Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Spin-labeling coronary MR angiography with steady-state free precession and radial k-space sampling: initial results in healthy volunteers.

The purpose of this study was to prospectively compare free-breathing navigator-gated cardiac-triggered three-dimensional steady-state free precession (SSFP) spin-labeling coronary magnetic resonance (MR) angiography performed by using Cartesian k-space sampling with that performed by using radial k-space sampling. A new dedicated placement of the two-dimensional selective labeling pulse and an individually adjusted labeling delay time approved by the institutional review board were used. In 14 volunteers (eight men, six women; mean age, 28.8 years) who gave informed consent, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), vessel sharpness, vessel length, and subjective image quality were investigated. Differences between groups were analyzed with nonparametric tests (Wilcoxon, Pearson chi2). Radial imaging, as compared with Cartesian imaging, resulted in a significant reduction in the severity of motion artifacts, as well as an increase in SNR (26.9 vs 12.0, P < .05) in the coronary arteries and CNR (23.1 vs 8.8, P < .05) between the coronary arteries and the myocardium. A tendency toward improved vessel sharpness and vessel length was also found with radial imaging. Radial SSFP imaging is a promising technique for spin-labeling coronary MR angiography.

Selective three-dimensional visualization of the coronary arterial lumen using arterial spin tagging.

Conventional coronary magnetic resonance angiography (MRA) techniques display the coronary blood-pool along with the surrounding structures, including the myocardium, the ventricular and atrial blood-pool, and the great vessels. This representation of the coronary lumen is not directly analogous to the information provided by x-ray coronary angiography, in which the coronary lumen displayed by iodinated contrast agent is seen. Analogous "luminographic" data may be obtained using MR arterial spin tagging (projection coronary MRA) techniques. Such an approach was implemented using a 2D selective "pencil" excitation for aortic spin tagging in concert with a 3D interleaved segmented spiral imaging sequence with free-breathing, and real-time navigator technology. This technique allows for selective 3D visualization of the coronary lumen blood-pool, while signal from the surrounding structures is suppressed.

Three-dimensional high-resolution fast spin-echo coronary magnetic resonance angiography.

Due to SNR constraints, current "bright-blood" 3D coronary MRA approaches still suffer from limited spatial resolution when compared to conventional x-ray coronary angiography. Recent 2D fast spin-echo black-blood techniques maximize signal for coronary MRA at no loss in image spatial resolution. This suggests that the extension of black-blood coronary MRA with a 3D imaging technique would allow for a further signal increase, which may be traded for an improved spatial resolution. Therefore, a dual-inversion 3D fast spin-echo imaging sequence and real-time navigator technology were combined for high-resolution free-breathing black-blood coronary MRA. In-plane image resolution below 400 microm was obtained. Magn Reson Med 45:206-211, 2001.

Free-breathing renal magnetic resonance angiography with steady-state free-precession and slab-selective spin inversion combined with radial k-space sampling and water-selective excitation.

The impact of radial k-space sampling and water-selective excitation on a novel navigator-gated cardiac-triggered slab-selective inversion prepared 3D steady-state free-precession (SSFP) renal MR angiography (MRA) sequence was investigated. Renal MRA was performed on a 1.5-T MR system using three inversion prepared SSFP approaches: Cartesian (TR/TE: 5.7/2.8 ms, FA: 85 degrees), radial (TR/TE: 5.5/2.7 ms, FA: 85 degrees) SSFP, and radial SSFP combined with water-selective excitation (TR/TE: 9.9/4.9 ms, FA: 85 degrees). Radial data acquisition lead to significantly reduced motion artifacts (P < 0.05). SNR and CNR were best using Cartesian SSFP (P < 0.05). Vessel sharpness and vessel length were comparable in all sequences. The addition of a water-selective excitation could not improve image quality. In conclusion, radial k-space sampling reduces motion artifacts significantly in slab-selective inversion prepared renal MRA, while SNR and CNR are decreased. The addition of water-selective excitation could not improve the lower CNR in radial scanning.

Bandwidth allocation based on real time calculations using the convolution approach

This paper focuses on one of the methods for bandwidth allocation in an ATM network: the convolution approach. The convolution approach permits an accurate study of the system load in statistical terms by accumulated calculations, since probabilistic results of the bandwidth allocation can be obtained. Nevertheless, the convolution approach has a high cost in terms of calculation and storage requirements. This aspect makes real-time calculations difficult, so many authors do not consider this approach. With the aim of reducing the cost we propose to use the multinomial distribution function: the enhanced convolution approach (ECA). This permits direct computation of the associated probabilities of the instantaneous bandwidth requirements and makes a simple deconvolution process possible. The ECA is used in connection acceptance control, and some results are presented

