Parallel density matrix propagation in spin dynamics simulations

Several methods for density matrix propagation in distributed computing environments, such as clusters and graphics processing units, are proposed and evaluated. It is demonstrated that the large communication overhead associated with each propagation step (two-sided multiplication of the density matrix by an exponential propagator and its conjugate) may be avoided and the simulation recast in a form that requires virtually no inter-thread communication. Good scaling is demonstrated on a 128-core (16 nodes, 8 cores each) cluster.Comment: Submitted for publicatio

Conformational analysis of small organic molecules using NOE and RDC data: A discussion of strychnine and a-methylene-y-butyrolactone

To understand the properties and/or reactivity of an organic molecule, an understanding of its three-dimensional structure is necessary. Simultaneous determination of configuration and conformation often poses a daunting challenge. Thus, the more information accessible for a given molecule, the better. Additionally to (3)J-couplings, two sources of information, quantitative NOE and more recently also RDCs, are used for conformational analysis by NMR spectroscopy. In this paper, we compare these sources of conformational information in two molecules: the configurationally well-characterized strychnine 1, and the only recently configurationally and conformationally characterized ?-methylene-?-butyrolactone 2. We discuss possible sources of error in the measurement and analysis process, and how to exclude them. By this means, we are able to bolster the previously proposed flexibility for these two molecules

A quantum mechanical NMR simulation algorithm for protein-scale spin systems

Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling simulation methods have not so far been available. Here, we report such a method and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of spin relaxation processes) on isotopically enriched human ubiquitin - a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analyzing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set. In the examples provided, the resulting reduction in the quantum mechanical simulation time is by many orders of magnitude.Comment: Submitted for publicatio

Can randomness alone tune the fractal dimension?

We present a generalized stochastic Cantor set by means of a simple {\it cut and delete process} and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, $m$ and $b$, are introduced which tune the relative strength of the two processes and the degree of randomness respectively. In doing so, we have identified a new set with a wide spectrum of subsets produced by tuning either $m$ or $b$. Measuring the size of the resulting set in terms of fractal dimension, we show that the fractal dimension increases with increasing order and reaches its maximum value when the randomness is completely ceased.Comment: 6 pages 2-column RevTeX, Two figures (presented in the APCTP International Symposium on Slow Dynamical Processes in Nature, Nov. 2001, Seoul, Korea

Mapping Short Association Fibers in the Early Cortical Visual Processing Stream Using In Vivo Diffusion Tractography

Short association fibers (U-fibers) connect proximal cortical areas and constitute the majority of white matter connections in the human brain. U-fibers play an important role in brain development, function, and pathology but are underrepresented in current descriptions of the human brain connectome, primarily due to methodological challenges in diffusion magnetic resonance imaging (dMRI) of these fibers. High spatial resolution and dedicated fiber and tractography models are required to reliably map the U-fibers. Moreover, limited quantitative knowledge of their geometry and distribution makes validation of U-fiber tractography challenging. Submillimeter resolution diffusion MRI-facilitated by a cutting-edge MRI scanner with 300 mT/m maximum gradient amplitude-was used to map U-fiber connectivity between primary and secondary visual cortical areas (V1 and V2, respectively) in vivo. V1 and V2 retinotopic maps were obtained using functional MRI at 7T. The mapped V1-V2 connectivity was retinotopically organized, demonstrating higher connectivity for retinotopically corresponding areas in V1 and V2 as expected. The results were highly reproducible, as demonstrated by repeated measurements in the same participants and by an independent replication group study. This study demonstrates a robust U-fiber connectivity mapping in vivo and is an important step toward construction of a more complete human brain connectome

Quantitative MRI maps of human neocortex explored using cell type-specific gene expression analysis

Quantitative magnetic resonance imaging (qMRI) allows extraction of reproducible and robust parameter maps. However, the connection to underlying biological substrates remains murky, especially in the complex, densely packed cortex. We investigated associations in human neocortex between qMRI parameters and neocortical cell types by comparing the spatial distribution of the qMRI parameters longitudinal relaxation rate (⁠R1⁠), effective transverse relaxation rate (⁠R2∗⁠), and magnetization transfer saturation (MTsat) to gene expression from the Allen Human Brain Atlas, then combining this with lists of genes enriched in specific cell types found in the human brain. As qMRI parameters are magnetic field strength-dependent, the analysis was performed on MRI data at 3T and 7T. All qMRI parameters significantly covaried with genes enriched in GABA- and glutamatergic neurons, i.e. they were associated with cytoarchitecture. The qMRI parameters also significantly covaried with the distribution of genes enriched in astrocytes (⁠R2∗ at 3T, R1 at 7T), endothelial cells (⁠R1 and MTsat at 3T), microglia (⁠R1 and MTsat at 3T, R1 at 7T), and oligodendrocytes and oligodendrocyte precursor cells (⁠R1 at 7T). These results advance the potential use of qMRI parameters as biomarkers for specific cell types

