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

Jupiter’s Atmosphere

In this paper the two model of Jupiter’s atmosphere, vi., adiabatic and isothermal, have been considered. The variability of the period of rotation of the atmosphere depending on the latitude and the variation of gravity have both been taken into account.The datum level of Jupiter is the effective radiating and absorbing layer probably a cloud layer at a certain height in the atmosphere It has the observed temperature of 150°Absolute. The authors have investigated the relation between pressure and density at any depth below the datum level and at any height above the datum level, in each of the two cases, viz., (i) when the atmosphere consists of methhae only, and (2) when it consists of a mixture of one part of methane and six parts of hydrogen Even taking the atmosphere to be in adiabatic condition below the datum level and in isothermal condition above the datum level the authors have found that the total thickness of the atmospheric layer cannot, in any ease exceed 1900kms., and possibly it is below 1300 kms

A time frequency analysis of wave packet fractional revivals

We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.Comment: 9 pages, 4 figure

On Kaufmann's theory of the impact of the pianoforte hammer

This article does not have an abstract

Correcting CIV-Based Virial Black Hole Masses

The CIV broad emission line is visible in optical spectra to redshifts exceeding z~5. CIV has long been known to exhibit significant displacements to the blue and these `blueshifts' almost certainly signal the presence of strong outflows. As a consequence, single-epoch virial black hole (BH) mass estimates derived from CIV velocity-widths are known to be systematically biased compared to masses from the hydrogen Balmer lines. Using a large sample of 230 high-luminosity (log $L_{\rm Bol}$ = 45.5-48 erg/s), redshift 1.5<z<4.0 quasars with both CIV and Balmer line spectra, we have quantified the bias in CIV BH masses as a function of the CIV blueshift. CIV BH masses are shown to be a factor of five larger than the corresponding Balmer-line masses at CIV blueshifts of 3000 km/s and are over-estimated by almost an order of magnitude at the most extreme blueshifts, >5000 km/s. Using the monotonically increasing relationship between the CIV blueshift and the mass ratio BH(CIV)/BH(H$\alpha$) we derive an empirical correction to all CIV BH-masses. The scatter between the corrected CIV masses and the Balmer masses is 0.24 dex at low CIV blueshifts (~0 km/s) and just 0.10 dex at high blueshifts (~3000 km/s), compared to 0.40 dex before the correction. The correction depends only on the CIV line properties - i.e. full-width at half maximum and blueshift - and can therefore be applied to all quasars where CIV emission line properties have been measured, enabling the derivation of un-biased virial BH mass estimates for the majority of high-luminosity, high-redshift, spectroscopically confirmed quasars in the literature.Comment: Accepted for publication in MNRAS; fixed typo in CIV wavelengt

Network Theoretic Tools in the Analysis of Complex Diseases

In this thesis we consider the application of network theoretic tools in the analysis of genome wide gene-expression data describing complex diseases, displaying defects in differentiation. After considering the literature, we motivate the construction of entropy based network rewiring methodologies, postulating that such an approach may provide a systems level correlate of the differentiation potential of a cellular sample, and may prove informative in the analysis of pathology. We construct, analytically investigate and validate three such network theoretic tools: Network Transfer Entropy, Signalling Entropy and Interactome Sparsification and Rewiring (InSpiRe). By considering over 1000 genome wide gene expression samples corresponding to healthy cells at different levels of differentiation, we demonstrate that signalling entropy is a strong correlate of cell potency confirming our initial postulate. The remainder of the thesis applies our network theoretic tools to two ends of the developmental pathology spectrum. Firstly we consider cancer, in which the power of cell differentiation is hijacked, to develop a malicious new tissue. Secondly, we consider muscular dystrophy, in which cell differentiation is inhibited, resulting in the poor development of muscle tissue. In the case of cancer we demonstrate that signalling entropy is a measure of tumour anaplasia and intra-tumour heterogeneity, which displays distinct values in different cancer subtypes. Moreover, we find signalling entropy to be a powerful prognostic indicator in epithelial cancer, outperforming conventional gene expression based assays. In the case of muscular dystrophy we focus on the most prevalent: facioscapulohumeral muscular dystrophy (FSHD). We demonstrate that muscle differentiation is perturbed in FSHD and that signalling entropy is elevated in myoblasts over-expressing the primary FSHD candidate gene DUX4. We subsequently utilise InSpiRe, performing a meta-analysis of FSHD muscle biopsy gene-expression data, uncovering a network of DUX4 driven rewired interactions in the pathology, and a novel therapeutic target which we validate experimentally