Probabilistic Aspects of Dirichlet Series

We investigate and generalise some properties of a family of probability distributions closely related to the Riemann zeta function. Random variables that have the property that divisibility by a set of distinct primes occurs as a set of independent events are characterised in terms of functions that are well known in number theory. We refer to random variables with this independence property as Khinchin random variables. In characterising the collection of Khinchin random variables, we make a connection between the probabilistic theory of discrete distributions and the number-theoretic concept of Dirichlet series. We outline some interesting correspondences between discrete probability distributions and arithmetic functions. A subset of the Khinchin random variables have infinitely divisible logarithms. We establish the necessity of a condition, already known to be sufficient, that ensures infinite divisibility. Some Khinchin random variables admit a multiplicative decomposition into a product of random prime numbers. The number of terms in such a product follows a Poisson distribution. We explore two instances of this decomposition: one related to the zeta distribution, and the other related to the so-called prime zeta function. We use the zeta distribution to derive known results from number theory via probabilistic methods, and provide a generalisation of the distribution for other unique factorisation domains

An adaptive algorithm for rough differential equations

We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log- ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to the global error. By incorporating a cost model, our algorithm efficiently deter- mines whether to refine the time grid or increase the order of the log-ODE method. In addition, we provide several examples that demonstrate the effectiveness of our adapctive algorithm in solving RDEs

An Adaptive Algorithm for Rough Differential Equations

We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to the global error. By incorporating a cost model, our algorithm efficiently determines whether to refine the time grid or increase the order of the log-ODE method. In addition, we provide several examples that demonstrate the effectiveness of our adaptive algorithm in solving RDEs

Inference and parameter estimation for diffusion processes

Diffusion processes provide a natural way of modelling a variety of physical and economic phenomena. It is often the case that one is unable to observe a diffusion process directly, and must instead rely on noisy observations that are discretely spaced in time. Given these discrete, noisy observations, one is faced with the task of inferring properties of the underlying diffusion process. For example, one might be interested in inferring the current state of the process given observations up to the present time (this is known as the filtering problem). Alternatively, one might wish to infer parameters governing the time evolution the diffusion process. In general, one cannot apply Bayes’ theorem directly, since the transition density of a general nonlinear diffusion is not computationally tractable. In this thesis, we investigate a novel method of simplifying the problem. The stochastic differential equation that describes the diffusion process is replaced with a simpler ordinary differential equation, which has a random driving noise that approximates Brownian motion. We show how one can exploit this approximation to improve on standard methods for inferring properties of nonlinear diffusion processes

Impacts of the Primary School Free Breakfast Initiative on socio-economic inequalities in breakfast consumption among 9–11-year-old schoolchildren in Wales

Objectives - Universal interventions may widen or narrow inequalities if disproportionately effective among higher or lower socio-economic groups. The present paper examines impacts of the Primary School Free Breakfast Initiative in Wales on inequalities in children's dietary behaviours and cognitive functioning.<p></p> Design Cluster - randomised controlled trial. Responses were linked to free school meal (FSM) entitlement via the Secure Anonymised Information Linkage databank. Impacts on inequalities were evaluated using weighted school-level regression models with interaction terms for intervention × whole-school percentage FSM entitlement and intervention × aggregated individual FSM entitlement. Individual-level regression models included interaction terms for intervention × individual FSM entitlement.<p></p> Setting - Fifty-five intervention and fifty-six wait-list control primary schools.<p></p> Subjects - Approximately 4500 children completed measures of dietary behaviours and cognitive tests at baseline and 12-month follow-up.<p></p> Results School-level models indicated that children in intervention schools ate a greater number of healthy items for breakfast than children in control schools (b = 0·25; 95 % CI 0·07, 0·44), with larger increases observed in more deprived schools (interaction term b = 1·76; 95 % CI 0·36, 3·16). An interaction between intervention and household-level deprivation was not significant. Despite no main effects on breakfast skipping, a significant interaction was observed, indicating declines in breakfast skipping in more deprived schools (interaction term b = −0·07; 95 % CI −0·15, −0·00) and households (OR = 0·67; 95 % CI 0·46, 0·98). No significant influence on inequality was observed for the remaining outcomes.<p></p> Conclusions - Universal breakfast provision may reduce socio-economic inequalities in consumption of healthy breakfast items and breakfast skipping. There was no evidence of intervention-generated inequalities in any outcomes

