Twisted Frobenius-Schur indicators for Hopf algebras

The classical Frobenius-Schur indicators for finite groups are character sums defined for any representation and any integer m greater or equal to 2. In the familiar case m=2, the Frobenius-Schur indicator partitions the irreducible representations over the complex numbers into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bump and Ginzburg, building on earlier work of Mackey, have defined versions of these indicators which are twisted by an automorphism of the group. In another direction, Linchenko and Montgomery have defined Frobenius-Schur indicators for semisimple Hopf algebras. In this paper, the authors construct twisted Frobenius-Schur indicators for semisimple Hopf algebras; these include all of the above indicators as special cases and have similar properties.Comment: 12 pages. Minor revision

Chiral symmetry breaking in a uniform external magnetic field II. Symmetry restoration at high temperatures and chemical potentials

Chiral symmetry is dynamically broken in quenched, ladder QED at weak gauge couplings when an external magnetic field is present. In this paper, we show that chiral symmetry is restored above a critical chemical potential and the corresponding phase transition is of first order. In contrast, the chiral symmetry restoration at high temperatures (and at zero chemical potential) is a second order phase transition.Comment: Latex; 12 pages; 8 postscript figures include

Cardio-Protection Afforded by Β-Blockade Is Maintained During Resistance Exercise

Objectives Whether or not the cardio-protective effect of β-adrenergic blockade is retained during resistance exercise has not been systematically evaluated. Therefore the purpose of this study was to measure selected cardiorespiratory responses to isometric exercise involving hand-gripping, single-leg extension, or double-leg dead-lift, under placebo (control), β1-selective (atenolol), and non-selective (propranolol) adrenergic blockade conditions. Design Eleven young male adults were evaluated in a randomized, double-blinded, repeated measures study design and performed all three exercise modalities at 30% of maximal voluntary contraction under placebo, atenolol and propranolol conditions. Methods Heart rate, systolic and diastolic blood pressure, rate-pressure product, oxygen uptake, cardiac output, stroke volume and total peripheral resistance were directly measured or calculated at rest and during the third minute of each of the three exercise modes. Results Irrespective of drug condition, a graded pressor response was observed going from rest to exercise so that rest \u3c handgrip \u3c leg extension \u3c dead-lift for heart rate, systolic and diastolic blood pressures, rate-pressure product and oxygen uptake (p \u3c 0.05 for all). Cardiac output only increased with the dead-lift mode of exercise (p \u3c 0.01). Importantly β-adrenergic blockade with either atenolol or propranolol similarly attenuated the rise in heart rate, and systolic blood pressure; thus rate-pressure product demonstrated a mode-of-exercise by drug interaction effect (p \u3c 0.001) with the greatest reductions seen with the dead-lift procedure. Conclusions The findings indicate that cardio-protection afforded by selective or non-selective β-blockade at rest is preserved during isometric exercise and even enhanced once heart rate increases above 100 beats min−1

A simple thermodynamic description of phase separation of Nup98 FG domains

The permeability barrier of nuclear pore complexes (NPCs) controls nucleocytoplasmic transport. It retains inert macromolecules but allows facilitated passage of nuclear transport receptors that shuttle cargoes into or out of nuclei. The barrier can be described as a condensed phase assembled from cohesive FG repeat domains, including foremost the charge-depleted FG domain of Nup98. We found that Nup98 FG domains show an LCST-type phase separation, and we provide comprehensive and orthogonal experimental datasets for a quantitative description of this behaviour. A derived thermodynamic model correlates saturation concentration with repeat number, temperature, and ionic strength. It allows estimating the enthalpy, entropy, and ΔG (∼0.2 kJ/mol, 0.1 kBgT) contributions per repeat to phase separation and inter-repeat cohesion. While changing the cohesion strength strongly impacts the strictness of barrier, these numbers provide boundary conditions for in-depth modelling not only of barrier assembly but also of NPC passage

From computation to black holes and space-time foam

We show that quantum mechanics and general relativity limit the speed $\tilde{\nu}$ of a simple computer (such as a black hole) and its memory space $I$ to \tilde{\nu}^2 I^{-1} \lsim t_P^{-2}, where $t_P$ is the Planck time. We also show that the life-time of a simple clock and its precision are similarly limited. These bounds and the holographic bound originate from the same physics that governs the quantum fluctuations of space-time. We further show that these physical bounds are realized for black holes, yielding the correct Hawking black hole lifetime, and that space-time undergoes much larger quantum fluctuations than conventional wisdom claims -- almost within range of detection with modern gravitational-wave interferometers.Comment: A misidentification of computer speeds is corrected. Our results for black hole computation now agree with those given by S. Lloyd. All other conclusions remain unchange

Factor structure and psychometric properties of the body appreciation scale among adults in Hong Kong

Previous research has suggested that the factor structure of Body Appreciation Scale (BAS), a widely-used measure of positive body image, may not be cross-culturally equivalent. Here, we used confirmatory factor analysis to evaluate the conceptual equivalence of a Chinese (Cantonese) translation of the BAS among women (n = 1,319) and men (n = 1,084) in Hong Kong. Results showed that neither the one-dimensional nor proposed two-dimensional factor structures had adequate fit. Instead, a modified two-dimensional structure, which retained 9 of the 13 BAS items in two factors, had the best fit. However, only one these factors, reflective of General Body Appreciation, had adequate internal consistency. This factor also had good patterns of construct validity, as indicated through significant correlations with participant body mass index, self-esteem, and (among women) actual-ideal weight discrepancy. The present results suggest that there may be cultural differences in the concept and experience of body appreciation

A study of energy concentration and drain in incompressible fluids

In this paper we examine two opposite scenarios of energy behavior for solutions of the Euler equation. We show that if $u$ is a regular solution on a time interval $[0,T)$ and if $u \in L^rL^\infty$ for some $r\geq \frac{2}{N}+1$, where $N$ is the dimension of the fluid, then the energy at the time $T$ cannot concentrate on a set of Hausdorff dimension samller than $N - \frac{2}{r-1}$. The same holds for solutions of the three-dimensional Navier-Stokes equation in the range $5/3<r<7/4$. Oppositely, if the energy vanishes on a subregion of a fluid domain, it must vanish faster than (T-t)^{1-\d}, for any \d>0. The results are applied to find new exclusions of locally self-similar blow-up in cases not covered previously in the literature.Comment: an update of the previous versio