On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Meter-baseline tests of sterile neutrinos at Daya Bay

We explore the sensitivity of an experiment at the Daya Bay site, with a point radioactive source and a few meter baseline, to neutrino oscillations involving one or more eV mass sterile neutrinos. We find that within a year, the entire 3+2 and 1+3+1 parameter space preferred by global fits can be excluded at the 3\sigma level, and if an oscillation signal is found, the 3+1 and 3+2 scenarios can be distinguished from each other at more than the 3\sigma level provided one of the sterile neutrinos is lighter than 0.5 eV.Comment: 4 pages, 5 figures, 1 table. Version to appear in PL

Astronomy: Starbursts near and far

Observations of intensely bright star-forming galaxies both close by and in the distant Universe at first glance seem to emphasize their similarity. But look a little closer, and differences emerge.Comment: 6 pages including 1 figur

Generic dark matter signature for gamma-ray telescopes

We describe a characteristic signature of dark matter (DM) annihilation or decay into gamma-rays. We show that if the total angular momentum of the initial DM particle(s) vanishes, and helicity suppression operates to prevent annihilation/decay into light fermion pairs, then the amplitude for the dominant 3-body final state f^+f^-\gamma has a unique form dictated by gauge invariance. This amplitude and the corresponding energy spectra hold for annihilation of DM Majorana fermions or self-conjugate scalars, and for decay of DM scalars, thus encompassing a variety of possibilities. Within this scenario, we analyze Fermi LAT, PAMELA and HESS data, and predict a hint in future Fermi gamma-ray data that portends a striking signal at atmospheric Cherenkov telescopes (ACTs).Comment: 9 pages, 4 figures. Version to appear in PR

Prevention and control of Zika fever as a mosquito-borne and sexually transmitted disease

The ongoing Zika virus (ZIKV) epidemic poses a major global public health emergency. It is known that ZIKV is spread by \textit{Aedes} mosquitoes, recent studies show that ZIKV can also be transmitted via sexual contact and cases of sexually transmitted ZIKV have been confirmed in the U.S., France, and Italy. How sexual transmission affects the spread and control of ZIKV infection is not well-understood. We presented a mathematical model to investigate the impact of mosquito-borne and sexual transmission on spread and control of ZIKV and used the model to fit the ZIKV data in Brazil, Colombia, and El Salvador. Based on the estimated parameter values, we calculated the median and confidence interval of the basic reproduction number R0=2.055 (95% CI: 0.523-6.300), in which the distribution of the percentage of contribution by sexual transmission is 3.044 (95% CI: 0.123-45.73). Our study indicates that R0 is most sensitive to the biting rate and mortality rate of mosquitoes while sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. In order to prevent and control the transmission of ZIKV, it must be treated as not only a mosquito-borne disease but also a sexually transmitted disease