On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time $n$ the particle is typically at a distance of order $O(n^\kappa)$ from the origin, $\kappa\in(0,1)$. We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time $n$, the particle is at a distance of order $O(n^{\nu_0})$ from the origin, $\nu_0\in (0,\kappa)$), and speedup (at time $n$, the particle is at a distance of order $n^{\nu_1}$ from the origin, $\nu_1\in (\kappa,1)$), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time $n$, the particle is located around $(-n^\nu)$, thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.Comment: 43 pages, 4 figures; to appear in Probability Theory and Related Field

Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional L\'{e}vy's modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.Comment: AMS-LaTeX, 23 page

The maximum of the local time of a diffusion process in a drifted Brownian potential

We consider a one-dimensional diffusion process $X$ in a $(-\kappa/2)$-drifted Brownian potential for $\kappa\neq 0$. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from the behaviour of the maximum local time of the transient random walk in random environment. We also obtain the convergence in law of the maximum local time of $X$ under the annealed law after suitable renormalization when $\kappa \geq 1$. Moreover, we characterize all the upper and lower classes for the hitting times of $X$, in the sense of Paul L\'evy, and provide laws of the iterated logarithm for the diffusion $X$ itself. To this aim, we use annealed technics.Comment: 38 pages, new version, merged with hal-00013040 (arXiv:math/0511053), with some additional result

Self-intersection local times of random walks: Exponential moments in subcritical dimensions

Fix $p>1$, not necessarily integer, with $p(d-2)<d$. We study the $p$-fold self-intersection local time of a simple random walk on the lattice $\Z^d$ up to time $t$. This is the $p$-norm of the vector of the walker's local times, $\ell_t$. We derive precise logarithmic asymptotics of the expectation of $\exp\{\theta_t \|\ell_t\|_p\}$ for scales $\theta_t>0$ that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of $t$ and $\theta_t$, and the precise rate is characterized in terms of a variational formula, which is in close connection to the {\it Gagliardo-Nirenberg inequality}. As a corollary, we obtain a large-deviation principle for $\|\ell_t\|_p/(t r_t)$ for deviation functions $r_t$ satisfying t r_t\gg\E[\|\ell_t\|_p]. Informally, it turns out that the random walk homogeneously squeezes in a $t$-dependent box with diameter of order $\ll t^{1/d}$ to produce the required amount of self-intersections. Our main tool is an upper bound for the joint density of the local times of the walk.Comment: 15 pages. To appear in Probability Theory and Related Fields. The final publication is available at springerlink.co

Prospective International Multicenter Pelvic Floor Study:Short-Term Follow-Up and Clinical Findings for Combined Pectopexy and Native Tissue Repair

Efforts to use traditional native tissue strategies and reduce the use of meshes have been made in several countries. Combining native tissue repair with sufficient mesh applied apical repair might provide a means of effective treatment. The study group did perform and publish a randomized trial focusing on the combination of traditional native tissue repair with pectopexy or sacrocolpopexy and observed no severe or hitherto unknown risks for patients (No&eacute; G.K. J Endourol 2015;29(2):210&ndash;215). The short-term follow-up of this international multicenter study carried out now is presented in this article. Material and Methods: Eleven clinics and 13 surgeons in four European counties participated in the trial. In order to ensure a standardized approach and obtain comparable data, all surgeons were obliged to follow a standardized approach for pectopexy, focusing on the area of fixation and the use of a prefabricated mesh (PVDF PRP 3 &times; 15 Dynamesh). The mesh was solely used for apical repair. All other clinically relevant defects were treated with native tissue repair. Colposuspension or TVT were used for the treatment of incontinence. Data were collected independently for 14 months on a secured server; 501 surgeries were registered and evaluated. Two hundred and sixty-four patients out of 479 (55.1%) returned for the physical examination and interview after 12&ndash;18 months. Main Outcome and Results: The mean duration of follow-up was 15 months. The overall success of apical repair was rated positively by 96.9%, and the satisfaction score was rated positively by 95.5%. A positive general recommendation was expressed by 95.1% of patients. Pelvic pressure was reduced in 95.2%, pain in 98.0%, and urgency in 86.0% of patients. No major complications, mesh exposure, or mesh complication occurred during the follow-up period. Conclusion: In clinical routine, pectopexy and concomitant surgery, mainly using native tissue approaches, resulted in high satisfaction rates and favorable clinical findings. The procedure may also be recommended for use by general urogynecological practitioners with experience in laparoscopy

The future of patient safety: Surgical trainees accept virtual reality as a new training tool