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

A new all-round density functional based on spin states and SN2 barriers

We report here a new empirical density functional that is constructed based on the performance of OPBE and PBE for spin states and SN 2 reaction barriers and how these are affected by different regions of the reduced gradient expansion. In a previous study [Swart, Sol̀, and Bickelhaupt, J. Comput. Methods Sci. Eng. 9, 69 (2009)] we already reported how, by switching between OPBE and PBE, one could obtain both the good performance of OPBE for spin states and reaction barriers and that of PBE for weak interactions within one and the same (SSB-sw) functional. Here we fine tuned this functional and include a portion of the KT functional and Grimme's dispersion correction to account for π- π stacking. Our new SSB-D functional is found to be a clear improvement and functions very well for biological applications (hydrogen bonding, π -π stacking, spin-state splittings, accuracy of geometries, reaction barriers)

Continuous arterial spin labeling of mouse cerebral blood flow using an actively-detuned two-coil system at 9.4T.

Among numerous magnetic resonance imaging (MRI) techniques, perfusion MRI provides insight into the passage of blood through the brain's vascular network non-invasively. Studying disease models and transgenic mice would intrinsically help understanding the underlying brain functions, cerebrovascular disease and brain disorders. This study evaluates the feasibility of performing continuous arterial spin labeling (CASL) on all cranial arteries for mapping murine cerebral blood flow at 9.4 T. We showed that with an active-detuned two-coil system, a labeling efficiency of 0.82 ± 0.03 was achieved with minimal magnetization transfer residuals in brain. The resulting cerebral blood flow of healthy mouse was 99 ± 26 mL/100g/min, in excellent agreement with other techniques. In conclusion, high magnetic fields deliver high sensitivity and allowing not only CASL but also other MR techniques, i.e. (1)H MRS and diffusion MRI etc, in studying murine brains.

Use of the FACTS solvation model for protein-ligand docking calculations. Application to EADock.

Protein-ligand docking has made important progress during the last decade and has become a powerful tool for drug development, opening the way to virtual high throughput screening and in silico structure-based ligand design. Despite the flattering picture that has been drawn, recent publications have shown that the docking problem is far from being solved, and that more developments are still needed to achieve high successful prediction rates and accuracy. Introducing an accurate description of the solvation effect upon binding is thought to be essential to achieve this goal. In particular, EADock uses the Generalized Born Molecular Volume 2 (GBMV2) solvent model, which has been shown to reproduce accurately the desolvation energies calculated by solving the Poisson equation. Here, the implementation of the Fast Analytical Continuum Treatment of Solvation (FACTS) as an implicit solvation model in small molecules docking calculations has been assessed using the EADock docking program. Our results strongly support the use of FACTS for docking. The success rates of EADock/FACTS and EADock/GBMV2 are similar, i.e. around 75% for local docking and 65% for blind docking. However, these results come at a much lower computational cost: FACTS is 10 times faster than GBMV2 in calculating the total electrostatic energy, and allows a speed up of EADock by a factor of 4. This study also supports the EADock development strategy relying on the CHARMM package for energy calculations, which enables straightforward implementation and testing of the latest developments in the field of Molecular Modeling.

Accurate calculations of intermolecular interaction energies using explicitly correlated coupled cluster wave functions and a dispersion-weighted MP2 method.

Explicitly correlated coupled-cluster calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented. Results obtained with the recently proposed CCSD(T)-F12a method and augmented double-zeta basis sets are found to be in very close agreement with basis set extrapolated conventional CCSD(T) results. Furthermore, we propose a dispersion-weighted MP2 (DW-MP2) approximation that combines the good accuracy of MP2 for complexes with predominately electrostatic bonding and SCS-MP2 for dispersion-dominated ones. The MP2-F12 and SCS-MP2-F12 correlation energies are weighted by a switching function that depends on the relative HF and correlation contributions to the interaction energy. For the S22 set, this yields a mean absolute deviation of 0.2 kcal/mol from the CCSD(T)-F12a results. The method, which allows obtaining accurate results at low cost, is also tested for a number of dimers that are not in the training set.

Systematic trends in self-consistent calculations of linear quantum wires

Systematic trends in the properties of a linear split-gate heterojunction are studied by solving iteratively the Poisson and Schrödinger equations for different gate potentials and temperatures. A two-dimensional approximation is presented that is much simpler in the numerical implementation and that accurately reproduces all significant trends. In deriving this approximation, we provide a rigorous and quantitative basis for the formulation of models that assumes a two-dimensional character for the electron gas at the junction.

Spin and density longitudinal response of quantum dots in the time-dependent local-spin-density approximation

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local-spin-density-functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single-particle excitations have a sizable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor (v) related. We have found that the spin dipole mode is especially soft for even-n values. Results for selected numbers of electrons and confining potentials are discussed.