First-passage times for non-Markovian processes: Multivalued noise

A new method for the calculation of first-passage times for non-Markovian processes is presented. In addition to the general formalism, some familiar examples are worked out in detail.

Life Times, Summer 2009

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Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Extreme times in financial markets.

We apply the theory of continuous time random walks (CTRWs) to study some aspects involving extreme events in financial time series. We focus our attention on the mean exit time (MET). We derive a general equation for this average and compare it with empirical results coming from high-frequency data of the U.S. dollar and Deutsche mark futures market. The empirical MET follows a quadratic law in the return length interval which is consistent with the CTRW formalism.

Mean first-passage times for systems driven by gamma and McFadden dichotomous noise

We consider mean first-passage times (MFPTs) for systems driven by non-Markov gamma and McFadden dichotomous noises. A simplified derivation is given of the underlying integral equations and the theory for ordinary renewal processes is extended to modified and equilibrium renewal processes. The exact results are compared with the MFPT for Markov dichotomous noise and with the results of Monte Carlo simulations.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Social Investment Policies in Times of Permanent Austerity

The objective of this paper is to identify the political conditions that are most likely to be conducive to the development of social investment policies. It starts from the view put forward by theorists of welfare retrenchment that in the current context of permanent austerity, policy is likely to be dominated by retrenchment and implemented in a way that allows governments to minimise the risk of electoral punishment (blame avoidance). It is argued that this view is inconsistent with developments observed in several European countries, were some welfare state expansion has taken place mostly in the fields of childcare and active labour market policy. An alternative model is put forward, that emphasises the notion of "affordable credit claiming". It is argued that even under strong budgetary pressures, governments maintain a preference for policies that allow them to claim credit for their actions. Since the traditional redistributive policies tend to be off the menu for cost reasons, governments have tended to favour investments in childcare and active labour market policy as credit claiming tools. Policies developed in this way while they have a social investment flavour, tend to be rather limited in the extent to which they genuinely improve prospects of disadvantaged people by investing in their human capital. A more ambitious strategy of social investment sees unlikely to develop on the basis of affordable credit claiming. The paper starts by presenting the theoretical argument, which is then illustrated with examples taken from European countries both in the pre-crisis and in the post-crisis years.

Retention half times in the skeleton of plutonium and Sr-90 from above-ground nuclear tests: A retrospective study of the Swiss population

Plutonium and Sr-90 are considered to be among the most radiotoxic nuclides produced by the nuclear fission process. In spite of numerous studies on mammals and humans there is still no general agreement on the retention half time of both radionuclides in the skeleton in the general population. Here we determined plutonium and Sr-90 in human vertebrae in individuals deceased between 1960 and 2004 in Switzerland. Plutonium was measured by sensitive SF-ICP-MS techniques and Sr-90 by radiometric methods. We compared our results to the ones obtained for other environmental compartments to reveal the retention half time of NBT fallout Pu-239 and Sr-90 in trabecular bones of the Swiss population. Results show that plutonium has a retention half time of 40 +/- 14 years. In contrast Sr-90 has a shorter retention half time of 13.5 +/- 1.0 years. Moreover Sr-90 retention half time in vertebrae is shown to be linked to the retention half time in food and other environmental compartments. These findings demonstrate that the renewal of the vertebrae through calcium homeostatic control is faster for Sr-90 excretion than for plutonium excretion. The precise determination of the retention half time of plutonium in the skeleton will improve the biokinetic model of plutonium metabolism in humans. (C) 2010 Elsevier Ltd. All rights reserved.

Novel anesthetics and other treatment strategies for refractory status epilepticus

