Nucleation for one-dimensional long-range Ising models

In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory with two examples (exponentially and polynomially decaying interaction) and we show that the critical droplet can be macroscopic or mesoscopic, according to the value of the external magnetic field.Comment: 15 pages, 3 figure

Основні віхи розвитку української гірничої термінології

Ідеться про розвиток термінології й номенклатури гірничої справи, зокрема частково шахтобудування, яка активно розвивалася впродовж 20–З0-х рр. ХХ ст. Наголошено на спірних моментах в історії становлення цієї лексичної групи. Зроблено висновок про те, що нині гірнича термінологія української мови практично повністю унормована завдяки ретельній праці лексикографів та фахівців-гірників.The paper examines the ways mining terminology and nomenclature was developed. Special attention is drawn to the period of the 20th – 30th of the 20th century, when the term system was formed. The research focuses on disputable moments in the history of lexical group development; it concludes that mining terminology is normalized in the present-day Ukrainian language thanks to the careful work of lexicographers and mining specialist

Sharp asymptotics for stochastic dynamics with parallel updating rule with self-interaction

In this paper we study metastability for a stochastic dynamics with a parallel updating rule in particular for a probabilistic cellular automata. The problem is addressed in the Freidlin Wentzel regime, i.e., finite volume, small magnetic field, and in the limit when temperature tends to zero. We are interested in how the system nucleates, i.e., in properties of the transition from the metastable state (the configuration with all minuses) to the stable state (the configuration with all pluses). In this paper we show that the nucleation time divided by its average converges to an exponential random variable and we express the proportionality constant for the average nucleation time in terms of parameters of the model. Our approach combines geometric and potential theoretic arguments. A special feature of parallel dynamics is the existence of many fixed points and cyclic pairs of the zero temperature dynamics, in which the system can be trapped in its way to the stable phase. These cyclic points are corresponding to chessboard kind of configurations that under the parallel dynamics alternate between even and odd

Sum of exit times in series of metastable states in probabilistic cellular automata

\u3cp\u3eReversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs-like measures. For those models the dynamics can be trapped for a very long time in states which are very different from the ones typical of stationarity. This phenomenon can be recasted in the framework of metastability theory which is typical of Statistical Mechanics. In this paper we consider a model presenting two not degenerate in energy metastable states which form a series, in the sense that, when the dynamics is started at one of them, before reaching stationarity, the system must necessarily visit the second one. We discuss a rule for combining the exit times from each of the metastable states.\u3c/p\u3

Homogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures

In this paper, we study metastability in large volumes at low temperatures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let ß denote the inverse temperature and let ¿ß¿Z2 be a square box with periodic boundary conditions such that limß¿8|¿ß|=8. We run the dynamics on ¿ß, starting from a random initial configuration where all of the droplets (clusters of plus-spins and clusters of particles, respectively) are small. For large ß and for interaction parameters that correspond to the metastable regime, we investigate how the transition from the metastable state (with only small droplets) to the stable state (with one or more large droplets) takes place under the dynamics. This transition is triggered by the appearance of a single critical droplet somewhere in ¿ß. Using potential-theoretic methods, we compute the average nucleation time (the first time a critical droplet appears and starts growing) up to a multiplicative factor that tends to 1 as ß¿8. It turns out that this time grows as KeGß/|¿ß| for Glauber dynamics and as KßeGß/|¿ß| for Kawasaki dynamics, where G is the local canonical (resp. grand-canonical) energy, to create a critical droplet and K is a constant reflecting the geometry of the critical droplet, provided these times tend to infinity (which puts a growth restriction on |¿ß|). The fact that the average nucleation time is inversely proportional to |¿ß| is referred to as homogeneous nucleation because it says that the critical droplet for the transition appears essentially independently in small boxes that partition ¿ß

The attributable mortality of delirium in critically ill patients: Prospective cohort study

Objective: To determine the attributable mortality caused by delirium in critically ill patients. Design: Prospective cohort study. Setting: 32 mixed bed intensive care unit in the Netherlands, January 2011 to July 2013. Participants: 1112 consecutive adults admitted to an intensive care unit for a minimum of 24 hours. Exposures: Trained observers evaluated delirium daily using a validated protocol. Logistic regression and competing risks survival analyses were used to adjust for baseline variables and a marginal structural model analysis to adjust for confounding by evolution of disease severity before the onset of delirium. Main outcome measure: Mortality during admission to an intensive care unit. Results: Among 1112 evaluated patients, 558 (50.2%) developed at least one episode of delirium, with a median duration of 3 days (interquartile range 2-7 days). Crude mortality was 94/558 (17%) in patients with delirium compared with 40/554 (7%) in patients without delirium (P<0.001). Delirium was significantly associated with mortality in the multivariable logistic regression analysis (odds ratio 1.77, 95% confidence interval 1.15 to 2.72) and survival analysis (subdistribution hazard ratio 2.08, 95% confidence interval 1.40 to 3.09). However, the association disappeared after adjustment for time varying confounders in the marginal structural model (subdistribution hazard ratio 1.19, 95% confidence interval 0.75 to 1.89). Using this approach, only 7.2% (95% confidence interval -7.5% to 19.5%) of deaths in the intensive care unit were attributable to delirium, with an absolute mortality excess in patients with delirium of 0.9% (95% confidence interval -0.9% to 2.3%) by day 30. In post hoc analyses, however, delirium that persisted for two days or more remained associated with a 2.0% (95% confidence interval 1.2% to 2.8%) absolute mortality increase. Furthermore, competing risk analysis showed that delirium of any duration was associated with a significantly reduced rate of discharge from the intensive care unit (cause specific hazard ratio 0.65, 95% confidence interval 0.55 to 0.76). Conclusions: Overall, delirium prolongs admission in the intensive care unit but does not cause death in critically ill patients. Future studies should focus on episodes of persistent delirium and its long term sequelae rather than on acute mortality

