Applications of Continued Fractions in Cryptography and Diophantine Equations

The theory of continued fractions has applications in cryptographic problems and in solution methods for Diophantine equations. We will first examine the basic properties of continued fractions such as convergents and approximations to real numbers. Then we will discuss a computationally efficient attack on the RSA cryptosystem (Wiener\u27s attack) based on continued fractions. Finally, using continued fractions and solutions of Pell\u27s equation, we will show that the Diophantine equation x^4-kx^2y^2+y^4 = 2^j (k,j are natural numbers) has no nontrivial solutions for j=9,10,11 given that k \u3e 2 and k is not a perfect square

Preliminary Evidence of Increased Hippocampal Myelin Content in Veterans with Posttraumatic Stress Disorder.

Recent findings suggest the formation of myelin in the central nervous system by oligodendrocytes is a continuous process that can be modified with experience. For example, a recent study showed that immobilization stress increased oligodendrogensis in the dentate gyrus of adult rat hippocampus. Because changes in myelination represents an adaptive form of brain plasticity that has a greater reach in the adult brain than other forms of plasticity (e.g., neurogenesis), the objective of this "proof of concept" study was to examine whether there are differences in myelination in the hippocampi of humans with and without post-traumatic stress disorder (PTSD). We used the ratio of T1-weighted/T2-weighted magnetic resonance image (MRI) intensity to estimate the degree of hippocampal myelination in 19 male veterans with PTSD and 19 matched trauma-exposed male veterans without PTSD (mean age: 43 ± 12 years). We found that veterans with PTSD had significantly more hippocampal myelin than trauma-exposed controls. There was also found a positive correlation between estimates of hippocampal myelination and PTSD and depressive symptom severity. To our knowledge, this is the first study to examine hippocampal myelination in humans with PTSD. These results provide preliminary evidence for stress-induced hippocampal myelin formation as a potential mechanism underlying the brain abnormalities associated with vulnerability to stress

Unique growth pattern of human mammary epithelial cells induced by polymeric nanoparticles.

Due to their unique properties, engineered nanoparticles (NPs) have found broad use in industry, technology, and medicine, including as a vehicle for drug delivery. However, the understanding of NPs' interaction with different types of mammalian cells lags significantly behind their increasing adoption in drug delivery. In this study, we show unique responses of human epithelial breast cells when exposed to polymeric Eudragit® RS NPs (ENPs) for 1-3 days. Cells displayed dose-dependent increases in metabolic activity and growth, but lower proliferation rates, than control cells, as evidenced in tetrazolium salt (WST-1) and 5-bromo-2'-deoxyuridine (BrdU) assays, respectively. Those effects did not affect cell death or mitochondrial fragmentation. We attribute the increase in metabolic activity and growth of cells culture with ENPs to three factors: (1) high affinity of proteins present in the serum for ENPs, (2) adhesion of ENPs to cells, and (3) activation of proliferation and growth pathways. The proteins and genes responsible for stimulating cell adhesion and growth were identified by mass spectrometry and Microarray analyses. We demonstrate a novel property of ENPs, which act to increase cell metabolic activity and growth and organize epithelial cells in the epithelium as determined by Microarray analysis

The Stellar Parameters and Evolutionary State of the Primary in the d'-Symbiotic System StH\alpha190

We report on a high-resolution, spectroscopic stellar parameter and abundance analysis of a d' symbiotic star: the yellow component of StH\alpha190. This star has recently been discovered, and confirmed here, to be a rapidly rotating (vsini=100 km/s) subgiant, or giant, that exhibits radial-velocity variations of probably at least 40 km/s, indicating the presence of a companion (a white dwarf star). It is found that the cool stellar component has Teff=5300K and log g=3.0. The iron and calcium abundances are close to solar, however, barium is overabundant, relative to Fe and Ca, by about +0.5 dex. The barium enhancement reflects mass-transfer of s-process enriched material when the current white dwarf was an asymptotic giant branch (AGB) star. The past and future evolution of this binary system depends critically on its current orbital period, which is not yet known. Concerted and frequent radial-velocity measurements are needed to provide crucial physical constraints to this d' symbiotic system.Comment: 9 pages, 1 table, 3 figures. In press to Astrophysical Journal Letter

