On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type

We propose a noncommutative version of the Euclidean Lie algebra E 2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra

DNA-based Self-Assembly of Chiral Plasmonic Nanostructures with Tailored Optical Response

Surface plasmon resonances generated in metallic nanostructures can be utilized to tailor electromagnetic fields. The precise spatial arrangement of such structures can result in surprising optical properties that are not found in any naturally occurring material. Here, the designed activity emerges from collective effects of singular components equipped with limited individual functionality. Top-down fabrication of plasmonic materials with a predesigned optical response in the visible range by conventional lithographic methods has remained challenging due to their limited resolution, the complexity of scaling, and the difficulty to extend these techniques to three-dimensional architectures. Molecular self-assembly provides an alternative route to create such materials which is not bound by the above limitations. We demonstrate how the DNA origami method can be used to produce plasmonic materials with a tailored optical response at visible wavelengths. Harnessing the assembly power of 3D DNA origami, we arranged metal nanoparticles with a spatial accuracy of 2 nm into nanoscale helices. The helical structures assemble in solution in a massively parallel fashion and with near quantitative yields. As a designed optical response, we generated giant circular dichroism and optical rotary dispersion in the visible range that originates from the collective plasmon-plasmon interactions within the nanohelices. We also show that the optical response can be tuned through the visible spectrum by changing the composition of the metal nanoparticles. The observed effects are independent of the direction of the incident light and can be switched by design between left- and right-handed orientation. Our work demonstrates the production of complex bulk materials from precisely designed nanoscopic assemblies and highlights the potential of DNA self-assembly for the fabrication of plasmonic nanostructures.Comment: 5 pages, 4 figure

Heterotic-Type II duality in the hypermultiplet sector

We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective moduli spaces at the level of the classical effective actions. We determine the parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal form. From the expression of the holomorphic prepotential we are led to conjecture that both X and its mirror must be K3 fibrations in order for the type IIA theory to have an heterotic dual. We then focus on the region of the moduli space where the metric is expressed in terms of a prepotential on both sides of the duality. Applying the duality we derive the heterotic hypermultiplet metric for a gauge bundle which is reduced to 24 point-like instantons. This result is confirmed by using the duality between the heterotic theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on the moduli space of an SU(2) bundle on K3.Comment: 27 pages; references added, typos correcte

Ecological Guild Evolution and the Discovery of the World's Smallest Vertebrate

Living vertebrates vary drastically in body size, yet few taxa reach the extremely minute size of some frogs and teleost fish. Here we describe two new species of diminutive terrestrial frogs from the megadiverse hotspot island of New Guinea, one of which represents the smallest known vertebrate species, attaining an average body size of only 7.7 mm. Both new species are members of the recently described genus Paedophryne, the four species of which are all among the ten smallest known frog species, making Paedophryne the most diminutive genus of anurans. This discovery highlights intriguing ecological similarities among the numerous independent origins of diminutive anurans, suggesting that minute frogs are not mere oddities, but represent a previously unrecognized ecological guild

Measurement of the hadronic photon structure function F_{2}^{γ} at LEP2

The hadronic structure function of the photon F_{2}^{γ} (x, Q²) is measured as a function of Bjorken x and of the photon virtuality Q² using deep-inelastic scattering data taken by the OPAL detector at LEP at e⁺e⁻ centre-of-mass energies from 183 to 209 GeV. Previous OPAL measurements of the x dependence of F_{2}^{γ} are extended to an average Q² of 〈Q²〉=780 GeV² using data in the kinematic range 0.15<x<0.98. The Q² evolution of F_{2}^{γ} is studied for 12.1<〈Q²〉<780 GeV² using three ranges of x. As predicted by QCD, the data show positive scaling violations in F_{2}^{γ} with F_{2}^{γ} (Q²)/α = (0.08±0.02⁺⁰·⁰⁵_₀.₀₃) + (0.13±0.01⁺⁰·⁰¹_₀.₀₁) lnQ², where Q² is in GeV², for the central x region 0.10–0.60. Several parameterisations of F_{2}^{γ} are in qualitative agreement with the measurements whereas the quark-parton model prediction fails to describe the data

