Optimal solutions to matrix-valued Nehari problems and related limit theorems

In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries can be efficiently approximated by certain functions defined in terms of finite dimensional restrictions of the Hankel operator. In this paper it is shown that these approximants appear as optimal solutions to restricted Nehari problems. The latter problems can be solved using relaxed commutant lifting theory. This observation is used to extent the Helton and Young approximation result to a matrix-valued setting. As in the Helton and Young paper the rate of convergence depends on the choice of the initial space in the approximation scheme.Comment: 22 page

On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere

Producción CientíficaSeparable Hamiltonian systems either in sphero-conical coordinates on an S2 sphere or in elliptic coordinates on a R2 plane are described in a unified way. A back and forth route connecting these Liouville Type I separable systems is unveiled. It is shown how the gnomonic projection and its inverse map allow us to pass from a Liouville Type I separable system with a spherical configuration space to its Liouville Type I partners where the configuration space is a plane and back. Several selected spherical separable systems and their planar cousins are discussed in a classical context

Isotopic variation of parity violation in atomic ytterbium

We report on measurements of atomic parity violation, made on a chain of ytterbium isotopes with mass numbers A=170, 172, 174, and 176. In the experiment, we optically excite the 6s2 1S0 -> 5d6s 3D1 transition in a region of crossed electric and magnetic fields, and observe the interference between the Stark- and weak-interaction-induced transition amplitudes, by making field reversals that change the handedness of the coordinate system. This allows us to determine the ratio of the weak-interaction-induced electric-dipole (E1) transition moment and the Stark-induced E1 moment. Our measurements, which are at the 0.5% level of accuracy for three of the four isotopes measured, allow a definitive observation of the isotopic variation of the weak-interaction effects in an atom, which is found to be consistent with the prediction of the Standard Model. In addition, our measurements provide information about an additional Z' boson.Comment: 19 pages, 4 figures, 2 table

The Supernova Gamma-Ray Burst Connection

The chief distinction between ordinary supernovae and long-soft gamma-ray bursts (GRBs) is the degree of differential rotation in the inner several solar masses when a massive star dies, and GRBs are rare mainly because of the difficulty achieving the necessary high rotation rate. Models that do provide the necessary angular momentum are discussed, with emphasis on a new single star model whose rapid rotation leads to complete mixing on the main sequence and avoids red giant formation. This channel of progenitor evolution also gives a broader range of masses than previous models, and allows the copious production of bursts outside of binaries and at high redshifts. However, even the production of a bare helium core rotating nearly at break up is not, by itself, a sufficient condition to make a gamma-ray burst. Wolf-Rayet mass loss must be low, and will be low in regions of low metallicity. This suggests that bursts at high redshift (low metallicity) will, on the average, be more energetic, have more time structure, and last longer than bursts nearby. Every burst consists of three components: a polar jet (~0.1 radian), high energy, subrelativistic mass ejection (~1 radian), and low velocity equatorial mass that can fall back after the initial explosion. The relative proportions of these three components can give a diverse assortment of supernovae and high energy transients whose properties may vary with redshift.Comment: 10 pages, to appear in AIP Conf. Proc. "Gamma Ray Bursts in the Swift Era", Eds. S. S. Holt, N. Gehrels, J. Nouse

Topological Crystalline Insulators in the SnTe Material Class

Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe, by identifying its nonzero topological index. We predict that as a manifestation of this nontrivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust against disorder and topologically protected by reflection symmetry of the crystal with respect to {110} mirror plane. Breaking this mirror symmetry via elastic strain engineering or applying an in-plane magnetic field can open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectrics, infrared detection, and tunable electronics. Closely related semiconductors PbTe and PbSe also become topological crystalline insulators after band inversion by pressure, strain and alloying.Comment: submitted on Feb. 10, 2012; to appear in Nature Communications; 5 pages, 4 figure

Gateway vectors for efficient artificial gene assembly in vitro and expression in yeast Saccharomyces cerevisiae

Peer reviewedPublisher PD

Cancer and thrombosis: Managing the risks and approaches to thromboprophylaxis

Patients with cancer are at increased risk of venous thromboembolism (VTE) compared with patients without cancer. This results from both the prothrombotic effects of the cancer itself and iatrogenic factors, such as chemotherapy, radiotherapy, indwelling central venous devices and surgery, that further increase the risk of VTE. Although cancer-associated thrombosis remains an important cause of morbidity and mortality, it is often underdiagnosed and undertreated. However, evidence is accumulating to support the use of low-molecular-weight heparins (LMWHs) in the secondary prevention of VTE in patients with cancer. Not only have LMWHs been shown to be at least as effective as coumarin derivatives in this setting, but they have a lower incidence of complications, including bleeding, and are not associated with the practical problems of warfarin therapy. Furthermore, a growing number of studies indicate that LMWHs may improve survival among patients with cancer due to a possible antitumor effect. Current evidence suggests that LMWHs should increasingly be considered for the long-term management of VTE in patients with cancer

Transmembrane helix dynamics of bacterial chemoreceptors supports a piston model of signalling.

Transmembrane α-helices play a key role in many receptors, transmitting a signal from one side to the other of the lipid bilayer membrane. Bacterial chemoreceptors are one of the best studied such systems, with a wealth of biophysical and mutational data indicating a key role for the TM2 helix in signalling. In particular, aromatic (Trp and Tyr) and basic (Arg) residues help to lock α-helices into a membrane. Mutants in TM2 of E. coli Tar and related chemoreceptors involving these residues implicate changes in helix location and/or orientation in signalling. We have investigated the detailed structural basis of this via high throughput coarse-grained molecular dynamics (CG-MD) of Tar TM2 and its mutants in lipid bilayers. We focus on the position (shift) and orientation (tilt, rotation) of TM2 relative to the bilayer and how these are perturbed in mutants relative to the wildtype. The simulations reveal a clear correlation between small (ca. 1.5 Å) shift in position of TM2 along the bilayer normal and downstream changes in signalling activity. Weaker correlations are seen with helix tilt, and little/none between signalling and helix twist. This analysis of relatively subtle changes was only possible because the high throughput simulation method allowed us to run large (n = 100) ensembles for substantial numbers of different helix sequences, amounting to ca. 2000 simulations in total. Overall, this analysis supports a swinging-piston model of transmembrane signalling by Tar and related chemoreceptors

Three computational approaches to weakly nonlocal Poisson brackets

We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, pseudo‐differential operators, and Poisson vertex algebras, respectively. We show that the three approaches lead to similar computations and same results