A unified way of analyzing some greedy algorithms

A unified way of analyzing different greedy-type algorithms in Banach spaces is presented. We define a class of Weak Biorthogonal Greedy Algorithms and prove convergence and rate of convergence results for algorithms from this class. In particular, the following well known algorithms --- Weak Chebyshev Greedy Algorithm and Weak Greedy Algorithm with Free Relaxation --- belong to this class. We consider here one more algorithm --- Rescaled Weak Relaxed Greedy Algorithm --- from the above class. We also discuss modifications of these algorithms, which are motivated by applications. We analyze convergence and rate of convergence of the algorithms under assumption that we may perform steps of these algorithms with some errors. We call such algorithms approximate greedy algorithms. We prove convergence and rate of convergence results for the Approximate Weak Biorthogonal Greedy Algorithms. These results guarantee stability of Weak Biorthogonal Greedy Algorithms

SDSS J1254+0846: A Binary Quasar Caught in the Act of Merging

We present the first luminous, spatially resolved binary quasar that clearly inhabits an ongoing galaxy merger. SDSS J125455.09+084653.9 and SDSS J125454.87+084652.1 (SDSS J1254+0846 hereafter) are two luminous z=0.44 radio quiet quasars, with a radial velocity difference of just 215 km/s, separated on the sky by 21 kpc in a disturbed host galaxy merger showing obvious tidal tails. The pair was targeted as part of a complete sample of binary quasar candidates with small transverse separations drawn from SDSS DR6 photometry. We present follow-up optical imaging which shows broad, symmetrical tidal arm features spanning some 75 kpc at the quasars' redshift. Numerical modeling suggests that the system consists of two massive disk galaxies prograde to their mutual orbit, caught during the first passage of an active merger. This demonstrates rapid black hole growth during the early stages of a merger between galaxies with pre-existing bulges. Neither of the two luminous nuclei show significant instrinsic absorption by gas or dust in our optical or X-ray observations, illustrating that not all merging quasars will be in an obscured, ultraluminous phase. We find that the Eddington ratio for the fainter component B is rather normal, while for the A component L/LEdd is quite (>3sigma) high compared to quasars of similar luminosity and redshift, possibly evidence for strong merger-triggered accretion. More such mergers should be identifiable at higher redshifts using binary quasars as tracers.Comment: 15 pages, 5 figures, accepted to the Astrophysical Journal for the February 2010 - 20 v710 issue. Latest version corrects author lis

A Full Year's Chandra Exposure on SDSS Quasars from the Chandra Multiwavelength Project

We study the spectral energy distributions and evolution of a large sample of optically selected quasars from the Sloan Digital Sky Survey (SDSS) that were observed in 323 Chandra images analyzed by the Chandra Multiwavelength Project (ChaMP). Our highest-confidence matched sample includes 1135 X-ray detected quasars in the redshift range 0.2<z<5.4, representing some 36Msec of effective exposure. Spectroscopic redshifts are available for about 1/3 of the detected sample; elsewhere, redshifts are estimated photometrically. With 56 z>3 QSOs detected, we find no evidence for evolution out to z~5 for either the X-ray photon index Gamma or for the ratio of optical/UV to X-ray flux alpha_ox. About 10% of detected QSOs are obscured (Nh>1E22), but the fraction might reach ~1/3 if most non-detections are absorbed. We confirm a significant correlation between alpha_ox and optical luminosity, but it flattens or disappears for fainter AGN alone. Gamma hardens significantly both towards higher X-ray luminosity, and for relatively X-ray loud quasars. These trends may represent a relative increase in non-thermal X-ray emission, and our findings thereby strengthen analogies between Galactic black hole binaries and AGN.Comment: 28 pages, 21 figures. Accepted (26 Aug 2008) for publication in ApJS. Electronic datafiles (for tables 2 and 3) and high resolution figures available at http://hea-www.harvard.edu/CHAMP

The changing ISM of massive elliptical galaxies and cosmic evolution of radio galaxies and quasars

