Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction

We introduce and begin a systematic study of sublinearly contracting projections. We give two characterizations of Morse quasi-geodesics in an arbitrary geodesic metric space. One is that they are sublinearly contracting; the other is that they have completely superlinear divergence. We give a further characterization of sublinearly contracting projections in terms of projections of geodesic segments.Comment: 24 pages, 5 figures. v2: 22 pages, 5 figures. Correction in proof of Thm 7.1. Proof of Prop 4.2 revised for improved clarity. Other minor changes per referee comments. To appear in Documenta Mathematic

Negative curvature in graphical small cancellation groups

We use the interplay between combinatorial and coarse geometric versions of negative curvature to investigate the geometry of infinitely presented graphical $Gr'(1/6)$ small cancellation groups. In particular, we characterize their 'contracting geodesics', which should be thought of as the geodesics that behave hyperbolically. We show that every degree of contraction can be achieved by a geodesic in a finitely generated group. We construct the first example of a finitely generated group $G$ containing an element $g$ that is strongly contracting with respect to one finite generating set of $G$ and not strongly contracting with respect to another. In the case of classical $C'(1/6)$ small cancellation groups we give complete characterizations of geodesics that are Morse and that are strongly contracting. We show that many graphical $Gr'(1/6)$ small cancellation groups contain strongly contracting elements and, in particular, are growth tight. We construct uncountably many quasi-isometry classes of finitely generated, torsion-free groups in which every maximal cyclic subgroup is hyperbolically embedded. These are the first examples of this kind that are not subgroups of hyperbolic groups. In the course of our analysis we show that if the defining graph of a graphical $Gr'(1/6)$ small cancellation group has finite components, then the elements of the group have translation lengths that are rational and bounded away from zero.Comment: 40 pages, 14 figures, v2: improved introduction, updated statement of Theorem 4.4, v3: new title (previously: "Contracting geodesics in infinitely presented graphical small cancellation groups"), minor changes, to appear in Groups, Geometry, and Dynamic

The peculiar velocity field: constraining the tilt of the Universe

A large bulk flow, which is in tension with the Lambda Cold Dark Matter ($\Lambda$CDM) cosmological model, has been observed. In this paper, we provide a physically plausible explanation of this bulk flow, based on the assumption that some fraction of the observed dipole in the cosmic microwave background is due to an intrinsic fluctuation, so that the subtraction of the observed dipole leads to a mismatch between the cosmic microwave background (CMB) defined rest frame and the matter rest frame. We investigate a model that takes into account the relative velocity (hereafter the tilted velocity) between the two frames, and develop a Bayesian statistic to explore the likelihood of this tilted velocity. By studying various independent peculiar velocity catalogs, we find that: (1) the magnitude of the tilted velocity $u$ is around 400 km/s, and its direction is close to what is found from previous bulk flow analyses; for most catalogs analysed, u=0 is excluded at about the $2.5 \sigma$ level;(2) constraints on the magnitude of the tilted velocity can result in constraints on the duration of inflation, due to the fact that inflation can neither be too long (no dipole effect) nor too short (very large dipole effect); (3) Under the assumption of a super-horizon isocurvature fluctuation, the constraints on the tilted velocity require that inflation lasts at least 6 e-folds longer (at the 95% confidence interval) than that required to solve the horizon problem. This opens a new window for testing inflation and models of the early Universe from observations of large scale structure.Comment: 7 pages, 7 figures, match the published version in Phys.Rev.

Identification and analysis of mutational hotspots in oncogenes and tumour suppressors

Background: The key to interpreting the contribution of a disease-associated mutation in the development and progression of cancer is an understanding of the consequences of that mutation both on the function of the affected protein and on the pathways in which that protein is involved. Protein domains encapsulate function and position-specific domain based analysis of mutations have been shown to help elucidate their phenotypes. Results: In this paper we examine the domain biases in oncogenes and tumour suppressors, and find that their domain compositions substantially differ. Using data from over 30 different cancers from whole-exome sequencing cancer genomic projects we mapped over one million mutations to their respective Pfam domains to identify which domains are enriched in any of three different classes of mutation; missense, indels or truncations. Next, we identified the mutational hotspots within domain families by mapping small mutations to equivalent positions in multiple sequence alignments of protein domains We find that gain of function mutations from oncogenes and loss of function mutations from tumour suppressors are normally found in different domain families and when observed in the same domain families, hotspot mutations are located at different positions within the multiple sequence alignment of the domain. Conclusions: By considering hotspots in tumour suppressors and oncogenes independently, we find that there are different specific positions within domain families that are particularly suited to accommodate either a loss or a gain of function mutation. The position is also dependent on the class of mutation. We find rare mutations co-located with well-known functional mutation hotspots, in members of homologous domain superfamilies, and we detect novel mutation hotspots in domain families previously unconnected with cancer. The results of this analysis can be accessed through the MOKCa database (http://strubiol.icr.ac.uk/ extra/MOKCa)

