Large deviations for Brownian motion in a random scenery

We prove large deviations principles in large time, for the Brownian occupation time in random scenery. The random scenery is constant on unit cubes, and consist of i.i.d. bounded variables, independent of the Brownian motion. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large deviations principles in ``quenched'' and ``annealed'' settings.Comment: 29 page

Quenched large deviations for diffusions in a random Gaussian shear flow drift

We prove a full large deviations principle in large time, for a diffusion process with random drift V, which is a centered Gaussian shear flow random field. The large deviations principle is established in a ``quenched'' setting, i.e. is valid almost surely in the randomness of V.Comment: 29 page

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

Facilitated spin models: recent and new results

Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the surrounding configuration fulfills a simple local constraint which \emph{does not involve} the chosen variable itself. Such simple models are quite popular in the glass community since they display some of the peculiar features of glassy dynamics, in particular they can undergo a dynamical arrest reminiscent of the liquid/glass transitiom. Due to the fact that the jumps rates of the Markov process can be zero, the whole analysis of the long time behavior becomes quite delicate and, until recently, KCSM have escaped a rigorous analysis with the notable exception of the East model. In these notes we will mainly review several recent mathematical results which, besides being applicable to a wide class of KCSM, have contributed to settle some debated questions arising in numerical simulations made by physicists. We will also provide some interesting new extensions. In particular we will show how to deal with interacting models reversible w.r.t. to a high temperature Gibbs measure and we will provide a detailed analysis of the so called one spin facilitated model on a general connected graph.Comment: 30 pages, 3 figure

Dynamical aspects of mean field plane rotators and the Kuramoto model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur

Eight Weeks of Treatment With Glecaprevir/Pibrentasvir Is Safe and Efficacious in an Integrated Analysis of Treatment-Naïve Patients With Hepatitis C Virus Infection

BACKGROUND & AIMS: The direct-acting antiviral combination glecaprevir/pibrentasvir has been approved by the Food and Drug Administration for 8 weeks of treatment in treatment-naïve patients with hepatitis C virus (HCV) infection without cirrhosis or with compensated cirrhosis. We performed an integrated analysis of data from trials to evaluate the overall efficacy and safety of 8 weeks of glecaprevir/pibrentasvir in treatment-naïve patients without cirrhosis or with compensated cirrhosis. METHODS: We pooled data from 8 phase 2 or phase 3 trials of treatment-naïve patients with HCV genotype 1 to 6 infections, without cirrhosis or with compensated cirrhosis, who received 8 weeks of glecaprevir/pibrentasvir. RESULTS: Of 1248 patients, 343 (27%) had cirrhosis. Most patients were white (80%) and had HCV genotype 1 infection (47%) or genotype 3 infection (22%); the median age was 54 years. Overall rates of sustained virologic response at post-treatment week 12 were 97.6% (1218 of 1248) in the intention to treat (ITT) and 99.3% (1218 of 1226) in the modified ITT populations. When we excluded patients with genotype 3 infections with compensated cirrhosis (consistent with the European label), rates of sustained virologic response at post-treatment week 12 were 97.6% in the ITT and 99.4% in the modified ITT populations. Eight virologic failures (7 in patients without cirrhosis and 1 in a patient with cirrhosis) occurred in the ITT population. Virologic failure was not associated with markers of advanced liver disease or populations of interest (current alcohol use, opioid substitution therapy, history of injection-drug use, and severe renal impairment). Treatment-emergent adverse events (AEs) occurred in 58% of patients. The most frequent AEs (>10%) were headache (12%) and fatigue (12%). Serious AEs and AEs that led to glecaprevir/pibrentasvir discontinuation were reported in 2% and less than 1% of patients, respectively. CONCLUSIONS: In a pooled analysis of data from 8 trials, we found that 8 weeks of treatment with glecaprevir/pibrentasvir is efficacious and well tolerated in treatment-naïve patients with HCV genotype 1 to 6 infections, with or without cirrhosis.status: publishe

Eradicating hepatitis C:Are novel screening strategies for people who inject drugs cost-effective?

