The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

The Essential Role of Human Databases for Learning in and Validation of Affectively Competent Agents.

This output is an invited and refereed chapter in the second of the two book length outputs resulting from the EU HUMAINE grant and follow-on grants. The book is in the OUP Affective Science Series and is intended to provide a theoretically oriented state of the art model for those working in the area of affective computing. Each chapter provides a synthesis of a specific area and presents new data/findings/approaches developed by the author(s) which take the area further. This chapter is in the section on ‘Approaches to developing expression corpora and databases.’ The chapter provides a critical synthesis of the issues involved in databases for affective computing and introduces the SEMAINE SAL Database, developed as an integral part of the EU SEMAINE Project (The Sensitive Agent Project 2008-2011) which is an interdisciplinary project. The project aimed to develop a computer interface that would allow a human to interact with an artificial agent in an emotional manner.

On the spectrum of frequently hypercyclic operators

A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question.

Infrared spectrum of an extremely cool white-dwarf star

White dwarfs are the remnant cores of stars that initially had masses of less than 8 solar masses. They cool gradually over billions of years, and have been suggested(1,2) to make up much of the 'dark matter' in the halo of the Milky way. But extremely cool white dwarfs have proved difficult to detect, owing to both their faintness and their anticipated similarity in colour to other classes of dwarf stars. Recent improved models(3-5) indicate that white dwarfs are much more blue than previously supposed, suggesting that the earlier searches may have been looking for the wrong kinds of objects. Here we report an infrared spectrum of an extremely cool white dwarf that is consistent with the new models. We determine the star's temperature to be 3,500 +/- 200 K, making it the coolest known white dwarf. The kinematics of this star indicate that it is in the halo of the Milky Way, and the density of such objects implied by the serendipitous discovery of this star is consistent with white dwarfs dominating the dark matter in the halo.

Dense spectrum of resonances and particle capture in a near-black-hole metric

We show that a quantum scalar particle in the gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, possesses a dense spectrum of narrow resonances. Their lifetimes and density tend to infinity in the limit R?rs. We determine the cross section of the particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus, a nonsingular static metric acquires black-hole properties before the actual formation of a black hole.

BRCA1 is an essential mediator of vinorelbine-induced apoptosis in mesothelioma

Therapeutic options for malignant pleural mesothelioma (MPM) are limited despite the increasing incidence globally. The vinca alkaloid vinorelbine exhibits clinical activity; however, to date, treatment optimization has not been achieved using biomarkers. BRCA1 regulates sensitivity to microtubule poisons; however, its role in regulating vinorelbine-induced apoptosis in mesothelioma is unknown. Here we demonstrate that BRCA1 plays an essential role in mediating vinorelbine-induced apoptosis, as evidenced by (1) the strong correlation between vinorelbine sensitivity and BRCA1 expression level; (2) induction of resistance to vinorelbine by BRCA1 using siRNA oligonucleotides; (3) dramatic down-regulation of BRCA1 following selection for vinorelbine resistance; and (4) the re-activation of vinorelbine-induced apoptosis following re-expression of BRCA1 in resistant cells. To determine whether loss of BRCA1 expression in mesothelioma was potentially relevant in vivo, BRCA1 immunohistochemistry was subsequently performed on 144 primary mesothelioma specimens. Loss of BRCA1 protein expression was identified in 38.9% of samples. Together, these data suggest that BRCA1 plays a critical role in mediating apoptosis by vinorelbine in mesothelioma, warranting its clinical evaluation as a predictive biomarker.

Detection of magnetic dipole lines of Fe XII in the ultraviolet spectrum of the dwarf star ε Eri

We report observations of the dwarf star e Eri (K2V) made with the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope. The high sensitivity of the STIS instrument has allowed us to detect the magnetic dipole transitions of Fe XII at 1242.00 and 1349 38 Å for the first time in a star other than the Sun. The width of the stronger line at 1242.00 Å has also been measured; such measurements are not possible for the permitted lines of Fe XII in the extreme-ultraviolet. To within the accuracy of the measurements the N v and the Fe XII lines occur at their rest wavelengths. Electron densities and linewidths have been measured from other transition region lines. Together, these can be used to investigate the non-thermal energy flux in the lower and upper transition regions, which is useful in constraining possible heating processes. The Fe XII lines are also present in archival STIS spectra of other G/K-type dwarfs.

Evidence for relativistic features in the X-ray spectrum of Mrk 335

We present an analysis of hard X-ray features in the spectrum of the bright Sy 1 galaxy Mrk 335 observed by the XMM-Newton satellite. Our analysis confirms the presence of a broad, ionized Fe Ka emission line in the spectrum, first found by Gondoin et al. The broad line can be modelled successfully by relativistic accretion disc reflection models. This interpretation is unusually robust in the case of Mrk 335 because of the lack of any ionized ('warm') absorber and the absence a clear narrow core to the line. Partial covering by neutral gas cannot, however, be ruled out statistically as the origin of the broad residuals. Regardless of the underlying continuum we report, for the first time in this source, the detection of a narrow absorption feature at the rest frame energy of ~5.9 keV. If the feature is identified with a resonance absorption line of iron in a highly ionized medium, the redshift of the line corresponds to an inflow velocity of ~0.11-0.15c. We present a simple model for the inflow, accounting approximately for relativistic and radiation pressure effects, and use Monte Carlo methods to compute synthetic spectra for qualitative comparison with the data. This modelling shows that the absorption feature can plausibly be reproduced by infalling gas providing that the feature is identified with Fe xxvi. We require the inflowing gas to extend over a limited range of radii at a few tens of r to match the observed feature. The mass accretion rate in the flow corresponds to 60 per cent of the Eddington limit, in remarkable agreement with the observed rate. The narrowness of the absorption line tends to argue against a purely gravitational origin for the redshift of the line, but given the current data quality we stress that such an interpretation cannot be ruled out. © 2006 The Authors.

Mutational spectrum of the ZEB1 gene in corneal dystrophies supports a genotype-phenotype correlation

Mutations in ZEB1 have been reported in posterior polymorphous corneal dystrophy (PPCD3; MIM #609141) and Fuchs' endothelial corneal dystrophy (FECD6; MIM #613270). Although PPCD and keratoconus are clinically and pathologically distinct, PPCD has been associated with keratoconus, suggesting a common genetic basis. The purpose of our study was to perform mutational screening of the ZEB1 gene in patients affected with keratoconus or PPCD.