A Sums-of-Squares Extension of Policy Iterations

In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative computation of policies, starting from a post-fixpoint. Computing each policy and the associated invariant relies on a sequence of numerical optimizations. While the early research efforts relied on linear programming (LP) to address linear properties of linear programs, the current state of the art is still limited to the analysis of linear programs with at most quadratic invariants, relying on semidefinite programming (SDP) solvers to compute policies, and LP solvers to refine invariants. We propose here to extend the class of programs considered through the use of Sums-of-Squares (SOS) based optimization. Our approach enables the precise analysis of switched systems with polynomial updates and guards. The analysis presented has been implemented in Matlab and applied on existing programs coming from the system control literature, improving both the range of analyzable systems and the precision of previously handled ones.Comment: 29 pages, 4 figure

Are Remakes Doing as Well as Originals? A note.

This paper compares originals and remakes from the standpoint of artistic quality and financial return. It appears that on average remakes are of lower quality and have smaller financial returns than originals.

The Chabauty space of closed subgroups of the three-dimensional Heisenberg group

When equipped with the natural topology first defined by Chabauty, the closed subgroups of a locally compact group $G$ form a compact space \Cal C(G). We analyse the structure of \Cal C(G) for some low-dimensional Lie groups, concentrating mostly on the 3-dimensional Heisenberg group $H$. We prove that \Cal C(H) is a 6-dimensional space that is path--connected but not locally connected. The lattices in $H$ form a dense open subset \Cal L(H) \subset \Cal C(H) that is the disjoint union of an infinite sequence of pairwise--homeomorphic aspherical manifolds of dimension six, each a torus bundle over $(\bold S^3 \smallsetminus T) \times \bold R$, where $T$ denotes a trefoil knot. The complement of \Cal L(H) in \Cal C(H) is also described explicitly. The subspace of \Cal C(H) consisting of subgroups that contain the centre $Z(H)$ is homeomorphic to the 4--sphere, and we prove that this is a weak retract of \Cal C(H).Comment: Minor edits. Final version. To appear in the Pacific Journal. 41 pages, no figure

Human Papillomavirus Infection and Vaccination Policies in the American South

In the United States, the South has a disproportionate burden of cervical cancer, yet research reporting regional prevalence of human papillomavirus (HPV) infection is scarce. Since 2008, Virginia has passed a HPV vaccine mandate and Louisiana a HPV education bill. This dissertation estimated the prevalence of HPV infection among females and assessed the impact of Virginia’s and Louisiana’s HPV vaccination policy on vaccination among adolescent females. The first manuscript estimated the prevalence of HPV infection using data from 4,250 females collected during the 2007–2010 National Health and Nutrition Examination Survey. Among 14–26 year-olds, the prevalence of high-risk oncogenic HPV was 25.6% (95% CI: 22.4 ̶ 33.3) in the South and 29.1% (95% CI: 24.8 ̶ 33.8) in the rest of the country (p= 0.15). Among 27–59 year-olds, infection rates were 20.9% (95% CI: 17.4 ̶ 24.9) for the South and 14.5% (95% CI: 12.9 ̶ 16.3) for the rest of the country (p=0.0001). The second manuscript assessed the impact of Virginia’s HPV vaccine mandate on vaccination using National Immunization Survey-Teen 2008-2012 data (n=3,203). A difference-in-differences estimation and logistic regression analysis were performed with South Carolina and Tennessee serving as comparison states. Virginia’s mandate was not associated with an increase in vaccination rates. Physician recommendation was strongly associated with vaccination in the Virginia-South Carolina (aOR=10.3; p=0.0001) and Virginia-Tennessee analyses (aOR=9.33; 95%CI: 6.11 ̶ 14.3). The third manuscript assessed the impact of Louisiana’s HPV education policy on vaccination using difference-in-differences estimation and logistic regression analysis, with Alabama and Mississippi as comparison states (n=2,327). There was no evidence that the policy increased vaccination rates. Physician recommendation was associated with vaccination in the Louisiana-Alabama (aOR=7.74; 95% CI: 5.22 ̶ 11.5) and Louisiana-Mississippi comparison (aOR=7.05; 95% CI: 4.6 ̶ 10.5). This study found a higher prevalence of HPV infection among females aged 27 ̶ 59 years in the South compared to the rest of the country. Additionally, physician recommendation was strongly associated with vaccination despite HPV policy implementation. These findings highlight the importance of physician recommendation for HPV vaccination and the need for recommended cervical cancer screening, particularly in the South