Contraction Bidimensionality: the Accurate Picture

We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory -- the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters

Nearest Neighbor Distances on a Circle: Multidimensional Case

We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels change for various choices of E, particularly when E goes to infinity. Primarily, we study the case in which the spring constant is a badly approximable vector. We first give the proof by Boshernitzan-Dyson that the number of distinct spacings has a uniform bound independent of E. Then, if the spring constant has components forming a basis of an algebraic number field, we show that, when normalized up to a unit, the spacings are from a finite set. Moreover, in the specific case that the field has one fundamental unit, the probability distribution of these spacings behaves quasiperiodically in log E. We conclude by studying the spacings in the case that the spring constant is not badly approximable, providing examples for which the number of distinct spacings is unbounded.Comment: Version 2 is updated to include more discussion of previous works. 17 pages with five figures. To appear in the Journal of Statistical Physic

Phase II randomised discontinuation trial of brivanib in patients with advanced solid tumours

Background: Brivanib is a selective inhibitor of vascular endothelial growth factor and fibroblast growth factor (FGF) signalling. We performed a phase II randomised discontinuation trial of brivanib in 7 tumour types (soft-tissue sarcomas [STS], ovarian cancer, breast cancer, pancreatic cancer, non-small-cell lung cancer [NSCLC], gastric/esophageal cancer and transitional cell carcinoma [TCC]). Patients and methods: During a 12-week open-label lead-in period, patients received brivanib 800 mg daily and were evaluated for FGF2 status by immunohistochemistry. Patients with stable disease at week 12 were randomised to brivanib or placebo. A study steering committee evaluated week 12 response to determine if enrolment in a tumour type would continue. The primary objective was progression-free survival (PFS) for brivanib versus placebo in patients with FGF2-positive tumours. Results: A total of 595 patients were treated, and stable disease was observed at the week 12 randomisation point in all tumour types. Closure decisions were made for breast cancer, pancreatic cancer, NSCLC, gastric cancer and TCC. Criteria for expansion were met for STS and ovarian cancer. In 53 randomised patients with STS and FGF2-positive tumours, the median PFS was 2.8 months for brivanib and 1.4 months for placebo (hazard ratio [HR]: 0.58, p = 0.08). For all randomised patients with sarcomas, the median PFS was 2.8 months (95% confidence interval [CI]: 1.4–4.0) for those treated with brivanib compared with 1.4 months (95% CI: 1.3–1.6) for placebo (HR = 0.64, 95% CI: 0.38–1.07; p = 0.09). In the 36 randomised patients with ovarian cancer and FGF2-positive tumours, the median PFS was 4.0 (95% CI: 2.6–4.2) months for brivanib and 2.0 months (95% CI: 1.2–2.7) for placebo (HR: 0.56, 95% CI: 0.26–1.22). For all randomised patients with ovarian cancer, the median PFS in those randomised to brivanib was 4.0 months (95% CI: 2.6–4.2) and was 2.0 months (95% CI: 1.2–2.7) in those randomised to placebo (HR = 0.54, 95% CI: 0.25–1.17; p = 0.11). Conclusion: Brivanib demonstrated activity in STS and ovarian cancer with an acceptable safety profile. FGF2 expression, as defined in the protocol, is not a predictive biomarker of the efficacy of brivanib

Graph Minors and Parameterized Algorithm Design

Abstract. The Graph Minors Theory, developed by Robertson and Sey-mour, has been one of the most influential mathematical theories in pa-rameterized algorithm design. We present some of the basic algorithmic techniques and methods that emerged from this theory. We discuss its direct meta-algorithmic consequences, we present the algorithmic appli-cations of core theorems such as the grid-exclusion theorem, and we give a brief description of the irrelevant vertex technique

Non-AIDS defining cancers in the D:A:D Study-time trends and predictors of survival : a cohort study

BACKGROUND:Non-AIDS defining cancers (NADC) are an important cause of morbidity and mortality in HIV-positive individuals. Using data from a large international cohort of HIV-positive individuals, we described the incidence of NADC from 2004-2010, and described subsequent mortality and predictors of these.METHODS:Individuals were followed from 1st January 2004/enrolment in study, until the earliest of a new NADC, 1st February 2010, death or six months after the patient's last visit. Incidence rates were estimated for each year of follow-up, overall and stratified by gender, age and mode of HIV acquisition. Cumulative risk of mortality following NADC diagnosis was summarised using Kaplan-Meier methods, with follow-up for these analyses from the date of NADC diagnosis until the patient's death, 1st February 2010 or 6 months after the patient's last visit. Factors associated with mortality following NADC diagnosis were identified using multivariable Cox proportional hazards regression.RESULTS:Over 176,775 person-years (PY), 880 (2.1%) patients developed a new NADC (incidence: 4.98/1000PY [95% confidence interval 4.65, 5.31]). Over a third of these patients (327, 37.2%) had died by 1st February 2010. Time trends for lung cancer, anal cancer and Hodgkin's lymphoma were broadly consistent. Kaplan-Meier cumulative mortality estimates at 1, 3 and 5 years after NADC diagnosis were 28.2% [95% CI 25.1-31.2], 42.0% [38.2-45.8] and 47.3% [42.4-52.2], respectively. Significant predictors of poorer survival after diagnosis of NADC were lung cancer (compared to other cancer types), male gender, non-white ethnicity, and smoking status. Later year of diagnosis and higher CD4 count at NADC diagnosis were associated with improved survival. The incidence of NADC remained stable over the period 2004-2010 in this large observational cohort.CONCLUSIONS:The prognosis after diagnosis of NADC, in particular lung cancer and disseminated cancer, is poor but has improved somewhat over time. Modifiable risk factors, such as smoking and low CD4 counts, were associated with mortality following a diagnosis of NADC

Excluding a group-labelled graph

This paper contains a first step towards extending the Graph Minors Project of Robertson and Seymour to group-labelled graphs. For a finite abelian group G and G-labelled graph G, we describe the class of G-labelled graphs that do not contain a minor isomorphic to G

Tangles, tree-decompositions and grids in matroids

A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of a tangle is equal to the branch-width. We prove that: (i) there is a tree decomposition of a matroid that "displays" all of the maximal tangles, and (ii) when M is representable over a finite field, each tangle of sufficiently large order "dominates" a large grid-minor. This extends results of Robertson and Seymour concerning Graph Minors