Cover zone properties influencing acoustic emission due to corrosion

The deterioration of reinforced concrete is a serviceability problem world-wide. The cover zone plays an important role in the durability and serviceability of concrete and provides the initial barrier to aggressive species. The research presented investigates the potential of acoustic emission (AE) as a means of identifying corrosion at an early stage, before any significant cover damage has occurred. The purpose of part of the study was to identify the influential cover zone factors that affect the magnitude of the acoustic emission measurements per gram of steel loss. Prisms with various combinations of strength, cover thickness, aggregate and rebar diameters were studied to ascertain the important variables likely to be encountered on reinforced structures. The experimental results confirmed that early corrosion, verified by internal visual inspection and mass loss, can be detected by AE and before any external signs of cracking. They also show that the most influential parameter affecting the AE measurement is concrete strength, being exponentially related to the AE Energy. Material properties such as cover thickness had a negligible effect on AE Energy during the initial stages of reinforcement corrosion, whereas from this initial work, the rebar diameter indicated a promising relationship with AE Energy per gram of steel loss

The Importance of the Meaning and Measurement of “Affordable” in the Affordable Care Act

This paper focuses on the practical importance of a critical but under-explored interpretation of a provision in the Affordable Care Act (ACA): whether “affordable” refers to the cost of single coverage alone, or to family or single coverage as applicable to the worker, in determining the employer’s mandated coverage requirement and workers’ (and their dependents’) access to subsidized exchange coverage. Since the average annual total premium for family coverage is substantially higher than that for single coverage (on average $12,298 vs.$4,386 in 2008) this is a non-trivial distinction. Using data on workers from the Current Population Survey merged with estimates of employer and exchange policy premiums, we investigate the impact of the affordability decision on the fraction of workers who could then access exchange coverage subsidies and on the correspondingly lower employer sponsored insurance (ESI) coverage rates. We do via a series of calculations for each worker that first shows the financial incentives at stake in deciding between ESI and subsidized exchange coverage. We then show how many of those who stand to gain from exchange coverage could do so under the two different affordability rules and different levels of employee contributions. Finally, we show the extent to which a single affordability rule would cause low-income workers with families to fall into a “no-man’s land” with no source of affordable family coverage. We estimate that choosing a family affordability rule could initially lead to as many as 1.3 million more workers accessing exchange subsidies for themselves and their families than under a single affordability rule. If employees pay 50 percent of the premiums in the future, this number increases to 6 million. Increased use of exchange subsidies would be accompanied by reductions in ESI coverage and increased costs to taxpayers. Alternatively, choosing a single affordability rule would initially result in close to 4 million dependents of workers with affordable single coverage not having affordable health insurance. This would grow to close to 13 million if employees pay 50 percent of the premium.

Influence of diurnal and seasonal temperature variations on the detection of corrosion in reinforced concrete by acoustic emission

Chloride rich reinforced concrete prisms were coupled to chloride free prisms and exposed to diurnal and seasonal temperature cycles typical of those found in the UK. Acoustic Emissions (AE) and galvanic currents were continuously monitored and correlated with ambient temperature. AE and galvanic currents were found to emulate the evolution of temperature in the diurnal cycles, although no specific relationship between AE and galvanic current could be obtained. The influence of seasonal variations in galvanic current had no obvious influence on AE Energy per second over the range of corrosion rates studied. The findings suggest that AE is more sensitive to short term (diurnal) changes in corrosion rates than the longer (seasonal) effects. It was hypothesised that this is due to transitory changes in the internal microclimate of the concrete

Condition monitoring of reinforced concrete structures at risk from reinforcement corrosion

The corrosion of reinforced concrete structures is a major issue in the UK and worldwide, both structurally and from a maintenance management aspect. Damage induced by the corrosion of the steel can dramatically reduce the designed service life of the structure through loss of bond between the steel and concrete, or from localised loss of section of the corroding rebars. Failure to manage the maintenance of reinforced concrete may result in the premature replacement of the structure or in extreme cases, structural failure. Avoiding such scenarios can be aided through improved detection and monitoring of corrosion in concrete. In addition, combining this with a condition management tool, capable of benchmarking, index testing and prioritising areas of the concrete structure(s) for remedial action, would provide robust facilities management techniques for structural assets. This paper suggests how the results of a novel non-destructive corrosion detection technique, currently being developed, could be incorporated into a condition-monitoring tool for the facilities management of structures. The development of protocols based on laboratory and field data enable the formation of a condition-monitoring tool forming part of a longterm maintenance strategy for estate owners and managers

'Breakfast: how important is it really?' A response

No abstract available