The recently discovered apparent dramatic expansion in the effective radii of massive elliptical galaxies from $z \simeq 2$ to $z \simeq 0.1$ has been interpreted in terms of either galaxy mergers or the rapid loss of cold gas due to AGN feedback. In examining the latter case we have quantified the extent of the expansion, which is uncertain observationally, in terms of the star formation parameters and time of the expulsion of the cold gas. In either case, the large global decrease in stellar density should translate into a major drop in the ISM density and pressure, and a much steeper radial decline in those quantities with cosmic epoch. These cosmological changes are expected to have a major influence on the gas accretion mode, which will shift from `cold' thin disk accretion at high redshifts toward `hot' Bondi fed ADAF accretion at low redshifts. The decline of angular momentum inflow would then lead to a spin down of the black hole, for which we have calculated more precise time scales; a value of about 0.2 Gyr is typical for a $10^9 M_\odot$ central black hole. These results have implications for the different cosmological evolutionary patterns found for the luminosity functions of powerful and weak radio galaxies.Comment: 9 pages, 4 figures, accepted in MNRA

Tropical tree growth driven by dry-season climate variability

Interannual variability in the global land carbon sink is strongly related to variations in tropical temperature and rainfall. This association suggests an important role for moisture-driven fluctuations in tropical vegetation productivity, but empirical evidence to quantify the responsible ecological processes is missing. Such evidence can be obtained from tree-ring data that quantify variability in a major vegetation productivity component: woody biomass growth. Here we compile a pantropical tree-ring network to show that annual woody biomass growth increases primarily with dry-season precipitation and decreases with dry-season maximum temperature. The strength of these dry-season climate responses varies among sites, as reflected in four robust and distinct climate response groups of tropical tree growth derived from clustering. Using cluster and regression analyses, we find that dry-season climate responses are amplified in regions that are drier, hotter and more climatically variable. These amplification patterns suggest that projected global warming will probably aggravate drought-induced declines in annual tropical vegetation productivity. Our study reveals a previously underappreciated role of dry-season climate variability in driving the dynamics of tropical vegetation productivity and consequently in influencing the land carbon sink.We acknowledge financial support to the co-authors provided by Agencia Nacional de Promoción Científica y Tecnológica, Argentina (PICT 2014-2797) to M.E.F.; Alberta Mennega Stichting to P.G.; BBVA Foundation to H.A.M. and J.J.C.; Belspo BRAIN project: BR/143/A3/HERBAXYLAREDD to H.B.; Confederação da Agricultura e Pecuária do Brasil - CNA to C.F.; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES, Brazil (PDSE 15011/13-5 to M.A.P.; 88881.135931/2016-01 to C.F.; 88887.199858/2018-00 to G.A.-P.; Finance Code 001 for all Brazilian collaborators); Conselho Nacional de Desenvolvimento Científico e Tecnológico - CNPq, Brazil (ENV 42 to O.D.; 1009/4785031-2 to G.C.; 311874/2017-7 to J.S.); CONACYT-CB-2016-283134 to J.V.-D.; CONICET to F.A.R.; CUOMO FOUNDATION (IPCC scholarship) to M.M.; Deutsche Forschungsgemeinschaft - DFG (BR 1895/15-1 to A.B.; BR 1895/23-1 to A.B.; BR 1895/29-1 to A.B.; BR 1895/24-1 to M.M.); DGD-RMCA PilotMAB to B.T.; Dirección General de Asuntos del Personal Académico of the UNAM (Mexico) to R.B.; Elsa-Neumann-Scholarship of the Federal State of Berlin to F.S.; EMBRAPA Brazilian Agricultural Research Corporation to C.F.; Equatorian Dirección de Investigación UNL (21-DI-FARNR-2019) to D.P.-C.; São Paulo Research Foundation FAPESP (2009/53951-7 to M.T.-F.; 2012/50457-4 to G.C.; 2018/01847‐0 to P.G.; 2018/24514-7 to J.R.V.A.; 2019/08783-0 to G.M.L.; 2019/27110-7 to C.F.); FAPESP-NERC 18/50080-4 to G.C.; FAPITEC/SE/FUNTEC no. 01/2011 to M.A.P.; Fulbright Fellowship to B.J.E.; German Academic Exchange Service (DAAD) to M.I. and M.R.; German Ministry of Education, Science, Research, and Technology (FRG 0339638) to O.D.; ICRAF through the Forests, Trees, and Agroforestry research programme of the CGIAR to M.M.; Inter-American Institute for Global Change Research (IAI-SGP-CRA 2047) to J.V.-D.; International Foundation for Science (D/5466-1) to M.I.; Lamont Climate Center to B.M.B.; Miquelfonds to P.G.; National Geographic Global Exploration Fund (GEFNE80-13) to I.R.; USA’s National Science Foundation NSF (IBN-9801287 to A.J.L.; GER 9553623 and a postdoctoral fellowship to B.J.E.); NSF P2C2 (AGS-1501321) to A.C.B., D.G.-S. and G.A.-P.; NSF-FAPESP PIRE 2017/50085-3 to M.T.-F., G.C. and G.M.L.; NUFFIC-NICHE programme (HEART project) to B.K., E.M., J.H.S., J.N. and R. Vinya; Peru ‘s CONCYTEC and World Bank (043-2019-FONDECYT-BM-INC.INV.) to J.G.I.; Peru’s Fondo Nacional de Desarrollo Científico, Tecnológico y de Innovación Tecnológica (FONDECYT-BM-INC.INV 039-2019) to E.J.R.-R. and M.E.F.; Programa Bosques Andinos - HELVETAS Swiss Intercooperation to M.E.F.; Programa Nacional de Becas y Crédito Educativo - PRONABEC to J.G.I.; Schlumberger Foundation Faculty for the Future to J.N.; Sigma Xi to A.J.L.; Smithsonian Tropical Research Institute to R. Alfaro-Sánchez.; Spanish Ministry of Foreign Affairs AECID (11-CAP2-1730) to H.A.M. and J.J.C.; UK NERC grant NE/K01353X/1 to E.G.Peer reviewe

