 is a crucial transcription factor, important for skeletal muscle development and expressed in myogenic progenitors in the dermomyotome of developing somites and in migratory muscle progenitors that populate the limb buds. Down-regulation of Pax3 is essential to ignite the myogenic program, including up-regulation of myogenic regulators, Myf-5 and MyoD. MicroRNAs (miRNAs) confer robustness to developmental timing by posttranscriptional repression of genetic programs that are related to previous developmental stages or to alternative cell fates. Here we demonstrate that the muscle-specific miRNAs miR-1 and miR-206 directly target Pax3. Antagomir-mediated inhibition of miR-1/miR-206 led to delayed myogenic differentiation in developing somites, as shown by transient loss of myogenin expression. This correlated with increased Pax3 and was phenocopied using Pax3-specific target protectors. Loss of myogenin after antagomir injection was rescued by Pax3 knockdown using a splice morpholino, suggesting that miR-1/miR-206 control somite myogenesis primarily through interactions with Pax3. Our studies reveal an important role for miR-1/miR-206 in providing precision to the timing of somite myogenesis. We propose that posttranscriptional control of Pax3 downstream of miR-1/miR-206 is required to stabilize myoblast commitment and subsequent differentiation. Given that mutually exclusive expression of miRNAs and their targets is a prevailing theme in development, our findings suggest that miRNA may provide a general mechanism for the unequivocal commitment underlying stem cell differentiation

Localization on quantum graphs with random vertex couplings

We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges

Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations

We present a method to solve initial-boundary value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A. S. Fokas to solve initial-boundary value problems for linear and integrable nonlinear partial differential equations via an extension of the inverse scattering transform. The method takes advantage of the Lax pair formulation for both linear and nonlinear equations, and is based on the simultaneous spectral analysis of both parts of the Lax pair. A key role is also played by the global algebraic relation that couples all known and unknown boundary values. Even though additional technical complications arise in discrete problems compared to continuum ones, we show that a similar approach can also solve initial-boundary value problems for linear and integrable nonlinear differential-difference equations. We demonstrate the method by solving initial-boundary value problems for the discrete analogue of both the linear and the nonlinear Schrodinger equations, comparing the solution to those of the corresponding continuum problems. In the linear case we also explicitly discuss Robin-type boundary conditions not solvable by Fourier series. In the nonlinear case we also identify the linearizable boundary conditions, we discuss the elimination of the unknown boundary datum, we obtain explicitly the linear and continuum limit of the solution, and we write down the soliton solutions.Comment: 41 pages, 3 figures, to appear in Inverse Problem

Local host response following an intramammary challenge with Staphylococcus fleurettii and different strains of Staphylococcus chromogenes in dairy heifers

Coagulase-negative staphylococci (CNS) are a common cause of subclinical mastitis in dairy cattle. The CNS inhabit various ecological habitats, ranging between the environment and the host. In order to obtain a better insight into the host response, an experimental infection was carried out in eight healthy heifers in mid-lactation with three different CNS strains: a Staphylococcus fleurettii strain originating from sawdust bedding, an intramammary Staphylococcus chromogenes strain originating from a persistent intramammary infection (S. chromogenes IM) and a S. chromogenes strain isolated from a heifer's teat apex (S. chromogenes TA). Each heifer was inoculated in the mammary gland with 1.0 x 10(6) colony forming units of each bacterial strain (one strain per udder quarter), whereas the remaining quarter was infused with phosphate-buffered saline. Overall, the CNS evoked a mild local host response. The somatic cell count increased in all S. fleurettii-inoculated quarters, although the strain was eliminated within 12 h. The two S. chromogenes strains were shed in larger numbers for a longer period. Bacterial and somatic cell counts, as well as neutrophil responses, were higher after inoculation with S. chromogenes IM than with S. chromogenes TA. In conclusion, these results suggest that S. chromogenes might be better adapted to the mammary gland than S. fleurettii. Furthermore, not all S. chromogenes strains induce the same local host response

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

The inverse spectral transform for the Zakharov-Shabat equation on the semi-line is reconsidered as a Hilbert problem. The boundary data induce an essential singularity at large k to one of the basic solutions. Then solving the inverse problem means solving a Hilbert problem with particular prescribed behavior. It is demonstrated that the direct and inverse problems are solved in a consistent way as soon as the spectral transform vanishes with 1/k at infinity in the whole upper half plane (where it may possess single poles) and is continuous and bounded on the real k-axis. The method is applied to stimulated Raman scattering and sine-Gordon (light cone) for which it is demonstrated that time evolution conserves the properties of the spectral transform.Comment: LaTex file, 1 figure, submitted to J. Phys.