Influence of diffraction on the spectrum and wavefunctions of an open system

In this paper, we demonstrate the existence and significance of diffractive orbits in an open microwave billiard, both experimentally and theoretically. Orbits that diffract off of a sharp edge of the system are found to have a strong influence on the transmission spectrum of the system, especially in the regime where there are no stable classical orbits. On resonance, the wavefunctions are influenced by both classical and diffractive orbits. Off resonance, the wavefunctions are determined by the constructive interference of multiple transient, nonperiodic orbits. Experimental, numerical, and semiclassical results are presented.Comment: 27 pages, 29 figures, and 3 tables. Submitted to Physical Review E. A copy with higher resolution figures is available at http://monsoon.harvard.edu/~hersch/papers.htm

Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

Association between Adiposity and disability in the Lc65+ Cohort.

To examine the longitudinal association between body mass index (BMI) and waist circumference (WC) with mortality and incident disability in Lc65+ cohort. Population-based cohort of non-institutionalized adults with up to 8.9 years of follow-up. City of Lausanne, Switzerland. 1,293 individuals aged 65 to 70 at baseline (58% women). BMI, WC and covariates were measured at baseline in 2004-2005. Vital status was obtained up to the 31st December 2013 and difficulty with basic activities of daily living (BADL) was reported in a self-administered questionnaire sent to participants every year. Main outcomes were total mortality and disability, defined as difficulty with BADL for ≥2 years or institutionalization. Cox regression was used with BMI/WC quintiles 2 as the reference. 130 persons died over a median follow-up of 8.47 years (crude mortality rate, men: 16.5/1,000 person-years, women: 9.7/1,000 person-years). In Cox regression adjusted for age, sex, education, financial situation, smoking and involuntary weight loss (IWL) at baseline, mortality was significantly associated with neither BMI nor WC, but there were trends towards non-significant J-curves across both BMI and WC quintiles. Disability (231 cases) tended to increase monotonically across both BMI and WC quintiles and was significantly associated with BMI quintile 5 (HR=2.44, 95% CI [1.65-3.63]), and WC quintiles 4 (HR=1.81 [1.15-2.85]) and 5 (HR=2.58, [1.67-4.00]). Almost half of the study population had a substantially increased HR of disability, as compared to the reference BMI/WC categories. This observation emphasizes the need for life-long strategies aimed at preventing excess weight, muscle loss and functional decline through adequate nutrition and regular physical activity, starting at early age and extending throughout life

Observation of diffractive orbits in the spectrum of excited NO in a magnetic field

We investigate the experimental spectra of excited NO molecules in the diamagnetic regime and develop a quantitative semiclassical framework to account for the results. We show the dynamics can be interpreted in terms of classical orbits provided that in addition to the geometric orbits, diffractive effects are appropriately taken into account. We also show how individual orbits can be extracted from the experimental signal and use this procedure to reveal the first experimental manifestation of inelastic diffractive orbits.Comment: 4 fig

Scattering Theory of Kondo Mirages and Observation of Single Kondo Atom Phase Shift

We explain the origin of the Kondo mirage seen in recent quantum corral Scanning Tunneling Microscope (STM) experiments with a scattering theory of electrons on the surfaces of metals. Our theory combined with experimental data provides the first direct observation of a single Kondo atom phase shift. The Kondo mirage at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the walls of the corral in a manner analagous to the formation of a real image in optics. We demonstrate our theory with direct quantitive comparision to experimental data.Comment: 13 pages; significant clarifications of metho

Divergent Protein Motifs Direct EF-P Mediated Translational Regulation in \u3cem\u3eSalmonella\u3c/em\u3e and \u3cem\u3eEscherichia coli\u3c/em\u3e

Elongation factor P (EF-P) is a universally conserved bacterial translation factor homologous to eukaryotic/archaeal initiation factor 5A. In Salmonella, deletion of the efp gene results in pleiotropic phenotypes, including increased susceptibility to numerous cellular stressors. Only a limited number of proteins are affected by the loss of EF-P, and it has recently been determined that EF-P plays a critical role in rescuing ribosomes stalled at PPP and PPG peptide sequences. Here we present an unbiased in vivo investigation of the specific targets of EF-P by employing stable isotope labeling of amino acids in cell culture (SILAC) to compare the proteomes of wild-type and efp mutant Salmonella. We found that metabolic and motility genes are prominent among the subset of proteins with decreased production in the Δefp mutant. Furthermore, particular tripeptide motifs are statistically overrepresented among the proteins downregulated in efp mutant strains. These include both PPP and PPG but also additional motifs, such as APP and YIRYIR, which were confirmed to induce EF-P dependence by a translational fusion assay. Notably, we found that many proteins containing polyproline motifs are not misregulated in an EF-P-deficient background, suggesting that the factors that govern EF-P-mediated regulation are complex. Finally, we analyzed the specific region of the PoxB protein that is modulated by EF-P and found that mutation of any residue within a specific GSCGPG sequence eliminates the requirement for EF-P. This work expands the known repertoire of EF-P target motifs and implicates factors beyond polyproline motifs that are required for EF-P-mediated regulation

Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

(R)-β-lysine Modified Elongation Factor P Functions in Translation Elongation

Post-translational modification of bacterial elongation factor P (EF-P) with (R)-β-lysine at a conserved lysine residue activates the protein in vivo and increases puromycin reactivity of the ribosome in vitro. The additional hydroxylation of EF-P at the same lysine residue by the YfcM protein has also recently been described. The roles of modified and unmodified EF-P during different steps in translation, and how this correlates to its physiological role in the cell, have recently been linked to the synthesis of polyproline stretches in proteins. Polysome analysis indicated that EF-P functions in translation elongation, rather than initiation as proposed previously. This was further supported by the inability of EF-P to enhance the rate of formation of fMet-Lys or fMet-Phe, indicating that the role of EF-P is not to specifically stimulate formation of the first peptide bond. Investigation of hydroxyl-(β)-lysyl-EF-P showed 30% increased puromycin reactivity but no differences in dipeptide synthesis rates when compared with the β-lysylated form. Unlike disruption of the other genes required for EF-P modification, deletion of yfcM had no phenotypic consequences in Salmonella. Taken together, our findings indicate that EF-P functions in translation elongation, a role critically dependent on post-translational β-lysylation but not hydroxylation