Coral development: from classical embryology to molecular control

The phylum Cnidaria is the closest outgroup to the triploblastic metazoans and as such offers unique insights into evolutionary questions at several levels. In the post-genomic era, a knowledge of the gene complement of representative cnidarians will be important for understanding the relationship between the expansion of gene families and the evolution of morphological complexity among more highly evolved metazoans. Studies of cnidarian development and its molecular control will provide information about the origins of the major bilaterian body axes, the origin of the third tissue layer, the mesoderm, and the evolution of nervous system patterning. We are studying the cnidarian Acropora millepora, a reef building scleractinian coral, and a member of the basal cnidarian class, the Anthozoa. We review ourwork on descriptive embryology and studies of selected transcription factor gene families, where our knowledge from Acropora is particularly advanced relative to other cnidarians. We also describe a recent preliminary whole genome initiative, a coral EST database.Eldon E. Ball, David C. Hayward, John S. Reece-Hoyes, Nikki R. Hislop, Gabrielle Samuel, Robert Saint, Peter L. Harrison and David J. Mille

Twisted duality of the CAR-Algebra

We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use modular theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof. As a byproduct of the proof we obtain an explicit and simple formula for the graph of the modular operator. This formula can be also applied to fermionic free nets, hence giving a formula of the modular operator for any double cone.Comment: 32 pages, Latex2e, to appear in Journal of Mathematical Physic

Clinical effectiveness and cost-effectiveness of imatinib dose escalation for the treatment of unresectable and/or metastatic gastrointestinal stromal tumours that have progressed on treatment at a dose of 400 mg/day : a systematic review and economic evaluation

Peer reviewedPublisher PD

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.Comment: 14 pages, no figure

Modular Structure and Duality in Conformal Quantum Field Theory

Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge region and the vacuum vector concides with the evolution given by the rescaled pure Lorentz transformations preserving the wedge. A similar geometric description is valid for the algebras associated with double cones. Moreover essential duality holds on the Minkowski space $M$, and Haag duality for double cones holds provided the net of local algebras is extended to a pre-cosheaf on the superworld $\tilde M$, i.e. the universal covering of the Dirac-Weyl compactification of $M$. As a consequence a PCT symmetry exists for any algebraic conformal field theory in even space-time dimension. Analogous results hold for a Poincar\'e covariant theory provided the modular groups corresponding to wedge algebras have the expected geometrical meaning and the split property is satisfied. In particular the Poincar\'e representation is unique in this case.Comment: 23 pages, plain TeX, TVM26-12-199

Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis

We study the Unruh effect for an observer with a finite lifetime, using the thermal time hypothesis. The thermal time hypothesis maintains that: (i) time is the physical quantity determined by the flow defined by a state over an observable algebra, and (ii) when this flow is proportional to a geometric flow in spacetime, temperature is the ratio between flow parameter and proper time. An eternal accelerated Unruh observer has access to the local algebra associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a field theory over this algebra is proportional to a flow in spacetime and the associated temperature is the Unruh temperature. An observer with a finite lifetime has access to the local observable algebra associated to a finite spacetime region called a "diamond". The flow defined by the Minkowski vacuum of a (four dimensional, conformally invariant) quantum field theory over this algebra is also proportional to a flow in spacetime. The associated temperature generalizes the Unruh temperature to finite lifetime observers. Furthermore, this temperature does not vanish even in the limit in which the acceleration is zero. The temperature associated to an inertial observer with lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b T).This temperature is related to the fact that a finite lifetime observer does not have access to all the degrees of freedom of the quantum field theory.Comment: One reference correcte

Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and "almost" linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.Comment: 14 pages, 5 figure

Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps

We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrodinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1d and 2d localization below the ground state of such an operator. Furthermore, we extend our results to 1d and 2d localization in d dimensions; for example, a linear or planar defect in a 3d crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.Comment: 9 pages, 3 figure