NMR-microscopy with TrueFISP at 11.75T

The purpose of this paper is to demonstrate that a fully balanced gradient echo technique (TrueFISP) can be used for microscopic experiments at high static magnetic field strengths. TrueFISP experiments were successfully performed on homogeneous and inhomogeneous objects at 11.75T. High-resolution TrueFISP images were obtained from phantoms, plants, formalin-fixed samples, and from an isolated beating rat heart with an in-plane resolution of 78 micro m and a slice thickness of 500 micro m. The signal-to-noise ratio (SNR) gain of TrueFISP compared to conventional gradient echo or spin echo sequences will allow faster acquisition times or an improvement in spatial resolution for microscopic experiments.     

High-dimensional model representations generated from low order terms--lp-RS-HDMR

High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. RS-HDMR is a particular form of HDMR based on random sampling (RS) of the input variables. The component functions in an HDMR expansion are optimal choices tailored to the n-variate function f(x) being represented over the desired domain of the n-dimensional vector x. The high-order terms (usually larger than second order, or equivalently beyond cooperativity between pairs of variables) in the expansion are often negligible. When it is necessary to go beyond the first and the second order RS-HDMR, this article introduces a modified low-order term product (lp)-RS-HDMR method to approximately represent the high-order RS-HDMR component functions as products of low-order functions. Using this method the high-order truncated RS-HDMR expansions may be constructed without directly computing the original high-order terms. The mathematical foundations of lp-RS-HDMR are presented along with an illustration of its utility in an atmospheric chemical kinetics model.     

Constructing irregular surfaces to enclose macromolecular complexes for mesoscale modeling using the discrete surface charge optimization (DISCO) algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular structures and dynamics. Because macromolecular systems modeled at atomic resolution contain thousands of solute atoms, the electrostatic computations constitute an expensive part of the force and energy calculations. Implicit solvent models are one way to simplify the model and associated calculations, but they are generally used in combination with standard atomic models for the solute. To approximate electrostatics interactions in models on the polymer level (e.g., supercoiled DNA) that are simulated over long times (e.g., milliseconds) using Brownian dynamics, Beard and Schlick have developed the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO represents a macromolecular complex by a few hundred discrete charges on a surface enclosing the system modeled by the Debye-Hückel (screened Coulombic) approximation to the Poisson-Boltzmann equation, and treats the salt solution as continuum solvation. DiSCO can represent the nucleosome core particle (>12,000 atoms), for example, by 353 discrete surface charges distributed on the surfaces of a large disk for the nucleosome core particle and a slender cylinder for the histone tail; the charges are optimized with respect to the Poisson-Boltzmann solution for the electric field, yielding a approximately 5.5% residual. Because regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for certain systems, we develop a general method to construct irregular models tailored to the geometry of macromolecules. We also compare charge optimization based on both the electric field and electrostatic potential refinement. Results indicate that irregular surfaces can lead to a more accurate approximation (lower residuals), and the refinement in terms of the electric field is more robust. We also show that surface smoothing for irregular models is important, that the charge optimization (by the TNPACK minimizer) is efficient and does not depend on the initial assigned values, and that the residual is acceptable when the distance to the model surface is close to, or larger than, the Debye length. We illustrate applications of DiSCO's model-building procedure to chromatin folding and supercoiled DNA bound to Hin and Fis proteins. DiSCO is generally applicable to other interesting macromolecular systems for which mesoscale models are appropriate, to yield a resolution between the all-atom representative and the polymer level.     

The first self-assembled trimetallic lanthanide helicates driven by positive cooperativity

