A second look at the toric h-polynomial of a cubical complex

We provide an explicit formula for the toric $h$-contribution of each cubical shelling component, and a new combinatorial model to prove Clara Chan's result on the non-negativity of these contributions. Our model allows for a variant of the Gessel-Shapiro result on the $g$-polynomial of the cubical lattice, this variant may be shown by simple inclusion-exclusion. We establish an isomorphism between our model and Chan's model and provide a reinterpretation in terms of noncrossing partitions. By discovering another variant of the Gessel-Shapiro result in the work of Denise and Simion, we find evidence that the toric $h$-polynomials of cubes are related to the Morgan-Voyce polynomials via Viennot's combinatorial theory of orthogonal polynomials.Comment: Minor correction

What's wrong with the scrum laws in rugby union? - Judgment, truth and refereeing

Officiating and the role of officials in sport are crucial and often decisive factors in sports contests. Notable contributions in philosophy of sport include Collins (2012), Russell (1997; 1999), McFee (2011) & Mumford (2006) have brought a sharp philosophical focus to highlight that justice and desert of sport contests, in part, rely on officiating truths (performances) that arise from an appropriate admixture of epistemic (judgments) and metaphysical (actions) ingredients. This paper provides a rigorous and original philosophical analysis of the problems of obeying the rules and of applying the rules of sport. The paper focuses on a particular phase of play in rugby union, namely the scrum. It is fair to say that the scrum has become a focus of criticism and bewilderment. Elite televised rugby is damaged as a spectacle because too much time is wasted setting and re-setting scrums. Furthermore, our trust in the fairness of games is eroded because the scrum is a ‘lottery’ when it comes to officiating. In this paper, we identify two fundamental structural problems which contribute to the scrum controversy. First, drawing on Mumford (2006) and Collins (2012) we argue that officials cannot make reliable judgments about scrums because they cannot see what they need to see. Secondly, we argue that players cannot follow the laws of the scrum even if they have a strong desire to do so. Laws which can’t be followed are, according to Fuller (2000) defective. Consequently, the scrum is not only potentially dangerous but also flawed in terms of its capacity to actualize an intended part of the game

Disordered eating behaviour is associated with blunted cortisol and cardiovascular reactions to acute psychological stress

Research suggests a potential dysregulation of the stress response in individuals with bulimia nervosa. This study measured both cardiovascular and cortisol reactions to a standardised laboratory stress task in individuals identified as showing disordered eating behaviour to determine whether dysregulation of the stress response is characteristic of the two branches of the stress response system. Female students (N = 455) were screened using two validated eating disorder questionnaires. Twelve women with disordered eating, including self-induced vomiting, and 12 healthy controls were selected for laboratory stress testing. Salivary cortisol and cardiovascular activity, via Doppler imaging and semi-automatic blood pressure monitoring, were measured at resting baseline and during and after exposure to a 10-min mental arithmetic stress task. Compared to controls the disordered eating group showed blunted cortisol, cardiac output, heart rate, and stroke volume reactions to the acute stress, as well as an attenuated vasodilatory reaction. These effects could not be accounted for in terms of group differences in stress task performance, subjective task impact/engagement, age, BMI, neuroticism, cardiorespiratory fitness, or co-morbid exercise dependence. Our findings suggest that disordered eating is characterised by a dysregulation of the autonomic stress-response system. As such, they add further weight to the general contention that blunted stress reactivity is characteristic of a number of maladaptive behaviours and states

Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes

We study the renormalized stress-energy tensor (RSET) for static quantum states on (n+1)-dimensional, static, spherically symmetric black holes. By solving the conservation equations, we are able to write the stress-energy tensor in terms of a single unknown function of the radial co-ordinate, plus two arbitrary constants. Conditions for the stress-energy tensor to be regular at event horizons (including the extremal and ``ultra-extremal'' cases) are then derived using generalized Kruskal-like co-ordinates. These results should be useful for future calculations of the RSET for static quantum states on spherically symmetric black hole geometries in any number of space-time dimensions.Comment: 9 pages, no figures, RevTeX4, references added, accepted for publication in General Relativity and Gravitatio

Nonlinear dynamics for vortex lattice formation in a rotating Bose-Einstein condensate

We study the response of a trapped Bose-Einstein condensate to a sudden turn-on of a rotating drive by solving the two-dimensional Gross-Pitaevskii equation. A weakly anisotropic rotating potential excites a quadrupole shape oscillation and its time evolution is analyzed by the quasiparticle projection method. A simple recurrence oscillation of surface mode populations is broken in the quadrupole resonance region that depends on the trap anisotropy, causing stochastization of the dynamics. In the presence of the phenomenological dissipation, an initially irrotational condensate is found to undergo damped elliptic deformation followed by unstable surface ripple excitations, some of which develop into quantized vortices that eventually form a lattice. Recent experimental results on the vortex nucleation should be explained not only by the dynamical instability but also by the Landau instability; the latter is necessary for the vortices to penetrate into the condensate.Comment: RevTex4, This preprint includes no figures. You can download the complete article and figures at http://matter.sci.osaka-cu.ac.jp/bsr/cond-mat.htm

Tradable Credits Scheme on Urban Travel Demand: A Linear Expenditure System Approach and Simulation in Beijing

Using a linear expenditure system (LES) approach, we investigate the influences of a new mobility management measure, a tradable credits scheme (TCS), on the pattern of daily trips measured in kilometres. Generally, we assume that an individuals’ travel consists of a car mode and a non-car mode. The effects of the TCS are discussed from a microeconomic perspective and using a scenario simulation study for the municipality of Beijing. Whilst other research has shown that travellers trade their credits and are generally inclined to non-car mode, the implementation of the tradable credits scheme demonstrated here is that travellers are likely to restrain their use of both car and non-car travel modes. Furthermore, both car and non-car mode trips are shown to be price inelastic, whilst the cross-price elasticity for different districts demonstrates a complementary relationship between car and bus modes

Cosmological distance indicators

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time delays from strongly lensed quasars currently provide constraints on $H_0$ with < 4% uncertainty, and with 1% within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to z <~ 0.8 with galaxies and z ~ 2 with Ly-$\alpha$ forest, providing precise distance measurements and $H_0$ with < 2% uncertainty in flat $\Lambda$CDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at z ~ 0.8 and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach 1% uncertainty in determining $H_0$, to assess the current tension in $H_0$ measurements that could indicate new physics.Comment: Review article accepted for publication in Space Science Reviews (Springer), 45 pages, 10 figures. Chapter of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Ag