Time Epochs Research Articles

Electrical source imaging of interictal spikes using multiple sparse volumetric priors for presurgical epileptogenic focus localization.

Electrical source imaging of interictal spikes observed in EEG recordings of patients with refractory epilepsy provides useful information to localize the epileptogenic focus during the presurgical evaluation. However, the selection of the time points or time epochs of the spikes in order to estimate the origin of the activity remains a challenge. In this study, we consider a Bayesian EEG source imaging technique for distributed sources, i.e. the multiple volumetric sparse priors (MSVP) approach. The approach allows to estimate the time courses of the intensity of the sources corresponding with a specific time epoch of the spike. Based on presurgical averaged interictal spikes in six patients who were successfully treated with surgery, we estimated the time courses of the source intensities for three different time epochs: (i) an epoch starting 50 ms before the spike peak and ending at 50% of the spike peak during the rising phase of the spike, (ii) an epoch starting 50 ms before the spike peak and ending at the spike peak and (iii) an epoch containing the full spike time period starting 50 ms before the spike peak and ending 230 ms after the spike peak. To identify the primary source of the spike activity, the source with the maximum energy from 50 ms before the spike peak till 50% of the spike peak was subsequently selected for each of the time windows. For comparison, the activity at the spike peaks and at 50% of the peaks was localized using the LORETA inversion technique and an ECD approach. Both patient-specific spherical forward models and patient-specific 5-layered finite difference models were considered to evaluate the influence of the forward model. Based on the resected zones in each of the patients, extracted from post-operative MR images, we compared the distances to the resection border of the estimated activity. Using the spherical models, the distances to the resection border for the MSVP approach and each of the different time epochs were in the same range as the LORETA and ECD techniques. We found distances smaller than 23 mm, with robust results for all the patients. For the finite difference models, we found that the distances to the resection border for the MSVP inversions of the full spike time epochs were generally smaller compared to the MSVP inversions of the time epochs before the spike peak. The results also suggest that the inversions using the finite difference models resulted in slightly smaller distances to the resection border compared to the spherical models. The results we obtained are promising because the MSVP approach allows to study the network of the estimated source-intensities and allows to characterize the spatial extent of the underlying sources.

System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy

In this paper, we deal with a discrete-time $Geo/G/1$ queueing system under the control of Min($N, V$)-policy in which the server takes single vacation whenever the system becomes empty. The Min($N, V$)-policy means that the server commences its service once the number of waiting customers reaches threshold $N$ or when its vacation time ends with at least one but less than $N$ customers waiting for processing, whichever occurs first. Otherwise, if no customer is presenting at the end of the server vacation, the server remains idle until the first arrival occurs. Under these assumptions, the $z$-transform expressions for the transient queue size distribution at time epoch $n^+$ are obtained by employing the renewal process theory and the total probability decomposition technique. Based on the transient analysis, the explicit recursive formulas of the steady-state queue length distribution at time epochs $n^+$, $n$, $n^-$ and outside observer's time epoch are derived, respectively. Additionally, the stochastic decomposition structure is presented and some other performance measures are also discussed. Furthermore, some computational experiments are implemented to demonstrate the significant application value of the recursive formulas for the steady-state queue size in designing system capacity. Finally, the optimal threshold of $N$ for economizing the system cost is numerically determined.

Neonatal outcomes by hospital of birth in Nova Scotia between 1988 and 2012: improvements in mortality and morbidity

Objectives: (1) To describe differences in newborn outcomes with respect to hospital of birth, place of maternal residence, and time epoch for infants born in Nova Scotia between 1988 and 2012. (2) To examine the possible impacts that regionalization of maternal newborn health services between 1988 and 2012 have had on neonatal mortality rates in Nova Scotia. Methods: Data on all infants delivered in Nova Scotia between January 1, 1988 and December 31, 2012 was extracted from the Nova Scotia Perinatal Atlee Database. Infant perinatal mortality and neonatal morbidity rates were calculated in 5-year time epochs and examined by delivery hospital classification (community, regional or tertiary), and maternal driving distance from hospital. Trends by epoch, delivery hospital and driving distance were examined. Results: From 1988 to 2012 perinatal mortality rates per 1000 for all births improved at both regional (from 9.8 to 5.7/1000) and tertiary hospitals (from 12.3 to 8.1/1000). Perinatal mortality rates for low risk births remained low and did not change significantly during this time period. Overall, neonatal morbidity rates fell across the province. Neonatal outcomes did not vary with increasing maternal distance from obstetrical services. Conclusions: Overall, infant perinatal morbidity and mortality outcomes have improved in Nova Scotia between 1988 and 2012. Regionalization of obstetrical care may have played a role in improving neonatal mortality rates among high-risk births. Increasing rural maternal isolation from obstetrical services did not impact infant perinatal mortality and morbidity outcomes when services remained available regionally.

