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Consider a nonuniformly hyperbolic map $ T $ modelled by a Young tower with tails of the form $ O(n^{-\beta}) $, $ \beta>2 $. We prove optimal moment bounds for Birkhoff sums $ \sum_{i=0}^{n-1}v\circ T^i $ and iterated sums $ \sum_{0\le i5$. Our method of proof is as follows; (i) prove that $ T $ satisfies an abstract functional correlation bound, (ii) use a weak dependence argument to show that the functional correlation bound implies moment estimates. Such iterated moment bounds arise when using rough path theory to prove deterministic homogenisation results. Indeed, by a recent result of Chevyrev, Friz, Korepanov, Melbourne & Zhang we have convergence an It\^o diffusion for fast-slow systems of the form \[ x^{(n)}_{k+1}=x_k^{(n)}+n^{-1}a(x_k^{(n)},y_k)+n^{-1/2}b(x_k^{(n)},y_k) , \quad y_{k+1}=T y_k \] in the optimal range $ \beta>2. $, Comment: 25 pages. Minor changes. To appear in Communications in Mathematical Physics

Simple Summary We investigated the influence of genetic variants, called single nucleotide polymorphisms (SNP) in the TP53 tumour suppressor gene, on cancer risk, clinical features and TP53 isoform levels. These SNPs were significantly over-represented in cohorts of mixed cancers versus controls, suggesting they confer increased cancer risk. Heterozygosity at rs1042522(GC) and either of the two SNPs rs9895829(TC) and rs2909430(AG) confer up to a 5-fold greater risk of developing cancer. The SNP combinations were associated with high Δ133TP53 and TP53β messenger RNA levels, elevated infiltrating immune cells and shorter patient survival for glioblastoma and prostate cancer. The data suggest that ∆133p53β protein levels are increased by the SNPs resulting in increased inflammation which contributes to more aggressive cancers. Abstract We investigated the influence of selected TP53 SNPs in exon 4 and intron 4 on cancer risk, clinicopathological features and expression of TP53 isoforms. The intron 4 SNPs were significantly over-represented in cohorts of mixed cancers compared to three ethnically matched controls, suggesting they confer increased cancer risk. Further analysis showed that heterozygosity at rs1042522(GC) and either of the two intronic SNPs rs9895829(TC) and rs2909430(AG) confer a 2.34–5.35-fold greater risk of developing cancer. These SNP combinations were found to be associated with shorter patient survival for glioblastoma and prostate cancer. Additionally, these SNPs were associated with tumor-promoting inflammation as evidenced by high levels of infiltrating immune cells and expression of the Δ133TP53 and TP53β transcripts. We propose that these SNP combinations allow increased expression of the Δ133p53 isoforms to promote the recruitment of immune cells that create an immunosuppressive environment leading to cancer progression.

Research from the wars in Afghanistan and Iraq have focused on traumatic brain injury (TBI) and mental health conditions; however, it is becoming clear that other health concerns, such as respiratory illnesses, warrant further scientific inquiry. Early reports from theater and postdeployment health assessments suggested an association with deployment-related exposures (e.g., sand, burn pits, chemical, etc.) and new-onset respiratory symptoms. We used data from Veterans Affairs medical encounters between fiscal years 2003 and 2011 to identify trends in chronic obstructive pulmonary disease, asthma, and interstitial lung disease in veterans. We used data from Veterans Affairs and Department of Defense sources to identify sociodemographic (age, sex, race), military (e.g., service branch, multiple deployments) and clinical characteristics (TBI, smoking) of individuals with and without chronic lung diseases. Generalized estimating equations found significant increases over time for chronic obstructive pulmonary disease and asthma in both unadjusted and adjusted analyses. Trends for interstitial lung disease were significant only in adjusted analyses. Age, smoking, and TBI were also significantly associated with chronic lung diseases; however, multiple deployments were not associated. Research is needed to identify which characteristics of deployment-related exposures are linked with chronic lung disease.