Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

The incidence of all stroke and stroke subtype in the United Kingdom, 1985 to 2008 : a systematic review

Background : There is considerable geographic variation in stroke mortality around the United Kingdom (UK). Whether this is due to geographical differences in incidence or case-fatality is unclear. We conducted a systematic review of high-quality studies documenting the incidence of any stroke and stroke subtypes, between 1985 and 2008 in the UK. We aimed to study geographic and temporal trends in relation to equivalent mortality trends.Methods : MEDLINE and EMBASE were searched, reference lists inspected and authors of included papers were contacted. All rates were standardised to the European Standard Population for those over 45, and between 45 and 74 years. Stroke mortality rates for the included areas were then calculated to produce rate ratios of stroke mortality to incidence for each location.Results : Five papers were included in this review. Geographic variation was narrow but incidence appeared to largely mirror mortality rates for all stroke. For men over 45, incidence (and confidence intervals) per 100,000 ranged from 124 (109-141) in South London, to 185 (164-208) in Scotland. For men, premature (45-74 years) stroke incidence per 100,000 ranged from 79 (67-94) in the North West, to 112 (95-132) in Scotland. Stroke subtype data was more geographically restricted, but did suggest there is no sizeable variation in incidence by subtype around the country. Only one paper, based in South London, had data on temporal trends. This showed that there has been a decline in stroke incidence since the mid 1990 s. This could not be compared to any other locations in this review.Conclusions : Geographic variations in stroke incidence appear to mirror variations in mortality rates. This suggests policies to reduce inequalities in stroke mortality should be directed at risk factor profiles rather than treatment after a first incident event. More high quality stroke incidence data from around the UK are needed before this can be confirmed.<br /

Polynomial Time Algorithms for Branching Markov Decision Processes and Probabilistic Min(Max) Polynomial Bellman Equations

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic max(min) polynomial equations, referred to as maxPPSs (and minPPSs, respectively), in time polynomial in both the encoding size of the system of equations and in log(1/epsilon), where epsilon > 0 is the desired additive error bound of the solution. (The model of computation is the standard Turing machine model.) We establish this result using a generalization of Newton's method which applies to maxPPSs and minPPSs, even though the underlying functions are only piecewise-differentiable. This generalizes our recent work which provided a P-time algorithm for purely probabilistic PPSs. These equations form the Bellman optimality equations for several important classes of infinite-state Markov Decision Processes (MDPs). Thus, as a corollary, we obtain the first polynomial time algorithms for computing to within arbitrary desired precision the optimal value vector for several classes of infinite-state MDPs which arise as extensions of classic, and heavily studied, purely stochastic processes. These include both the problem of maximizing and mininizing the termination (extinction) probability of multi-type branching MDPs, stochastic context-free MDPs, and 1-exit Recursive MDPs. Furthermore, we also show that we can compute in P-time an epsilon-optimal policy for both maximizing and minimizing branching, context-free, and 1-exit-Recursive MDPs, for any given desired epsilon > 0. This is despite the fact that actually computing optimal strategies is Sqrt-Sum-hard and PosSLP-hard in this setting. We also derive, as an easy consequence of these results, an FNP upper bound on the complexity of computing the value (within arbitrary desired precision) of branching simple stochastic games (BSSGs)

The Impatient May Use Limited Optimism to Minimize Regret

Discounted-sum games provide a formal model for the study of reinforcement learning, where the agent is enticed to get rewards early since later rewards are discounted. When the agent interacts with the environment, she may regret her actions, realizing that a previous choice was suboptimal given the behavior of the environment. The main contribution of this paper is a PSPACE algorithm for computing the minimum possible regret of a given game. To this end, several results of independent interest are shown. (1) We identify a class of regret-minimizing and admissible strategies that first assume that the environment is collaborating, then assume it is adversarial---the precise timing of the switch is key here. (2) Disregarding the computational cost of numerical analysis, we provide an NP algorithm that checks that the regret entailed by a given time-switching strategy exceeds a given value. (3) We show that determining whether a strategy minimizes regret is decidable in PSPACE

Light scattering study of the “pseudo-layer” compression elastic constant in a twist-bend nematic liquid crystal

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or “pseudo-layers”, each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining “layer” compression and bending ought to be characterized by an effective layer compression elastic constant Beff and average director splay constant Keff1. The magnitude of Keff1 is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, Beff could differ substantially from the typical value of ∼10⁶ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the “pseudo-layer” structure of the TB phase with Beff in the range 10³–10⁴ Pa. We show additionally that the temperature dependence of Beff at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director

