Traffic with an FBM limit: convergence of the workload process

Highly-aggregated traffic in communication networks is often modeled as fractional Brownian motion (fBm). This is justified by the theoretical result that the sum of a large number of on-off inputs, with either on-times or off-times having a heavy-tailed distribution with infinite variance, converges to fBm, after rescaling time appropriately. For performance analysis purposes, the key question is whether this convergence carries over to the stationary buffer content process. In this paper it is shown that, in a heavy-traffic queueing environment, this property indeed hold

Transient asymptotics of Lévy-driven queues

With (Qt)t denoting the stationary workload process in a queue fed by a L´evy input process (Xt)t, this paper focuses on the asymptotics of rare event probabilities of the type P(Q0 > pB,QTB > qB), for given positive numbers p, q, and a positive determinstic function TB. - We first identify conditions under which the probability of interest is dominated by the ‘most demanding event’, in the sense that it is asymptotically equivalent to P(Q > max{p, q}B) for B large, where Q denotes the steady-state workload. These conditions essentially reduce to TB being sublinear (i.e., TB/B ! 0 as B ! 1) - A second condition is derived under which the probability of interest essentially ‘decouples’, in that it is asymptotically equivalent to P(Q > pB)P(Q > qB) for B large. For various models considered in the literature this ‘decoupling condition’ reduces to requiring that TB is superlinear (i.e., TB/B ! 1as B ! 1). Notable exceptions are two ‘heavy-tailed’ cases, viz. the situations in which the L´evy input process corresponds to an -stable process, or to a compound Poisson process with regularly varying job sizes, in which the ‘decoupling condition’ reduces to TB/B2 ! 1. For these input processes we also establish the asymptotics of the probability under consideration for TB increasing superlinearly but subquadratically. We pay special attention to the case TB = RB for some R > 0; for light-tailed input we derive intuitively appealing asymptotics, intensively relying on sample-path large deviations results. The regimes obtained have appealing interpretations in terms of most likely paths to overflow

A tandem queue with Lévy input: a new representation of the downstream queue length.

In this paper we present a new representation for the steady state distribution of the workload of the second queue in a two-node tandem network. It involves the difference of two suprema over two adjacent intervals. In case of spectrally-positive

Extremes of multidimensional Gaussian processes

This paper considers extreme values attained by a centered, multidimensional Gaussian process t) = (X_1(t), ..., X_n(t)) minus drift d(t) = (d_1(t), ..., d_n(t)), on an arbitrary set T. Under mild regularity conditions, we establish the asymptotics of the logarithm of the probability that for some t in T, we have that (for all i = 1, ..., n) X_i(t) - d_i(t) > q_i u, for positive thresholds q_i > 0 and u large. Our findings generalize and extend previously known results for the single-dimensional and two-dimensional case. A number of examples illustrate the theory

Surface critical exponents at a uniaxial Lifshitz point

Using Monte Carlo techniques, the surface critical behaviour of three-dimensional semi-infinite ANNNI models with different surface orientations with respect to the axis of competing interactions is investigated. Special attention is thereby paid to the surface criticality at the bulk uniaxial Lifshitz point encountered in this model. The presented Monte Carlo results show that the mean-field description of semi-infinite ANNNI models is qualitatively correct. Lifshitz point surface critical exponents at the ordinary transition are found to depend on the surface orientation. At the special transition point, however, no clear dependency of the critical exponents on the surface orientation is revealed. The values of the surface critical exponents presented in this study are the first estimates available beyond mean-field theory.Comment: 10 pages, 7 figures include

Stochastic excitation of acoustic modes in stars

For more than ten years, solar-like oscillations have been detected and frequencies measured for a growing number of stars with various characteristics (e.g. different evolutionary stages, effective temperatures, gravities, metal abundances ...). Excitation of such oscillations is attributed to turbulent convection and takes place in the uppermost part of the convective envelope. Since the pioneering work of Goldreich & Keely (1977), more sophisticated theoretical models of stochastic excitation were developed, which differ from each other both by the way turbulent convection is modeled and by the assumed sources of excitation. We review here these different models and their underlying approximations and assumptions. We emphasize how the computed mode excitation rates crucially depend on the way turbulent convection is described but also on the stratification and the metal abundance of the upper layers of the star. In turn we will show how the seismic measurements collected so far allow us to infer properties of turbulent convection in stars.Comment: Notes associated with a lecture given during the fall school organized by the CNRS and held in St-Flour (France) 20-24 October 2008 ; 39 pages ; 11 figure

T-Cell Immune Dysregulation and Mortality in Women with Human Immunodeficiency Virus