Measurement of the charm structure function F_{2,c)^{γ} of the photon at LEP

The production of charm quarks is studied in deep-inelastic electron–photon scattering using data recorded by the OPAL detector at LEP at nominal e⁺e⁻ centre-of-mass energies from 183 to 209 GeV. The charm quarks have been identified by full reconstruction of charged D* mesons using their decays into D⁰π with the D⁰ observed in two decay modes with charged particle final states, Kπ and Kπππ. The cross-section σ^{D*} for production of charged D* in the reaction e⁺e⁻→e⁺e⁻D*Χ is measured in a restricted kinematical region using two bins in Bjorken x, 0.00140.1 the perturbative QCD calculation at next-to-leading order agrees perfectly with the measured cross-section. For x<0.1 the measured cross-section is 43.8±14.3±6.3±2.8 pb with a next-to-leading order prediction of 17.0⁺²·⁹_₂.₃ pb

Metabolomic Profiling of Drug Responses in Acute Myeloid Leukaemia Cell Lines

Combined bezafibrate (BEZ) and medroxyprogesterone acetate (MPA) exert unexpected antileukaemic activities against acute myeloid leukaemia (AML) and these activities are associated with the generation of reactive oxygen species (ROS) within the tumor cells. Although the generation of ROS by these drugs is supported by preceding studies including our own, the interrelationship between the cellular effects of the drugs and ROS generation is not well understood. Here we report the use of NMR metabolomic profiling to further study the effect of BEZ and MPA on three AML cell lines and to shed light on the underlying mechanism of action. For this we focused on drug effects induced during the initial 24 hours of treatment prior to the onset of overt cellular responses and examined these in the context of basal differences in metabolic profiles between the cell lines. Despite their ultimately profound cellular effects, the early changes in metabolic profiles engendered by these drugs were less pronounced than the constitutive metabolic differences between cell types. Nonetheless, drug treatments engendered common metabolic changes, most markedly in the response to the combination of BEZ and MPA. These responses included changes to TCA cycle intermediates consistent with recently identified chemical actions of ROS. Notable amongst these was the conversion of α-ketoglutarate to succinate which was recapitulated by the treatment of cell extracts with exogenous hydrogen peroxide. These findings indicate that the actions of combined BEZ and MPA against AML cells are indeed mediated downstream of the generation of ROS rather than some hitherto unsuspected mechanism. Moreover, our findings demonstrate that metabolite profiles represent highly sensitive markers for genomic differences between cells and their responses to external stimuli. This opens new perspectives to use metabolic profiling as a tool to study the rational redeployment of drugs in new disease settings

Feasibility and initial experience of assessment of mechanical dyssynchrony using cardiovascular magnetic resonance and semi-automatic border detection

<p>Abstract</p> <p>Background</p> <p>The systolic dyssynchrony index (SDI) has been introduced as a measure of mechanical dyssynchrony using three-dimensional echocardiography to select patients who may benefit from cardiac resynchronization therapy (CRT). However, three-dimensional echocardiography may be inadequate in a number of patients with suboptimal acoustic window and no single echocardiographic measure of dyssynchrony has proven to be of value in selecting patients for CRT. Thus, the aim of this study was to determine the value of cardiovascular magnetic resonance (CMR) for the assessment of the SDI in patients with reduced LV function as well as in healthy controls using semi-automatic border tracking.</p> <p>Methods</p> <p>We investigated a total of 45 patients including 35 patients (65 ± 8 years) with reduced LV function (EF 30 ± 11%) and a wide QRS complex as well as 10 control subjects (42 ± 21 years, EF 70 ± 11%). For cine imaging a standard SSFP imaging sequence was used with a temporal resolution of 40 frames per RR-interval. Quantitative analysis was performed off-line using a software prototype for semi-automatic border detection. Global volumes, ejection fraction and the SDI were calculated in each subject. SDI was compared with standard echocardiographic parameters of dyssynchrony.</p> <p>Results</p> <p>The mean SDI differed significantly between patients (14 ± 5%) and controls (5 ± 2%, p < 0.001). An exponential correlation between the EF and the SDI was observed (r = -0.84; p < 0.001). In addition, a significant association between the SDI and the standard deviation of time to peak systolic motion of 12 LV segments (Ts-SD) determined by echocardiography was observed (r = 0.66, p = 0.002).</p> <p>Conclusion</p> <p>The results of this preliminary study suggest that CMR with semi-automatic border detection may be useful for the assessment of mechanical dyssynchrony in patients with reduced LV function.</p> <p>No trial registration due to recruitment period between October 2004 and November 2006</p