An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution

We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational approximation by taking the minimum over the regular grid, which consists of rational points with denominator r (for given r). We show that the associated convergence rate is O(1/r^2 ) for quadratic polynomials. For general polynomials, if there exists a rational global minimizer over the simplex, we show that the convergence rate is also of the order O(1/r^2 ). Our results answer a question posed by De Klerk et al. [9] and improves on previously known O(1/r) bounds in the quadratic case

Convergence analysis for Lasserre's measure-based hierarchy of upper bounds for polynomial optimization

We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864 − 885], obtained by searching for an optimal pr

Orientation Dependence of the Ionization of CO and NO in an Intense Femtosecond Two-Color Laser Field

Two-color (800- and 400-nm) short (45-fs) linearly polarized pulses are used to ionize and dissociate CO and NO. The emission of Cq+, Nq+, and O⁺ fragments indicates that the higher ionization rate occurs when the peak electric field points from C to O in CO and from N to O in NO. This preferred direction is in agreement with that predicted by Stark-corrected strong-field-approximation calculations

Socially-mediated arousal and contagion within domestic chick broods

Emotional contagion – an underpinning valenced feature of empathy – is made up of simpler, potentially dissociable social processes which can include socially-mediated arousal and behavioural/physiological contagion. Previous studies of emotional contagion have often conflated these processes rather than examining their independent contribution to empathic response. We measured socially-mediated arousal and contagion in 9-week old domestic chicks (n = 19 broods), who were unrelated but raised together from hatching. Pairs of observer chicks were exposed to two conditions in a counterbalanced order: air puff to conspecifics (AP) (during which an air puff was applied to three conspecifics at 30 s intervals) and control with noise of air puff (C) (during which the air puff was directed away from the apparatus at 30 s intervals). Behaviour and surface eye temperature of subjects and observers were measured throughout a 10-min pre-treatment and 10-min treatment period. Subjects and observers responded to AP with increased freezing, and reduced preening and ground pecking. Subjects and observers also showed reduced surface eye temperature - indicative of stress-induced hyperthermia. Subject-Observer behaviour was highly correlated within broods during both C and AP conditions, but with higher overall synchrony during AP. We demonstrate the co-occurrence of socially-mediated behavioural and physiological arousal and contagion; component features of emotional contagion

Prolate-Spherical Shape Coexistence at N=28 in 44^{44}S

The structure of $^{44}$S has been studied using delayed $\gamma$ and electron spectroscopy at \textsc{ganil}. The decay rates of the 0$^+_2$ isomeric state to the 2$^+_1$ and 0$^+_1$ states have been measured for the first time, leading to a reduced transition probability B(E2~:~2$^{+}_1$$\rightarrow$0$^{+}_2)$= 8.4(26)~e$^2$fm$^4$ and a monopole strength $\rho^2$(E0~:~0$^{+}_2$$\rightarrow$0$^{+}_1)$ =~8.7(7)$\times$10$^{-3}$. Comparisons to shell model calculations point towards prolate-spherical shape coexistence and a phenomenological two level mixing model is used to extract a weak mixing between the two configurations.Comment: 5 pages, 3 figures, accepted for publication in Physical Review Letter

Parallel momentum distribution of the 28^{28}Si fragments from 29^{29}P

Distribution of the parallel momentum of $^{28}$Si fragments from the breakup of 30.7 MeV/nucleon $^{29}$P has been measured on C targets. The distribution has the FWHM with the value of 110.5 $\pm$ 23.5 MeV/c which is consistent quantitatively with Galuber model calculation assuming by a valence proton in $^{29}$P. The density distribution is also predicted by Skyrme-Hartree-Fock calculation. Results show that there might exist the proton-skin structure in $^{29}$P.Comment: 4 pages, 4 figure

Elements Discrimination in the Study of Super-Heavy Elements using an Ionization Chamber

Dedicated ionization chamber was built and installed to measure the energy loss of very heavy nuclei at 2.7 MeV/u produced in fusion reactions in inverse kinematics (beam of 208Pb). After going through the ionization chamber, products of reactions on 12C, 18O targets are implanted in a Si detector. Their identification through their alpha decay chain is ambiguous when their half-life is short. After calibration with Pb and Th nuclei, the ionization chamber signal allowed us to resolve these ambiguities. In the search for rare super-heavy nuclei produced in fusion reactions in inverse or symmetric kinematics, such a chamber will provide direct information on the nuclear charge of each implanted nucleus.Comment: submitted to NIMA, 10 pages+4 figures, Latex, uses elsart.cls and grahpic

Gemini Planet Imager Observational Calibrations VI: Photometric and Spectroscopic Calibration for the Integral Field Spectrograph

The Gemini Planet Imager (GPI) is a new facility instrument for the Gemini Observatory designed to provide direct detection and characterization of planets and debris disks around stars in the solar neighborhood. In addition to its extreme adaptive optics and corona graphic systems which give access to high angular resolution and high-contrast imaging capabilities, GPI contains an integral field spectrograph providing low resolution spectroscopy across five bands between 0.95 and 2.5 $\mu$m. This paper describes the sequence of processing steps required for the spectro-photometric calibration of GPI science data, and the necessary calibration files. Based on calibration observations of the white dwarf HD 8049B we estimate that the systematic error in spectra extracted from GPI observations is less than 5%. The flux ratio of the occulted star and fiducial satellite spots within coronagraphic GPI observations, required to estimate the magnitude difference between a target and any resolved companions, was measured in the $H$-band to be $\Delta m = 9.23\pm0.06$ in laboratory measurements and $\Delta m = 9.39\pm 0.11$ using on-sky observations. Laboratory measurements for the $Y$, $J$, $K1$ and $K2$ filters are also presented. The total throughput of GPI, Gemini South and the atmosphere of the Earth was also measured in each photometric passband, with a typical throughput in $H$-band of 18% in the non-coronagraphic mode, with some variation observed over the six-month period for which observations were available. We also report ongoing development and improvement of the data cube extraction algorithm.Comment: 15 pages, 6 figures. Proceedings of the SPIE, 9147-30