Psychophysiological Effectiveness of Calmvalera Hevert Tablets as Measured by EnkephaloVision in Anxious Subjects during Audio-Visual Cognitive and Emotional Challenges: A Double-Blind, Randomized, Placebo-Controlled, 2-Armed, Phase IV Study in Parallel Design

Subjects suffering from anxiety during examinations often take drugs with considerable side effects. As alternative, homeopathic preparations virtually lack side effects in general. However, clinical efficacy has to be demonstrated. This experimental series was initiated to provide evidence, that Calmvalera Hevert tablets, marketed for treatment of nervous restlessness and better coping with stress, have an influence on brain electric activity. In order to test this, a new clinical design was used: “EnkephaloVision”. It consists of the combination of quantitative EEG recording with time epochs of 364 ms (Neurocode-Tracking) with conventional Eye-Tracking. Seventeen channels of EEG and one channel EOG were recorded. After frequency analysis (FFT) current source density was calculated. Recording was performed in the presence of a video clip, which contained several different cognitive and emotional challenges in series. Twenty-four male and female subjects having a score >60 in an anxiety questionnaire (Prufungsangstfragebogen PAF-S) were recruited to participate. A correlation between the Hamilton anxiety score and spectral alpha1 power during the recording condition “eyes open” before drug intake was detected. Spectral power was averaged including Cz, F3 and F4 electrode positions. Audiovisual challenges induced spectral changes with respect to delta, theta and beta power, not in the alpha ranges, to a different but statistically significant degree. Intake of Calmvalera Hevert tablets resulted in statistically significant increases of alpha1 and alpha2 spectral power during most of the recording conditions within the left hemisphere. Increases of alpha activity have been related to relaxation and calmness as reported in the literature. Discriminant analysis of the whole data set revealed a clear difference between verum and placebo and a projection of the data into the vicinity of other plant-derived calming preparations. Performance of psychometric tasks was not disturbed. Efficacy of Calmvalera Hevert tablets points to active molecules contained due to low triturations (D2 - D8).

Psychophysiological Effects of Zembrin<sup>®</sup>Using Quantitative EEG Source Density in Combination with Eye-Tracking in 60 Healthy Subjects. A Double-Blind, Randomized, Placebo-Controlled, 3-Armed Study with Parallel Design

The endemic South African succulent plant Sceletium tortuosum (L.) N.E. Br., family Mesembryathemaceae, is known as kanna in Nama, kougoed in Afrikaans, and sceletium in English. The plant has been used as a tea and as a masticatory for millennia by indigenous San hunter-gatherers and Nama pastoralists for endurance and well-being. It has been reported that the plant “gives strength to their limbs, and takes away pain, and makes their memory strong”. The current investigation aimed at the psychophysiological characterization of 25.0 and 50.0 mg of a special extract marketed as Zembrin® in comparison to placebo using a new methodology called “EnkephaloVision”. This combination of EEG Neurocode-Tracking and Eye-Tracking allows for concomitant analysis of time epochs of only 364 ms duration. Spectral EEG analysis during cognitive and emotional challenges revealed statistically significant increases of delta (p < 0.01 during arithmetic calculation and watching a boring animal video) and theta spectral power (p < 0.10 during these same challenges) in the presence of Zembrin® within the frontal brain. It is these same increases of slow waves in the frontal brain that are described in the literature during performance of mental tests. This indicates a positive effect of Zembrin® on the electrical activity of the brain during cognitive processing. In addition, alpha1 and alpha2 spectral power in the frontal brain was increased during several challenges including brain teasing, arithmetic calculations and performance of a memory test. From the literature, increases of spectral alpha1 power indicate a greater degree of calmness and may represent decreased depressive symptoms, while increases in alpha2 waves have been related to memory. Beta2 waves increased during mental performance in the presence of the higher dosage of Zembrin® in parietal, occipital and temporal brain regions. In comparison to placebo, Zembrin® induced frequency changes in the brain, which have been related to enhanced attention and memory. These results may represent a positive action of Zembrin® on cognitive and emotional processes in the brain.

