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1. Fiber-Sampled Stochastic Mirror Descent for Tensor Decomposition with β-Divergence

   https://doi.org/10.1109/ICASSP39728.2021.9413830  

   Pu, Wenqiang ; Ibrahim, Shahana ; Fu, Xiao ; Hong, Mingyi ( June 2021 , IEEE ICASSP 2021)

   null (Ed.)

   Canonical polyadic decomposition (CPD) has been a workhorse for multimodal data analytics. This work puts forth a stochastic algorithmic framework for CPD under β-divergence, which is well-motivated in statistical learning—where the Euclidean distance is typically not preferred. Despite the existence of a series of prior works addressing this topic, pressing computational and theoretical challenges, e.g., scalability and convergence issues, still remain. In this paper, a unified stochastic mirror descent framework is developed for large-scale β-divergence CPD. Our key contribution is the integrated design of a tensor fiber sampling strategy and a flexible stochastic Bregman divergence-based mirror descent iterative procedure, which significantly reduces the computation and memory cost per iteration for various β. Leveraging the fiber sampling scheme and the multilinear algebraic structure of low-rank tensors, the proposed lightweight algorithm also ensures global convergence to a stationary point under mild conditions. Numerical results on synthetic and real data show that our framework attains significant computational saving compared with state-of-the-art methods. 

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2. New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 2. Linear-scaling computational algorithms and parallelization

   https://doi.org/10.1039/c9ra01983a  

   Manz, Thomas A. ; Chen, Taoyi ( October 2019 , RSC Advances)

   We present two algorithms to compute system-specific polarizabilities and dispersion coefficients such that required memory and computational time scale linearly with increasing number of atoms in the unit cell for large systems. The first algorithm computes the atom-in-material (AIM) static polarizability tensors, force-field polarizabilities, and C 6 , C 8 , C 9 , C 10 dispersion coefficients using the MCLF method. The second algorithm computes the AIM polarizability tensors and C 6 coefficients using the TS-SCS method. Linear-scaling computational cost is achieved using a dipole interaction cutoff length function combined with iterative methods that avoid large dense matrix multiplies and large matrix inversions. For MCLF, Richardson extrapolation of the screening increments is used. For TS-SCS, a failproof conjugate residual (FCR) algorithm is introduced that solves any linear equation system having Hermitian coefficients matrix. These algorithms have mathematically provable stable convergence that resists round-off errors. We parallelized these methods to provide rapid computation on multi-core computers. Excellent parallelization efficiencies were obtained, and adding parallel processors does not significantly increase memory requirements. This enables system-specific polarizabilities and dispersion coefficients to be readily computed for materials containing millions of atoms in the unit cell. The largest example studied herein is an ice crystal containing >2 million atoms in the unit cell. For this material, the FCR algorithm solved a linear equation system containing >6 million rows, 7.57 billion interacting atom pairs, 45.4 billion stored non-negligible matrix components used in each large matrix-vector multiplication, and ∼19 million unknowns per frequency point (>300 million total unknowns). 

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3. Semi-implicit hybrid discrete (H$^T_N$) approximation of thermal radiative transfer

   https://doi.org/https://link.springer.com/article/10.1007/s10915-021-01686-7  

   R.G. McClarren, J.A. Rossmanith ( November 2021 , Journal of scientific computing)

   The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing accurate and efficient numerical solutions TRT are challenging for several reasons, the first of which is that TRT is defined on a high-dimensional phase space that includes the independent variables of time, space, and velocity. In order to reduce the dimensionality of the phase space, classical approaches such as the P$_N$ (spherical harmonics) or the S$_N$ (discrete ordinates) ansatz are often used in the literature. In this work, we introduce a novel approach: the hybrid discrete (H$^T_N$) approximation to the radiative thermal transfer equations. This approach acquires desirable properties of both P$_N$ and S$_N$, and indeed reduces to each of these approximations in various limits: H$^1_N$ $\equiv$ P$_N$ and H$^T_0$ $\equiv$ S$_T$. We prove that H$^T_N$ results in a system of hyperbolic partial differential equations for all $T\ge 1$ and $N\ge 0$. Another challenge in solving the TRT system is the inherent stiffness due to the large timescale separation between propagation and collisions, especially in the diffusive (i.e., highly collisional) regime. This stiffness challenge can be partially overcome via implicit time integration, although fully implicit methods may become computationally expensive due to the strong nonlinearity and system size. On the other hand, explicit time-stepping schemes that are not also asymptotic-preserving in the highly collisional limit require resolving the mean-free path between collisions, making such schemes prohibitively expensive. In this work we develop a numerical method that is based on a nodal discontinuous Galerkin discretization in space, coupled with a semi-implicit discretization in time. In particular, we make use of a second order explicit Runge-Kutta scheme for the streaming term and an implicit Euler scheme for the material coupling term. Furthermore, in order to solve the material energy equation implicitly after each predictor and corrector step, we linearize the temperature term using a Taylor expansion; this avoids the need for an iterative procedure, and therefore improves efficiency. In order to reduce unphysical oscillation, we apply a slope limiter after each time step. Finally, we conduct several numerical experiments to verify the accuracy, efficiency, and robustness of the H$^T_N$ ansatz and the numerical discretizations. 

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4. High-dimension to high-dimension screening for detecting genome-wide epigenetic and noncoding RNA regulators of gene expression

   https://doi.org/10.1093/bioinformatics/btac518  

   Ke, Hongjie ; Ren, Zhao ; Qi, Jianfei ; Chen, Shuo ; Tseng, George C. ; Ye, Zhenyao ; Ma, Tianzhou ; Alkan, ed., Can ( July 2022 , Bioinformatics)

   The advancement of high-throughput technology characterizes a wide variety of epigenetic modifications and noncoding RNAs across the genome involved in disease pathogenesis via regulating gene expression. The high dimensionality of both epigenetic/noncoding RNA and gene expression data make it challenging to identify the important regulators of genes. Conducting univariate test for each possible regulator–gene pair is subject to serious multiple comparison burden, and direct application of regularization methods to select regulator–gene pairs is computationally infeasible. Applying fast screening to reduce dimension first before regularization is more efficient and stable than applying regularization methods alone.

   We propose a novel screening method based on robust partial correlation to detect epigenetic and noncoding RNA regulators of gene expression over the whole genome, a problem that includes both high-dimensional predictors and high-dimensional responses. Compared to existing screening methods, our method is conceptually innovative that it reduces the dimension of both predictor and response, and screens at both node (regulators or genes) and edge (regulator–gene pairs) levels. We develop data-driven procedures to determine the conditional sets and the optimal screening threshold, and implement a fast iterative algorithm. Simulations and applications to long noncoding RNA and microRNA regulation in Kidney cancer and DNA methylation regulation in Glioblastoma Multiforme illustrate the validity and advantage of our method.

   The R package, related source codes and real datasets used in this article are provided at https://github.com/kehongjie/rPCor.

   Supplementary data are available at Bioinformatics online.

    

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5. Addressing CT metal artifacts using photon‐counting detectors and one‐step spectral CT image reconstruction

   https://doi.org/10.1002/mp.15621  

   Schmidt, Taly Gilat ; Sammut, Barbara A. ; Barber, Rina Foygel ; Pan, Xiaochuan ; Sidky, Emil Y. ( April 2022 , Medical Physics)

   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.

   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.

   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.

   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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