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

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

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

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

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

An impact and feasibility evaluation of a 6 week (9 hour) active play intervention on fathers' engagement with their preschool children: A feasibility study

Research has demonstrated the benefits of father involvement with their children and a link between uninvolved fatherhood and societal problems. Children’s Centres (n=15) received 6 x 90 minute active play sessions designed to foster six aspects of parental engagement. Fathers’ engagement and attitudes to child PA were measured pre- and post-intervention via questionnaire. Acceptability of the intervention was explored through participant and staff focus groups. Results showed no effect on overall time fathers spent with their child during the week (t (36) = 0.178, p = 0.860) and the weekend (t (36) =1.166, p = 0.252). Qualitative results demonstrated the sessions provided opportunities for fathers to spend quality time with their children. Parenting self-efficacy increased across the subscale control, t (36) = -2.97, p = 0.04. Fathers increased awareness of their role in motivating their child to play (z = -2.46, p = 0.01). Further longitudinal research is recommended. Key Words: fathers’ engagement; childcare settings; parenting programmes; active play; parenting self-efficac

Force-length recording of eye muscles during local-anesthesia surgery in 32 strabismus patients

Abstract. Force-length recordings were made from isolated human eye muscles during strabismus surgery in local, eye-drop anesthesia in 32 adult patients. From each muscle three recordings were made: (1) while the patient looked with the other eye into the field of action of the recorded muscle, (2) looked ahead, and (3) looked out of the field of action of the recorded muscle. Non-innervated eye muscles (state 3) had an approximately exponential relation between force and length. During contraction evoked by letting the patient look ahead or into the field of action of the muscle (states I or 2), the relation between force and length was grossly linear. The approximate spring constants of horizontal rectus muscles that had not been operated on before ranged from 2 to 4 g/mm. In palsies, the degree of muscle paresis could be quantified accurately using this method and, accordingly, cases of true superior oblique palsy could be well differentiated from strabismus sursoadductorius (= upshoot in adduction) that may mimic a superior oblique palsy. In seven patients with Graves' disease of recent onset, affected muscles were found to be very stiff when the other eye looked ahead. It was expected that these stiff muscles would be able to shorten to some extent but would not be able to lengthen, due to fibrosis of the muscle. We found, however, that the affected muscles lengthened considerably when the other eye looked out of the field of action of the muscle. This implies that, in these cases of Graves' disease of recent onset, the raised muscle tension and reduced elasticity of the affected muscles and, hence, the strabismus were primarily caused by active muscle contraction, not by fibrosis

Involvement of calpains in adult neurogenesis: implications for stroke

Calpains are ubiquitous proteases involved in cell proliferation, adhesion and motility. In the brain, calpains have been associated with neuronal damage in both acute and neurodegenerative disorders, but their physiological function in the nervous system remains elusive. During brain ischemia, there is a large increase in the levels of intracellular calcium, leading to the activation of calpains. Inhibition of these proteases has been shown to reduce neuronal death in a variety of stroke models. On the other hand, after stroke, neural stem cells (NSC) increase their proliferation and newly formed neuroblasts migrate towards the site of injury. However, the process of forming new neurons after injury is not efficient and finding ways to improve it may help with recovery after lesion. Understanding the role of calpains in the process of neurogenesis may therefore open a new window for the treatment of stroke. We investigated the involvement of calpains in NSC proliferation and neuroblast migration in two highly neurogenic regions in the mouse brain, the dentate gyrus (DG) and the subventricular zone (SVZ). We used mice that lack calpastatin, the endogenous calpain inhibitor, and calpains were also modulated directly, using calpeptin, a pharmacological calpain inhibitor. Calpastatin deletion impaired both NSC proliferation and neuroblast migration. Calpain inhibition increased NSC proliferation, migration speed and migration distance in cells from the SVZ. Overall, our work suggests that calpains are important for neurogenesis and encourages further research on their neurogenic role. Prospective therapies targeting calpain activity may improve the formation of new neurons following stroke, in addition to affording neuroprotection.Foundation for Science and Technology, (FCT, Portugal); COMPETE; FEDER [PTDC/SAU-NMC/112183/2009, PEst-C/SAU/LA0001/2013-2014, PEst-OE/EQB/LA0023/2013-2014]; NIH [GM 23244]; FCT [SFRH/BPD/78901/2011, SFRH/BD/38127/2007, SFRH/BD/78050/2011]info:eu-repo/semantics/publishedVersio