Probing active site geometry using high pressure and secondary isotope effects in an enzyme-catalysed 'deep' H-tunnelling reaction

We report the first study of the effects of hydrostatic pressure on α-2° KIEs for an enzyme-catalysed H-transfer reaction that occurs by 'deep' tunnelling. High pressure causes a significant decrease in the observed α-2° KIE on the pre-steady-state hydride transfer from NADH to FMN in the flavoprotein morphinone reductase. We have recently shown that high pressure causes a reduction in macroscopic reaction barrier width for this reaction. Using DFT vibrational analysis of a simple active site model, we posit that the decrease in α-2° KIE with pressure may arise due to a decrease in the vibrational coupling between the NADH primary (transferred) and secondary hydrogens in the 'tunnelling ready configuration', which more closely resembles the reactant state than the transition state.     

Stable base loci, movable curves, and small modifications, for toric varieties

We show that the dual of the cone of divisors on a complete -factorial toric variety X whose stable base loci have dimension less than k is generated by curves on small modifications of X that move in families sweeping out the birational transforms of k-dimensional subvarieties of X. We give an example showing that it does not suffice to consider curves on X itself. Supported by a Graduate Research Fellowship from the NSF     

First principle study of unzipped boron nitride nanotubes

Systematic first principle calculations have been used to explain the dangling bonds behaviour in the rolling up of a boron nitride nanoribbon (BNNR) to construct a single-walled boron nitride nanotube (BNNT). We found in armchair BNNR two degenerate dangling bonds split and move up to higher energies due to symmetry breaking of system. While in zigzag BNNR changing the topology of system does not affect on metallic features of the band structure, but in unzipped BNNT case a metallic-semimetallic phase transition occurs. Considering the width dependent electronic properties of hydrogen passivated armchair BNNRs, exhibit zigzag behaviour of energy gap in agreement with previous results.     

Wavelet Analysis of Big Data Contaminated by Large Noise in an fMRI Study of Neuroplasticity

Functional magnetic resonance imaging (fMRI) allows researchers to analyze brain activity on a voxel level, but using this ability is complicated by dealing with Big Data and large noise. A traditional remedy is averaging over large parts of brain in combination with more advanced technical innovations in reducing fMRI noise. In this paper a novel statistical approach, based on a wavelet analysis of standard fMRI data, is proposed and its application to an fMRI study of neuron plasticity of 24 healthy adults is presented. The aim of that study was to recognize changes in connectivity between left and right motor cortices (the neuroplasticity) after button clicking training sessions. A conventional method of the data analysis, based on averaging images, has implied that for the group of 24 participants the connectivity increased after the training. The proposed wavelet analysis suggests to analyze pathways between left and right hemispheres on a voxel-to-voxel level and for each participant via estimation of corresponding cross-correlations. This immediately necessitates statistical analysis of large-p-small-n correlation matrices contaminated by large noise. Furthermore, distributions that we are dealing in the analysis are neither Gaussian nor sub-Gaussian but sub-exponential. The paper explains how the problem may be solved and presents results of a dynamic analysis of the ability of a human brain to reorganize itself for 24 healthy adults. Results show that the ability of a brain to reorganize itself varies widely even among healthy individuals, and this observation is important for our understanding of a human brain and treatment of brain diseases.     

Dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain

The longitudinal spin structure factor for the XXZ-chain at small wave vector q is obtained using Bethe ansatz, field theory methods, and the density matrix renormalization group. It consists of a peak with a peculiar, non-Lorentzian shape and a high-frequency tail. We show that the width of the peak is proportional to q2 for finite magnetic field compared to q3 for a zero field. For the tail we derive an analytic formula without any adjustable parameters and demonstrate that the integrability of the model directly affects the line shape.     

Spinful fermionic ladders at incommensurate filling: Phase diagram,local perturbations,and ionic potentials

We study the effect of external potential on transport properties of the fermionic two-leg ladder model. The response of the system to a local perturbation is strongly dependent on the ground state properties of the system and especially on the dominant correlations. We categorize all phases and transitions in the model (for incommensurate filling) and introduce “hopping-driven transitions” that the system undergoes as the inter-chain hopping is increased from zero. We also describe the response of the system to an ionic potential. The physics of this effect is similar to that of the single impurity, except that the ionic potential can affect the bulk properties of the system and in particular induce true long range order.     

2009 SSRL School on X-ray Spectroscopy Techniques in Environmental and Materials Sciences: Theory and Application

More than 50 students, post-docs, and career scientists from US national laboratories, academic institutions, and the international user community participated in this four-day school, held from June 2–5, 2009, which delved deeply into theoretical and practical aspects of synchrotron X-ray spectroscopy. The fourth annual school on synchrotron techniques in environmental and materials sciences, organized by the Stanford Synchrotron Radiation Lightsource (SSRL) at the SLAC National Accelerator Laboratory, was designed to introduce new and prospective users to theoretical underpinnings and capabilities of the techniques, data collection procedures, and data analysis approaches. More advanced topics, particularly in data analysis, were also discussed to reinforce and clarify important concepts that are fundamental to data interpretation. Although the school focused principally on applications in environmental and materials sciences, diverse and cross-cutting disciplinary backgrounds were represented, from environmental remediation science and geochemistry, to heterogeneous catalysis and bioinorganic chemistry, to materials sciences and applied physics.     

A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options

We propose a general framework to model equity volatility for a firm financed by equity and additional non-equity sources of funds. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities. Second, we show for the first time in the option literature, that instantaneous equity volatility is a solution of a partial differential equation similar to Black-Scholes', although it is non-linear and in general does not have any analytical solution. However, analytical approximations for equity volatility are proposed for different capital structures: (1) equity and debt, (2) equity and warrants, and (3) equity, debt and warrants. They are shown to be very accurate.