BRAVO for many-server QED systems with finite buffers

This paper demonstrates the occurrence of the feature called BRAVO (Balancing Reduces Asymptotic Variance of Output) for the departure process of a finite-buffer Markovian many-server system in the QED (Quality and Efficiency-Driven) heavy-traffic regime. The results are based on evaluating the limit of a formula for the asymptotic variance of death counts in finite birth--death processes

Modeling information cascades with self-exciting processes via generalized epidemic models

© 2020 Association for Computing Machinery. Epidemic models and self-exciting processes are two types of models used to describe diffusion phenomena online and offline. These models were originally developed in different scientific communities, and their commonalities are under-explored. This work establishes, for the first time, a general connection between the two model classes via three new mathematical components. The first is a generalized version of stochastic Susceptible-Infected-Recovered (SIR) model with arbitrary recovery time distributions; the second is the relationship between the (latent and arbitrary) recovery time distribution, recovery hazard function, and the infection kernel of self-exciting processes; the third includes methods for simulating, fitting, evaluating and predicting the generalized process. On three large Twitter diffusion datasets, we conduct goodness-of-fit tests and holdout log-likelihood evaluation of self-exciting processes with three infection kernels — exponential, power-law and Tsallis Q-exponential. We show that the modeling performance of the infection kernels varies with respect to the temporal structures of diffusions, and also with respect to user behavior, such as the likelihood of being bots. We further improve the prediction of popularity by combining two models that are identified as complementary by the goodness-of-fit tests

The occupation of a box as a toy model for the seismic cycle of a fault

We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around 6 that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.Comment: Final version of the published paper, with an erratum and an unpublished appendix with some proof

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Renewal function asymptotics refined à la Feller

 RENEWAL FUNCTION ASYMPTOTICS REFINED À LA FELLERFeller’s volume 2 shows how to use the Key Renewal Theorem to prove that in the limit x!1, the renewal function Ux of a renewal process with nonarithmetic generic lifetime X with finite mean EX=1=and second moment differs from its linear asymptote x by the quantity 122EX2. His first edition 1966 but not the second in 1971 asserted that a similar approach would refine this asymptotic result when X has finite higher order moments. The paper shows how higher order moments may justify drawing conclusions from a recurrence relation that exploits a general renewal equation and further appeal to the Key Renewal Theorem. RENEWAL FUNCTION ASYMPTOTICS REFINED À LA FELLERFeller’s volume 2 shows how to use the Key Renewal Theorem to prove that in the limit x!1, the renewal function Ux of a renewal process with nonarithmetic generic lifetime X with finite mean EX=1=and second moment differs from its linear asymptote x by the quantity 122EX2. His first edition 1966 but not the second in 1971 asserted that a similar approach would refine this asymptotic result when X has finite higher order moments. The paper shows how higher order moments may justify drawing conclusions from a recurrence relation that exploits a general renewal equation and further appeal to the Key Renewal Theorem

Two lilypond systems of finite line-segments

The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points P = {Pi} in R2 with which are associated directions {i}. At time zero, for each and every i, a line-segment Li starts growing at unit rate around the point Pi in the direction i, the point Pi remaining at the centre of Li; each line-segment, under Model 1, ceases growth when one of its ends hits another line, while under Model 2, its growth ceases either when one of its ends hits another line or when it is hit by the growing end of some other line.The paper shows that these procedures are well defined and gives constructive algorithms to compute the half-lengths Ri of all Li. Moreover, it specifies assumptions under which stochastic versions, i.e. models based on point processes, exist. Afterwards, it deals with the question as to whether there is percolation in Model 1. The paper concludes with a section containing several conjectures and final remarks.The paper discusses two models for non-overlapping finite line-segments constructed via the lilypond protocol, operating here on a given array of points P = {Pi} in R2 with which are associated directions {i}. At time zero, for each and every i, a line-segment Li starts growing at unit rate around the point Pi in the direction i, the point Pi remaining at the centre of Li; each line-segment, under Model 1, ceases growth when one of its ends hits another line, while under Model 2, its growth ceases either when one of its ends hits another line or when it is hit by the growing end of some other line.The paper shows that these procedures are well defined and gives constructive algorithms to compute the half-lengths Ri of all Li. Moreover, it specifies assumptions under which stochastic versions, i.e. models based on point processes, exist. Afterwards, it deals with the question as to whether there is percolation in Model 1. The paper concludes with a section containing several conjectures and final remarks