Electronic properties of metal induced gap states at insulator/metal interfaces -- dependence on the alkali halide and the possibility of excitonic mechanism of superconductivity

Motivated from the experimental observation of metal induced gap states (MIGS) at insulator/metal interfaces by Kiguchi {\it et al.} [Phys. Rev. Lett. {\bf 90}, 196803 (2003)], we have theoretically investigated the electronic properties of MIGS at interfaces between various alkali halides and a metal represented by a jellium with the first-principles density functional method. We have found that, on top of the usual evanescent state, MIGS generally have a long tail on halogen sites with a $p_z$-like character, whose penetration depth ($\lambda$) is as large as half the lattice constant of bulk alkali halides. This implies that $\lambda$, while little dependent on the carrier density in the jellium, is dominated by the lattice constant (hence by energy gap) of the alkali halide, where $\lambda_{\rm LiF} < \lambda_{\rm LiCl} < \lambda_{\rm LiI}$. We also propose a possibility of the MIGS working favorably for the exciton-mediated superconductivity.Comment: 7 pages, 9 figure

Composition of objectively measured physical activity and sedentary behaviour participation across the school-day, influence of gender and weight status: cross-sectional analyses among disadvantaged Victorian school children

BACKGROUND: The after-school period has been described as the \u27critical window\u27 for physical activity (PA) participation. However, little is known about the importance of this window compared with the before and during-school period among socioeconomically disadvantaged children, and influence of gender and weight status. METHODS: 39 out of 156 (RR=25%) invited primary schools across 26 local government areas in Victoria, Australia, consented to participate with 856 children (RR=36%) participating in the wider study. The analysis sample included 298 Grade 4 and Grade 6 children (mean age: 11.2&plusmn;1.1; 44% male) whom met minimum accelerometry wear-time criteria and had complete height, weight and health-behaviours questionnaire data. Accelerometry measured duration in daily light-intensity PA (LPA), moderate-to-vigorous PA (MVPA) and sedentary time (ST) was calculated for before-school=8-8:59, during-school=9:00-15:29 and after-school=15:30-18:00. Bivariate and multivariable linear regression analyses were conducted. RESULTS: During-school represented the greatest accumulation of LPA and MVPA compared with the before and after-school periods. Boys engaged in 102 min/day of LPA (95% CI 98.5 to 104.9) and 62 min/day of MVPA (95% CI 58.9 to 64.7) during-school; girls engaged in 103 min/day of LPA (95% CI 99.7 to 106.5) and 45 min/day of MVPA (95% CI 42.9 to 47.4). Linear regression models indicated that girls with overweight or obesity engaged in significantly less LPA, MVPA and more time in ST during-school. CONCLUSIONS: This study highlights the importance of in-school PA compared with after-school PA among socioeconomically disadvantage children whom may have fewer resources to participate in after-school PA

Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers

The nematic twist-bend (NTB) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The NTB phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The NTB structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, NTB-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like ``pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the NTB state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two

Sleep duration and risk of obesity among a sample of Victorian school children

Abstract Background Insufficient sleep is potentially an important modifiable risk factor for obesity and poor physical activity and sedentary behaviours among children. However, inconsistencies across studies highlight the need for more objective measures. This paper examines the relationship between sleep duration and objectively measured physical activity, sedentary time and weight status, among a sample of Victorian Primary School children. Methods A sub-sample of 298 grades four (n = 157) and six (n = 132) Victorian primary school children (aged 9.2-13.2 years) with complete accelerometry and anthropometry data, from 39 schools, were taken from a pilot study of a larger state based cluster randomized control trial in 2013. Data comprised: researcher measured height and weight; accelerometry derived physical activity and sedentary time; and self-reported sleep duration and hypothesised confounding factors (e.g. age, gender and environmental factors). Results Compared with sufficient sleepers (67 %), those with insufficient sleep (<10 hrs/day) were significantly more likely to be overweight (OR 1.97, 95 % CI:1.11-3.48) or obese (OR 2.43, 95 % CI:1.26-4.71). No association between sleep and objectively measured physical activity levels or sedentary time was found. Conclusion The strong positive relationship between weight status and sleep deprivation merits further research though PA and sedentary time do not seem to be involved in the relationship. Strategies to improve sleep duration may help obesity prevention initiatives in the future