Aspects of Discrete Breathers and New Directions

We describe results concerning the existence proofs of Discrete Breathers (DBs) in the two classes of dynamical systems with optical linear phonons and with acoustic linear phonons. A standard approach is by continuation of DBs from an anticontinuous limit. A new approach, which is purely variational, is presented. We also review some numerical results on intraband DBs in random nonlinear systems. Some non-conventional physical applications of DBs are suggested. One of them is understanding slow relaxation properties of glassy materials. Another one concerns energy focusing and transport in biomolecules by targeted energy transfer of DBs. A similar theory could be used for describing targeted charge transfer of nonlinear electrons (polarons) and, more generally, for targeted transfer of several excitations (e.g. Davydov soliton).Comment: to appear in the Proceedings of NATO Advanced Research Workshop "Nonlinearity and Disorder: Theory and Applications", Tashkent,Uzbekistan,October 1-6, 200

Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

Cryotomography of budding influenza a virus reveals filaments with diverse morphologies that mostly do not bear a genome at their distal end

Influenza viruses exhibit striking variations in particle morphology between strains. Clinical isolates of influenza A virus have been shown to produce long filamentous particles while laboratory-adapted strains are predominantly spherical. However, the role of the filamentous phenotype in the influenza virus infectious cycle remains undetermined. We used cryo-electron tomography to conduct the first three-dimensional study of filamentous virus ultrastructure in particles budding from infected cells. Filaments were often longer than 10 microns and sometimes had bulbous heads at their leading ends, some of which contained tubules we attribute to M1 while none had recognisable ribonucleoprotein (RNP) and hence genome segments. Long filaments that did not have bulbs were infrequently seen to bear an ordered complement of RNPs at their distal ends. Imaging of purified virus also revealed diverse filament morphologies; short rods (bacilliform virions) and longer filaments. Bacilliform virions contained an ordered complement of RNPs while longer filamentous particles were narrower and mostly appeared to lack this feature, but often contained fibrillar material along their entire length. The important ultrastructural differences between these diverse classes of particles raise the possibility of distinct morphogenetic pathways and functions during the infectious process

The Impact of NOD2 Variants on Fecal Microbiota in Crohn's Disease and Controls Without Gastrointestinal Disease.

BACKGROUND/AIMS: Current models of Crohn's disease (CD) describe an inappropriate immune response to gut microbiota in genetically susceptible individuals. NOD2 variants are strongly associated with development of CD, and NOD2 is part of the innate immune response to bacteria. This study aimed to identify differences in fecal microbiota in CD patients and non-IBD controls stratified by NOD2 genotype. METHODS: Patients with CD and non-IBD controls of known NOD2 genotype were identified from patients in previous UK IBD genetics studies and the Cambridge bioresource (genotyped/phenotyped volunteers). Individuals with known CD-associated NOD2 mutations were matched to those with wild-type genotype. We obtained fecal samples from patients in clinical remission with low fecal calprotectin (<250 µg/g) and controls without gastrointestinal disease. After extracting DNA, the V1-2 region of 16S rRNA genes were polymerase chain reaction (PCR)-amplified and sequenced. Analysis was undertaken using the mothur package. Volatile organic compounds (VOC) were also measured. RESULTS: Ninety-one individuals were in the primary analysis (37 CD, 30 bioresource controls, and 24 household controls). Comparing CD with nonIBD controls, there were reductions in bacterial diversity, Ruminococcaceae, Rikenellaceae, and Christensenellaceae and an increase in Enterobacteriaceae. No significant differences could be identified in microbiota by NOD2 genotype, but fecal butanoic acid was higher in Crohn's patients carrying NOD2 mutations. CONCLUSIONS: In this well-controlled study of NOD2 genotype and fecal microbiota, we identified no significant genotype-microbiota associations. This suggests that the changes associated with NOD2 genotype might only be seen at the mucosal level, or that environmental factors and prior inflammation are the predominant determinant of the observed dysbiosis in gut microbiota.Funding was supported by CORE, the Digestive Diseases Foundation and the Wellcome Trust [grant number 097943 to NAK, 093885 to CAL and 098051 to Alan W Walker and Julian Parkhill . Dr. Walker receives core funding support from the Scottish Government Rural and Environmental Science and Analysis Service (RESAS). We also acknowledge the NIHR Biomedical Research Centre awards to Addenbrooke’s Hospital/University of Cambridge School of Clinical Medicine and acknowledge the NIHR Newcastle Biomedical Research Centre

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444

Lax pair and first integrals for two of nonlinear coupled oscillators

The system of two nonlinear coupled oscillators is studied. As partial case this system of equation is reduced to the Duffing oscillator which has many applications for describing physical processes. It is well known that the inverse scattering transform is one of the most powerful methods for solving the Cauchy problems of partial differential equations. To solve the Cauchy problem for nonlinear differential equations we can use the Lax pair corresponding to this equation. The Lax pair for ordinary differential or systems or for system ordinary differential equations allows us to find the first integrals, which also allow us to solve the question of integrability for differential equations. In this report we present the Lax pair for the system of coupled oscillators. Using the Lax pair we get two first integrals for the system of equations. The considered system of equations can be also reduced to the fourth-order ordinary differential equation and the Lax pair can be used for the ordinary differential equation of fourth order. Some special cases of the system of equations are considered.Comment: 9 page