The model of the Nociceptive Withdrawal Reflex in horses

In equine pain research, the Nociceptive Withdrawal Reflex (NWR) model has been proposed as an alternative to classical thermal, mechanical and electrical models to investigate the physiology of nociception. This model does not only allow a more reliable definition of the nociceptive threshold through neurophysiological characterization of the elicited response , but also consents plotting a stimulus-response curve as well as the evaluation of temporal summation mechanisms. Aim of this report is to summarize the experience and results obtained using the NWR model in horses over the last 15 years, firstly with the purpose of describing its physiological characteristics and secondly with the aim of evaluating its pharmacological modulation through analgesic and anaesthetic compounds. The NWR can be elicited in horses through electrical transcutaneous stimulation of a peripheral sensory nerve and is recorded through electromyographic electrodes from the muscles involved in the withdrawal reaction. As the non-nociceptive fibres have lower threshold to electrical stimuli than the nociceptive one, it is impossible to differentiate between the two groups on the stimulus side. So, the only guidance to assess the quality of the stimulus and the recruitment of nociceptive afferents should rely on the characteristics of the electromyographic response, most of all on the timing of its various components. A reflex response can be considered to be a true NWR only if it appears within a time epoch compatible with the conduction velocity of the Aδ fibers. Furthermore a clearly recognizable EMG burst in the epoch of interest has to be accompanied by a consistent aversive behavioural reaction, thus allowing the definition of a reliable NWR threshold. Responses to stimulation intensities below and above thresholds can be quantified to draw a stimulus response curve. Furthermore, through repeated stimulation at subthreshold intensities, it is possible to elicit the phenomenon of temporal summation, considered to be the early phase of the wind up phenomenon and of relevant interest to study central integrative mechanisms of pain processing. Alpha-2 agonists, opioids, systemic lidocaine, ketamine and inhalation anaesthetics have been investigated using the NWR model in horses. Drug-specific modulation of NWR threshold, stimulus-response curves and temporal summation are summarized for each tested compound.

Steady state analysis of bulk arrival and bulk service queueing model with multiple working vacations

This paper studies a single server queue with variable batch size general service, Poisson bulk arrival and multiple working vacations where the server works with different rate rather than completely stops the service during the vacation period. In this model, the servers with variable batch size (a, b) in regular service period whereas, during the working vacation period the server starts the service if he finds even one customer in queue with a maximum of 'b' customers with different service time. Service time in working vacation and in regular period follows general distribution. The probability generating function of a queue size at an arbitrary time epochs as well as other completion epochs are derived. Expected queue length in a steady state is also obtained. Numerical illustration is presented.

Modeling the Throughput of the Linux-Based Agile-SD Transmission Control Protocol

Agile-SD is one of the latest versions of loss-based congestion control algorithm (CCA), which has been proposed to improve the total performance of transmission control protocol (TCP) over high-speed and short-distance networks. It has introduced a new mechanism, called agility factor mechanism, which shortens the epoch time to reduce the sensitivity to packet losses and in turn to increase the average throughput. Agile-SD has only been tested via simulation; however, it has not been mathematically proven or evaluated. The contribution of this paper is twofold. First, a new mathematical model for the throughput of NewReno and Agile-SD is proposed. This model is designed using the well-known Markov chains to validate the correctness of Agile-SD and to show the impact of buffer size, multiplicative decrease factor, and maximum limit of agility factor ({\lambda}max ) on the total performance. Second, an automated algorithm configuration and parameter tuning (AACPT) technique is employed to optimize and automate the configuration of {\lambda}max . Furthermore, the numerical results for both NewReno and Agile-SD are compared with the simulation results, in which the validity of the proposed model is confirmed. Moreover, the output of the AACPT is exploited to formulate a new equation, which calculates the optimal {\lambda}max from a given \b{eta} in order to conserve the standard interface of the TCP. This equation increases the scalability of Agile-SD and improves its total performance.

