Effective Circle Count for Apollonian packings and Closed horospheres

The main result of this paper is an effective count for Apollonian circle packings that are either bounded or contain two parallel lines. We obtain this by proving an effective equidistribution of closed horospheres in the unit tangent bundle of a geometrically finite hyperbolic 3-manifold of infinite volume, whose fundamental group has critical exponent bigger than 1. We also discuss applications to Affine sieves. Analogous results for surfaces are treated as well.Comment: 43 pages, 2 figures, To appear in GAF

Highly efficient source for frequency-entangled photon pairs generated in a 3rd order periodically poled MgO-doped stoichiometric LiTaO3 crystal

We present a highly efficient source for discrete frequency-entangled photon pairs based on spontaneous parametric down-conversion using 3rd order type-0 quasi-phase matching in a periodically poled MgO-doped stoichiometric LiTaO3 crystal pumped by a 355.66 nm laser. Correlated two-photon states were generated with automatic conservation of energy and momentum in two given spatial modes. These states have a wide spectral range, even under small variations in crystal temperature, which consequently results in higher discreteness. Frequency entanglement was confirmed by measuring two-photon quantum interference fringes without any spectral filtering.Comment: 4 pages, 4 figures, to be published in Optics Letter

Naphthalimide Trifluoroacetyl Acetonate: A Hydrazine-Selective Chemodosimetric Sensor

The trifluoroacetyl acetonate naphthalimide derivative 1 has been synthesized in good yield. In acetonitrile solution, compound 1 reacts selectively with hydrazine (NH2NH2) to give a five-membered ring. This leads to OFF-ON fluorescence with a maximum intensity at 501 nm as well as easily discernible color changes. Based on a readily discernible and reproducible 3.9% change in overall fluorescence intensity, the limit of detection for 1 is 3.2 ppb (0.1 mu M), which is below the accepted limit for hydrazine set by the U.S. Environmental Protection Agency (EPA). Compound 1 is selective for hydrazine over other amines, including NH4OH, NH2OH, ethylenediamine, methylamine, n-butylamine, piperazine, dimethylamine, triethylamine, pyridine, and is not perturbed by environmentally abundant metal ions. When supported on glass-backed silica gel TLC plates, compound 1 acts as a fluorimetric and colorimetric probe for hydrazine vapor at a partial pressure of 9.0 mm Hg, with selectivity over other potentially interfering volatile analytes, including ammonia, methylamine, n-butylamine, formaldehyde, acetaldehyde, H2O2, HCl, and CO2 being observed. Probe 1 can also be used for the detection of hydrazine in HeLa cells and does so without appreciable interference from other biologically abundant amines and metal ions.U.S. National Science Foundation CHE-1057904Robert A. Welch Foundation F-1018CRI project grant from National Research Foundation of Korea (NRF)Korea government (MSIP) 2009-0081566Chemistr

Taurine reduces ER stress in C. elegans

<p>Abstract</p> <p>Background</p> <p>ER stress is a strong indicator of whether or not a cell is undergoing physiological stress. C. elegans is a practical system of characterizing the effect of ER stress at the <it>in vivo</it> or organismal level.</p> <p>Methods</p> <p>This study characterized taurine’s anti-ER stress potential employing western blotting on ER stress markers and assays of motility, lifespan comparison, and fecundity measurement.</p> <p>Results</p> <p>When treated with tunicamycin, C. elegans showed the typical ER stress symptoms. It showed a higher expression of hsp-70 and skn-1 than the non-treated control. Survivorship significantly decreased under tunicamycin treatment, and the offspring number also decreased. During the synchronized culture under ER stress conditions, the C. elegans showed early signs of aging especially between L3 and L4 within their life span, along with lowered motility. The worms, however, showed a positive response to the taurine treatment under ER stress conditions.</p> <p>Conclusions</p> <p>When C. elegans were treated with taurine before or after the tunicamycin treatment, they showed a less severe level of ER stress, including an enhanced survivorship, increased motility, and augmented fecundity. Taken together, these results strongly indicate that taurine works positively to cope with ER stress from the organismal perspective.</p