The evolution of lung cancer and impact of subclonal selection in TRACERx

Lung cancer is the leading cause of cancer-associated mortality worldwide. Here we analysed 1,644 tumour regions sampled at surgery or during follow-up from the first 421 patients with non-small cell lung cancer prospectively enrolled into the TRACERx study. This project aims to decipher lung cancer evolution and address the primary study endpoint: determining the relationship between intratumour heterogeneity and clinical outcome. In lung adenocarcinoma, mutations in 22 out of 40 common cancer genes were under significant subclonal selection, including classical tumour initiators such as TP53 and KRAS. We defined evolutionary dependencies between drivers, mutational processes and whole genome doubling (WGD) events. Despite patients having a history of smoking, 8% of lung adenocarcinomas lacked evidence of tobacco-induced mutagenesis. These tumours also had similar detection rates for EGFR mutations and for RET, ROS1, ALK and MET oncogenic isoforms compared with tumours in never-smokers, which suggests that they have a similar aetiology and pathogenesis. Large subclonal expansions were associated with positive subclonal selection. Patients with tumours harbouring recent subclonal expansions, on the terminus of a phylogenetic branch, had significantly shorter disease-free survival. Subclonal WGD was detected in 19% of tumours, and 10% of tumours harboured multiple subclonal WGDs in parallel. Subclonal, but not truncal, WGD was associated with shorter disease-free survival. Copy number heterogeneity was associated with extrathoracic relapse within 1 year after surgery. These data demonstrate the importance of clonal expansion, WGD and copy number instability in determining the timing and patterns of relapse in non-small cell lung cancer and provide a comprehensive clinical cancer evolutionary data resource

