The inverse resonance problem for perturbations of algebro-geometric potentials

We prove that a compactly supported perturbation of a rational or simply periodic algebro-geometric potential of the one-dimensional Schr\"odinger equation on the half line is uniquely determined by the location of its Dirichlet eigenvalues and resonances.Comment: 14 page

The spectral problem for the dispersionless Camassa-Holm equation

We present a spectral and inverse spectral theory for the zero dispersion spectral problem associated with the Camassa-Holm equation. This is an alternative approach to that in [10] by Eckhardt and Teschl

Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page

Monitoring the immune response to vaccination with an inactivated vaccine associated to bovine neonatal pancytopenia by deep sequencing transcriptome analysis in cattle

Bovine neonatal pancytopenia (BNP) is a new fatal, alloimmune/alloantibody mediated disease of new-born calves induced by ingestion of colostrum from cows, which had been vaccinated with a specific vaccine against the Bovine Virus Diarrhoea Virus (BVDV). The hypothesis of pathogenic MHC class I molecules in the vaccine had been put up, but no formal proof of specific causal MHC class I alleles has been provided yet. However, the unique features of the vaccine obviously result in extremely high specific antibody titres in the vaccinated animals, but apparently also in further molecules inducing BNP. Thus, a comprehensive picture of the immune response to the vaccine is essential. Applying the novel approach of next generation RNA sequencing (RNAseq), our study provides a new holistic, comprehensive analysis of the blood transcriptome regulation after vaccination with the specific BVDV vaccine. Our RNAseq approach identified a novel cytokine-like gene in the bovine genome that is highly upregulated after vaccination. This gene has never been described before in any other species and might be specific to ruminant immune response. Furthermore, our data revealed a very coordinated immune response to double-stranded (ds) RNA or a dsRNA analogue after vaccination with the inactivated single-stranded (ss) RNA vaccine. This would suggest either a substantial contamination of the vaccine with dsRNA from host cells after virus culture or a dsRNA analogue applied to the vaccine. The first option would highlight the potential risks associated with virus culture on homologous cells during vaccine production; the latter option would emphasise the potential risks associated with immune stimulating adjuvants used in vaccine production

Characterization of PRLR and PPARGC1A genes in buffalo (Bubalus bubalis)

More than 40 million households in India depend at least partially on livestock production. Buffaloes are one of the major milk producers in India. The prolactin receptor (PRLR) gene and peroxisome proliferators activated receptor-γ coactivator 1-alpha (PPARGC1A) gene are reportedly associated with milk protein and milk fat yields in Bos taurus. In this study, we sequenced the PRLR and PPARGC1A genes in the water buffalo Bubalus bubalis. The PRLR and PPARGC1A genes coded for 581 and 819 amino acids, respectively. The B. bubalis PRLR gene differed from the corresponding Bos taurus at 21 positions and four differences with an additional arginine at position 620 in the PPARGC1A gene were found in the amino acid sequence. All of the changes were confirmed by cDNA sequencing. Twelve buffalo-specific single nucleotide polymorphisms (SNPs) were identified in both genes, with five of them being non-synonymous

Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field

We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analyzing the Hamiltonian equations we derive the Poincar\'e return map associated to the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a 4-dimensional space time, the oscillatory regime here constructed overlap the usual Belinski-Khalatnikov-Liftshitz one.Comment: 9 pages, published on Classical and Quantum Gravit

On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schr{\"o}dinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions.Comment: In this slightly revised version we have reworded some of the theorems, and we updated two reference

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too

The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case

We present a technique for reconstructing a semi-infinite Jacobi operator in the limit circle case from the spectra of two different self-adjoint extensions. Moreover, we give necessary and sufficient conditions for two real sequences to be the spectra of two different self-adjoint extensions of a Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result