Intra-tumour signalling entropy determines clinical outcome in breast and lung cancer.

The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample's genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers

Heavily reddened type 1 quasars at z > 2 I: Evidence for significant obscured black-hole growth at the highest quasar luminosities

We present a new population of z>2 dust-reddened, Type 1 quasars with 0.5<E(B-V)<1.5, selected using near infra-red (NIR) imaging data from the UKIDSS-LAS, ESO-VHS and WISE surveys. NIR spectra obtained using the Very Large Telescope (VLT) for 24 new objects bring our total sample of spectroscopically confirmed hyperluminous (>10^{13}L_0), high-redshift dusty quasars to 38. There is no evidence for reddened quasars having significantly different H$\alpha$ equivalent widths relative to unobscured quasars. The average black-hole masses (~10^9-10^10 M_0) and bolometric luminosities (~10^{47} erg/s) are comparable to the most luminous unobscured quasars at the same redshift, but with a tail extending to very high luminosities of ~10^{48} erg/s. Sixty-six per cent of the reddened quasars are detected at $>3\sigma$ at 22um by WISE. The average 6um rest-frame luminosity is log10(L6um/erg/s)=47.1+/-0.4, making the objects among the mid-infrared brightest AGN currently known. The extinction-corrected space-density estimate now extends over three magnitudes (-30 < M_i < -27) and demonstrates that the reddened quasar luminosity function is significantly flatter than that of the unobscured quasar population at z=2-3. At the brightest magnitudes, M_i < -29, the space density of our dust-reddened population exceeds that of unobscured quasars. A model where the probability that a quasar becomes dust-reddened increases at high luminosity is consistent with the observations and such a dependence could be explained by an increase in luminosity and extinction during AGN-fuelling phases. The properties of our obscured Type 1 quasars are distinct from the heavily obscured, Compton-thick AGN that have been identified at much fainter luminosities and we conclude that they likely correspond to a brief evolutionary phase in massive galaxy formation.Comment: 16 pages, 9 figures (+ 2 appendices), Accepted for publication in MNRA

Off Resonant Pumping for Transition from Continuous to Discrete Spectrum and Quantum Revivals in Systems in Coherent States

We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the non-linear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomena as an optical analog of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.Comment: 5 pages, 4 figures, submitted to Jnl. of Optics

Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states

We consider the evolution of a two-mode system of bosons under the action of a Hamiltonian that generates linear SU(2) transformations. The Hamiltonian is generic in that it represents a host of entanglement mechanisms, which can thus be treated in a unified way. We start by solving the quantum dynamics analytically when the system is initially in a Fock state. We show how the two modes get entangled by evolution to produce a coherent superposition of vortex states in general, and a single vortex state under certain conditions. The degree of entanglement between the modes is measured by finding the explicit analytical dependence of the Von Neumann entropy on the system parameters. The reduced state of each mode is analyzed by means of its correlation function and spatial coherence function. Remarkably, our analysis is shown to be equally as valid for a variety of initial states that can be prepared from a two-mode Fock state via a unitary transformation and for which the results can be obtained by mere inspection of the corresponding results for an initial Fock state. As an example, we consider a quantum vortex as the initial state and also find conditions for its revival and charge conjugation. While studying the evolution of the initial vortex state, we have encountered and explained an interesting situation in which the entropy of the system does not evolve whereas its wave function does. Although the modal concept has been used throughout the paper, it is important to note that the theory is equally applicable for a two-particle system in which each particle is represented by its bosonic creation and annihilation operators.Comment: 6 figure

Age and growth studies on the Indian mackerel Rastrelliger kanagurta (Cuvier) with special reference to length-frequency data collected at cochin

Length-frequency studies on the Indian mackerel Rastrelliger kanagurta (Cuvier) have been made by Pradhan (1956), Sekharan (1958) and Balakristman (1962-MS). but there has been no agreement with regard to the interpretation of age and growth rate of the fish. Since little work has been done on study of hard parts of the fish, tagging or rearing of the fish under captivity, verification of any of the conclusions arrived at by length-frequency studies has not been possible. Mention may be made in this connection of the work of Seshappa (1958) to interpret the significance of the scale rings of the fish

