Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Nonlinear spectra of spinons and holons in short GaAs quantum wires.

One-dimensional electronic fluids are peculiar conducting systems, where the fundamental role of interactions leads to exotic, emergent phenomena, such as spin-charge (spinon-holon) separation. The distinct low-energy properties of these 1D metals are successfully described within the theory of linear Luttinger liquids, but the challenging task of describing their high-energy nonlinear properties has long remained elusive. Recently, novel theoretical approaches accounting for nonlinearity have been developed, yet the rich phenomenology that they predict remains barely explored experimentally. Here, we probe the nonlinear spectral characteristics of short GaAs quantum wires by tunnelling spectroscopy, using an advanced device consisting of 6000 wires. We find evidence for the existence of an inverted (spinon) shadow band in the main region of the particle sector, one of the central predictions of the new nonlinear theories. A (holon) band with reduced effective mass is clearly visible in the particle sector at high energies.This work was supported by the UK EPSRC [Grant Nos. EP/J01690X/1 and EP/J016888/1].This is the final version of the article. It first appeared from Nature Publishing Group via http://dx.doi.org/10.1038/NCOMMS12784

Nature of the many-body excitations in a quantum wire: Theory and experiment

The natural excitations of an interacting one-dimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of $\mathcal{R}^{2}/L^{2}$, where $\mathcal{R}$ is a length-scale related to interactions and $L$ is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analysed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to non-linear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.We acknowledge financial support from the UK EPSRC through Grants No. EP/J01690X/1 and No. EP/J016888/1 and from the DFG through SFB/TRR 49. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevB.93.07514

Hierarchy of modes in an interacting one-dimensional system.

Studying interacting fermions in one dimension at high energy, we find a hierarchy in the spectral weights of the excitations theoretically, and we observe evidence for second-level excitations experimentally. Diagonalizing a model of fermions (without spin), we show that levels of the hierarchy are separated by powers of R^{2}/L^{2}, where R is a length scale related to interactions and L is the system length. The first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We measure momentum-resolved tunneling of electrons (fermions with spin) from or to a wire formed within a GaAs heterostructure, which shows parabolic dispersion of the first-level mode and well-resolved spin-charge separation at low energy with appreciable interaction strength. We find structure resembling the second-level excitations, which dies away quite rapidly at high momentum.We acknowledge financial support from the UK EPSRC through Grant No. EP/J01690X/1 and EP/J016888/1.This is the accepted manuscript. The final version is available at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.196401

The effect of S-substitution at the O6-guanine site on the structure and dynamics of a DNA oligomer containing a G:T mismatch

The effect of S-substitution on the O6 guanine site of a 13-mer DNA duplex containing a G:T mismatch is studied using molecular dynamics. The structure, dynamic evolution and hydration of the S-substituted duplex are compared with those of a normal duplex, a duplex with Ssubstitution on guanine, but no mismatch and a duplex with just a G:T mismatch. The S-substituted mismatch leads to cell death rather than repair. One suggestion is that the G:T mismatch recognition protein recognises the S-substituted mismatch (GS:T) as G:T. This leads to a cycle of futile repair ending in DNA breakage and cell death. We find that some structural features of the helix are similar for the duplex with the G:T mismatch and that with the S-substituted mismatch, but differ from the normal duplex, notably the helical twist. These differences arise from the change in the hydrogen-bonding pattern of the base pair. However a marked feature of the S-substituted G:T mismatch duplex is a very large opening. This showed considerable variability. It is suggested that this enlarged opening would lend support to an alternative model of cell death in which the mismatch protein attaches to thioguanine and activates downstream damage-response pathways. Attack on the sulphur by reactive oxygen species, also leading to cell death, would also be aided by the large, variable opening

Opicapone in UK clinical practice: effectiveness, safety and cost analysis in patients with Parkinson's disease.

Aim: This subanalysis of the OPTIPARK study aimed to confirm the effectiveness and safety of opicapone in patients with Parkinson's disease and motor fluctuations in clinical practice specifically in the UK and to assess the impact of opicapone on treatment costs. Methods: Patients received opicapone added to levodopa for 6 months. Clinical outcomes were assessed at 3 and 6 months and treatment costs at 6 months. Results: Most patients' general condition improved at 3 months, with sustained improvements reported at 6 months. Opicapone improved motor and non-motor symptoms at both timepoints, was generally well tolerated and reduced total treatment costs by GBP 3719. Conclusion: Opicapone added to levodopa resulted in clinical improvements and reduced treatment costs across UK clinical practice