Background: In developed countries, people who inject drugs (PWID) have a high prevalence of hepatitis C virus (HCV), yet they are often under-diagnosed. The World Health Organization has set 2030 as a target year for HCV elimination. To meet this target, improving screening in convenient community settings in order to reach infected undiagnosed individuals is a priority. This study assesses the cost-effectiveness of alternative novel strategies for diagnosing HCV infection in PWID. Methods: A cost-effectiveness analysis was undertaken to compare HCV screening at needle exchange centres, substance misuse services and at community pharmacies, with the standard practice of detection during general practitioners’ consultations. A decision tree model was developed to assess the incremental cost per positive diagnosis, and a Markov model explored the net monetary benefit (NMB) and the cost per Quality Adjusted Life Years (QALYs) gained over a lifetime horizon. Results: Needle exchange services provided a 7.45-fold increase in detecting positive individuals and an incremental cost of £12,336 per QALY gained against current practice (NMB £163,827), making this the most cost-effective strategy over a lifetime horizon. Screening at substance misuse services and pharmacies was cost-effective only at a £30,000/QALY threshold. With a 24% discount to HCV treatment list prices, all three screening strategies become cost-effective at £20,000/QALY. Conclusions: Targeting PWID populations with screening at needle exchange services is a highly cost-effective strategy for reaching undiagnosed HCV patients. When applying realistic discounts to list prices of drug treatments, all three strategies were highly cost-effective from a UK NHS perspective. All of these strategies have the potential to make a cost-effective contribution to the eradication of HCV by 2030

Sofosbuvir and Velpatasvir for HCV Genotype 1, 2, 4, 5, and 6 Infection

published_or_final_versio

Glecaprevir-Pibrentasvir for 8 or 12 Weeks in HCV Genotype 1 or 3 Infection

The trials (NCT02604017, NCT02640157) were funded by AbbVie Inc

IL28B genotype is associated with cirrhosis or transition to cirrhosis in treatment-naive patients with chronic HCV genotype 1 infection: the international observational Gen-C study

Background and purpose: Contradictory data exist on the association between host interleukin-28B (IL28B) rs12979860 genotype and liver fibrosis in patients with chronic hepatitis C (CHC). This large, international, observational study (NCT01675427/MV25600) investigated relationships between IL28B rs12979860 genotype and liver fibrosis stage in CHC patients. Methods: A total of 3003 adult, treatment-naive CHC patients were enrolled into the study. Patients made one study visit to provide a blood sample for genotyping; other data were obtained from medical records. Results: 2916 patients comprised the analysis population; the majority were enrolled in Europe (n = 2119), were Caucasian (n = 2582) and had hepatitis C virus (HCV) genotype (G) 1 infection (n = 1702) (G2 = 323, G3 = 574, G4 = 260). Distribution of IL28B genotypes varied according to region of enrolment, patient ethnicity and HCV genotype. A significant association was observed between increasing number of IL28B T alleles and the prevalence of cirrhosis/transition to cirrhosis (based on biopsy or non-invasive assessments) in G1-infected patients (CC = 22.2% [111/499], CT = 27.5% [255/928], TT = 32.3% [87/269]; p = 0.0018). The association was significant in the large subgroup of European Caucasian G1 patients (n = 1245) but not in the smaller Asian (n = 25), Latin American (n = 137) or Middle Eastern (n = 289) G1 subgroups. IL28B genotype was not associated with liver fibrosis stage in patients with HCV G2, G3 or G4 infection. Conclusion: This large, international study found that IL28B rs12979860 genotype is significantly associated with liver fibrosis stage in CHC patients with HCV G1 infection. This association was evident in European Caucasians but not in G1-infected patients from Asia, Latin America or the Middle EastF. Hoffmann-La Roche Ltd, Basel, Switzerlan