A Lindley-type equation arising from a carousel problem

Abstract: In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phasetype distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley’s equation for the waiting time in the P H/U/1 queue. Although the latter equation has no simple solution, it appears that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the P H/U/1 queue depends on to the complete inter-arrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution

Decentralised Learning MACs for Collision-free Access in WLANs

By combining the features of CSMA and TDMA, fully decentralised WLAN MAC schemes have recently been proposed that converge to collision-free schedules. In this paper we describe a MAC with optimal long-run throughput that is almost decentralised. We then design two \changed{schemes} that are practically realisable, decentralised approximations of this optimal scheme and operate with different amounts of sensing information. We achieve this by (1) introducing learning algorithms that can substantially speed up convergence to collision free operation; (2) developing a decentralised schedule length adaptation scheme that provides long-run fair (uniform) access to the medium while maintaining collision-free access for arbitrary numbers of stations

Feto-Placental Atherosclerotic Lesions in Intrauterine Fetal Demise: Role of Parental Cigarette Smoking

The atherogenic effect of cigarette smoking is already recognizable in coronary arteries of fetuses in the last gestational weeks. In this study we analyzed the atherogenic effect of mother’s and father’s smoking habit on coronary arteries and even on adnexa of 30 human fresh fetuses died from 32 to 41 gestational weeks. In 12 cases only the mothers of the victims were cigarette smokers, in 7 cases only the fathers were smokers, whereas in 11 cases nobody smoked

Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech. (2007) P10008, doi:10.1088/1742-5468/2007/10/P10008

Stakeholder ownership: a theoretical framework for cross national understanding and analyses of stakeholder involvement in issues of substance use, problem use and addiction

This project contributes to understanding of the role of different stakeholder groups in the formulation and implementation of policy in the addictions field in Austria, Denmark, Finland, Italy, Poland and the UK. It comprises a number of case studies which draw on a range of theoretical frameworks to examine stakeholder dynamics at international, national and local levels. Mainly qualitative methods were used: interviews, policy and documentation analyses, webcrawler network analysis, and simple surveys; one case study was based on a survey only. The case studies fall into four main categories: three focus on controversial issues in drug treatment policy and practice – opioid substitution treatment, drug consumption rooms, and heroin assisted treatment; three look at stakeholder activity in alcohol control and public health; one pilot case study considers the potential role of researchers in the development of a scientific network around gambling; and one looks at the role of nurses in implementing brief interventions. In addition, themes explored across case studies included the role of evidence and stakeholder activity, drug users as stakeholders, and the role of external stakeholders on national policy. Professional stakeholders at implementation level and families and drug users as stakeholders are also considered. The case studies revealed that, in many instances, the addictions field is characterised by tensions between groups, by entrenched relationships between some addiction-specific stakeholder groups and powerful political stakeholders, and by the dominance of some forms of evidence over other forms of knowledge. Science and scientists are only influential in policy terms if their scientific findings ‘fit’ with the wider political context. Nevertheless, at least within the European context, there are opportunities for new stakeholder groups to emerge and gain policy salience and there are opportunities for stakeholders to challenge prevailing frames of understanding the addictions and prevailing modes of responding to problems of substance misuse and addiction

Getters for improved technetium containment in cementitious waste forms.

A cementitious waste form, Cast Stone, is a possible candidate technology for the immobilization of low activity nuclear waste (LAW) at the Hanford site. This work focuses on the addition of getter materials to Cast Stone that can sequester Tc from the LAW, and in turn, lower Tc release from the Cast Stone. Two getters which produce different products upon sequestering Tc from LAW were tested: Sn(II) apatite (Sn-A) that removes Tc as a Tc(IV)-oxide and potassium metal sulfide (KMS-2) that removes Tc as a Tc(IV)-sulfide species, allowing for a comparison of stability of the form of Tc upon entering the waste form. The Cast Stone with KMS-2 getter had the best performance with addition equivalent to ∼0.08wt% of the total waste form mass. The observed diffusion (Dobs) of Tc decreased from 4.6±0.2×10-12cm2/s for Cast Stone that did not contain a getter to 5.4±0.4×10-13cm2/s for KMS-2 containing Cast Stone. It was found that Tc-sulfide species are more stable against re-oxidation within getter containing Cast Stone compared with Tc-oxide and is the origin of the decrease in Tc Dobs when using the KMS-2

A Markovian event-based framework for stochastic spiking neural networks

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks

Systemic Risk and Default Clustering for Large Financial Systems

As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as law of large numbers and central limit theorems allow to approximate the distribution in large systems and study quantities such as the loss distribution in large portfolios. Large deviations analysis allow us to study the tail of the loss distribution and to identify pathways to default clustering. Sensitivity analysis allows to understand the most likely ways in which different effects, such as contagion and systematic risks, combine to lead to large default rates. Such results could give useful insights into how to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015