Lingering random walks in random environment on a strip

We consider a recurrent random walk (RW) in random environment (RE) on a strip. We prove that if the RE is i. i. d. and its distribution is not supported by an algebraic subsurface in the space of parameters defining the RE then the RW exhibits the "(log t)-squared" asymptotic behaviour. The exceptional algebraic subsurface is described by an explicit system of algebraic equations. One-dimensional walks with bounded jumps in a RE are treated as a particular case of the strip model. If the one dimensional RE is i. i. d., then our approach leads to a complete and constructive classification of possible types of asymptotic behaviour of recurrent random walks. Namely, the RW exhibits the $(\log t)^{2}$ asymptotic behaviour if the distribution of the RE is not supported by a hyperplane in the space of parameters which shall be explicitly described. And if the support of the RE belongs to this hyperplane then the corresponding RW is a martingale and its asymptotic behaviour is governed by the Central Limit Theorem

Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems

A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov exponents. The sequence, taking the values $\pm 1$, is pairwise independent (but not independent) ergodic sequence with infinite range dependence. The model corresponds to the motion of a particle on an infinite cylinder, hopping backward and forward along its axis, with a transversal acceleration parameter $\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded continuous fraction representation, all these moments are finite and bounded with respect to n.Comment: To be published in J. Phys.

The key neuroendocrine regulators of the onset of puberty in the Atlantic bluefin tuna (Thunnus thynnus)

Recently, significant progress on spawning induction in captive bluefin tuna (BFT, Thunnus thynnus), has been achieved providing the basis for the species' domestication. To further promote the development of a self- sustained BFT aquaculture, we investigated first sexual maturity in BFT reared from an immature stage in captivity. Accordingly, our major objectives were to evaluate: (i) maturational status of the brain-pituitary-gonadal (BPG) axis, and (ii) responsiveness of the BPG to exogenous hormones. Special emphasis was given to characterize the gonadotropins follicle stimulating hormone (FSH) and luteinizing hormone (LH) that act as central regulators of gonadal development and gamete maturation. The growth parameters recorded for the captive BFT juveniles are consistent with the length-weight relationship established for wild Mediterranean BFT stocks. The histological analyses of the gonads indicate advanced sexual maturation in BFT males compared to females, yet it is not yet clear whether this phenomenon typifies wild stocks or is induced due to the culture conditions. The hormone measurements show expression and accumulation of both gonadotropins in the pituitaries of immature and mature BFT. The pituitary LH content increased concomitantly with the age of the fish, exhibiting sex dimorphic patterns (i.e. 3-fold higher levels in females) in adult but not in juvenile BFT. The pituitary FSH levels, however, were elevated in 2Y immature males and in fully mature adults. Comparable to mammals, the intra-pituitary FSH/LH ratio was found to be higher (>1) in sexually immature than in maturing or pubertal BFT. Nevertheless, in the 3Y BFT females, which were all immature, the onset of puberty appears to require some other prerequisites, such as a rise in the LH storage above a minimal threshold. Our in vitro trials further demonstrated the capacity of rFSH and to a lesser extent that of rLH to stimulate cell proliferation in the immature ovarian and testicular fragments. Both rFSH and rLH have failed to stimulate steroidogenesis, yet pre-treatment with KiSS containing EVAc implants appeared to potentiate FSH-stimulated steroidogenesis in the immature testes. On the other hand, the expression levels of both the GtH-R and IGF I genes in the testicular fragments, derived from BFT juveniles and further exposed to the rLH treatment, showed dose-dependent pattern. Future studies testing the effects of captivity and hormone-based treatments on precocious maturity at relatively small body size are expected to facilitate the handling in confined environments, and to greatly improve the cost-efficiency of BFT farming.Postprin

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Epidural steroid injections compared with gabapentin for lumbosacral radicular pain: multicenter randomized double blind comparative efficacy study