BACKGROUND: The use of virtual reality (VR) has gained increasing interest to acquire laparoscopic skills outside the operating theatre and thus increasing patients' safety. The aim of this study was to evaluate trainees' acceptance of VR for assessment and training during a skills course and at their institution. METHODS: All 735 surgical trainees of the International Gastrointestinal Surgery Workshop 2006-2008, held in Davos, Switzerland, were given a minimum of 45 minutes for VR training during the course. Participants' opinion on VR was analyzed with a standardized questionnaire. RESULTS: Fivehundred-twenty-seven participants (72%) from 28 countries attended the VR sessions and answered the questionnaires. The possibility of using VR at the course was estimated as excellent or good in 68%, useful in 21%, reasonable in 9% and unsuitable or useless in 2%. If such VR simulators were available at their institution, most course participants would train at least one hour per week (46%), two or more hours (42%) and only 12% wouldn't use VR. Similarly, 63% of the participants would accept to operate on patients only after VR training and 55% to have VR as part of their assessment. CONCLUSION: Residents accept and appreciate VR simulation for surgical assessment and training. The majority of the trainees are motivated to regularly spend time for VR training if accessible

Ovine Fetal Thymus Response to Lipopolysaccharide-Induced Chorioamnionitis and Antenatal Corticosteroids

RATIONALE: Chorioamnionitis is associated with preterm delivery and involution of the fetal thymus. Women at risk of preterm delivery receive antenatal corticosteroids which accelerate fetal lung maturation and improve neonatal outcome. However, the effects of antenatal corticosteroids on the fetal thymus in the settings of chorioamnionitis are largely unknown. We hypothesized that intra-amniotic exposure to lipopolysaccharide (LPS) causes involution of the fetal thymus resulting in persistent effects on thymic structure and cell populations. We also hypothesized that antenatal corticosteroids may modulate the effects of LPS on thymic development. METHODS: Time-mated ewes with singleton fetuses received an intra-amniotic injection of LPS 7 or 14 days before preterm delivery at 120 days gestational age (term = 150 days). LPS and corticosteroid treatment groups received intra-amniotic LPS either preceding or following maternal intra-muscular betamethasone. Gestation matched controls received intra-amniotic and maternal intra-muscular saline. The fetal intra-thoracic thymus was evaluated. RESULTS: Intra-amniotic LPS decreased the cortico-medullary (C/M) ratio of the thymus and increased Toll-like receptor (TLR) 4 mRNA and CD3 expression indicating involution and activation of the fetal thymus. Increased TLR4 and CD3 expression persisted for 14 days but Foxp3 expression decreased suggesting a change in regulatory T-cells. Sonic hedgehog and bone morphogenetic protein 4 mRNA, which are negative regulators of T-cell development, decreased in response to intra-amniotic LPS. Betamethasone treatment before LPS exposure attenuated some of the LPS-induced thymic responses but increased cleaved caspase-3 expression and decreased the C/M ratio. Betamethasone treatment after LPS exposure did not prevent the LPS-induced thymic changes. CONCLUSION: Intra-amniotic exposure to LPS activated the fetal thymus which was accompanied by structural changes. Treatment with antenatal corticosteroids before LPS partially attenuated the LPS-induced effects but increased apoptosis in the fetal thymus. Corticosteroid administration after the inflammatory stimulus did not inhibit the LPS effects on the fetal thymus

Volume and outcomes relationship in laparoscopic diaphragmatic hernia repair

BackgroundThere is no published data regarding the relationship between hospital volume and outcomes in patients undergoing laparoscopic diaphragmatic hernia repair. We hypothesize that hospitals performing high case volume have improved outcomes compared to low-volume hospitals.Materials and methodsWe reviewed the National Inpatient Sample (NIS) database between 2008 and 2012 for adults with the diagnosis of diaphragmatic hernia who underwent elective laparoscopic repair of diaphragmatic Hernia and/or Nissen fundoplication. Pediatric, emergent, and open cases were excluded. Main outcome measures included logistic regression analysis of factors predictive of in-hospital mortality and outcomes according to annual hospital case volume.ResultsA total of 31,228 laparoscopic diaphragmatic hernia operations were analyzed. The overall in-hospital mortality was 0.14%. Risk factors for higher in-hospital mortality included renal failure (AOR: 6.26; 95% CI: 2.48-15.78; p &lt; 0.001), age&gt;60 years (AOR: 5.06; 95% CI: 2.38-10.76; p &lt; 0.001), and CHF (AOR: 3.80; 95% CI: 1.39-10.38; p = 0.009) while an incremental increase in volume of 10 cases/year (AOR: 0.89; 95% CI: 0.81-0.98; p = 0.019) and diabetes (AOR: 0.34; 95% CI: 0.12-0.93; p = 0.036) decreases mortality. There was a small but significant inverse relationship between hospital case volume and mortality with a 10% reduction in adjusted odds of in-hospital mortality for every increase in 10 cases per year. Using 10 cases per year as the volume threshold, low-volume hospitals (≤10 cases/year) had almost a twofold higher mortality compared to high-volume hospitals (0.23 vs. 0.12%, respectively, p = 0.02).ConclusionsThere was a small but significant inverse relationship between the hospitals' case volume and mortality in laparoscopic diaphragmatic hernia repair