A Neurohospitalist Discharge Clinic Shortens the Transition From Inpatient to Outpatient Care.

Medicine hospitalist programs have effectively incorporated hospitalist-run discharge clinics into clinical practice to help bridge the vulnerable transition periods after hospital discharge. A neurohospitalist discharge clinic would similarly allow continuity with the inpatient provider while addressing challenges in the coordination of neurologic care. We anticipated that this would afford a greater total number of patients to be seen and at a shorter interval. The number of posthospital discharge patients who were seen in general continuity per month in the 6 months prior to establishment of neurohospitalist discharge clinic and those seen over 1 full calendar year 6 months after clinic began was compared by reviewing medical records. Average length of time between discharge from hospital and first clinic visit was compared between patients seen in general neurology continuity clinic and those seen in discharge clinic. There was a significant increase in the average number of postdischarge visits per month after initiation of neurohospitalist discharge clinic compared to prior (16.1 visits vs 10.5 visits, P = .001). Patients were seen significantly sooner after hospitalization in discharge clinic (35.9 ± 4.3 days) compared to those seen in general continuity clinic during the same time epoch (57.6 ± 4.1 days; p < 0.001). Creation of a neurohospitalist discharge clinic was effective in increasing posthospital discharge follow-up frequency and shortening duration of time to follow-up.

ON A M^[X]/G/1 QUEUEING SYSTEM WITH GENERALIZED COXIAN-2 SERVICE AND OPTIONAL GENERALIZED COXIAN-2 VACATION

We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times G1 is compulsory and the second service with general service times G2 is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server may take a vacation of random length of time with general vacation times V1. After completion of the first phase of vacation the server may or may not take the second optional vacation with general vacation times V2. We term this two phase vacation as optional generalized Coxian-2 sever vacation. We obtain steady state probability generating functions for the queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.

Doppler imaging of LQ Hydrae for 1998–2002

We study the spot distribution on the surface of LQ~Hya during the observing seasons October 1998 -- November 2002. We look for persistent active longitudes, trends in the level of spot activity and compare to photometric data, specifically to the derived time epochs of the lightcurve minima. We apply the Doppler Imaging technique on photospheric spectral lines using an inversion code to retrieve images of the surface temperature. We present new temperature maps using multiple spectral lines for a total of 7 seasons. We calculate spot coverage fractions from each map, and as a result we find a general trend that is interpreted to be an indication of a spot cycle. There is a minimum during the observing season of March 1999. After this the activity increases until November 2000, followed by a general decrease in activity again. We find no evidence for active longitudes persisting over multiple observing seasons. The spot activity appears to be concentrated to two latitude regions. The high latitude spots are particularly strong when the spot coverage is at a maximum. Using the currently accepted rotation period, we find spot structures to show a trend in the phase-time plot, indicative of a need for a longer period. We conclude that the long-term activity of LQ~Hya is more chaotic than that of some magnetically active binary stars analyzed with similar methods, but still with clear indications of an activity cycle.

Pharmacoepidemiology of opiate use in the neonatal ICU: Increasing cumulative doses and iatrogenic opiate withdrawal.

Neonatal intensive care unit (ICU) care involves use of opiates to treat postoperative, ventilated, or chronically ill infants. Opiates provide necessary analgesia and sedation, but the morbidities include prolonged neonatal abstinence syndrome (NAS) and extended length of stay for dose tapering. Our objective was to quantify trends in opiate exposure in a tertiary care NICU. The authors hypothesize that medical opiate exposure and resultant ICU-acquired NAS would increase over time. Retrospective cross-sectional cohort study. Tertiary care NICU. High-risk inborn infants admitted in fiscal years 2003-2004, 2007-2008, and 2010-2011. Average cumulative morphine exposure (all opiate doses converted to morphine equivalents) per time epoch was compared in cohorts of clinically similar infants. Linear regression was used to assess the primary outcome, assessing changes in opiate exposure over time. Sixty-three infants were included in the final analysis. The primary analysis assessing cumulative opiate exposure per infant showed an increase of 134 mg per time epoch (95% CI-12, 279 mg, p-value 0.071). There was a statistically significant increase in the percent of infants with a diagnosis of iatrogenic NAS, increasing from 9 to 35 to 50 percent (p-value 0.012).