Objective To evaluate whether an epidural steroid injection or gabapentin is a better treatment for lumbosacral radiculopathy. Design A multicenter randomized study conducted between 2011 and 2014. Computer generated randomization was stratified by site. Patients and evaluating physicians were blinded to treatment outcomes. Settings Eight military, Veterans Administration, and civilian hospitals. Participants 145 people with lumbosacral radicular pain secondary to herniated disc or spinal stenosis for less than four years in duration and in whom leg pain is as severe or more severe than back pain. Interventions Participants received either epidural steroid injection plus placebo pills or sham injection plus gabapentin. Main outcome measures Average leg pain one and three months after the injection on a 0-10 numerical rating scale. A positive outcome was defined as a ≥2 point decrease in leg pain coupled with a positive global perceived effect. All patients had one month follow-up visits; patients whose condition improved remained blinded for their three month visit. Results There were no significant differences for the primary outcome measure at one month (mean pain score 3.3 (SD 2.6) and mean change from baseline −2.2 (SD 2.4) in epidural steroid injection group versus 3.7 (SD 2.6) and −1.7 (SD 2.6) in gabapentin group; adjusted difference 0.4, 95% confidence interval −0.3 to 1.2; P=0.25) and three months (mean pain score 3.4 (SD 2.7) and mean change from baseline −2.0 (SD 2.6) versus 3.7 (SD 2.8) and −1.6 (SD 2.7), respectively; adjusted difference 0.3, −0.5 to 1.2; P=0.43). Among secondary outcomes, one month after treatment those who received epidural steroid injection had greater reductions in worst leg pain (−3.0, SD 2.8) than those treated with gabapentin (−2.0, SD 2.9; P=0.04) and were more likely to experience a positive successful outcome (66% v 46%; number needed to treat=5.0, 95% confidence interval 2.8 to 27.0; P=0.02). At three months, there were no significant differences between treatments. Conclusions Although epidural steroid injection might provide greater benefit than gabapentin for some outcome measures, the differences are modest and are transient for most people. Trial registration ClinicalTrials.gov Identifier: NCT01495923

Interleukin-2 therapy in patients with HIV infection

BACKGROUND Used in combination with antiretroviral therapy, subcutaneous recombinant interleukin-2 raises CD4+ cell counts more than does antiretroviral therapy alone. The clinical implication of these increases is not known. METHODS We conducted two trials: the Subcutaneous Recombinant, Human Interleukin-2 in HIV-Infected Patients with Low CD4+ Counts under Active Antiretroviral Therapy (SILCAAT) study and the Evaluation of Subcutaneous Proleukin in a Randomized International Trial (ESPRIT). In each, patients infected with the human immunodeficiency virus (HIV) who had CD4+ cell counts of either 50 to 299 per cubic millimeter (SILCAAT) or 300 or more per cubic millimeter (ESPRIT) were randomly assigned to receive interleukin-2 plus antiretroviral therapy or antiretroviral therapy alone. The interleukin-2 regimen consisted of cycles of 5 consecutive days each, administered at 8-week intervals. The SILCAAT study involved six cycles and a dose of 4.5 million IU of interleukin-2 twice daily; ESPRIT involved three cycles and a dose of 7.5 million IU twice daily. Additional cycles were recommended to maintain the CD4+ cell count above predefined target levels. The primary end point of both studies was opportunistic disease or death from any cause. RESULTS In the SILCAAT study, 1695 patients (849 receiving interleukin-2 plus antiretroviral therapy and 846 receiving antiretroviral therapy alone) who had a median CD4+ cell count of 202 cells per cubic millimeter were enrolled; in ESPRIT, 4111 patients (2071 receiving interleukin-2 plus antiretroviral therapy and 2040 receiving antiretroviral therapy alone) who had a median CD4+ cell count of 457 cells per cubic millimeter were enrolled. Over a median follow-up period of 7 to 8 years, the CD4+ cell count was higher in the interleukin-2 group than in the group receiving antiretroviral therapy alone--by 53 and 159 cells per cubic millimeter, on average, in the SILCAAT study and ESPRIT, respectively. Hazard ratios for opportunistic disease or death from any cause with interleukin-2 plus antiretroviral therapy (vs. antiretroviral therapy alone) were 0.91 (95% confidence interval [CI], 0.70 to 1.18; P=0.47) in the SILCAAT study and 0.94 (95% CI, 0.75 to 1.16; P=0.55) in ESPRIT. The hazard ratios for death from any cause and for grade 4 clinical events were 1.06 (P=0.73) and 1.10 (P=0.35), respectively, in the SILCAAT study and 0.90 (P=0.42) and 1.23 (P=0.003), respectively, in ESPRIT. CONCLUSIONS Despite a substantial and sustained increase in the CD4+ cell count, as compared with antiretroviral therapy alone, interleukin-2 plus antiretroviral therapy yielded no clinical benefit in either study. (ClinicalTrials.gov numbers, NCT00004978 [ESPRIT] and NCT00013611 [SILCAAT study].