Measuring serial correlation of residuals in econometric relations

The inter-relationship of economic variables, such as incomes, employment and the ruling rate of interest, is a popularly accepted fact. "Econometric relations" arise when these inter-relationships are quantified, and expressed in mathematical form. An example is the simple set of simultaneous equations arising from the elementary economic analysis of savings, investment, consumption and national income

Novel use Of Hydroxyurea in an African Region with Malaria (NOHARM): a trial for children with sickle cell anemia

Hydroxyurea treatment is recommended for children with sickle cell anemia (SCA) living in high-resource malaria-free regions, but its safety and efficacy in malaria-endemic sub-Saharan Africa, where the greatest sickle-cell burden exists, remain unknown. In vitro studies suggest hydroxyurea could increase malaria severity, and hydroxyurea-associated neutropenia could worsen infections. NOHARM (Novel use Of Hydroxyurea in an African Region with Malaria) was a randomized, double-blinded, placebo-controlled trial conducted in malaria-endemic Uganda, comparing hydroxyurea to placebo at 20 ± 2.5 mg/kg per day for 12 months. The primary outcome was incidence of clinical malaria. Secondary outcomes included SCA-related adverse events (AEs), clinical and laboratory effects, and hematological toxicities. Children received either hydroxyurea (N = 104) or placebo (N = 103). Malaria incidence did not differ between children on hydroxyurea (0.05 episodes per child per year; 95% confidence interval [0.02, 0.13]) vs placebo (0.07 episodes per child per year [0.03, 0.16]); the hydroxyurea/placebo malaria incidence rate ratio was 0.7 ([0.2, 2.7]; P = .61). Time to infection also did not differ significantly between treatment arms. A composite SCA-related clinical outcome (vaso-occlusive painful crisis, dactylitis, acute chest syndrome, splenic sequestration, or blood transfusion) was less frequent with hydroxyurea (45%) than placebo (69%; P = .001). Children receiving hydroxyurea had significantly increased hemoglobin concentration and fetal hemoglobin, with decreased leukocytes and reticulocytes. Serious AEs, sepsis episodes, and dose-limiting toxicities were similar between treatment arms. Three deaths occurred (2 hydroxyurea, 1 placebo, and none from malaria). Hydroxyurea treatment appears safe for children with SCA living in malaria-endemic sub-Saharan Africa, without increased severe malaria, infections, or AEs. Hydroxyurea provides SCA-related laboratory and clinical efficacy, but optimal dosing and monitoring regimens for Africa remain undefined. This trial was registered at www.clinicaltrials.gov as #NCT01976416

Mutational patterns in oncogenes and tumour suppressors

All cancers depend upon mutations in critical genes, which confer a selective advantage to the tumour cell. Knowledge of these mutations is crucial to understanding the biology of cancer initiation and progression, and to the development of targeted therapeutic strategies. The key to understanding the contribution of a disease-associated mutation to the development and progression of cancer, comes from an understanding of the consequences of that mutation on the function of the affected protein, and the impact on the pathways in which that protein is involved. In this paper we examine the mutation patterns observed in oncogenes and tumour suppressors, and discuss different approaches that have been developed to identify driver mutations within cancers that contribute to the disease progress. We also discuss the MOKCa database where we have developed an automatic pipeline that structurally and functionally annotates all proteins from the human proteome that are mutated in cancer

At Our Own Peril: DoD Risk Assessment in a Post-Primacy World

The U.S. Department of Defense (DoD) faces persistent fundamental change in its strategic and operating environments. This report suggests this reality is the product of the United States entering or being in the midst of a new, more competitive, post-U.S. primacy environment. Post-primacy conditions promise far-reaching impacts on U.S. national security and defense strategy. Consequently, there is an urgent requirement for DoD to examine and adapt how it develops strategy and describes, identifies, assesses, and communicates corporate-level risk. This report takes on the latter risk challenge. It argues for a new post-primacy risk concept and its four governing principles of diversity, dynamism, persistent dialogue, and adaptation. The authors suggest that this approach is critical to maintaining U.S. military advantage into the future. Absent change in current risk convention, the report suggests DoD exposes current and future military performance to potential failure or gross under-performance.https://press.armywarcollege.edu/monographs/1410/thumbnail.jp