Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness

The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an effective scheme for finding computationally feasible SDP approximations of polynomial optimization over compact semi-algebraic sets. In this paper, we show that, for convex polynomial optimization, the Lasserre hierarchy with a slightly extended quadratic module always converges asymptotically even in the face of non-compact semi-algebraic feasible sets. We do this by exploiting a coercivity property of convex polynomials that are bounded below. We further establish that the positive definiteness of the Hessian of the associated Lagrangian at a saddle-point (rather than the objective function at each minimizer) guarantees finite convergence of the hierarchy. We obtain finite convergence by first establishing a new sum-of-squares polynomial representation of convex polynomials over convex semi-algebraic sets under a saddle-point condition. We finally prove that the existence of a saddle-point of the Lagrangian for a convex polynomial program is also necessary for the hierarchy to have finite convergence.Comment: 17 page

A single amino acid determines preference between phospholipids and reveals length restriction for activation ofthe S1P₄ receptor

Background<br/><br/> Sphingosine-1-phosphate and lysophosphatidic acid (LPA) are ligands for two related families of G protein-coupled receptors, the S1P and LPA receptors, respectively. The lysophospholipid ligands of these receptors are structurally similar, however recognition of these lipids by these receptors is highly selective. A single residue present within the third transmembrane domain (TM) of S1P receptors is thought to determine ligand selectivity; replacement of the naturally occurring glutamic acid with glutamine (present at this position in the LPA receptors) has previously been shown to be sufficient to change the specificity of S1P<sub>1</sub> from S1P to 18:1 LPA.<br/><br/> Results<br/><br/> We tested whether mutation of this "ligand selectivity" residue to glutamine could confer LPA-responsiveness to the related S1P receptor, S1P<sub>4</sub>. This mutation severely affected the response of S1P<sub>4</sub> to S1P in a [<sup>35</sup>S]GTPγS binding assay, and imparted sensitivity to LPA species in the order 14:0 LPA > 16:0 LPA > 18:1 LPA. These results indicate a length restriction for activation of this receptor and demonstrate the utility of using LPA-responsive S1P receptor mutants to probe binding pocket length using readily available LPA species. Computational modelling of the interactions between these ligands and both wild type and mutant S1P<sub>4</sub> receptors showed excellent agreement with experimental data, therefore confirming the fundamental role of this residue in ligand recognition by S1P receptors.<br/><br/> Conclusions<br/><br/> Glutamic acid in the third transmembrane domain of the S1P receptors is a general selectivity switch regulating response to S1P over the closely related phospholipids, LPA. Mutation of this residue to glutamine confers LPA responsiveness with preference for short-chain species. The preference for short-chain LPA species indicates a length restriction different from the closely related S1P<sub>1</sub> receptor

Chiral Anomaly Effects and the BaBar Measurements of the γγ∗→π0\gamma\gamma^{*}\to \pi^{0} Transition Form Factor

The recent BaBar measurements of the $\gamma\gamma^{*}\to \pi^{0}$ transition form factor show spectacular deviation from perturbative QCD prediction for large space-like $Q^{2}$ up to $34\,\rm GeV^{2}$. When plotted against $Q^{2}$, $Q^{2}F(Q^{2})$ shows steady increase with $Q^{2}$ in contrast with the flat $Q^{2}$ behavior predicted by perturbative QCD, and at $34\,\rm GeV^{2}$ is more than 50% larger than the QCD prediction. Stimulated by the BaBar measurements, we revisit our previous paper on the cancellation of anomaly effects in high energy processes $Z^{0}\to \pi^{0}\gamma$, $e^{+}e^{-}\to \pi^{0}\gamma$ and apply our results to the $\gamma^{*}\gamma\to \pi^{0}$ transition form factor measured in the $e^{+}e^{-}\to e^{+}e^{-}\pi^{0}$ process with one highly virtual photon. We find that, the transition form factor $F(Q^{2})$ behaves as $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ and produces a striking agreement with the BaBar data for $Q^{2}F(Q^{2})$ with $m=132\,\rm MeV$ which also reproduces very well the CLEO data at lower $Q^{2}$.Comment: v4, LaTeX, 8 pages, one figure, minor changes(references), to appear in Int. J. Mod. Phys.

