Grassmann extensions of Yang-Baxter maps

In this paper we show that there are explicit Yang–Baxter (YB) maps with Darboux–Lax representation between Grassman extensions of algebraic varieties. Motivated by some recent results on noncommutative extensions of Darboux transformations, we first derive a Darboux matrix associated with the Grassmann-extended derivative nonlinear Schrödinger (DNLS) equation, and then we deduce novel endomorphisms of Grassmann varieties, which possess the YB property. In particular, we present ten-dimensional maps which can be restricted to eight-dimensional YB maps on invariant leaves, related to the Grassmann-extended NLS and DNLS equations. We consider their vector generalisations

Fully Anisotropic String Cosmologies, Maxwell Fields and Primordial Shear

We present a class of exact cosmological solutions of the low energy string effective action in the presence of a homogeneous magnetic fields. We discuss the physical properties of the obtained (fully anisotropic) cosmologies paying particular attention to their vacuum limit and to the possible isotropization mechanisms. We argue that quadratic curvature corrections are able to isotropize fully anisotropic solutions whose scale factors describe accelerated expansion. Moreover, the degree of isotropization grows with the duration of the string phase. We follow the fate of the shear parameter in a decelerated phase where, dilaton, magnetic fields and radiation fluid are simultaneously present. In the absence of any magnetic field a long string phase immediately followed by radiation is able to erase large anisotropies. Conversely, if a short string phase is followed by a long dilaton dominated phase the anisotropies can be present, in principle, also at later times. The presence of magnetic seeds after the end of the string phase can induce further anisotropies which can be studied within the formalism reported in this paper.Comment: 19 pages in Revtex style, 14 Encapsulated figure

Massive fermion production in nonsingular superstring cosmology

We study massive spin-1/2 fermion production in nonsingular superstring cosmology, taking into account one-loop quantum corrections to a superstring effective action with dilaton and modulus fields. While no creation occurs in the massless limit, massive fermions can be produced by the existence of a time-dependent frequency. Due to the increase of the Hubble expansion rate during the modulus-driven phase, the occupation of number of fermions continues to grow until the point of the graceful exit, after which fermion creation ceases with the decrease of the Hubble rate.Comment: 5 pages, 3 figure

The structure of Chariklo's rings from stellar occultations

Two narrow and dense rings (called C1R and C2R) were discovered around the Centaur object (10199) Chariklo during a stellar occultation observed on 2013 June 3. Following this discovery, we planned observations of several occultations by Chariklo's system in order to better characterize the physical properties of the ring and main body. Here, we use 12 successful occulations by Chariklo observed between 2014 and 2016. They provide ring profiles (physical width, opacity, edge structure) and constraints on the radii and pole position. Our new observations are currently consistent with the circular ring solution and pole position, to within the $\pm 3.3$ km formal uncertainty for the ring radii derived by Braga-Ribas et al. The six resolved C1R profiles reveal significant width variations from $\sim 5$ to 7.5 km. The width of the fainter ring C2R is less constrained, and may vary between 0.1 and 1 km. The inner and outer edges of C1R are consistent with infinitely sharp boundaries, with typical upper limits of one kilometer for the transition zone between the ring and empty space. No constraint on the sharpness of C2R's edges is available. A 1$\sigma$ upper limit of $\sim 20$ m is derived for the equivalent width of narrow (physical width <4 km) rings up to distances of 12,000 km, counted in the ring plane

Static dilaton solutions and singularities in six dimensional warped compactification with higher derivatives

Static solutions with a bulk dilaton are derived in the context of six dimensional warped compactification. In the string frame, exponentially decreasing warp factors are identified with critical points of the low energy $\beta$-functions truncated at a given order in the string tension corrections. The stability of the critical points is discussed in the case of the first string tension correction. The singularity properties of the obtained solutions are analyzed and illustrative numerical examples are provided.Comment: 35 pages. Revised version. Accepted in Phys. Rev.

