Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves

In this paper we present a new method to construct a polynomial $u(x) \in \mathbb{Z}[x]$ which will make $\mathrm{\Phi}_{k}(u(x))$ reducible. We construct a finite separable extension of $\mathbb{Q}(\zeta_{k})$, denoted as $\mathbb{E}$. By primitive element theorem, there exists a primitive element $\theta \in \mathbb{E}$ such that $\mathbb{E}=\mathbb{Q}(\theta)$. We represent the primitive $k$-th root of unity $\zeta_{k}$ by $\theta$ and get a polynomial $u(x) \in \mathbb{Q}[x]$ from the representation. The resulting $u(x)$ will make $\mathrm{\Phi}_{k}(u(x))$ factorable

Using surface waves recorded by a large mesh of three-element arrays to detect and locate disparate seismic sources

Author Posting. © The Authors, 2018. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 215 (2018): 942–958, doi:10.1093/gji/ggy316.Surface waves recorded by global arrays have proven useful for locating tectonic earthquakes and in detecting slip events depleted in high frequency, such as glacial quakes. We develop a novel method using an aggregation of small- to continental-scale arrays to detect and locate seismic sources with Rayleigh waves at 20–50 s period. The proposed method is a hybrid approach including first dividing a large aperture aggregate array into Delaunay triangular subarrays for beamforming, and then using the resolved surface wave propagation directions and arrival times from the subarrays as data to formulate an inverse problem to locate the seismic sources and their origin times. The approach harnesses surface wave coherence and maximizes resolution of detections by combining measurements from stations spanning the whole U.S. continent. We tested the method with earthquakes, glacial quakes and landslides. The results show that the method can effectively resolve earthquakes as small as ∼M3 and exotic slip events in Greenland. We find that the resolution of the locations is non-uniform with respect to azimuth, and decays with increasing distance between the source and the array when no calibration events are available. The approach has a few advantages: the method is insensitive to seismic event type, it does not require a velocity model to locate seismic sources, and it is computationally efficient. The method can be adapted to real-time applications and can help in identifying new classes of seismic sources.WF is currently supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Weston Howland Jr. Postdoctoral Scholarship. This work was supported by National Science Foundation grant EAR-1358520 at Scripps Institution of Oceanography, UC San Diego

Bufalin Induces Lung Cancer Cell Apoptosis via the Inhibition of PI3K/Akt Pathway

Bufalin is a class of toxic steroids which could induce the differentiation and apoptosis of leukemia cells, and induce the apoptosis of gastric, colon and breast cancer cells. However, the anti-tumor effects of bufalin have not been demonstrated in lung cancer. In this study we used A549 human lung adenocarcinoma epithelial cell line as the experimental model to evaluate the potential of bufalin in lung cancer chemotherapy. A549 cells were treated with bufalin, then the proliferation was detected by MTT assay and apoptosis was detected by flow cytometry analysis and Giemsa staining. In addition, A549 cells were treated by Akt inhibitor LY294002 in combination with bufalin and the activation of Akt and Caspase-3 as well as the expression levels of Bax, Bcl-2 and livin were examined by Western blot analysis. The results showed that Bufalin inhibited the proliferation of A549 cells and induced the apoptosis of A549 cells in a dose and time dependent manner. Mechanistically, we found that bufalin inhibited the activation of Akt. Moreover, bufalin synergized with Akt inhibitor to induce the apoptosis of A549 cells and this was associated with the upregulation of Bax expression, the downregulation of Bcl-2 and livin expression, and the activation of Caspase-3. In conclusion, our findings demonstrate that bufalin induces lung cancer cell apoptosis via the inhibition of PI3K/Akt pathway and suggest that bufalin is a potential regimen for combined chemotherapy to overcome the resistance of lung cancer cells to chemotherapeutics induced apoptosis

