Correction of spin diffusion during iterative automated NOE assignment

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus beta-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.     

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

Convergence rates of cascade algorithms

We consider solutions of a refinement equation of the form

where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.

Our main result gives estimates for the convergence rate of the cascade algorithm. Let be the normalized solution of the above refinement equation with the dilation matrix being isotropic. Suppose lies in the Lipschitz space , where 0$"> and . Under appropriate conditions on , the following estimate will be established:

where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.

     

Continuous-Time Controlled Markov Chains with Discounted Rewards

This paper studies denumerable state continuous-time controlled Markov chains with the discounted reward criterion and a Borel action space. The reward and transition rates are unbounded, and the reward rates are allowed to take positive or negative values. First, we present new conditions for a nonhomogeneous Q(t)-process to be regular. Then, using these conditions, we give a new set of mild hypotheses that ensure the existence of -optimal (0) stationary policies. We also present a martingale characterization of an optimal stationary policy. Our results are illustrated with controlled birth and death processes.     

Continuous-flow optical pumping NMR in a closed circuit system

In a typical continuous-flow optical pumping setup, the chemical shift of xenon in the adsorbed phase depends on the gas flow rate due to warming of the sample surface by the gas stream. Calibration of the system using the (207)Pb resonance of solid lead nitrate is necessary to determine the actual sample temperature. Optimum pulse repetition rates are strongly affected by gas flow and spin-lattice relaxation rates. The interplay of flow and pulse repetition rate alters signal intensity ratios and may lead to the complete suppression of signals.     

Finite-difference approach for the high-precision analysis of rotating-frame diffusion images

A finite-difference approach has been developed for precisely determining diffusion coefficient and T₁ relaxation time in fluid samples analyzed by magnetization-grating rotating-frame imaging (MAGROFI) with either a surface coil or a toroid cavity detector (TCD). This approach avoids shortcomings of phenomenologically based approximations, such as neglect of sample geometries with singularities at the confines of the sample volume, and accounts for the diffusive edge enhancement observed in fluid imaging. Error limits are discussed. The new method has been applied to the determination of the self-diffusion coefficient for MAGROFI experiments using TCDs filled with acetone.     

Transmutation of 129I, 237Np, 238Pu, 239Pu, and 241Am using neutrons produced in target-blanket system ‘Energy plus Transmutation’ by relativistic protons

Target-blanket facility ‘Energy + Transmutation’ was irradiated by proton beam extracted from the Nuclotron Accelerator in Laboratory of High Energies of Joint Institute for Nuclear Research in Dubna, Russia. Neutrons generated by the spallation reactions of 0.7, 1.0, 1.5 and 2 GeV protons and lead target interact with subcritical uranium blanket. In the neutron field outside the blanket, radioactive iodine, neptunium, plutonium and americium samples were irradiated and transmutation reaction yields (residual nuclei production yields) have been determined using γ-spectroscopy. Neutron field's energy distribution has also been studied using a set of threshold detectors. Results of transmutation studies of ¹²⁹I, ²³⁷Np, ²³⁸Pu, ²³⁹Pu and ²⁴¹Am are presented.      

The matrix rate of return

In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous analysis of evolution of baskets parameterized by complex variables in both continuous and discrete time models.     

Double peaks on ac magnetization in a superconducting Pb-porous glass nanocomposite

Studies of temperature dependences of ac magnetization were carried out for a superconducting lead-porous glass nanocomposite. Double peaks were found on the imaginary part of ac magnetization which were accompanied with double steps on the real part. The lower-temperature anomalies in ac magnetization differed noticeably when they were obtained upon cooling and warming. The double peaks were treated as two phase transitions in the vortex system: the liquid-solid transition which occurs close to the onset of superconductivity and solid-solid one which is triggered by superconductivity in confined lead islands.     

The expectation hypothesis of interest rates and network theory: The case of Brazil

This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity.