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

Quality of Prenatal Care and Pregnancy Outcomes: Centering Pregnancy Versus Traditional Prenatal Care

Prenatal care provides a unique opportunity for healthcare providers to improve outcomes for women and their families and by extension community health. Therefore, prenatal care has the opportunity to become the cornerstone of healthcare in our nation. It can influence the health of the mother, newborn, and family unit long beyond the course of a 9-month pregnancy. However, evidence supporting positive outcomes from current tradition based models of prenatal care is lacking. The current United States prenatal system limits the patient-provider relationship, does not empower the patient, lacks emphasis on education, and is not woman-centered. The aim of the study was to compare an alternative prenatal care model, Centering Pregnancy, to individual prenatal care. An initial comparative concept analysis of power and empowerment focused on the nurse’s role in cultivating empowerment in the pregnant woman. Subsequently, a study exploring the differences in outcomes for women in two different prenatal care groups was conducted. Differences examined included quality of prenatal care and pregnancy-related empowerment from the patient’s perspective. Also comparison of birth weight and gestational age at time of birth for a sample size of 51 pregnant patients (n =14 in Centering Pregnancy, n=37 in individual prenatal care). Findings from this feasibility study revealed no statistical significance between the two independent groups in quality of prenatal care and gestational age. Differences in pregnancy-related empowerment (p = 0.083) and birth weight (p = 0.088) were noted to be approaching significance. Participants receiving individual prenatal care demonstrated higher post pregnancy-related empowerment. Centering Pregnancy participants had higher birth weights. The results call for further research into the effect of Centering Pregnancy on empowerment and birth weight with a larger sample size to determine if true significance exists

Commodity Price Pass-Through in Differentiated Retail Food Markets

Prices for nearly all basic commodity rose at unprecedented rates throughout early 2008, only to fall nearly as fast as financial markets and global economies began to collapse. Rising food prices in 2008 led to concerns that commodity price spikes would lead to more general food inflation, but by early 2009 interest focused more on the seeming inability of food prices to fall back down with commodity prices. This study provides an empirical investigation into the pass-through of commodity prices to retail prices for two different types of food products: potatoes and fluid milk. The results show that pass-through depends on the nature of the food in question, but is generally consistent with theoretical models of pricing by sellers of multiple, differentiated products. In particular, pass-through rates tend to be lower for processed (differentiated) products during periods of falling input prices than when input prices are rising. For less processed products, pass-through tends to be higher during regimes of both rising and falling input prices. Our results show that pass-through depends on the degree of pricing power possessed by all channel members and, more generally, suggest a nuanced approach to understanding retail food price inflation.commodity prices, conduct, industrial organization, inflation, market power, nested logit, pass-through, random parameters model, Consumer/Household Economics, Demand and Price Analysis, Industrial Organization, C35, D12, D43, L13, L41, Q13,

Current occupational health policy issues for universities in the United Kingdom

Universities are large organisations with diverse occupational hazards and some unusual features as employers. They need expert professional advice for generalist managers on occupational health matters and they need specialist services such as immunisations for medical students and respiratory health surveillance for staff and students whose research involves the use of animals. We have reviewed these varied occupational health needs in detail in a separate paper (Venables and Allender 2006). Universities need an occupational health response which is proportionate to their needs.<br /

On Resource-bounded versions of the van Lambalgen theorem

The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences $A$ and $B$, $B$ is Martin-L\"of random and $A$ is Martin-L\"of random relative to $B$ if and only if the interleaved sequence $A \uplus B$ is Martin-L\"of random. This implies that $A$ is relative random to $B$ if and only if $B$ is random relative to $A$ \cite{vanLambalgen}, \cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this phenomenon for different notions of time-bounded relative randomness. We prove the classical van Lambalgen theorem using martingales and Kolmogorov compressibility. We establish the failure of relative randomness in these settings, for both time-bounded martingales and time-bounded Kolmogorov complexity. We adapt our classical proofs when applicable to the time-bounded setting, and construct counterexamples when they fail. The mode of failure of the theorem may depend on the notion of time-bounded randomness

A parameterized halting problem, the linear time hierarchy, and the MRDP theorem

The complexity of the parameterized halting problem for nondeterministic Turing machines p-Halt is known to be related to the question of whether there are logics capturing various complexity classes [10]. Among others, if p-Halt is in para-AC0, the parameterized version of the circuit complexity class AC0, then AC0, or equivalently, (+, x)-invariant FO, has a logic. Although it is widely believed that p-Halt ∉. para-AC0, we show that the problem is hard to settle by establishing a connection to the question in classical complexity of whether NE ⊈ LINH. Here, LINH denotes the linear time hierarchy. On the other hand, we suggest an approach toward proving NE ⊈ LINH using bounded arithmetic. More specifically, we demonstrate that if the much celebrated MRDP (for Matiyasevich-Robinson-Davis-Putnam) theorem can be proved in a certain fragment of arithmetic, then NE ⊈ LINH. Interestingly, central to this result is a para-AC0 lower bound for the parameterized model-checking problem for FO on arithmetical structures.Peer ReviewedPostprint (author's final draft

The stability of weight status through the early to middle childhood years in Australia: a longitudinal study

OBJECTIVES: To investigate the sociodemographic and behavioural factors associated with incidence, persistence or remission of obesity in a longitudinal sample of Australian children aged 4-10 years. SETTING: Nationally representative Longitudinal Study of Australian Children (LSAC). PARTICIPANTS: The sample for this analysis included all children in the Kinder cohort (aged 4-5 years at wave 1) who participated in all four waves of LSAC (wave 1, 2004, aged 4-5 years; wave 2, 2006, aged 6-7 years; wave 3, 2008, aged 8-9 years and wave 4, 2010, aged 10-11 years). Of the 4983 children who participated in the baseline (wave 1) survey, 4169 (83.7%) children completed all four waves of data collection. PRIMARY AND SECONDARY OUTCOME MEASURES: Movement of children between weight status categories over time and individual-level predictors of weight status change (sociodemographic characteristics, selected dietary and activity behaviours). RESULTS: The study found tracking of weight status across this period of childhood. There was an inverse association observed between socioeconomic position and persistence of overweight/obesity. Sugar-sweetened beverages and fruit and vegetable intake and screen time appeared to be important predictors of stronger tracking. CONCLUSIONS: Overweight and obesity established early in childhood tracks strongly to the middle childhood years in Australia, particularly among children of lower socioeconomic position and children participating in some unhealthy behaviour patterns