The development and optimisation of an HPLC-based in vitro serum stability assay for a calcitonin gene-related peptide receptor antagonist peptide

Evaluation of the stability of peptide drug candidates in biological fluids, such as blood serum, is of high importance during the lead optimisation phase. Here, we describe the optimisation and validation of a method for the evaluation of the stability of a lead calcitonin gene-related peptide antagonist peptide (P006) in blood serum. After initially determining appropriate peptide and human serum concentrations and selection of the quenching reagent, the HPLC method optimisation used two experimental designs, Plackett–Burman design and Taguchi design. The analytical method was validated as complying with the International Council for Harmonisation of Technical Requirements for Pharmaceuticals for Human Use guidelines. The optimised method allowed the successful resolution of the parent peptide from its metabolites using RP-HPLC and identification of the major metabolites of P006 by mass spectrometry. This paradigm may be widely adopted as a robust early-stage platform for screening peptide stability to rule out candidates with low in vitro stability, which would likely translate into poor in vivo pharmacokinetics

Window screening, ceilings and closed eaves as sustainable ways to control malaria in Dar es Salaam, Tanzania.

BACKGROUND\ud \ud Malaria transmission in Africa occurs predominantly inside houses where the primary vectors prefer to feed. Human preference and investment in blocking of specific entry points for mosquitoes into houses was evaluated and compared with known entry point preferences of the mosquitoes themselves.\ud \ud METHODS\ud \ud Cross-sectional household surveys were conducted in urban Dar es Salaam, Tanzania to estimate usage levels of available options for house proofing against mosquito entry, namely window screens, ceilings and blocking of eaves. These surveys also enabled evaluation of household expenditure on screens and ceilings and the motivation behind their installation.\ud \ud RESULTS\ud \ud Over three quarters (82.8%) of the 579 houses surveyed in Dar es Salaam had window screens, while almost half (48.9%) had ceilings. Prevention of mosquito entry was cited as a reason for installation of window screens and ceilings by 91.4% (394/431) and 55.7% (127/228) of respondents, respectively, but prevention of malaria was rarely cited (4.3%, 22/508). The median cost of window screens was between US $21-30 while that of ceilings was between US$301-400. The market value of insecticide-treated nets, window screening and ceilings currently in use in the city was estimated as 2, 5 and 42 million US$. More than three quarters of the respondents that lacked them said it was too expensive to install ceilings (82.2%) or window screens (75.5%).\ud \ud CONCLUSION\ud \ud High coverage and spending on screens and ceilings implies that these techniques are highly acceptable and excellent uptake can be achieved in urban settings like Dar es Salaam. Effective models for promotion and subsidization should be developed and evaluated, particularly for installation of ceilings that prevent entry via the eaves, which are the most important entry point for mosquitoes that cause malaria, a variety of neglected tropical diseases and the nuisance which motivates uptake

Constitutive relations for compressible granular flow in the inertial regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the μ(I),Φ(I)-rheology, which postulates that the bulk friction coefficient μ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction ϕ are functions of the inertial number I only. Although the μ(I),Φ(I)-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the μ(I),Φ(I)-rheology that does not suffer from such defects is proposed. In the framework of compressible I-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established μ(I) and Φ(I) relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations

Prevalence and Progression of Ametropias in Medical Students

Background: Uncorrected refractive errors (Myopia, Hyperopia and Astigmatism) are one of the main causes of poor vision, attributing to 43% of vision deficiencies. Myopia is the most common visual disorder in the world and can progress up until the age of 20-25, when many people are in university. The etiological factors that cause myopia are still unclear and deserve to be studied. Our aim was to identify the prevalence of ametropias and self-perception of ophthalmic health in medical students at the Centro Universitário Saúde ABC/FMABC. Methods: This is a cross-sectional study with data collected at Centro Universitário Saúde ABC/FMABC from medical students. A total of 232 students participated in the survey, from the 1st to the 4th year of study. Data was obtained through a questionnaire, which evaluates ophthalmologic health, ametropia, and self-perception. Results: It was observed that 74.57% of the students had some type of ametropia, myopia being the most recurrent (59.05%). The study shows significant data of an increase in the grade of students from 1st to 4th grade throughout college. It was observed that the average daily study time of the students was 9.68 hours and abuse in the use of electronic devices. Conclusion: This study presented a high prevalence of ametropias among medical students at the Centro Universitário ABC/FMABC, in addition to a high prevalence of multifactorial myopia and an increased need to update their diopters (degrees) during the course of university