Multimodal probes : superresolution and transmission electron microscopy imaging of mitochondria, and oxygen mapping of cells, using small-molecule Ir(III) luminescent complexes

We describe an Ir(III)-based small-molecule, multimodal probe for use in both light and electron microscopy. The direct correlation of data between light- and electron-microscopy-based imaging to investigate cellular processes at the ultrastructure level is a current challenge, requiring both dyes that must be brightly emissive for luminescence imaging and scatter electrons to give contrast for electron microscopy, at a single working concentration suitable for both methods. Here we describe the use of Ir(III) complexes as probes that provide excellent image contrast and quality for both luminescence and electron microscopy imaging, at the same working concentration. Significant contrast enhancement of cellular mitochondria was observed in transmission electron microscopy imaging, with and without the use of typical contrast agents. The specificity for cellular mitochondria was also confirmed with MitoTracker using confocal and 3D-structured illumination microscopy. These phosphorescent dyes are part of a very exclusive group of transition-metal complexes that enable imaging beyond the diffraction limit. Triplet excited-state phosphorescence was also utilized to probe the O2 concentration at the mitochondria in vitro, using lifetime mapping techniques

Combining navigator and optical prospective motion correction for high-quality 500 μm resolution quantitative multi-parameter mapping at 7T

PURPOSE: High-resolution quantitative multi-parameter mapping shows promise for non-invasively characterizing human brain microstructure but is limited by physiological artifacts. We implemented corrections for rigid head movement and respiration-related B0-fluctuations and evaluated them in healthy volunteers and dementia patients. METHODS: Camera-based optical prospective motion correction (PMC) and FID navigator correction were implemented in a gradient and RF-spoiled multi-echo 3D gradient echo sequence for mapping proton density (PD), longitudinal relaxation rate (R1) and effective transverse relaxation rate (R2*). We studied their effectiveness separately and in concert in young volunteers and then evaluated the navigator correction (NAVcor) with PMC in a group of elderly volunteers and dementia patients. We used spatial homogeneity within white matter (WM) and gray matter (GM) and scan-rescan measures as quality metrics. RESULTS: NAVcor and PMC reduced artifacts and improved the homogeneity and reproducibility of parameter maps. In elderly participants, NAVcor improved scan-rescan reproducibility of parameter maps (coefficient of variation decreased by 14.7% and 11.9% within WM and GM respectively). Spurious inhomogeneities within WM were reduced more in the elderly than in the young cohort (by 9% vs. 2%). PMC increased regional GM/WM contrast and was especially important in the elderly cohort, which moved twice as much as the young cohort. We did not find a significant interaction between the two corrections. CONCLUSION: Navigator correction and PMC significantly improved the quality of PD, R1, and R2* maps, particularly in less compliant elderly volunteers and dementia patients

The effect of ring size on the selective carboxylation of cycloalkene oxides

Carbon dioxide utilisation technology can contribute to the reduction of atmospheric CO2 levels both through its sequestration from flue gases and indirectly by relieving pressure on conventional feedstocks in chemical manufacturing. A promising approach is to employ CO2 to produce valuable cyclic carbonates (CCs) in reaction with suitable epoxides. This also has the advantage that carbon dioxide replaces toxic and hazardous reactants such as phosgene. In earlier work we have investigated the synthesis of epoxides from cycloalkenes using supported gold and gold–palladium nanoparticles as catalysts and oxygen from air as the oxidant under solvent free conditions. A strong dependence of epoxide selectivity on ring size was observed with C5 < C6 < C7 ≪ C8. In this study we extend this work to the investigation of cycloaddition of CO2 to different cycloalkene oxides with the ultimate aim of designing a process in which both epoxidation of an alkene and incorporation of CO2 could be achieved in a single process. However, we have found the opposite trend for the selectivity to carbonates: smaller ring cycloalkene oxides giving the highest carbonate selectivities while large rings do not yield CCs at all. The product distributions suggest that an alternative ring opening of the epoxides to yield alcohols and ketones is preferred under all the experimental conditions explored for larger ring systems. Additionally, the mechanism of the CC synthesis using a quaternary ammonium salt and ZnBr2 as the catalyst system was investigated using DFT methods. The results of the calculations support the experimental findings

Convergence Acceleration via Combined Nonlinear-Condensation Transformations

A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating series. In the second step, the convergence of the transformed series is accelerated with the help of suitable nonlinear sequence transformations that are known to be particularly powerful for alternating series. Some theoretical aspects of our approach are discussed. The efficiency, numerical stability, and wide applicability of the combined nonlinear-condensation transformation is illustrated by a number of examples. We discuss the evaluation of special functions close to or on the boundary of the circle of convergence, even in the vicinity of singularities. We also consider a series of products of spherical Bessel functions, which serves as a model for partial wave expansions occurring in quantum electrodynamic bound state calculations.Comment: 24 pages, LaTeX, 12 tables (accepted for publication in Comput. Phys. Comm.