Arithmetic of split Kummer surfaces: Montgomery endomorphism of Edwards products

International audienceLet $E$ be an elliptic curve, $\mathcal{K}_1$ its Kummer curve $E/\{\pm1\}$, $E^2$ its square product, and $\mathcal{K}_2$ the split Kummer surface $E^2/\{\pm1\}$. The addition law on $E^2$ gives a large endomorphism ring, which induce endomorphisms of $\mathcal{K}_2$. With a view to the practical applications to scalar multiplication on $\mathcal{K}_1$, we study the explicit arithmetic of $\mathcal{K}_2$

Spontaneous Calcium Release in Cardiac Myocytes: Store Overload and Electrical Dynamics

Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca2+) mishandling in cardiac muscle cells. We adapt Izu\u27s et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes implemented by Gobbert, and analyzed in Coulibaly et al. to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca2+ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with known biological models and principles, giving us a thorough understanding of several factors that influence Ca2+ dynamics in cardiac myocytes. Specifically, dynamic calcium store will cap previous calcium blow-up seen in the model. Calcium channels located in spatial opposition of calcium release units produce more predictable intracellular calcium propagation. And we used multi-parametric calcium dynamics tables, which act as a multidimensional bifurcation diagram, to visualize parameter boundaries between different biophysical dynamics

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

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Comparison of Structural Properties and Solar Cell Performance of a-Si:H Films Prepared at Various Deposition Rates using 13.56 and 70 MHz PECVD Methods

ABSTRACT The advantage of using very high frequencies for preparation of a-Si:H materials at high rates (above 5 Å/s) for intrinsic layers (i-layer) of solar cells has been well documented. In an effort to identify film properties which may be related to this superior device performance, a study of the structural, optical and electrical properties of films made at various deposition rates between 1 and 15 Å/s using rf frequencies of 13.56 and 70 MHz has been made. The films were characterized using a number of techniques including small-angle x-ray scattering, infrared absorption spectroscopy, and scanning electron microscopy. For the films made using the 70 MHz frequency, the amount of nanovoids with sizes of < 100Å increases systematically as the deposition rates increases beyond 5 Å/s. Accompanying the increase in void fraction in the films are increases in the hydrogen content and the amount of 2070 cm -1 mode in the infrared absorption spectra. In addition to an increase in the amount of nanovoids in the films as the deposition rate exceeds 5 Å/s, the films made using the 13.56 MHz and high deposition rates have large amounts of SAXS related to scattering features with sizes > 200 Å. This scattering is associated with large bulk density fluctuations and/or enhanced surface roughness. None of the films in the study displayed signs of having columnar-like microstructures. The nanovoids are not related to changes in the solar cells with increasing i-layer deposition rate for both fabrication processes, perhaps due to the relatively small volume fractions of less than 0.2% and/or good void-surface passivation. However, the larger-scale structures detected in the films made using the 13.56 MHz technique could cause poorer performance in cells prepared at high growth rates

Complex electrophysiological remodeling in postinfarction ischemic heart failure

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