Local constancy of dimensions of Hecke eigenspaces of automorphic forms

We use a method of Buzzard to study p-adic families of Hilbert modular forms and modular forms over imaginary quadratic fields. In the case of Hilbert modular forms, we get local constancy of dimensions of spaces of fixed slope and varying weight. For imaginary quadratic fields we obtain bounds independent of the weight on the dimensions of such spaces.     

Controlled interparticle spacing for surface-modified gold nanoparticle aggregates

Aggregation of gold nanoparticles of increasing size has been studied as a consequence of adsorption of 2-aminothiophenol (ATP) on gold nanoparticle surfaces. The capping property of ATP in the acidic pH range has been accounted from UV-vis absorption spectroscopy and surface-enhanced Raman scattering (SERS) studies. The effect of nanoparticle size (8-55 nm) on the nature of aggregation as well as the variation in the optical response due to variable degree of interparticle coupling effects among the gold particles have been critically examined. Various techniques such as transmission electron microscopy, X-ray diffraction, zeta-potential, and average particle size measurement were undertaken to characterize the nanoparticle aggregates. The aggregate size, interparticle distances, and absorption band wavelengths were found to be highly dependent on the pH of the medium and the concentration of the capping agent, ATP. The acquired SERS spectra of ATP relate the interparticle spacing. It has been observed that the SERS signal intensities are different for different sized gold nanoparticles.     

Analytical aspects of some organic acids Part III

Summary m-Phenylenedioxydiacetic acid gives a white precipitate with thorium even in the absence of an electrolyte which is quantitative up toph 4. Be²⁺, Mg²⁺, Ca²⁺, Zn²⁺, Pb²⁺ and Mn²⁺ ions are removed by single precipitation and Al³⁺, UO₂ ²⁺ and trivalent cerite earth ions are removed by double precipitation. Sn²⁺, Sn⁴⁺ and Cr³⁺ ions interfere.Part II: See. Z. analyt. Chem.165, 343 (1959).     

Using path sampling to build better Markovian state models: predicting the folding rate and mechanism of a tryptophan zipper beta hairpin

We propose an efficient method for the prediction of protein folding rate constants and mechanisms. We use molecular dynamics simulation data to build Markovian state models (MSMs), discrete representations of the pathways sampled. Using these MSMs, we can quickly calculate the folding probability (P(fold)) and mean first passage time of all the sampled points. In addition, we provide techniques for evaluating these values under perturbed conditions without expensive recomputations. To demonstrate this method on a challenging system, we apply these techniques to a two-dimensional model energy landscape and the folding of a tryptophan zipper beta hairpin.     

Solvent viscosity dependence of the folding rate of a small protein: distributed computing study

By using distributed computing techniques and a supercluster of more than 20,000 processors we simulated folding of a 20-residue Trp Cage miniprotein in atomistic detail with implicit GB/SA solvent at a variety of solvent viscosities (gamma). This allowed us to analyze the dependence of folding rates on viscosity. In particular, we focused on the low-viscosity regime (values below the viscosity of water). In accordance with Kramers' theory, we observe approximately linear dependence of the folding rate on 1/gamma for values from 1-10(-1)x that of water viscosity. However, for the regime between 10(-4)-10(-1)x that of water viscosity we observe power-law dependence of the form k approximately gamma(-1/5). These results suggest that estimating folding rates from molecular simulations run at low viscosity under the assumption of linear dependence of rate on inverse viscosity may lead to erroneous results.     

Defibrillation via the elimination of spiral turbulence in a model for ventricular fibrillation

Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart make it incapable of any concerted pumping action. Methods of controlling ventricular fibrillation include electrical defibrillation as well as injected medication. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often counterproductive, electrical shocks. We propose a defibrillation method that uses a very low-amplitude shock (of order mV) applied for a brief duration (of order 100 ms) and over a coarse mesh of lines on our model ventricle.     

Accelerating molecular dynamic simulation on graphics processing units

We describe a complete implementation of all‐atom protein molecular dynamics running entirely on a graphics processing unit (GPU), including all standard force field terms, integration, constraints, and implicit solvent. We discuss the design of our algorithms and important optimizations needed to fully take advantage of a GPU. We evaluate its performance, and show that it can be more than 700 times faster than a conventional implementation running on a single CPU core. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

On the solutions of the Wick-Cutkosky model in the instantaneous approximation

By reexamining the analysis of Basu and Biswas, based on the stereographic projection method of Fock and Levy, it is shown that the general solution of the Wick-Cutkosky model in the instantaneous approximation, hitherto unreported, involves only one quantum number; this is contrasted with the well-known solution which involves two quantum numbers, but for which the spectrum is degenerate with respect to one of them. The latter situation is shown to hold under a rather special circumstance.