The evolution of non-small cell lung cancer metastases in TRACERx

Metastatic disease is responsible for the majority of cancer-related deaths. We report the longitudinal evolutionary analysis of 126 non-small cell lung cancer (NSCLC) tumours from 421 prospectively recruited patients in TRACERx who developed metastatic disease, compared with a control cohort of 144 non-metastatic tumours. In 25% of cases, metastases diverged early, before the last clonal sweep in the primary tumour, and early divergence was enriched for patients who were smokers at the time of initial diagnosis. Simulations suggested that early metastatic divergence more frequently occurred at smaller tumour diameters (less than 8 mm). Single-region primary tumour sampling resulted in 83% of late divergence cases being misclassified as early, highlighting the importance of extensive primary tumour sampling. Polyclonal dissemination, which was associated with extrathoracic disease recurrence, was found in 32% of cases. Primary lymph node disease contributed to metastatic relapse in less than 20% of cases, representing a hallmark of metastatic potential rather than a route to subsequent recurrences/disease progression. Metastasis-seeding subclones exhibited subclonal expansions within primary tumours, probably reflecting positive selection. Our findings highlight the importance of selection in metastatic clone evolution within untreated primary tumours, the distinction between monoclonal versus polyclonal seeding in dictating site of recurrence, the limitations of current radiological screening approaches for early diverging tumours and the need to develop strategies to target metastasis-seeding subclones before relapse

Genomic–transcriptomic evolution in lung cancer and metastasis

Intratumour heterogeneity (ITH) fuels lung cancer evolution, which leads to immune evasion and resistance to therapy. Here, using paired whole-exome and RNA sequencing data, we investigate intratumour transcriptomic diversity in 354 non-small cell lung cancer tumours from 347 out of the first 421 patients prospectively recruited into the TRACERx study. Analyses of 947 tumour regions, representing both primary and metastatic disease, alongside 96 tumour-adjacent normal tissue samples implicate the transcriptome as a major source of phenotypic variation. Gene expression levels and ITH relate to patterns of positive and negative selection during tumour evolution. We observe frequent copy number-independent allele-specific expression that is linked to epigenomic dysfunction. Allele-specific expression can also result in genomic–transcriptomic parallel evolution, which converges on cancer gene disruption. We extract signatures of RNA single-base substitutions and link their aetiology to the activity of the RNA-editing enzymes ADAR and APOBEC3A, thereby revealing otherwise undetected ongoing APOBEC activity in tumours. Characterizing the transcriptomes of primary–metastatic tumour pairs, we combine multiple machine-learning approaches that leverage genomic and transcriptomic variables to link metastasis-seeding potential to the evolutionary context of mutations and increased proliferation within primary tumour regions. These results highlight the interplay between the genome and transcriptome in influencing ITH, lung cancer evolution and metastasis

Antibodies against endogenous retroviruses promote lung cancer immunotherapy

B cells are frequently found in the margins of solid tumours as organized follicles in ectopic lymphoid organs called tertiary lymphoid structures (TLS). Although TLS have been found to correlate with improved patient survival and response to immune checkpoint blockade (ICB), the underlying mechanisms of this association remain elusive. Here we investigate lung-resident B cell responses in patients from the TRACERx 421 (Tracking Non-Small-Cell Lung Cancer Evolution Through Therapy) and other lung cancer cohorts, and in a recently established immunogenic mouse model for lung adenocarcinoma. We find that both human and mouse lung adenocarcinomas elicit local germinal centre responses and tumour-binding antibodies, and further identify endogenous retrovirus (ERV) envelope glycoproteins as a dominant anti-tumour antibody target. ERV-targeting B cell responses are amplified by ICB in both humans and mice, and by targeted inhibition of KRAS(G12C) in the mouse model. ERV-reactive antibodies exert anti-tumour activity that extends survival in the mouse model, and ERV expression predicts the outcome of ICB in human lung adenocarcinoma. Finally, we find that effective immunotherapy in the mouse model requires CXCL13-dependent TLS formation. Conversely, therapeutic CXCL13 treatment potentiates anti-tumour immunity and synergizes with ICB. Our findings provide a possible mechanistic basis for the association of TLS with immunotherapy response