Geographies of the Anthropocene

Introduction If humans have become a rival to Nature, then the epic nomenclature of the great forces – the eras, periods, and epochs of geological time – have finally been reconciled with the social, something geographers might cheer or lament. For over a century, there have been calls to recognise human impact with its own geological epoch. The most recent of these calls – and the most significant given the unprecedented shift in Earth system functioning (Steffen et al., 2011) – proposes the name the Anthropocene (Crutzen and Stoermer, 2000). To date, the Anthropocene has been also the most successful in terms of its academic and popular reception. The proposal has led to an explosion of popular and academic debate among both scientific and social thinkers, and for both groups the proposal has refreshed long-standing exploration of the purported division between science and society (Rittel and Webber, 1973; Funtowicz and Ravetz, 1993). This paper introduces concepts and debates within a special issue of Geographical Research that deals with the Anthropocene. Our aim is to contribute to and help consolidate the rapidly expanding discourse that explores humanity as akin to a geological force, but with the added emphasis on geography and geographers. Geographers have a history of both being wary of ‘buzzwords’, only with hindsight to lament missed opportunities when those buzzwords are adopted by other disciplines and become the convention (see environmental studies). Is the ‘Anthropocene’ a fad, an important idea that should be embraced by geographers, or something altogether different? The notion of the Anthropocene is not so far settled that it cannot be influenced by the discipline of Geography, and there is reason to think that Geography has much to offer regardless of whether the concept becomes widely or popularly adopted or discarded. More important than the issue of its definition are the moral, cultural, and political challenges that the Anthropocene is amplifying. Geographers, then, have an opportunity to consider the concept during its ‘adolescence’ (cf Castree, 2014c) and to, simultaneously, consider whether and how the discipline might capitalise on what appears to be a rapid ascension. This ‘opportunity-challenge’ has been recognised and explored by geographers elsewhere (e.g. Dalby, 2007; Gibson-Graham, 2011; Yusoff, 2013b; Castree, 2014a; 2014b; 2014c; Johnson et al., 2014; Whitehead, 2014; Young, 2014), leading us to take up a promising and daunting issue to emerge from those Anthropocene-Geography discussions: whether and how this concept might present a ‘meeting place’ for the heterogeneous groups, framings, and sub-disciplinary specialisms that make up the discipline. The Anthropocene is a concept that is being adopted in wide and divergent ways. Our goal here is not in any way to establish consensus or impose direction, but to explore emergent themes in the context of Geography. The Anthropocene requires a sophisticated approach to space, time, knowledge, politics, social action, and, perhaps most of all, interactions between human and environmental systems, including the empirical and ontological blurring of these categories. As bs_bs_banner

A Fluid EOQ Model with Markovian Environment

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

A Fluid EOQ Model with Markovian Environment

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

A Fluid EOQ Model with Markovian Environment

We consider a production-inventory model operating in a stochastic environment that is modulated by a finite state continuous-time Markov chain. When the inventory level reaches zero, an order is placed from an external supplier. The costs (purchasing and holding costs) are modulated by the state at the order epoch time. Applying a matrix analytic approach, fluid flow techniques, and martingales, we develop methods to obtain explicit equations for these cost functionals in the discounted case and under the long-run average criterion. Finally, we extend the model to allow backlogging.

Expressions for moments of order statistics and records from the skew-normal distribution in terms of multivariate normal orthant probabilities

In designs of experiments and reliability analyze, order statistics (OS) are used for various purposes including model checking, estimations of parameters and prediction. Most of these procedures are defined on the basis of expectations of OS problems. In this paper, explicit expressions for central moments of OS coming from the skew-normal (SN) distribution are derived. The SN model enjoys interesting properties from the normal distribution while captures asymmetric behavior in the parent population. Another important topic which is related to OS is record statistics. These data are arising in some practical situations including shock models, sports and epoch times of a non-homogeneous Poisson processes. Here, we derive moments of the upper and the lower record values arising from the skew normal distribution. The obtained results may be used for prediction purposes such as predictive maintenance in a repairable system and prediction of performance of a transmission oil pipeline. Some real data sets are analyzed using the results obtained for illustration purposes.