Refractory status epilepticus (RSE)-that is, seizures resistant to at least two antiepileptic drugs (AEDs)-is generally managed with barbiturates, propofol, or midazolam, despite a low level of evidence (Rossetti, 2007). When this approach fails, the need for alternative pharmacologic and nonpharmacologic strategies emerges. These have been investigated even less systematically than the aforementioned compounds, and are often used, sometimes in succession, in cases of extreme refractoriness (Robakis & Hirsch, 2006). Several possibilities are reviewed here. In view of the marked heterogeneity of reported information, etiologies, ages, and comedications, it is extremely difficult to evaluate a given method, not to say to compare different strategies among them. Pharmacologic Approaches Isoflurane and desflurane may complete the armamentarium of anesthetics,' and should be employed in a ''close'' environment, in order to prevent intoxication of treating personnel. c-Aminobutyric acid (GABA)A receptor potentiation represents the putative mechanism of action. In an earlier report, isoflurane was used for up to 55 h in nine patients, controlling seizures in all; mortality was, however, 67% (Kofke et al., 1989). More recently, the use of these inhalational anesthetics was described in seven subjects with RSE, for up to 26 days, with an endtidal concentration of 1.2-5%. All patients required vasopressors, and paralytic ileus occurred in three; outcome was fatal in three patients (43%) (Mirsattari et al., 2004). Ketamine, known as an emergency anesthetic because of its favorable hemodynamic profile, is an N-methyl-daspartate (NMDA) antagonist; the interest for its use in RSE derives from animal works showing loss of GABAA efficacy and maintained NMDA sensitivity in prolonged status epilepticus (Mazarati & Wasterlain, 1999). However, to avoid possible neurotoxicity, it appears safer to combine ketamine with GABAergic compounds (Jevtovic-Todorovic et al., 2001; Ubogu et al., 2003), also because of a likely synergistic effect (Martin & Kapur, 2008). There are few reported cases in humans, describing progressive dosages up to 7.5 mg/kg/h for several days (Sheth & Gidal, 1998; Quigg et al., 2002; Pruss & Holtkamp, 2008), with moderate outcomes. Paraldehyde acts through a yet-unidentified mechanism, and appears to be relatively safe in terms of cardiovascular tolerability (Ramsay, 1989; Thulasimani & Ramaswamy, 2002), but because of the risk of crystal formation and its reactivity with plastic, it should be used only as fresh prepared solution in glass devices (Beyenburg et al., 2000). There are virtually no recent reports regarding its use in adults RSE, whereas rectal paraldehyde in children with status epilepticus resistant to benzodiazepines seems less efficacious than intravenous phenytoin (Chin et al., 2008). Etomidate is another anesthetic agent for which the exact mechanism of action is also unknown, which is also relatively favorable regarding cardiovascular side effects, and may be used for rapid sedation. Its use in RSE was reported in eight subjects (Yeoman et al., 1989). After a bolus of 0.3 mg/kg, a drip of up to 7.2 mg/kg/h for up to 12 days was administered, with hypotension occurring in five patients; two patients died. A reversible inhibition of cortisol synthesis represents an important concern, limiting its widespread use and implying a careful hormonal substitution during treatment (Beyenburg et al., 2000). Several nonsedating approaches have been reported. The use of lidocaine in RSE, a class Ib antiarrhythmic agent modulating sodium channels, was reviewed in 1997 (Walker & Slovis, 1997). Initial boluses up to 5 mg/kg and perfusions of up to 6 mg/kg/h have been mentioned; somewhat surprisingly, at times lidocaine seemed to be successful in controlling seizures in patients who were refractory to phenytoin. The aforementioned dosages should not be overshot, in order to keep lidocaine levels under 5 mg/L and avoid seizure induction (Hamano et al., 2006). A recent pediatric retrospective survey on 57 RSE episodes (37 patients) described a response in 36%, and no major adverse events; mortality was not given (Hamano et al., 2006 Verapamil, a calcium-channel blocker, also inhibits P-glycoprotein, a multidrug transporter that may diminish AED availability in the brain (Potschka et al., 2002). Few case reports on its use in humans are available; this medication nevertheless appears relatively safe (under cardiac monitoring) up to dosages of 360 mg/day (Iannetti et al., 2005). Magnesium, a widely used agent for seizures elicited by eclampsia, has also been anecdotally reported in RSE (Fisher et al., 1988; Robakis & Hirsch, 2006), but with scarce results even at serum levels of 14 mm. The rationale may be found in the physiologic blockage of NMDA channels by magnesium ions (Hope & Blumenfeld, 2005). Ketogenic diet has been prescribed for decades, mostly in children, to control refractory seizures. Its use in RSE as ''ultima ratio'' has been occasionally described: three of six children (Francois et al., 2003) and one adult (Bodenant et al., 2008) were responders. This approach displays its effect subacutely