Khinchin theorem for integral points on quadratic varieties

We prove an analogue the Khinchin theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories visit a family of shrinking subsets infinitely often.Comment: 19 page

Evolution and oncological outcomes of a contemporary radical prostatectomy practice in a UK regional tertiary referral centre.

OBJECTIVE: To investigate the clinical and pathological trends, over a 10-year period, in robot-assisted laparoscopic prostatectomy (RALP) in a UK regional tertiary referral centre. PATIENTS AND METHODS: In all, 1 500 consecutive patients underwent RALP between October 2005 and January 2015. Prospective data were collected on clinicopathological details at presentation as well as surgical outcomes and compared over time. RESULTS: The median (range) age of patients throughout the period was 62 (35-78) years. The proportion of preoperative high-grade cases (Gleason score 8-10) rose from 4.6% in 2005-2008 to 18.2% in 2013-2015 (P < 0.001). In the same periods the proportion of clinical stage T3 cases operated on rose from 2.4% to 11.4% (P < 0.001). The median prostate-specific antigen (PSA) level at diagnosis did not alter significantly. Overall, 11.6% of men in 2005-2008 were classified preoperatively as high-risk by National Institute for Health and Care Excellence criteria, compared with 33.6% in 2013-2015 (P < 0.001). The corresponding proportions for low-risk cases were 48.6% and 17.3%, respectively. Final surgical pathology showed an increase in tumour stage, Gleason grade, and nodal status over time. The proportion of pT3 cases rose from 43.2% in 2005-2008 to 55.5% in 2013-2015 (P < 0.001), Gleason score 9-10 tumours increased from 1.8% to 9.1% (P < 0.001) and positive nodal status increased from 1.6% to 12.9% (P < 0.001) between the same periods. Despite this, positive surgical margin rates showed a downward trend in all pT groups across the different eras (P = 0.72). CONCLUSION: This study suggests that the patient profile for RALP in our unit is changing, with increasing proportions of higher stage and more advanced disease being referred and operated on. However, surgical margin outcomes have remained good.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1111/bju.1351

Investigating the Effect of Galaxy Interactions on Star Formation at 0.5<z<3.0

Observations and simulations of interacting galaxies and mergers in the local universe have shown that interactions can significantly enhance the star formation rates (SFR) and fueling of Active Galactic Nuclei (AGN). However, at higher redshift, some simulations suggest that the level of star formation enhancement induced by interactions is lower due to the higher gas fractions and already increased SFRs in these galaxies. To test this, we measure the SFR enhancement in a total of 2351 (1327) massive ($M_*>10^{10}M_\odot$) major ($1<M_1/M_2<4$) spectroscopic galaxy pairs at 0.5<z<3.0 with $\Delta V <5000$ km s$^{-1}$ (1000 km s$^{-1}$) and projected separation <150 kpc selected from the extensive spectroscopic coverage in the COSMOS and CANDELS fields. We find that the highest level of SFR enhancement is a factor of 1.23$^{+0.08}_{-0.09}$ in the closest projected separation bin (<25 kpc) relative to a stellar mass-, redshift-, and environment-matched control sample of isolated galaxies. We find that the level of SFR enhancement is a factor of $\sim1.5$ higher at 0.5<z<1 than at 1<z<3 in the closest projected separation bin. Among a sample of visually identified mergers, we find an enhancement of a factor of 1.86$^{+0.29}_{-0.18}$ for coalesced systems. For this visually identified sample, we see a clear trend of increased SFR enhancement with decreasing projected separation (2.40$^{+0.62}_{-0.37}$ vs.\ 1.58$^{+0.29}_{-0.20}$ for 0.5<z<1.6 and 1.6<z<3.0, respectively). The SFR enhancement seen in our interactions and mergers are all lower than the level seen in local samples at the same separation, suggesting that the level of interaction-induced star formation evolves significantly over this time period.Comment: 23 pages, 13 figures, Accepted for publication in Ap

Sequencing of prostate cancers identifies new cancer genes, routes of progression and drug targets

Prostate cancer represents a substantial clinical challenge because it is difficult to predict outcome and advanced disease is often fatal. We sequenced the whole genomes of 112 primary and metastatic prostate cancer samples. From joint analysis of these cancers with those from previous studies (930 cancers in total), we found evidence for 22 previously unidentified putative driver genes harboring coding mutations, as well as evidence for NEAT1 and FOXA1 acting as drivers through noncoding mutations. Through the temporal dissection of aberrations, we identified driver mutations specifically associated with steps in the progression of prostate cancer, establishing, for example, loss of CHD1 and BRCA2 as early events in cancer development of ETS fusion-negative cancers. Computational chemogenomic (canSAR) analysis of prostate cancer mutations identified 11 targets of approved drugs, 7 targets of investigational drugs, and 62 targets of compounds that may be active and should be considered candidates for future clinical trials

Analysis of the genetic phylogeny of multifocal prostate cancer identifies multiple independent clonal expansions in neoplastic and morphologically normal prostate tissue.