Long-term stability studies of a semiconductor photoelectrode in three-electrode configuration

Improving the stability of semiconductor materials is one of the major challenges for sustainable and economic photoelectrochemical water splitting. N-terminated GaN nanostructures have emerged as a practical protective layer for conventional high efficiency but unstable Si and III-V photoelectrodes due to their near-perfect conduction band-alignment, which enables efficient extraction of photo-generated electrons, and N-terminated surfaces, which protects against chemical and photo-corrosion. Here, we demonstrate that Pt-decorated GaN nanostructures on an n+-p Si photocathode can exhibit an ultrahigh stability of 3000 h (i.e., over 500 days for usable sunlight ∼5.5 h per day) at a large photocurrent density (>35 mA cm-2) in three-electrode configuration under AM 1.5G one-sun illumination. The measured applied bias photon-to-current efficiency of 11.9%, with an excellent onset potential of ∼0.56 V vs. RHE, is one of the highest values reported for a Si photocathode under AM 1.5G one-sun illumination. This study provides a paradigm shift for the design and development of semiconductor photoelectrodes for PEC water splitting: stability is no longer limited by the light absorber, but rather by co-catalyst particles

Liquid droplet generation

A pre-prototype segment of a droplet sheet generator for a liquid droplet radiator was designed, constructed and tested. The ability to achieve a uniform, non-diverging droplet sheet is limited by manufacturing tolerances on nozzle parallelism. For an array of 100, 100 micrometer diameters nozzles spaced 5 stream diameters apart, typical standard deviations in stream alignment were plus or minus 10 mrad. The drop to drop fractional speed variations of the drops in typical streams were similar and independent of position in the array. The absolute value of the speed dispersion depended on the amplitude of the disturbance applied to the stream. A second generation preliminary design of a 5200 stream segment of a droplet sheet generator was completed. The design is based on information developed during testing of the pre-prototype segment, along with the results of an acoustical analysis for the stagnation cavity pressure fluctuations used to break-up the streams into droplets

Low-Energy Properties of a One-dimensional System of Interacting bosons with Boundaries

The ground state properties and low-lying excitations of a (quasi) one-dimensional system of longitudinally confined interacting bosons are studied. This is achieved by extending Haldane's harmonic-fluid description to open boundary conditions. The boson density, one-particle density matrix, and momentum distribution are obtained accounting for finite-size and boundary effects. Friedel oscillations are found in the density. Finite-size scaling of the momentum distribution at zero momentum is proposed as a method to obtain from the experiment the exponent that governs phase correlations. The strong correlations between bosons induced by reduced dimensionality and interactions are displayed by a Bijl-Jastrow wave function for the ground state, which is also derived.Comment: Final published version. Minor changes with respect to the previous versio

Activation-induced deoxycytidine deaminase (AID) co-transcriptional scanning at single-molecule resolution

Activation-induced deoxycytidine deaminase (AID) generates antibody diversity in B cells by initiating somatic hypermutation (SHM) and class-switch recombination (CSR) during transcription of immunoglobulin variable (IgV) and switch region (IgS) DNA. Using single-molecule FRET, we show that AID binds to transcribed dsDNA and translocates unidirectionally in concert with RNA polymerase (RNAP) on moving transcription bubbles, while increasing the fraction of stalled bubbles. AID scans randomly when constrained in an 8 nt model bubble. When unconstrained on single-stranded (ss) DNA, AID moves in random bidirectional short slides/hops over the entire molecule while remaining bound for ~5 min. Our analysis distinguishes dynamic scanning from static ssDNA creasing. That AID alone can track along with RNAP during transcription and scan within stalled transcription bubbles suggests a mechanism by which AID can initiate SHM and CSR when properly regulated, yet when unregulated can access non-Ig genes and cause cancer