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  1. Abstract Purpose

    The constrained one‐step spectral CT image reconstruction (cOSSCIR) algorithm with a nonconvex alternating direction method of multipliers optimizer is proposed for addressing computed tomography (CT) metal artifacts caused by beam hardening, noise, and photon starvation. The quantitative performance of cOSSCIR is investigated through a series of photon‐counting CT simulations.

    Methods

    cOSSCIR directly estimates basis material maps from photon‐counting data using a physics‐based forward model that accounts for beam hardening. The cOSSCIR optimization framework places constraints on the basis maps, which we hypothesize will stabilize the decomposition and reduce streaks caused by noise and photon starvation. Another advantage of cOSSCIR is that the spectral data need not be registered, so that a ray can be used even if some energy window measurements are unavailable. Photon‐counting CT acquisitions of a virtual pelvic phantom with low‐contrast soft tissue texture and bilateral hip prostheses were simulated. Bone and water basis maps were estimated using the cOSSCIR algorithm and combined to form a virtual monoenergetic image for the evaluation of metal artifacts. The cOSSCIR images were compared to a “two‐step” decomposition approach that first estimated basis sinograms using a maximum likelihood algorithm and then reconstructed basis maps using an iterative total variation constrained least‐squares optimization (MLE+TV). Images were also compared to a nonspectral TV reconstruction of the total number of counts detected for each ray with and without normalized metal artifact reduction (NMAR) applied. The simulated metal density was increased to investigate the effects of increasing photon starvation. The quantitative error and standard deviation in regions of the phantom were compared across the investigated algorithms. The ability of cOSSCIR to reproduce the soft‐tissue texture, while reducing metal artifacts, was quantitatively evaluated.

    Results

    Noiseless simulations demonstrated the convergence of the cOSSCIR and MLE+TV algorithms to the correct basis maps in the presence of beam‐hardening effects. When noise was simulated, cOSSCIR demonstrated a quantitative error of −1 HU, compared to 2 HU error for the MLE+TV algorithm and −154 HU error for the nonspectral TV+NMAR algorithm. For the cOSSCIR algorithm, the standard deviation in the central iodine region of interest was 20 HU, compared to 299 HU for the MLE+TV algorithm, 41 HU for the MLE+TV+Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TV+NMAR algorithm. Increasing levels of photon starvation did not impact the bias or standard deviation of the cOSSCIR images. cOSSCIR was able to reproduce the soft‐tissue texture when an appropriate regularization constraint value was selected.

    Conclusions

    By directly inverting photon‐counting CT data into basis maps using an accurate physics‐based forward model and a constrained optimization algorithm, cOSSCIR avoids metal artifacts due to beam hardening, noise, and photon starvation. The cOSSCIR algorithm demonstrated improved stability and accuracy compared to a two‐step method of decomposition followed by reconstruction.

     
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  2. Geographic information systems deal with spatial data and its analysis. Spatial data contains many attributes with location information. Spatial autocorrelation is a fundamental concept in spatial analysis. It suggests that similar objects tend to cluster in geographic space. Hotspots, an example of autocorrelation, are statistically significant clusters of spatial data. Other autocorrelation measures like Moran’s I are used to quantify spatial dependence. Large scale spatial autocorrelation methods are compute- intensive. Fast methods for hotspots detection and analysis are crucial in recent times of COVID-19 pandemic. Therefore, we have developed parallelization methods on heterogeneous CPU and GPU environments. To the best of our knowledge, this is the first GPU and SIMD-based design and implementation of autocorrelation kernels. Earlier methods in literature introduced cluster-based and MapReduce-based parallelization. We have used Intrinsics to exploit SIMD parallelism on x86 CPU architecture. We have used MPI Graph Topology to minimize inter-process communication. Our benchmarks for CPU/GPU optimizations gain up to 750X relative speedup with a 8 GPU setup when compared to baseline sequential implementation. Compared to the best implementation using OpenMP + R-tree data structure on a single compute node, our accelerated hotspots benchmark gains a 25X speedup. For real world US counties and COVID data evolution calculated over 500 days, we gain up to 110X speedup reducing time from 33 minutes to 0.3 minutes. 
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  3. The activation of O 2 at thiolate–ligated iron( ii ) sites is essential to the function of numerous metalloenzymes and synthetic catalysts. Iron–thiolate bonds in the active sites of nonheme iron enzymes arise from either coordination of an endogenous cysteinate residue or binding of a deprotonated thiol-containing substrate. Examples of the latter include sulfoxide synthases, such as EgtB and OvoA, that utilize O 2 to catalyze tandem S–C bond formation and S -oxygenation steps in thiohistidine biosyntheses. We recently reported the preparation of two mononuclear nonheme iron–thiolate complexes (1 and 2) that serve as structural active-site models of substrate-bound EgtB and OvoA ( Dalton Trans. 2020, 49 , 17745–17757). These models feature monodentate thiolate ligands and tripodal N 4 ligands with mixed pyridyl/imidazolyl donors. Here, we describe the reactivity of 1 and 2 with O 2 at low temperatures to give metastable intermediates (3 and 4, respectively). Characterization with multiple spectroscopic techniques (UV-vis absorption, NMR, variable-field and -temperature Mössbauer, and resonance Raman) revealed that these intermediates are thiolate-ligated iron( iii ) dimers with a bridging oxo ligand derived from the four-electron reduction of O 2 . Structural models of 3 and 4 consistent with the experimental data were generated via density functional theory (DFT) calculations. The combined experimental and computational results illuminate the geometric and electronic origins of the unique spectral features of diiron( iii )-μ-oxo complexes with thiolate ligands, and the spectroscopic signatures of 3 and 4 are compared to those of closely-related diiron( iii )-μ-peroxo species. Collectively, these results will assist in the identification of intermediates that appear on the O 2 reaction landscapes of iron–thiolate species in both biological and synthetic environments. 
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