Genome-wide DNA sequencing was used to decrypt the phylogeny of multiple samples from distinct areas of cancer and morphologically normal tissue taken from the prostates of three men. Mutations were present at high levels in morphologically normal tissue distant from the cancer, reflecting clonal expansions, and the underlying mutational processes at work in morphologically normal tissue were also at work in cancer. Our observations demonstrate the existence of ongoing abnormal mutational processes, consistent with field effects, underlying carcinogenesis. This mechanism gives rise to extensive branching evolution and cancer clone mixing, as exemplified by the coexistence of multiple cancer lineages harboring distinct ERG fusions within a single cancer nodule. Subsets of mutations were shared either by morphologically normal and malignant tissues or between different ERG lineages, indicating earlier or separate clonal cell expansions. Our observations inform on the origin of multifocal disease and have implications for prostate cancer therapy in individual cases

Appraising the relevance of DNA copy number loss and gain in prostate cancer using whole genome DNA sequence data.

A variety of models have been proposed to explain regions of recurrent somatic copy number alteration (SCNA) in human cancer. Our study employs Whole Genome DNA Sequence (WGS) data from tumor samples (n = 103) to comprehensively assess the role of the Knudson two hit genetic model in SCNA generation in prostate cancer. 64 recurrent regions of loss and gain were detected, of which 28 were novel, including regions of loss with more than 15% frequency at Chr4p15.2-p15.1 (15.53%), Chr6q27 (16.50%) and Chr18q12.3 (17.48%). Comprehensive mutation screens of genes, lincRNA encoding sequences, control regions and conserved domains within SCNAs demonstrated that a two-hit genetic model was supported in only a minor proportion of recurrent SCNA losses examined (15/40). We found that recurrent breakpoints and regions of inversion often occur within Knudson model SCNAs, leading to the identification of ZNF292 as a target gene for the deletion at 6q14.3-q15 and NKX3.1 as a two-hit target at 8p21.3-p21.2. The importance of alterations of lincRNA sequences was illustrated by the identification of a novel mutational hotspot at the KCCAT42, FENDRR, CAT1886 and STCAT2 loci at the 16q23.1-q24.3 loss. Our data confirm that the burden of SCNAs is predictive of biochemical recurrence, define nine individual regions that are associated with relapse, and highlight the possible importance of ion channel and G-protein coupled-receptor (GPCR) pathways in cancer development. We concluded that a two-hit genetic model accounts for about one third of SCNA indicating that mechanisms, such haploinsufficiency and epigenetic inactivation, account for the remaining SCNA losses.We acknowledge support from Cancer Research UK (C5047/A22530, C309/A11566, C368/A6743, A368/A7990, C14303/A17197) and the Dallaglio Foundation. We also acknowledge support from the National Institute of Health Research (NIHR) (The Biomedical Research Centre at The Institute of Cancer Research & The Royal Marsden NHS Foundation Trust and the project "Prostate Cancer: Mechanisms of Progression and Treatment (PROMPT)" [G0500966/75466]). We thank the Wellcome Trust, Bob Champion Cancer Trust, The Orchid Cancer appeal, The RoseTrees Trust, The North West Cancer Research Fund, Big C, The King family, and The Masonic Charitable Foundation for funding. This research is supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001202), the UK Medical Research Council (FC001202), and the Wellcome Trust (FC001202). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Impact of COVID-19 on cardiovascular testing in the United States versus the rest of the world

