Iron is a tightly regulated micronutrient with no physiologic means of elimination and is necessary for cell division in normal tissue. Recent evidence suggests that dysregulation of iron regulatory proteins may play a role in cancer pathophysiology. We use public data from The Cancer Genome Atlas (TCGA) to study the association between survival and expression levels of 61 genes coding for iron regulatory proteins in patients with World Health Organization Grade II-III gliomas. Using a feature selection algorithm we identified a novel, optimized subset of eight iron regulatory genes (STEAP3, HFE, TMPRSS6, SFXN1, TFRC, UROS, SLC11A2, and STEAP4) whose differential expression defines two phenotypic groups with median survival differences of 52.3 months for patients with grade II gliomas (25.9 vs. 78.2 months, p< 10−3), 43.5 months for patients with grade III gliomas (43.9 vs. 87.4 months, p = 0.025), and 54.0 months when considering both grade II and III gliomas (79.9 vs. 25.9 months, p < 10−5).

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We prove exponential concentration estimates and a strong law of large numbers for a particle system that is the simplest representative of a general class of models for 2D grain boundary coarsening introduced in [14]. The system consists of n particles in (0, ∞) that move at unit speed to the left. Each time a particle hits the boundary point 0, it is removed from the system along with a second particle chosen uniformly from the particles in (0, ∞). Under the assumption that the initial empirical measure of the particle system converges weakly to a measure with density f0(x) ∈ L 1 + (0, ∞), the empirical measure of the particle system at time t is shown to converge to the measure with density f (x, t), where f is the unique solution to the kinetic equation with nonlinear boundary couplingand initial condition f (x, 0) = f0(x).The proof relies on a concentration inequality for an urn model studied by Pittel, and Maurey's concentration inequality for Lipschitz functions on the permutation group.MSC classification: 35R60, 60K25, 82C23, 82C70

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Let N (τ ) be a renewal process for holding times {Xi} k≥0 ,where {X k } k≥1 are iid with density p(x). If the associated residual time R(τ ) has a density u(x, t), its Kolmogorov forward equation is given bywith an initial holding time density u(x, 0) = u0(x). We derive a measurevalued solution formula for the density of residual times after an expected number of renewals occur. Solutions under this time scale are then shown to evolve continuously in the space of measures with the weak topology for a wide variety of holding times.