Anti-influenza hyperimmune intravenous immunoglobulin for adults with influenza A or B infection (FLU-IVIG): a double-blind, randomised, placebo-controlled trial

BACKGROUND: Since the 1918 influenza pandemic, non-randomised studies and small clinical trials have suggested that convalescent plasma or anti-influenza hyperimmune intravenous immunoglobulin (hIVIG) might have clinical benefit for patients with influenza infection, but definitive data do not exist. We aimed to evaluate the safety and efficacy of hIVIG in a randomised controlled trial. METHODS: This randomised, double-blind, placebo-controlled trial was planned for 45 hospitals in Argentina, Australia, Denmark, Greece, Mexico, Spain, Thailand, UK, and the USA over five influenza seasons from 2013-14 to 2017-18. Adults (≥18 years of age) were admitted for hospital treatment with laboratory-confirmed influenza A or B infection and were randomly assigned (1:1) to receive standard care plus either a single 500-mL infusion of high-titre hIVIG (0·25 g/kg bodyweight, 24·75 g maximum; hIVIG group) or saline placebo (placebo group). Eligible patients had a National Early Warning score of 2 points or greater at the time of screening and their symptoms began no more than 7 days before randomisation. Pregnant and breastfeeding women were excluded, as well as any patients for whom the treatment would present a health risk. Separate randomisation schedules were generated for each participating clinical site using permuted block randomisation. Treatment assignments were obtained using a web-based application by the site pharmacist who then masked the solution for infusion. Patients and investigators were masked to study treatment. The primary endpoint was a six-category ordinal outcome of clinical status at day 7, ranging in severity from death to resumption of normal activities after discharge. The choice of day 7 was based on haemagglutination inhibition titres from a pilot study. It was analysed with a proportional odds model, using all six categories to estimate a common odds ratio (OR). An OR greater than 1 indicated that, for a given category, patients in the hIVIG group were more likely to be in a better category than those in the placebo group. Prespecified primary analyses for safety and efficacy were based on patients who received an infusion and for whom eligibility could be confirmed. This trial is registered with ClinicalTrials.gov, NCT02287467. FINDINGS: 313 patients were enrolled in 34 sites between Dec 11, 2014, and May 28, 2018. We also used data from 16 patients enrolled at seven of the 34 sites during the pilot study between Jan 15, 2014, and April 10, 2014. 168 patients were randomly assigned to the hIVIG group and 161 to the placebo group. 21 patients were excluded (12 from the hIVIG group and 9 from the placebo group) because they did not receive an infusion or their eligibility could not be confirmed. Thus, 308 were included in the primary analysis. hIVIG treatment produced a robust rise in haemagglutination inhibition titres against influenza A and smaller rises in influenza B titres. Based on the proportional odds model, the OR on day 7 was 1·25 (95% CI 0·79-1·97; p=0·33). In subgroup analyses for the primary outcome, the OR in patients with influenza A was 0·94 (0·55-1·59) and was 3·19 (1·21-8·42) for those with influenza B (interaction p=0·023). Through 28 days of follow-up, 47 (30%) of 156 patients in the hIVIG group and in 45 (30%) of 152 patients in the placebo group had the composite safety outcome of death, a serious adverse event, or a grade 3 or 4 adverse event (hazard ratio [HR] 1·06, 95% CI 0·70-1·60; p=0·79). Six (4%) patients in the hIVIG group and five (3%) in the placebo group died, but these deaths were not necessarily related to treatment. INTERPRETATION: When administered alongside standard care (most commonly oseltamivir), hIVIG was not superior to placebo for adults hospitalised with influenza infection. By contrast with our prespecified subgroup hypothesis that hIVIG would result in more favourable responses in patients with influenza A than B, we found the opposite effect. The clinical benefit of hIVIG for patients with influenza B is supported by antibody affinity analyses, but confirmation is warranted. FUNDING: NIAID and NIH. Partial support was provided by the Medical Research Council (MRC_UU_12023/23) and the Danish National Research Foundation

Potential Economic Viability of Two Proposed Rifapentine-Based Regimens for Treatment of Latent Tuberculosis Infection

Rationale: Rifapentine-based regimens for treating latent tuberculosis infection (LTBI) are being considered for future clinical trials, but even if they prove effective, high drug costs may limit their economic viability. Objectives: To inform clinical trial design by estimating the potential costs and effectiveness of rifapentine-based regimens for treatment of latent tuberculosis infection (LTBI). Methods: We used a Markov model to estimate cost and societal benefits for three regimens for treating LTBI: Isoniazid/ rifapentine daily for one month, isoniazid/rifapentine weekly for three months (self-administered and directly-observed), and isoniazid daily for nine months; a strategy of ‘‘no treatment’ ’ used for comparison. Costs, quality-adjusted life-years gained, and instances of active tuberculosis averted were calculated for all arms. Results: Both daily isoniazid/rifapentine for one month and weekly isoniazid/rifapentine for three months were less expensive and more effective than other strategies under a wide variety of clinically plausibly parameter estimates. Daily isoniazid/rifapentine for one month was the least expensive and most effective regimen. Conclusions: Daily isoniazid/rifapentine for one month and weekly isoniazid/rifapentine for three months should be studied in a large-scale clinical trial for efficacy. Because both regimens performed well even if their efficacy is somewhat reduced