The Rigidly Rotating Magnetosphere of Sigma Ori E

We attempt to characterize the observed variability of the magnetic helium-strong star sigma Ori E in terms of a recently developed rigidly rotating magnetosphere model. This model predicts the accumulation of circumstellar plasma in two co-rotating clouds, situated in magnetohydrostatic equilibrium at the intersection between magnetic and rotational equators. We find that the model can reproduce well the periodic modulations observed in the star's light curve, H alpha emission-line profile, and longitudinal field strength, confirming that it furnishes an essentially correct, quantitative description of the star's magnetically controlled circumstellar environment.Comment: 4 pages, 3 figures, accepted by Ap

Multimessenger search for sources of gravitational waves and high-energy neutrinos: Initial results for LIGO-Virgo and IceCube

We report the results of a multimessenger search for coincident signals from the LIGO and Virgo gravitational-wave observatories and the partially completed IceCube high-energy neutrino detector, including periods of joint operation between 2007–2010. These include parts of the 2005–2007 run and the 2009–2010 run for LIGO-Virgo, and IceCube’s observation periods with 22, 59 and 79 strings. We find no significant coincident events, and use the search results to derive upper limits on the rate of joint sources for a range of source emission parameters. For the optimistic assumption of gravitational-wave emission energy of 10−2  M⊙c2 at ∼150  Hz with ∼60  ms duration, and high-energy neutrino emission of 1051  erg comparable to the isotropic gamma-ray energy of gamma-ray bursts, we limit the source rate below 1.6×10−2  Mpc−3 yr−1. We also examine how combining information from gravitational waves and neutrinos will aid discovery in the advanced gravitational-wave detector era. © 2014 The American Physical Societ

On the photometric variability of blue supergiants in NGC 300 and its impact on the Flux-weighted Gravity-Luminosity Relationship

We present a study of the photometric variability of spectroscopically confirmed supergiants in NGC 300, comprising 28 epochs extending over a period of five months. We find 15 clearly photometrically variable blue supergiants in a sample of nearly 70 such stars, showing maximum light amplitudes ranging from 0.08 to 0.23 magnitudes in the V band, and one variable red supergiant. We show their light curves, and determine semi-periods for two A2 Ia stars. Assuming that the observed changes correspond to similar variations in the bolometric luminosity, we test for the influence of this variability on the Flux-weighted Gravity--Luminosity Relationship and find a negligible effect, showing that the calibration of this relationship, which has the potential to measure extragalactic distances at the Cepheid accuracy level, is not affected by the stellar photometric variability in any significant way.Comment: 9 pages, 3 figures, 3 tables. Accepted for publication in the Astrophysical Journa

Interferometer readout-noise below the Standard Quantum Limit of a membrane

Here we report on the realization of a Michelson-Sagnac interferometer whose purpose is the precise characterization of the motion of membranes showing significant light transmission. Our interferometer has a readout noise spectral density (imprecision) of 3E-16 m/sqrt(Hz) at frequencies around the fundamental resonance of a SiN_x membrane at about 100 kHz, without using optical cavities. The readout noise demonstrated is more than 16 dB below the peak value of the membrane's standard quantum limit (SQL). This reduction is significantly higher than those of previous works with nano-wires [Teufel et al., Nature Nano. 4, 820 (2009); Anetsberger et al., Nature Phys. 5, 909 (2009)]. We discuss the meaning of the SQL for force measurements and its relation to the readout performance and conclude that neither our nor previous experiments achieved a total noise spectral density as low as the SQL

Evolution of the polarization of the optical afterglow of the gamma-ray burst GRB 030329

We report 31 polarimetric observations of the afterglow of GRB 030329 with high signal-to-noise and high sampling frequency. We establish the polarization light curve, detect sustained polarization at the percent level, and find significant variability of polarization degree and angle. The data imply that the afterglow magnetic field has small coherence length and is mostly random, probably generated by turbulence.Comment: Nature 426 (13. Nov. 2003), 2 figure

The most rapidly rotating He-strong emission line star: HR7355

Using archival spectroscopic and photometric data, we searched for massive stars with Balmer-emission consistent with magnetically confined circumstellar material. HR 7355 is a formerly unknown He-strong star showing Balmer emission. At V=6.02 mag, it is one of the brightest objects simultaneously showing anomalous helium absorption and hydrogen emission. Among similar objects, only sigma Ori E has so far been subjected to any systematic analysis of the circumstellar material responsible for the emission. We argue that the double-wave photometric period of 0.52d corresponds to the rotation period. In tandem with the high projected equatorial velocity, v sin i=320 km/s, this short period suggests that HR 7355 is the most rapidly rotating He-strong star known to date; a class that was hitherto expected to host stars with slow to moderate rotation only.Comment: 4 pages with 2 figures. Accepted for publication as Research Note by Astronomy and Astrophysic