Simulations of the OzDES AGN Reverberation Mapping Project

As part of the OzDES spectroscopic survey we are carrying out a large scale reverberation mapping study of $\sim$500 quasars over five years in the 30 deg$^2$ area of the Dark Energy Survey (DES) supernova fields. These quasars have redshifts ranging up to 4 and have apparent AB magnitudes between $16.8<r<22.5$ mag. The aim of the survey is to measure time lags between fluctuations in the quasar continuum and broad emission line fluxes of individual objects in order to measure black hole masses for a broad range of AGN and constrain the radius-luminosity ($R-L$) relationship. Here we investigate the expected efficiency of the OzDES reverberation mapping campaign and its possible extensions. We expect to recover lags for $\sim$35-45\% of the quasars. AGN with shorter lags and greater variability are more likely to yield a lag, and objects with lags $\lesssim$6 months or $\sim$1 year are expected be recovered the most accurately. The baseline OzDES reverberation mapping campaign is predicted to produce an unbiased measurement of the $R-L$ relationship parameters for H$\beta$, Mg II $\lambda$2798, and C IV $\lambda$1549. However, extending the baseline survey by either increasing the spectroscopic cadence, extending the survey season, or improving the emission line flux measurement accuracy will significantly improve the $R-L$ parameter constraints for all broad emission lines.Comment: Published online in MNRAS. 28 page

The Discovery of Gas-Rich, Dusty Starbursts in Luminous Reddened Quasars at z∼2.5z\sim2.5 with ALMA

We present ALMA observations of cold dust and molecular gas in four high-luminosity, heavily reddened (A$_{\rm{V}} \sim 2.5-6$ mag) Type 1 quasars at $z\sim2.5$ with virial M$_{\rm{BH}} \sim 10^{10}$M$_\odot$, to test whether dusty, massive quasars represent the evolutionary link between submillimetre bright galaxies (SMGs) and unobscured quasars. All four quasars are detected in both the dust continuum and in the $^{12}$CO(3-2) line. The mean dust mass is 6$\times$10$^{8}$M$_\odot$ assuming a typical high redshift quasar spectral energy distribution (T=41K, $\beta$=1.95 or T=47K, $\beta$=1.6). The implied star formation rates are very high - $\gtrsim$1000 M$_\odot$ yr$^{-1}$ in all cases. Gas masses estimated from the CO line luminosities cover $\sim$1-5$\times10^{10}$($\alpha_{\rm{CO}} / 0.8$)M$_\odot$ and the gas depletion timescales are very short - $\sim5-20$Myr. A range of gas-to-dust ratios is observed in the sample. We resolve the molecular gas in one quasar - ULASJ2315$+$0143 ($z=2.561$) - which shows a strong velocity gradient over $\sim$20 kpc. The velocity field is consistent with a rotationally supported gas disk but other scenarios, e.g. mergers, cannot be ruled out at the current resolution of these data. In another quasar - ULASJ1234+0907 ($z=2.503$) - we detected molecular line emission from two millimetre bright galaxies within 200 kpc of the quasar, suggesting that this quasar resides in a significant over-density. The high detection rate of both cold dust and molecular gas in these sources, suggests that reddened quasars could correspond to an early phase in massive galaxy formation associated with large gas reservoirs and significant star formation.MB acknowledges funding from the UK Science and Technology Facilities Council (STFC) via an Ernest Rutherford Fellowship. GJ is grateful for support from NRAO through the Grote Reber Doctoral Fellowship Program. RGM and PCH acknowledge funding from STFC via the Institute of Astronomy, Cambridge Consolidated Grant. SA-Z acknowledges support from Peterhouse, Cambridge

Coherent states of P{\"o}schl-Teller potential and their revival dynamics

A recently developed algebraic approach for constructing coherent states for solvable potentials is used to obtain the displacement operator coherent state of the P\"{o}schl-Teller potential. We establish the connection between this and the annihilation operator coherent state and compare their properties. We study the details of the revival structure arising from different time scales underlying the quadratic energy spectrum of this system.Comment: 13 pages, 6 figure

Far-infrared emission in luminous quasars accompanied by nuclear outflows

Combining large-area optical quasar surveys with the new far-infrared (FIR) Herschel-ATLAS Data Release 1, we search for an observational signature associated with the minority of quasars possessing bright FIR luminosities. We find that FIR-bright quasars show broad C IV emission-line blueshifts in excess of that expected from the optical luminosity alone, indicating particularly powerful nuclear outflows. The quasars show no signs of having redder optical colours than the general ensemble of optically selected quasars, ruling out differences in line-of-sight dust within the host galaxies. We postulate that these objects may be caught in a special evolutionary phase, with unobscured, high black hole accretion rates and correspondingly strong nuclear outflows. The high FIR emission found in these objects is then either a result of star formation related to the outflow, or is due to dust within the host galaxy illuminated by the quasar. We are thus directly witnessing coincident small-scale nuclear processes and galaxy-wide activity, commonly invoked in galaxy simulations that rely on feedback from quasars to influence galaxy evolution

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