Self-Diffusion in Simple Models: Systems with Long-Range Jumps

We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self diffusion coefficient, $D_N(\rho)$, in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set of $N$ neighboring sites. We obtain positive upper and lower bounds on $F_N(\rho)=N((1-\r)-[D_N(\rho)/D_N(0)])/(\rho(1-\rho))$ for $\rho\in [0,1]$. Computer simulations for the square, triangular and one dimensional lattice suggest that $F_N$ becomes effectively independent of $N$ for $N\ge 20$.Comment: 24 pages, in TeX, 1 figure, e-mail addresses: [email protected], [email protected], [email protected]

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation $\partial_t{\cal E} - {\cal D}\Delta {\cal E} = \lambda S^2{\cal E}$, where $S(x,t)$ is a Gaussian stochastic field with covariance $C(x-x',t,t')$, and $x\in {\mathbb R}^d$. It is shown that the coupling $\lambda_{cN}(t)$ at which the $N$-th moment diverges at time $t$, is always less or equal for ${\cal D}>0$ than for ${\cal D}=0$. Equality holds under some reasonable assumptions on $C$ and, in this case, $\lambda_{cN}(t)=N\lambda_c(t)$ where $\lambda_c(t)$ is the value of $\lambda$ at which diverges. The ${\cal D}=0$ case is solved for a class of $S$. The dependence of $\lambda_{cN}(t)$ on $d$ is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, ${\cal D}\to i{\cal D}$, the case of interest for backscattering instabilities in laser-plasma interaction.Comment: 19 pages, in LaTeX, e-mail addresses: [email protected], [email protected], [email protected], [email protected]

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

Новое в развитии пластической хирургии носа

Рассмотрены проблемы, возникающие при реконструктивных вмешательствах на структурах наружного носа и его внутренних полостях, характеристики трансплантатов и условия, способствующие возникновению осложнений. На основании собственных наблюдений сделан вывод о практической целесообразности использования гомо− и гетеротрансплантатов с учетом конкретных медико−социальных показаний.The problems arising at reconstructive surgery on the external structures of the nose and its inner cavities as well as characteristics of the implants and the conditions promoting complication development are featured. Basing on the original research the authors conclude about practical expediency of application of homo− and heterotransplants with the account of definite medical−social parameters

Final analysis of the international observational S-Collate study of peginterferon alfa-2a in patients with chronic hepatitis B

Background and aims Sustained off-treatment immune control is achievable in a proportion of patients with chronic hepatitis B treated with peginterferon alfa-2a. We evaluated on-treatment predictors of hepatitis B surface antigen (HBsAg) clearance 3 years after peginterferon alfa-2a treatment and determined the incidence of hepatocellular carcinoma. Methods A prospective, international, multicenter, observational study in patients with chronic hepatitis B who have been prescribed peginterferon alfa-2a (40KD) in a real-world setting. The primary endpoint was HBsAg clearance after 3 years' follow-up. Results The modified intention-to-treat population comprised 844 hepatitis B e antigen (HBeAg)positive patients (540 [64%] completed 3 years' follow-up), and 872 HBeAg-negative patients (614 [70%] completed 3 years' follow-up). At 3 years' follow-up, HBsAg clearance rates in HBeAg-positive and HBeAg-negative populations, respectively, were 2% (16/844) and 5% (41/872) in the modified intention-to-treat population and 5% [16/328] and 10% [41/ 394] in those with available data. In HBeAg-positive patients with data, Week 12 HBsAg levels &lt;1500, 1500-20,000, and &gt;20,000 IU/mL were associated with HBsAg clearance rates at 3 years' follow-up of 11%, 1%, and 5%, respectively (Week 24 predictability was similar). In HBeAg-negative patients with available data, a 6510% decline vs a &lt;10% decline in HBsAg at Week 12 was associated with HBsAg clearance rates of 16% vs 4%. Hepatocellular carcinoma incidence was lower than REACH-B (Risk Estimation for Hepatocellular Carcinoma in Chronic Hepatitis B) model predictions. Conclusions Sustained off-treatment immune control is achieved with peginterferon alfa-2a in a real-world setting. HBsAg clearance 3 years after completion of peginterferon alfa-2a can be predicted on the basis of on-treatment HBsAg kinetics

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

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

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