Factorization of the current algebra and integrable top-like systems

A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the Taylor series and some complementary subalgebra. In the case of the Lie algebra $so(3)$ our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows us to generate integrable deformations for known integrable models.Comment: 21 page

Integrable matrix equations related to pairs of compatible associative algebras

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we investigate in details the multiplications of the A-type and integrable matrix ODEs and PDEs generated by them.Comment: 12 pages, Late

From AKNS to derivative NLS hierarchies via deformations of associative products

Using deformations of associative products, derivative nonlinear Schrodinger (DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed method to obtain 'functional representations' can be applied. We actually consider hierarchies with dependent variables in any (possibly noncommutative) associative algebra, e.g., an algebra of matrices of functions. This also covers the case of hierarchies of coupled DNLS equations.Comment: 22 pages, 2nd version: title changed and material organized in a different way, 3rd version: introduction and first part of section 2 rewritten, taking account of previously overlooked references. To appear in J. Physics A: Math. Ge

Lattice vibrations of alpha'-NaV2O5

We have measured far infrared reflectance and transmittance spectra as well as Raman scattering spectra of \alpha'-NaV2O5 single crystals for all the principal polarizations. The temperature range above the phase transition temperature T_c=35 K was investigated, mainly. On the basis of this experimental study and of the lattice dynamics calculations we conclude that the symmetry of NaV2O5 in the high temperature phase is described by the centrosymmetric D_{2h}^{13} space group. The assignment of the observed phonons is given. Values of dielectric constants are obtained from the infrared data. Asymmetric shapes of several infrared lines as well as higher order infrared vibrational spectra are discussed. The crystal field energy levels of the 3d electron localized at the V^{4+} site have been calculated in the framework of the exchange charge model using the values of effective charges obtained from the lattice dynamics calculations. According to the results of these calculations, the earlier observed broad optical bands in the region of 1 eV can be interpreted as phonon assisted d-d transitions.Comment: 12 pages, 8 figures, 5 tables; submitted to PR

Folded modes in the infrared spectra of the spin-Peierls phase of CuGeO_3

Polarized far-infrared transmittance spectra of CuGeO_3 single crystals were measured at different temperatures (6K < T < 300K). Two spectral lines, at 284.2 cm-1 in E||c polarization and at 311.7 cm-1 in E||b polarization, appear at the temperature of the spin-Peierls transition and grow in intensity with decreasing temperature. Both of them are, most probably, folded modes of the dimerized lattice. We discuss a possible role of the spin-phonon interaction in the formation of the 311.7 cm-1 feature.Comment: 4 pages, 5 figures, 1 table; Submitted to Phys.Rev.B Second revision. Figures and text were slightly change

One-dimensional dynamics of the d-electrons in α′\alpha'-NaV2_{2}O5_{5}

We have studied the electronic properties of the ladder compound $\alpha'$-NaV$_{2}$O$_{5}$, adopting a joint experimental and theoretical approach. The momentum-dependent loss function was measured using electron energy-loss spectroscopy in transmission. The optical conductivity derived from the loss function by a Kramers-Kronig analysis agrees well with our results from LSDA+U band-structure calculations upon application of an antiferromagnetic alignment of the V~3$d_{xy}$ spins along the legs and an on-site Coulomb interaction U of between 2 and 3 eV. The decomposition of the calculated optical conductivity into contributions from transitions between selected energy regions of the DOS reveals the origin of the observed anisotropy of the optical conductivity. In addition, we have investigated the plasmon excitations related to transitions between the vanadium states within an effective 16 site vanadium cluster model. Good agreement between the theoretical and experimental loss function was obtained using the hopping parameters derived from the tight binding fit to the band-structure and moderate Coulomb interactions between the electrons within the ab plane.Comment: 23 pages, 8 figures; submitted to PR

A High-Resolution View of Genome-Wide Pneumococcal Transformation

Transformation is an important mechanism of microbial evolution through which bacteria have been observed to rapidly adapt in response to clinical interventions; examples include facilitating vaccine evasion and the development of penicillin resistance in the major respiratory pathogen Streptococcus pneumoniae. To characterise the process in detail, the genomes of 124 S. pneumoniae isolates produced through in vitro transformation were sequenced and recombination events detected. Those recombinations importing the selected marker were independent of unselected events elsewhere in the genome, the positions of which were not significantly affected by local sequence similarity between donor and recipient or mismatch repair processes. However, both types of recombinations were sometimes mosaic, with multiple non-contiguous segments originating from the same molecule of donor DNA. The lengths of the unselected events were exponentially distributed with a mean of 2.3 kb, implying that recombinations are stochastically resolved with a fixed per base probability of 4.4×10−4 bp−1. This distribution of recombination sizes, coupled with an observed under representation of large insertions within transferred sequence, suggests transformation has the potential to reduce the size of bacterial genomes, and is unlikely to act as an efficient mechanism for the uptake of accessory genomic loci