Clinical Non-Motor Phenotyping of Black and Asian Minority Ethnic Compared to White Individuals with Parkinson's Disease Living in the United Kingdom

BACKGROUND: Ethnic phenotypic differences in Parkinson's disease (PD) are important to understand the heterogeneity of PD and develop biomarkers and clinical trials. OBJECTIVE: To investigate (i) whether there are non-motor symptoms (NMS)-and comorbidity-based phenotypic differences between Black, Asian and Minority Ethnic (BAME) and White PD patients and (ii) whether clinically available biomarkers may help differentiate and explain the diversity. METHODS: This is a multicentre (four sites, London), real-life, cross-sectional study including PD patients of BAME or White ethnicity. The primary outcome was a detailed NMS assessment, additional measurements included disease and motor stage, comorbidity, sociodemographic parameters and brain MRI imaging. RESULTS: 271 PD patients (54 Asian, 71 Black, and 146 White) were included balanced for age, gender, and disease severity (HY). Black patients had a shorter disease duration compared to White and Asian populations. The SCOPA-Motor activities of daily living scores as well as the NMSS scores were significantly higher in both Black (total score and domain "miscellaneous") and Asian (total score and domains "sleep/fatigue", mood/apathy" and perception/hallucinations) than White individuals. Both BAME populations had higher prevalence of arterial hypertension, and the Black population had a higher prevalence of diabetes mellitus. Brain MRI revealed a greater severity of white matter changes in Black compared to the White and Asian cohorts. CONCLUSION: These findings suggest differences in phenotype of PD in BAME populations with greater burden of NMS and motor disability and a higher rate of cardiovascular comorbidities

Suppressing dimension-5 operators in general SU(5) models

We discuss dimension-5 operators in supersymmetric models containing extra hypercharge 1/3 color-triplets. We derive a general formula relating dimension-5 operator to the color-triplet mass matrix. We show that certain zeros in the triplet mass-matrix together with some triplet coupling selection rules can lead to elimination of dimension-5 operators. In particular we focus on SU(5) models and show that (a) Dimension-5 operators can be eliminated in the standard SU(5) model by the introduction of an extra pair of 5+5b Higgses with specific couplings (b) Flipped SU(5) models with extra 10+10b Higgses are free of dimension-5 operators (c) Flipped SU(5) models with extra 5+5b and/or extra 10+10b Higgses can be made free of dimension-5 operators for a textured form of the triplet mass-matrix accompanied by constraints on the 5-plet couplings to matter. Our analysis is motivated by the recently put forward M-theory phenomenological framework that requires a strong string coupling and reintroduces the problem of eliminating dimension-5 operators.Comment: 10 pages, Latex2e, minor changes, references adde

String-Inspired Higher-Curvature Terms and the Randall-Sundrum Scenario

We consider the O(a') string effective action, with Gauss-Bonnet curvature-squared and fourth-order dilaton-derivative terms, which is derived by a matching procedure with string amplitudes in five space-time dimensions. We show that a non-factorizable metric of the Randall-Sundrum (RS) type, with four-dimensional conformal factor Exp(-2 k|z|), can be a solution of the pertinent equations of motion. The parameter k is found proportional to the string coupling g_s and thus the solution appears to be non-perturbative. It is crucial that the Gauss-Bonnet combination has the right (positive in our conventions) sign, relative to the Einstein term, which is the case necessitated by compatibility with string (tree) amplitude computations. We study the general solution for the dilaton and metric functions, and thus construct the appropriate phase-space diagram in the solution space. In the case of an anti-de-Sitter bulk, we demonstrate that there exists a continuous interpolation between (part of) the RS solution at z=infinity and an (integrable) naked singularity at z=0. This implies the dynamical formation of domain walls (separated by an infinite distance), thus restricting the physical bulk space time to the positive z axis. Some brief comments on the possibility of fine-tuning the four-dimensional cosmological constant to zero are also presented.Comment: 28 pages Latex, three eps figures incorporated, minor change

Nature of singularities in anisotropic string cosmology

We study nature of singularities in anisotropic string-inspired cosmological models in the presence of a Gauss-Bonnet term. We analyze two string gravity models-- dilaton-driven and modulus-driven cases-- in the Bianchi type-I background without an axion field. In both scenarios singularities can be classified in two ways- the determinant singularity where the main determinant of the system vanishes and the ordinary singularity where at least one of the anisotropic expansion rates of the Universe diverges. In the dilaton case, either of these singularities inevitably appears during the evolution of the system. In the modulus case, nonsingular cosmological solutions exist both in asymptotic past and future with determinant $D=+\infty$ and D=2, respectively. In both scenarios nonsingular trajectories in either future or past typically meet the determinant singularity in past/future when the solutions are singular, apart from the exceptional case where the sign of the time-derivative of dilaton is negative. This implies that the determinant singularity may play a crucial role to lead to singular solutions in an anisotropic background.Comment: 21 pages, 8 figure