Epidemiology, Management, and Risk-Adjusted Mortality of ICU-Acquired Enterococcal Bacteremia.

BACKGROUND: Enterococcal bacteremia has been associated with high case fatality, but it remains unknown to what extent death is caused by these infections. We therefore quantified attributable mortality of intensive care unit (ICU)-acquired bacteremia caused by enterococci. METHODS: From 2011 to 2013 we studied consecutive patients who stayed >48 hours in 2 tertiary ICUs in the Netherlands, using competing risk survival regression and marginal structural modeling to estimate ICU mortality caused by enterococcal bacteremia. RESULTS: Among 3080 admissions, 266 events of ICU-acquired bacteremia occurred in 218 (7.1%) patients, of which 76 were caused by enterococci (incidence rate, 3.0 per 1000 patient-days at risk; 95% confidence interval [CI], 2.3-3.7). A catheter-related bloodstream infection (CRBSI) was suspected in 44 (58%) of these, prompting removal of 68% of indwelling catheters and initiation of antibiotic treatment for a median duration of 3 (interquartile range 1-7) days. Enterococcal bacteremia was independently associated with an increased case fatality rate (adjusted subdistribution hazard ratio [SHR], 2.68; 95% CI, 1.44-4.98). However, for patients with CRBSI, case fatality was similar for infections caused by enterococci and coagulase-negative staphylococci (CoNS; adjusted SHR, 0.91; 95% CI, .50-1.67). Population-attributable fraction of mortality was 4.9% (95% CI, 2.9%-6.9%) by day 90, reflecting a population-attributable risk of 0.8% (95% CI, .4%-1.1%). CONCLUSIONS: ICU-acquired enterococcal bacteremia is associated with increased case fatality; however, the mortality attributable to these infections is low from a population perspective. The virulence of enterococci and CoNS in a setting of CRBSI seems comparable

Cytomegalovirus Seroprevalence as a Risk Factor for Poor Outcome in Acute Respiratory Distress Syndrome

Objective: Cytomegalovirus reactivation may complicate critical illness in latent carriers of the virus, even in patients who were previously immunocompetent. Patients with acute respiratory distress syndrome are considered to be prone for reactivation. Prophylactic antiviral therapy in immunocompetent cytomegalovirus seropositive patients admitted to the ICU with acute respiratory distress syndrome has therefore been proposed. We assessed cytomegalovirus seroprevalence as a risk factor for morbidity and mortality in patients with acute respiratory distress syndrome. Design: Prospective observational cohort study. We used the number of days alive and free of mechanical ventilation on day 28 as a composite outcome measure and used multivariable ordinal logistic regression analyses to adjust for potential confounders. Setting: ICUs of two tertiary care hospitals in The Netherlands. Patients: We included all newly admitted patients with acute respiratory distress syndrome who received mechanical ventilation for at least 4 days. Patients with known immunocompromise and those receiving antiviral treatment prior to ICU admission were excluded. Interventions: None. Measurements and Main Results: Over a 2-year period, 306 patients were included, 209 (68%) of whom were cytomegalovirus seropositive. Cytonnegalovirus reactivation occurred in 53 of these cases (26%). One hundred patients (33%) died or continued to be mechanically ventilated by day 28. After adjustment for confounding, cytomegalovirus seroprevalence was not associated with the primary outcome (crude odds ratio, 1.09; 95% Cl, 0.70-1.70; adjusted odds ratio, 1.01; 95% Cl, 0.64-1.59). Seroprevalence was also not associated with poor outcome in any of the prespecified subgroup analyses. However, a significant association was found in a post hoc subgroup of patients who had, developed acute respiratory distress syndrome in a setting of septic shock (adjusted odds ratio, 2.86; 95% Cl, 1.32-6.23). The time course of pulmonary markers in survivors was comparable between the two serogroups. Conclusions: Cytomegalovirus serobrevalence is not associated with prolonged mechanical ventilation or increased mortality in critically ill patients with acute respiratory distress syndrome, with possible exception of patients presenting with septic shock. Therefore, a prevention strategy targeting an unselected cohort of seropositive patients with acute respiratory distress syndrome is unlikely to show any meaningful benefi