On finiteness conjectures for modular quaternion algebras

It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a number field of bounded degree. We explore this conjecture when restricted to quaternion endomorphism algebras of abelian surfaces of GL$_2$-type over Q by giving a moduli interpretation which translates the question into the diophantine arithmetic of Shimura curves embedded in Hilbert surfaces. We address the resulting problems on these curves by local and global methods, including Chabauty techniques on explicit equations of Shimura curves

Persistence and the Random Bond Ising Model in Two Dimensions

We study the zero-temperature persistence phenomenon in the random bond $\pm J$ Ising model on a square lattice via extensive numerical simulations. We find strong evidence for ` blocking\rq regardless of the amount disorder present in the system. The fraction of spins which {\it never} flips displays interesting non-monotonic, double-humped behaviour as the concentration of ferromagnetic bonds $p$ is varied from zero to one. The peak is identified with the onset of the zero-temperature spin glass transition in the model. The residual persistence is found to decay algebraically and the persistence exponent $\theta (p)\approx 0.9$ over the range $0.1\le p\le 0.9$. Our results are completely consistent with the result of Gandolfi, Newman and Stein for infinite systems that this model has ` mixed\rq behaviour, namely positive fractions of spins that flip finitely and infinitely often, respectively. [Gandolfi, Newman and Stein, Commun. Math. Phys. {\bf 214} 373, (2000).]Comment: 9 pages, 5 figure

K→(ππ)I=2K\to(\pi\pi)_{I=2} decays and twisted boundary conditions

We propose a new method to evaluate the Lellouch-L\"uscher factor which relates the $\Delta I=3/2$ $K\to\pi\pi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of partially twisted boundary conditions, which allow the s-wave $\pi\pi$ phase shift to be computed as an almost continuous function of the centre-of-mass relative momentum and hence for its derivative to be evaluated. We successfully demonstrate the feasibility of the technique in an exploratory computation.Comment: 19 pages, 7 figure

Correlation of Crystal Quality and Extreme Magnetoresistance of WTe2_2

High quality single crystals of WTe$_2$ were grown using a Te flux followed by a cleaning step involving self-vapor transport. The method is reproducible and yields consistently higher quality single crystals than are typically obtained via halide assisted vapor transport methods. Magnetoresistance (MR)values at 9 Tesla and 2 Kelvin as high as 1.75 million \%, nearly an order of magnitude higher than previously reported for this material, were obtained on crystals with residual resistivity ratio (RRR) of approximately 1250. The MR follows a near B$^2$ law (B = 1.95(1)) and, assuming a semiclassical model, the average carrier mobility for the highest quality crystal was found to be ~167,000 cm$^2$/Vs at 2 K. A correlation of RRR, MR ratio and average carrier mobility ($\mu_{avg}$) is found with the cooling rate during the flux growth.Comment: 7 pages, 3 figures, 1 tabl

The effect of the visual exercise environment on the response to psychological stress: a pilot study

Background: Performing physical activity whilst exposed to nature can improve health. However, there is little evidence of its impact on stress outcomes. The aim of this study was to examine the influence of the visual exercise environment on the response to a psychosocial stressor. Methods: Eighteen participants were randomised to one of three conditions: i. control; ii. Nature or; iii. Built condition. Participants exercised for 30min on a treadmill at 50% of their VO2max whilst viewing a video of either a natural or built environment or a blank screen. Following the exercise, participants completed the Trier Social Stress Test (TSST), a standardised laboratory stressor. Salivary samples were collected before, during and after the TSST to calculate cortisol reactivity and recovery. Results: One-way ANOVA revealed a significant effect of viewing condition on cortisol reactivity [F (2, 11) = 4.686, p = .034; n2p= .460]; with significantly lower reactivity in the built compared to the nature condition (p = .027, d=1.73). There was no effect of condition on cortisol recovery (P>0.05; n2p= .257). Conclusions: In the context of the adverse health impact of lower (i.e. blunted) cortisol responding, these findings could indicate a negative impact of the built environment on stress responses

The impacts of a nature-based mentorship program on students’ self-regulation: Harnessing the anticipation effect

Self-regulation is essential to youths’ long-term mental well-being and healthy functioning and positive anticipation of future events may support healthy emotional regulation. Green Chimneys, a school in New York that serves students with special education needs and psychosocial challenges, offers its students weekly one-on-one nature-based mentoring sessions with school staff. We used a modified version of the State Difficulties in Emotion Regulation Scale (S-DERS) to explore how these sessions impacted students’ emotional regulation both before and after their sessions. Results indicated that students’ behavior may improve in the 1-4 hours prior to participation. Further research is needed to test these findings