Objectives: This study sought to quantify and compare the decline in volumes of cardiovascular procedures between the United States and non-US institutions during the early phase of the coronavirus disease-2019 (COVID-19) pandemic. Background: The COVID-19 pandemic has disrupted the care of many non-COVID-19 illnesses. Reductions in diagnostic cardiovascular testing around the world have led to concerns over the implications of reduced testing for cardiovascular disease (CVD) morbidity and mortality. Methods: Data were submitted to the INCAPS-COVID (International Atomic Energy Agency Non-Invasive Cardiology Protocols Study of COVID-19), a multinational registry comprising 909 institutions in 108 countries (including 155 facilities in 40 U.S. states), assessing the impact of the COVID-19 pandemic on volumes of diagnostic cardiovascular procedures. Data were obtained for April 2020 and compared with volumes of baseline procedures from March 2019. We compared laboratory characteristics, practices, and procedure volumes between U.S. and non-U.S. facilities and between U.S. geographic regions and identified factors associated with volume reduction in the United States. Results: Reductions in the volumes of procedures in the United States were similar to those in non-U.S. facilities (68% vs. 63%, respectively; p = 0.237), although U.S. facilities reported greater reductions in invasive coronary angiography (69% vs. 53%, respectively; p < 0.001). Significantly more U.S. facilities reported increased use of telehealth and patient screening measures than non-U.S. facilities, such as temperature checks, symptom screenings, and COVID-19 testing. Reductions in volumes of procedures differed between U.S. regions, with larger declines observed in the Northeast (76%) and Midwest (74%) than in the South (62%) and West (44%). Prevalence of COVID-19, staff redeployments, outpatient centers, and urban centers were associated with greater reductions in volume in U.S. facilities in a multivariable analysis. Conclusions: We observed marked reductions in U.S. cardiovascular testing in the early phase of the pandemic and significant variability between U.S. regions. The association between reductions of volumes and COVID-19 prevalence in the United States highlighted the need for proactive efforts to maintain access to cardiovascular testing in areas most affected by outbreaks of COVID-19 infection

Mutational signatures of ionizing radiation in second malignancies

Ionizing radiation is a potent carcinogen, inducing cancer through DNA damage. The signatures of mutations arising in human tissues following in vivo exposure to ionizing radiation have not been documented. Here, we searched for signatures of ionizing radiation in 12 radiation-associated second malignancies of different tumour types. Two signatures of somatic mutation characterize ionizing radiation exposure irrespective of tumour type. Compared with 319 radiation-naive tumours, radiation-associated tumours carry a median extra 201 deletions genome-wide, sized 1-100 base pairs often with microhomology at the junction. Unlike deletions of radiation-naive tumours, these show no variation in density across the genome or correlation with sequence context, replication timing or chromatin structure. Furthermore, we observe a significant increase in balanced inversions in radiation-associated tumours. Both small deletions and inversions generate driver mutations. Thus, ionizing radiation generates distinctive mutational signatures that explain its carcinogenic potential.This work was supported by funding from the Wellcome Trust (grant reference 077012/Z/05/Z), Skeletal Cancer Action Trust, Rosetrees Trust UK, Bone Cancer Research Trust, the RNOH NHS Trust, the National Institute for Health Research Health Protection Research Unit in Chemical and Radiation Hazards and Threats at Newcastle University in partnership with Public Health England. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR, the Department of Health or Public Health England. Tissue was obtained from the RNOH Musculoskeletal Research Programme and Biobank, co-ordinated by Mrs Deidre Brooking and Mrs Ru Grinnell, Biobank staff, RNOH. Support was provided to AMF by the National Institute for Health Research, UCLH Biomedical Research Centre, and the CRUK UCL Experimental Cancer Centre. S.N.Z. and S.B. are personally funded through Wellcome Trust Intermediate Clinical Research Fellowships, P.J.C. through a Wellcome Trust Senior Clinical Research Fellowship

Retrospective evaluation of whole exome and genome mutation calls in 746 cancer samples

Funder: NCI U24CA211006Abstract: The Cancer Genome Atlas (TCGA) and International Cancer Genome Consortium (ICGC) curated consensus somatic mutation calls using whole exome sequencing (WES) and whole genome sequencing (WGS), respectively. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2,658 cancers across 38 tumour types, we compare WES and WGS side-by-side from 746 TCGA samples, finding that ~80% of mutations overlap in covered exonic regions. We estimate that low variant allele fraction (VAF < 15%) and clonal heterogeneity contribute up to 68% of private WGS mutations and 71% of private WES mutations. We observe that ~30% of private WGS mutations trace to mutations identified by a single variant caller in WES consensus efforts. WGS captures both ~50% more variation in exonic regions and un-observed mutations in loci with variable GC-content. Together, our analysis highlights technological divergences between two reproducible somatic variant detection efforts