Summary: In women with HIV, higher activation and exhaustion of CD4+ T cells were associated with risk of non-HIV-related mortality during a median of 13.3 years of follow-up, independent of baseline demographic, behavioral, HIV-related, and cardiometabolic factors and longitudinal HIV disease progression. Background: Dysregulation of adaptive immunity is a hallmark of human immunodeficiency virus (HIV) infection that persists on antiretroviral therapy (ART). Few long-term prospective studies have related adaptive immunity impairments to mortality in HIV, particularly in women. Methods: Among 606 women with HIV in the Women's Interagency HIV Study, peripheral blood mononuclear cells collected from 2002 to 2005 underwent multiparameter flow cytometry. Underlying cause of death was ascertained from the National Death Index up to 2018. We examined associations of CD4+ and CD8+ T-cell activation (%CD38+HLA-DR+), senescence (%CD57+CD28-), exhaustion (%PD-1+), and nonactivation/normal function (%CD57-CD28+) with natural-cause, HIV-related, and non-HIV-related mortality. Results: At baseline, median participant age was 41, and 67% were on ART. Among 100 deaths during a median of 13.3 years follow-up, 90 were natural-cause (53 non-HIV-related, 37 HIV-related). Higher activation and exhaustion of CD4+ T cells were associated with risk of natural-cause and non-HIV-related mortality, adjusting for age, demographic, behavioral, HIV-related, and cardiometabolic factors at baseline. Additional adjustment for time-varying viral load and CD4+ T-cell count did not attenuate these associations. CD8+ T-cell markers were not associated with any outcomes adjusting for baseline factors. Conclusions: Persistent CD4+ T-cell activation and exhaustion may contribute to excess long-term mortality risk in women with HIV, independent of HIV disease progression

Self-Reported Sexually Transmitted Infections after Incarceration in Women with or at Risk for HIV in the United States, 2007-2017

Background: U.S. women who have been incarcerated report high rates of sexual risk behavior and sexually transmitted infections (STIs). Materials and Methods: We estimated the effect of incarceration on the time to first incident STI in a multicenter cohort of U.S. women with or at risk for HIV. We used marginal structural models to compare time to first self-reported gonorrhea, chlamydia, or trichomonas infection for nonincarcerated women and incarcerated women. Covariates included demographic factors, HIV status, sex exchange, drug/alcohol use, and prior incarceration. Results: Three thousand hundred twenty-four women contributed a median of 4 at-risk years and experienced 213 first incident STI events. The crude incidence of STIs was 3.7 per 100 person-years for incarcerated women and 1.9 per 100 person-years for nonincarcerated women. The weighted hazard ratio for incident STIs was 4.05 (95% confidence interval: 1.61-10.19). Conclusion: Women with or at risk for HIV in the United States who have recently experienced incarceration may be at increased STI risk

Incarceration and Number of Sexual Partners after Incarceration among Vulnerable US Women, 2007-2017

Objectives. To examine whether women's incarceration increases numbers of total and new sexual partners. Methods. US women with or at risk for HIV in a multicenter cohort study answered incarceration and sexual partner questions semiannually between 2007 and 2017. We used marginal structural models to compare total and new partners at visits not following incarceration with all visits following incarceration and visits immediately following incarceration. Covariates included demographics, HIV status, sex exchange, drug or alcohol use, and housing instability. Results. Of the 3180 participants, 155 were incarcerated. Women reported 2 partners, 3 or more partners, and new partners at 5.2%, 5.2%, and 9.3% of visits, respectively. Relative to visits not occurring after incarceration, odds ratios were 2.41 (95% confidence interval [CI] = 1.20, 4.85) for 2 partners, 2.03 (95% CI = 0.97, 4.26) for 3 or more partners, and 3.24 (95% CI = 1.69, 6.22) for new partners at visits immediately after incarceration. Odds ratios were similar for all visits following incarceration. Conclusions. Women had more total partners and new partners immediately and at all visits following incarceration after confounders and loss to follow-up had been taken into account

Menopause Is Associated with Immune Activation in Women with HIV

Background: Persistent immune activation due to gut barrier dysfunction is a suspected cause of morbidity in HIV, but the impact of menopause on this pathway is unknown. Methods: In 350 women with HIV from the Women's Interagency HIV Study, plasma biomarkers of gut barrier dysfunction (intestinal fatty acid binding protein; IFAB), innate immune activation (soluble CD14 and CD163; sCD14, sCD163), and systemic inflammation (interleukin-6 and tumor necrosis factor receptor 1; IL-6, TNFR1) were measured at 674 person-visits spanning ≤2 years. Results: Menopause (post-vs premenopausal status) was associated with higher plasma sCD14 and sCD163 in linear mixed-effects regression adjusting for age and other covariates (β=161.89 ng/mL; 95% confidence interval [CI], 18.37-305.41 and 65.48 ng/mL, 95% CI, 6.64-124.33, respectively); but not with plasma IFAB, IL-6, or TNFR1. In piece-wise linear mixed-effects regression of biomarkers on years before/after the final menstrual period, sCD14 increased during the menopausal transition by 250.71 ng/mL per year (95% CI, 16.63-484.79; P=.04), but not in premenopausal or postmenopausal periods. Conclusions: In women with HIV, menopause may increase innate immune activation, but data did not support an influence on the gut barrier or inflammation. Clinical implications of immune activation during menopausal transition warrant further investigation