over several days to a few weeks. Because ''malignant RSE'' seems at times to be the consequence of immunologic processes (Holtkamp et al., 2005), a course of immunomodulatory treatment is often advocated in this setting, even in the absence of definite autoimmune etiologies (Robakis & Hirsch, 2006); steroids, adrenocorticotropic hormone (ACTH), plasma exchanges, or intravenous immunoglobulins may be used alone or in sequential combination. Nonpharmacologic Approaches These strategies are described somewhat less frequently than pharmacologic approaches. Acute implantation of vagus nerve stimulation (VNS) has been reported in RSE (Winston et al., 2001; Patwardhan et al., 2005; De Herdt et al., 2009). Stimulation was usually initiated in the operation room, and intensity progressively adapted over a few days up to 1.25 mA (with various regimens regarding the other parameters), allowing a subacute seizure control; one transitory episode of bradycardia/asystole has been described (De Herdt et al., 2009). Of course, pending identification of a definite seizure focus, resective surgery may also be considered in selected cases (Lhatoo & Alexopoulos, 2007). Low-frequency (0.5 Hz) transcranial magnetic stimulation (TMS) at 90% of the resting motor threshold has been reported to be successful for about 2 months in a patient with epilepsia partialis continua, but with a weaning effect afterward, implying the need for a repetitive use (Misawa et al., 2005). More recently, TMS was applied in a combination of a short ''priming'' high frequency (up to 100 Hz) and longer runs of low-frequency stimulations (1 Hz) at 90-100% of the motor threshold in seven other patients with simple-partial status, with mixed results (Rotenberg et al., 2009). Paradoxically at first glance, electroconvulsive treatment may be found in cases of extremely resistant RSE. A recent case report illustrates its use in an adult patient with convulsive status, with three sessions (three convulsions each) carried out over 3 days, resulting in a moderate recovery; the mechanism is believed to be related to modification of the synaptic release of neurotransmitters (Cline & Roos, 2007). Therapeutic hypothermia, which is increasingly used in postanoxic patients (Oddo et al., 2008), has been the object of a recent case series in RSE (Corry et al., 2008). Reduction of energy demand, excitatory neurotransmission, and neuroprotective effects may account for the putative mechanism of action. Four adult patients in RSE were cooled to 31_-34_C with an endovascular system for up to 90 h, and then passively rewarmed over 2-50 h. Seizures were controlled in two patients, one of whom died; also one of the other two patients in whom seizures continued subsequently deceased. Possible side effects are related to acid-base and electrolyte disturbances, and coagulation dysfunction including thrombosis, infectious risks, cardiac arrhythmia, and paralytic ileus (Corry et al., 2008; Cereda et al., 2009). Finally, anecdotic evidence suggests that cerebrospinal fluid (CSF)-air exchange may induce some transitory benefit in RSE (Kohrmann et al., 2006); although this approach was already in use in the middle of the twentieth century, the mechanism is unknown. Acknowledgment A wide spectrum of pharmacologic (sedating and nonsedating) and nonpharmacologic (surgical, or involving electrical stimulation) regimens might be applied to attempt RSE control. Their use should be considered only after refractoriness to AED or anesthetics displaying a higher level of evidence. Although it seems unlikely that these uncommon and scarcely studied strategies will influence the RSE outcome in a decisive way, some may be interesting in particular settings. However, because the main prognostic determinant in status epilepticus appears to be related to the underlying etiology rather than to the treatment approach (Rossetti et al., 2005, 2008), the safety issue should always represent a paramount concern for the prescribing physician. Conclusion The author confirms that he has read the Journal's position on issues involved in ethical publication and affirms that this paper is consistent with those guidelines.

Accès aux soins et maintien dans la communauté des personnes difficiles à engager dans un traitement psychiatrique [Access to care and maintenance in the community of persons who are difficult to engage in psychiatric treatment]

Psychotic patients to not access easily to psychiatric care. First, psychotic disorders are difficult to identify among a great number of non psychotic depressive and anxious disorders. Second, inpatient care has shortened and now focus on acute care rather than long stay. For some psychotic patients, desinstitutionalization means exclusion and marginalization. Intensive case management can answer these needs in collaboration with relatives and professionals of patient's social network. Results and care's steps of intensive case management as practiced in Lausanne are described and illustrated with cases vignettes.

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Sign of the Times, September-November 2012

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