The segmental tris-tridentate ligand L7 reacts with stoichiometric quantities of Ln(III) (Ln=La-Lu) in acetonitrile to give the complexes [Ln(2)(L7)(3)](6+) and [Ln(3)(L7)(3)](9+). Formation constants point to negligible size-discriminating effects along the lanthanide series, but Scatchard plots suggest that the self-assembly of the trimetallic triple-stranded helicates [Ln(3)(L7)(3)](9+) is driven to completion by positive cooperativity, despite strong intermetallic electrostatic repulsions. Crystallization provides quantitatively [Ln(3)(L7)(3)](CF(3)SO(3))(9) (Ln=La, Eu, Gd, Tb, Lu) and the X-ray crystal structure of [Eu(3)(L7)(3)](CF(3)SO(3))(9).(CH(3)CN)(9).(H(2)O)(2) (Eu(3)C(216)H(226)N(48)O(35)F(27)S(9), triclinic, P1, Z=2) shows the three ligand strands wrapped around a pseudo-threefold axis defined by the three metal ions rigidly held at about 9 A. Each metal ion is coordinated by nine donor atoms in a pseudo-trigonal prismatic arrangement, but the existence of terminal carboxamide units in the ligand strands differentiates the electronic properties of the terminal and the central metallic sites. Photophysical data confirm that the three coordination sites possess comparable pseudo-trigonal symmetries in the solid state and in solution. High-resolution luminescence analyses evidence a low-lying LMCT state affecting the central EuN(9) site, so that multi-metal-centered luminescence is essentially dominated by the emission from the two terminal EuN(6)O(3) sites in [Eu(3)(L7)(3)](9+). New multicenter equations have been developed for investigating the solution structure of [Ln(3)(L7)(3)](9+) by paramagnetic NMR spectroscopy and linear correlations for Ln=Ce-Tb imply isostructurality for these larger lanthanides. NMR spectra point to the triple helical structure being maintained in solution, but an inversion of the magnitude of the second-rank crystal-field parameters, obtained by LIS analysis, for the LnN(6)O(3) and LnN(9) sites with respect to the parameters extracted for Eu(III) from luminescence data, suggests that the geometry of the central LnN(9) site is somewhat relaxed in solution.     

Measuring a colloidal particle's interaction with a flat surface under nonequilibrium conditions

A new and general approach is proposed to analyze the dynamics of a colloidal particle interacting with a nearby wall. This analysis can be used to determine the acting forces even when the system is non-stationary. As an illustration, we use total internal reflection microscopy to investigate the forces acting on a polystyrene sulfate latex particle as it is receding from a charged glass surface. Received 10 October 2002 Published online: 16 April 2003 RID="a" ID="a"Present address: Department of Polymer Physics, BASF Aktiengesellschaft, 67056 Ludwigshafen, Germany RID="b" ID="b"Present address: Arryx. Inc., Chicago, IL 60601, USA     

Shift-tolerance Property of Optical Security System using Phase-based Virtual Image

The shift-tolerance property of the encrypted image or the Fourier decrypting key in the Fourier space is proposed based on a phase-encoded virtual image. The encrypted data is obtained by the Fourier transform of the product of a phase-encoded virtual image to camouflage the original one and a random phase image. Therefore, even if unauthorized users analyze the encrypted image, they cannot reconstruct the required image. This virtual image protects the original one from being counterfeited and from unauthorized access. We demonstrate the robustness to data loss and shift of the encrypted data or the Fourier decrypting key in the proposed decryption technique using an interferometer.     

Reduction of spin glasses applied to the Migdal-Kadanoff hierarchical lattice

A reduction procedure to obtain ground states of spin glasses on sparse graphs is developed and tested on the hierarchical lattice associated with the Migdal-Kadanoff approximation for low-dimensional lattices. While more generally applicable, these rules here lead to a complete reduction of the lattice. The stiffness exponent governing the scaling of the defect energy E with system size L, (E) ~L ^y, is obtained as y ₃ = 0.25546(3) by reducing the equivalent of lattices up to L = 2¹⁰⁰ in d = 3, and as y ₄ = 0.76382(4) for up to L = 2³⁵ in d = 4. The reduction rules allow the exact determination of the ground state energy, entropy, and also provide an approximation to the overlap distribution. With these methods, some well-know and some new features of diluted hierarchical lattices are calculated.     

Magnetic properties of Yb Mo O and Gd Mo O from rare earth Mössbauer measurements

Using ¹⁷⁰Yb and ¹⁵⁵Gd M?ssbauer measurements down to ∼ 0.03 K, we have examined the semiconducting pyrochlore Yb₂Mo₂O₇ where the Mo intra-sublattice interaction is anti-ferromagnetic and the metallic pyrochlore Gd₂Mo₂O₇ where this interaction is ferromagnetic. Additional information was obtained from susceptibility, magnetisation and ¹⁷²Yb perturbed angular correlation measurements. The microscopic measurements evidence lattice disorder which is important in Yb₂Mo₂O₇ and modest in Gd₂Mo₂O₇. Magnetic irreversibilities occur at 17 K in Yb₂Mo₂O₇ and at 75 K in Gd₂Mo₂O₇ and below these temperatures the rare earths carry magnetic moments which are induced through couplings with the Mo sublattice. In Gd₂Mo₂O₇, we observe the steady state Gd hyperfine populations at 0.027 K are out of thermal equilibrium, indicating that Gd and Mo spin fluctuations persist at very low temperatures. Frustration is thus operative in this essentially isotropic pyrochlore where the dominant Mo intra-sublattice interaction is ferromagnetic. Received 13 January 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: hodges@drecam.saclay.cea.fr     

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de