Lithosphere structure of the Earth from surface wave tomography

The lithosphere is commonly defined as the outermost rigid layer of the Earth, including the crust and the uppermost part of the mantle. It forms the rigid 'plate' in plate tectonic theory. To study its large-scale structure globally, I use fundamental mode surface waves with a period range between 25 s and 200 s. A large dataset including all long period seismograms publicly available for earthquakes with magnitudes larger than Mw=5.5 between 1977 and 2007 has been assembled. To analyze such a large dataset, an efficient measurement method has been developed based on a cluster analysis technique to measure the velocity and amplitude variations of the surface wave packages. These measurements are then inverted for a self- consistent global dispersion model for both Rayleigh and Love waves, which provides the basic input data for constraining the lithospheric structure at high resolution. These maps of surface wave phase/group velocities match surface tectonics very well. Slow anomalies are found beneath orogenic zones and other regions with thick crust, e.g. the Himalayas and Andes. The Basin and Range province in North America, mid-ocean ridges, and back-arc basins also show up as slow anomalies. Cratons can be seen in the low frequency maps as regions of anomalously high velocities. I also find that azimuthal anisotropy needs to be included in order to obtain reliable isotropic velocity variations for Rayleigh waves, and the uncertainties in earthquake locations can affect the resulting azimuthal anisotropy. In addition, I apply finite-frequency theory to account for the focusing- defocusing effect when modeling the amplitude data and present a set of 2D global attenuation maps for Rayleigh waves. The products from this thesis are expected to find wide use by the seismological and the broader geophysical community. One particular application would be to use the maps of phase/group velocity and attenuation to investigate the evolution of the oceanic lithosphere. All measurement and model files produced in this thesis have been made available on the Interne

Polynomials for Ate Pairing and Atei\mathbf{Ate}_{i} Pairing

The irreducible factor $r(x)$ of $\mathrm{\Phi}_{k}(u(x))$ and $u(x)$ are often used in constructing pairing-friendly curves. $u(x)$ and $u_{c} \equiv u(x)^{c} \pmod{r(x)}$ are selected to be the Miller loop control polynomial in Ate pairing and $\mathrm{Ate}_{i}$ pairing. In this paper we show that when $4|k$ or the minimal prime which divides $k$ is larger than $2$, some $u(x)$ and $r(x)$ can not be used as curve generation parameters if we want $\mathrm{Ate}_{i}$ pairing to be efficient. We also show that the Miller loop length can not reach the bound $\frac{\mathrm{log_{2}r}}{\varphi(k)}$ when we use the factorization of $\mathrm{\Phi}_{k}(u(x))$ to generate elliptic curves

Inhibition of Jak-STAT3 pathway enhances bufalin-induced apoptosis in colon cancer SW620 cells

Abstract Background The purpose of the research is to investigate the roles of Jak-STAT3 signaling pathway in bufalin-induced apoptosis in colon cancer SW620 cells. Methods The inhibitory effects of bufalin on cell proliferation were determined by MTT (Methyl thiazolyltetrazolium) assay. The morphological changes of cells were measured by Wright-Giemsa staining. The cell cycle arrest and apoptosis were tested by flow cytometry analysis. Western Blot was used to determine the protein expression of the apoptosis inhibitors livin and caspase-3, the apoptosis-related proteins Bax and Bcl-2, as well as the key protein kinases in the Jak-stat3 signaling pathway, stat3 and p-stat3. Results (1) Bufalin inhibited the proliferation of SW620 cells. IC50 at 24 h, 48 h and 72 h were 76.72 ± 6.21 nmol/L, 34.05 ± 4.21 nmol/L and 16.7 ± 6.37 nmol/L. (2) Bufalin induced SW620 cell cycle arrest and apoptosis, indicated by the appearance of apoptotic bodies; (3) The results from flow cytometry demonstrated that there was cell cycle G2/M phase arrest in 20 nmol/L bufalin treatment group (36.29 ± 2.11% vs 18.39 ± 1.74%, P Conclusions Bufalin not only inhibited the growth of colon cancer SW620 cells, but also induced apoptosis of SW620 cells. Activation of caspase-3, up-regulation of Bax, down-regulation of livin and Bcl-2, as well as inhibition of Jak-stat3 signaling pathway might be the important mechanisms for the bufalin-induced apoptosis.</p