X-ray emission from isolated neutron stars

X-ray emission is a common feature of all varieties of isolated neutron stars (INS) and, thanks to the advent of sensitive instruments with good spectroscopic, timing, and imaging capabilities, X-ray observations have become an essential tool in the study of these objects. Non-thermal X-rays from young, energetic radio pulsars have been detected since the beginning of X-ray astronomy, and the long-sought thermal emission from cooling neutron star's surfaces can now be studied in detail in many pulsars spanning different ages, magnetic fields, and, possibly, surface compositions. In addition, other different manifestations of INS have been discovered with X-ray observations. These new classes of high-energy sources, comprising the nearby X-ray Dim Isolated Neutron Stars, the Central Compact Objects in supernova remnants, the Anomalous X-ray Pulsars, and the Soft Gamma-ray Repeaters, now add up to several tens of confirmed members, plus many candidates, and allow us to study a variety of phenomena unobservable in "standard'' radio pulsars.Comment: Chapter to be published in the book of proceedings of the 1st Sant Cugat Forum on Astrophysics, "ICREA Workshop on the high-energy emission from pulsars and their systems", held in April, 201

Scattering Theory and PT\mathcal{P}\mathcal{T}-Symmetry

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we review various relevant concepts such as Jost solutions, transfer and scattering matrices, reciprocity principle, unidirectional reflection and invisibility, and spectral singularities. We discuss in some detail the mathematical conditions that imply or forbid reciprocal transmission, reciprocal reflection, and the presence of spectral singularities and their time-reversal. We also derive generalized unitarity relations for time-reversal-invariant and $\mathcal{P}\mathcal{T}$-symmetric scattering systems, and explore the consequences of breaking them. The results reported here apply to the scattering systems defined by a real or complex local potential as well as those determined by energy-dependent potentials, nonlocal potentials, and general point interactions.Comment: Slightly expanded revised version, 38 page

Adaptive remodeling of the bacterial proteome by specific ribosomal modification regulates Pseudomonas infection and niche colonisation

Post-transcriptional control of protein abundance is a highly important, underexplored regulatory process by which organisms respond to their environments. Here we describe an important and previously unidentified regulatory pathway involving the ribosomal modification protein RimK, its regulator proteins RimA and RimB, and the widespread bacterial second messenger cyclic-di-GMP (cdG). Disruption of rimK affects motility and surface attachment in pathogenic and commensal Pseudomonas species, with rimK deletion significantly compromising rhizosphere colonisation by the commensal soil bacterium P. fluorescens, and plant infection by the pathogens P. syringae and P. aeruginosa. RimK functions as an ATP-dependent glutamyl ligase, adding glutamate residues to the C-terminus of ribosomal protein RpsF and inducing specific effects on both ribosome protein complement and function. Deletion of rimK in P. fluorescens leads to markedly reduced levels of multiple ribosomal proteins, and also of the key translational regulator Hfq. In turn, reduced Hfq levels induce specific downstream proteomic changes, with significant increases in multiple ABC transporters, stress response proteins and non-ribosomal peptide synthetases seen for both ΔrimK and Δhfq mutants. The activity of RimK is itself controlled by interactions with RimA, RimB and cdG. We propose that control of RimK activity represents a novel regulatory mechanism that dynamically influences interactions between bacteria and their hosts; translating environmental pressures into dynamic ribosomal changes, and consequently to an adaptive remodeling of the bacterial proteome

Downregulation of miR-92a Is Associated with Aggressive Breast Cancer Features and Increased Tumour Macrophage Infiltration

BACKGROUND: MicroRNAs are small non-coding RNAs involved in the regulation of gene expression on a posttranscriptional level. These regulatory RNAs have been implicated in numerous cellular processes and are further deregulated in different cancer types, including breast cancer. MiR-92a is part of the miR-17∼92 cluster, which was first reported to be linked to tumourigenesis. However, little is known about the expression of miR-92a in breast cancer and potential associations to tumour properties. The expression of miR-92a was therefore characterized in 144 invasive breast cancer samples using in situ hybridization and related to clinico-pathological data as well as to selected key properties of the tumour stroma, including the presence of macrophages (CD68) and cancer activated fibroblasts (alpha-SMA). METHODOLOGY/PRINCIPAL FINDINGS: To measure miR-92a levels, an in situ hybridisation protocol was developed and validated using cell lines and miR-92a inhibitors. The expression in the tumour samples was objectively evaluated using digital image analysis program subtracting background activities. We found that the miR-92a expression varied between tumours and was inversely correlated to tumour grade (r = -0.276, p = 0.003) and recurrence-free survival (p = 0.008) and provided independent prognostic information in multivariate Cox analysis (HR: 0.375, CI: 0.145-0.972, p = 0.043). MiR-92a was moreover inversely correlated to the number of infiltrating macrophages in the tumour stroma (r = -0.357, p<0.001), and downregulation of miR-92a promoted cell migration (p<0.01). CONCLUSIONS/SIGNIFICANCE: This study demonstrates that downregulation of miR-92a in breast cancer is linked to key epithelial and stromal properties as well as clinical outcome