G254(P) The impact of an obstetric birth and neonatal emergency life support education project on staff competences, organisational capacity and patient outcomes in a resource – poor setting

Aims To design, deliver and evaluate the impact of a multi-structured educational programme on the management of obstetric and neonatal emergencies in a resource poor setting. Methods I assessed the impact of a unique multi structured educational programme on Obstetric Birth and Neonatal Emergency Life Support delivered to health care workers in North Eastern Uganda using the Kirkpartrick model. Quantitative assessment methods included analysis of results of a questionnaire assessment of participants’ pre and post course knowledge base and the number of early neonatal deaths pre and post course. T- test statistics was used to analyse the results. Qualitative assessment methods included structured and semi structured direct observation of skills and interviews with trained staff in the clinical settings 2 weeks and 6 months post course. Results 138 health care workers participated in the training course delivered over two days for qualified staff and one day for students. 85% of participants completed a before and after multiple choice questionnaire evaluating knowledge of obstetric birth emergencies. Across the whole group, there was a statistically significant increase in post course scores by 10% compared with pre course scores. 97.8% of the qualified staff that underwent a practical assessment of skills at new born resuscitation were considered competent. On site evaluation of skill and practice 2 weeks post course revealed that most students used their new skills competently in a resuscitation scenario but highlighted a ‘competency gap’ in some cases. Evaluation of staff progress at 6 months revealed significant organisational challenges that affected staff training and development. Analysis of neonatal deaths showed that there was a 30% reduction in number of deaths post course compared with a similar time epoch two years earlier. Conclusion This project demonstrated that UK style emergency life support courses on Obstetric Birth and Neonatal Life Emergencies can be delivered successfully in resource poor settings. The training led to newly acquired skill sets that in turn led to improvements in individual knowledge, organisational capabilities and neonatal mortality data. The challenge faced by organisers of educational programmes in similar settings is how to ensure that the new skills are embedded in order to sustain long term continuing improvements in clinical outcomes.

Simulation of Real Discrete Time Gaussian Multivariate Stationary Processes with Given Spectral Densities

In this article we establish a simulation procedure to generate values for a real discrete time multivariate stationary process, based on a factor of spectral density matrix. We prove the convergence of the simulator, at each time epoch, to the actual process, and provide the corresponding rate of convergence. We merely assume that the spectral density matrix is continuous and of bounded variation. By using the positive root factor, we provide an extended version for the Sun and Chaika () simulator, for real univariate stationary processes.

Statistics of the longest interval in renewal processes

We consider renewal processes where events, which can for instance be the zero crossings of a stochastic process, occur at random epochs of time. The intervals of time between events, τ1, τ2, …, are independent and identically distributed (i.i.d.) random variables with a common density ρ(τ). Fixing the total observation time to t induces a global constraint on the sum of these random intervals, which accordingly become interdependent. Here we focus on the largest interval among such a sequence on the fixed time interval (0, t). Depending on how the last interval is treated, we consider three different situations, indexed by α = I, II and III. We investigate the distribution of the longest interval and the probability Qα(t) that the last interval is the longest one. We show that if ρ(τ) admits a well defined first moment, i.e. if it decays faster than 1/τ2 for large τ, then the full statistics of is given, in the large t limit, by the standard theory of extreme value statistics for i.i.d. random variables, showing in particular that the global constraint on the intervals τi does not play any role at large times in this case. However, if ρ(τ) exhibits heavy tails, ρ(τ) ∼ τ−1−θ for large τ, with index 0 < θ < 1 (like the zero-crossings of random walks corresponding to θ = 1/2), we show that the fluctuations of are governed, in the large t limit, by a stationary non-trivial universal distribution (different from a Fréchet law) which depends on both θ and α, which we compute exactly. On the other hand, Qα(t) is generically different from its counterpart for i.i.d. variables (both for narrow or heavy tailed distributions ρ(τ)). In particular, in the case 0 < θ < 1, the large t behaviour of Qα(t) gives rise to universal non-trivial constants (depending also on both θ and α) which we compute exactly.