Environmental Enrichment Preceding Early Adulthood Methylphenidate Treatment Leads to Long Term Increase of Corticosterone and Testosterone in the Rat

Attention-deficit/hyperactivity disorder (ADD/ADHD) has been emerging as a world-wide psychiatric disorder. There appears to be an increasing rate of stimulant drug abuse, specifically methylphenidate (MPH) which is the most common treatment for ADHD, among individuals who do not meet the criteria for ADHD and particularly for cognitive enhancement among university students. However, the long term effects of exposure to MPH are unknown. Thus, in light of a developmental approach in humans, we aimed to test the effects of adolescence exposure to enriched environment (EE) followed by MPH administration during early adulthood, on reactions to stress in adulthood. Specifically, at approximate adolescence [post natal days (PND) 30–60] rats were reared in EE and were treated with MPH during early adulthood (PND 60–90). Adult (PND 90–92) rats were exposed to mild stress and starting at PND 110, the behavioral and endocrine effects of the combined drug and environmental conditions were assessed. Following adolescence EE, long term exposure to MPH led to decreased locomotor activity and increased sucrose preference. EE had a beneficial effect on PPI (attentive abilities), which was impaired by long term exposure to MPH. Finally, the interaction between EE and, exposure to MPH led to long-term elevated corticosterone and testosterone levels. In view of the marked increase in MPH consumption over the past decade, vigilance is crucial in order to prevent potential drug abuse and its long term detrimental consequences

Within-host evolution of Staphylococcus aureus during asymptomatic carriage

Background Staphylococcus aureus is a major cause of healthcare associated mortality, but like many important bacterial pathogens, it is a common constituent of the normal human body flora. Around a third of healthy adults are carriers. Recent evidence suggests that evolution of S. aureus during nasal carriage may be associated with progression to invasive disease. However, a more detailed understanding of within-host evolution under natural conditions is required to appreciate the evolutionary and mechanistic reasons why commensal bacteria such as S. aureus cause disease. Therefore we examined in detail the evolutionary dynamics of normal, asymptomatic carriage. Sequencing a total of 131 genomes across 13 singly colonized hosts using the Illumina platform, we investigated diversity, selection, population dynamics and transmission during the short-term evolution of S. aureus. Principal Findings We characterized the processes by which the raw material for evolution is generated: micro-mutation (point mutation and small insertions/deletions), macro-mutation (large insertions/deletions) and the loss or acquisition of mobile elements (plasmids and bacteriophages). Through an analysis of synonymous, non-synonymous and intergenic mutations we discovered a fitness landscape dominated by purifying selection, with rare examples of adaptive change in genes encoding surface-anchored proteins and an enterotoxin. We found evidence for dramatic, hundred-fold fluctuations in the size of the within-host population over time, which we related to the cycle of colonization and clearance. Using a newly-developed population genetics approach to detect recent transmission among hosts, we revealed evidence for recent transmission between some of our subjects, including a husband and wife both carrying populations of methicillin-resistant S. aureus (MRSA). Significance This investigation begins to paint a picture of the within-host evolution of an important bacterial pathogen during its prevailing natural state, asymptomatic carriage. These results also have wider significance as a benchmark for future systematic studies of evolution during invasive S. aureus disease

Geographical and temporal distribution of SARS-CoV-2 clades in the WHO European Region, January to June 2020

We show the distribution of SARS-CoV-2 genetic clades over time and between countries and outline potential genomic surveillance objectives. We applied three available genomic nomenclature systems for SARS-CoV-2 to all sequence data from the WHO European Region available during the COVID-19 pandemic until 10 July 2020. We highlight the importance of real-time sequencing and data dissemination in a pandemic situation. We provide a comparison of the nomenclatures and lay a foundation for future European genomic surveillance of SARS-CoV-2.Peer reviewe