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1. Partitioned Search with Column Resampling for Locating Array Construction

   https://doi.org/10.1109/ICSTW.2019.00056  

   Lanus, Erin; Colbourn, Charles J.; Montgomery, Douglas C. (April 2019, IEEE International Conference on Software Testing, Verification and Validation Workshops (ICSTW))

   Locating arrays are designs used in combinatorial testing with the property that every set of d t-way interactions appears in a unique set of tests. Using a locating array to conduct fault testing ensures that faulty interactions can be located when there are d or fewer faults. Locating arrays are fairly new and few techniques have been explored for their construction. Most of the available work is limited to finding only one fault. Known general methods require a covering array of strength t+d and produce many more tests than are needed. We present Partitioned Search with Column Resampling (PSCR), a randomized computational search algorithmic framework to verify if an array is (d t)-locating by partitioning the search space to decrease the number of comparisons. If a candidate array is not locating, random resampling is performed until a locating array is constructed or an iteration limit is reached. Results are compared against known locating array constructions from covering arrays of higher strength and against published results of mixed level locating arrays for parameters of real-world systems. The use of PSCR to build larger locating arrays from a variety of ingredient arrays is explored. 

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2. Robustness of Recovery in Locating Array-based Screening Experiments

   Seidel, S. A.; Colbourn, C. J.; Syrotiuk, V.R. (January 2019, Spring Simulation Multiconference)

   Locating arrays (LAs) are experimental designs for screening interactions in engineered systems. LAs are often highly unbalanced, requiring advanced techniques to recover the terms that significantly influence system performance. While perfect recovery is achieved in the absence of noise, real systems are noisy. Therefore, in this paper, we study the robustness of recovery in the presence of noise. Using known models to generate synthetic data, we investigate recovery accuracy as a function of noise. Separation is introduced into LAs to allow more coverage for each t-way interaction; when separation is higher, recovery in noisy scenarios should improve. We find that locating arrays are able to recover the influential terms even with high levels of noise and that separation appears to improve recovery. Under the pessimistic assumption that noise depends on the range of responses, it is no surprise that terms with small coefficients become indistinguishable from noise. 

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3. Detecting Arrays for Main Effects

   https://doi.org/10.1007/978-3-030-21363-3_10  

   Colbourn, C. J.; Syrotiuk, V. R. (January 2019, Lecture notes in computer science)

   Determining correctness and performance for complex engineered systems necessitates testing the system to determine how its behaviour is impacted by many factors and interactions among them. Of particular concern is to determine which settings of the factors (main effects) impact the behaviour significantly. Detecting arrays for main effects are test suites that ensure that the impact of each main effect is witnessed even in the presence of d or fewer other significant main effects. Separation in detecting arrays dictates the presence of at least a specified number of such witnesses. A new parameter, corroboration, enables the fusion of levels while maintaining the presence of witnesses. Detecting arrays for main effects, having various values for the separation and corroboration, are constructed using error-correcting codes and separating hash families. The techniques are shown to yield explicit constructions with few tests for large numbers of factors. 

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4. Introducing DDEC6 atomic population analysis: part 4. Efficient parallel computation of net atomic charges, atomic spin moments, bond orders, and more

   https://doi.org/10.1039/c7ra11829e  

   Limas, Nidia Gabaldon; Manz, Thomas A. (January 2018, RSC Advances)

   The DDEC6 method is one of the most accurate and broadly applicable atomic population analysis methods. It works for a broad range of periodic and non-periodic materials with no magnetism, collinear magnetism, and non-collinear magnetism irrespective of the basis set type. First, we show DDEC6 charge partitioning to assign net atomic charges corresponds to solving a series of 14 Lagrangians in order. Then, we provide flow diagrams for overall DDEC6 analysis, spin partitioning, and bond order calculations. We wrote an OpenMP parallelized Fortran code to provide efficient computations. We show that by storing large arrays as shared variables in cache line friendly order, memory requirements are independent of the number of parallel computing cores and false sharing is minimized. We show that both total memory required and the computational time scale linearly with increasing numbers of atoms in the unit cell. Using the presently chosen uniform grids, computational times of ∼9 to 94 seconds per atom were required to perform DDEC6 analysis on a single computing core in an Intel Xeon E5 multi-processor unit. Parallelization efficiencies were usually >50% for computations performed on 2 to 16 cores of a cache coherent node. As examples we study a B-DNA decamer, nickel metal, supercells of hexagonal ice crystals, six X@C 60 endohedral fullerene complexes, a water dimer, a Mn 12 -acetate single molecule magnet exhibiting collinear magnetism, a Fe 4 O 12 N 4 C 40 H 52 single molecule magnet exhibiting non-collinear magnetism, and several spin states of an ozone molecule. Efficient parallel computation was achieved for systems containing as few as one and as many as >8000 atoms in a unit cell. We varied many calculation factors ( e.g. , grid spacing, code design, thread arrangement, etc. ) and report their effects on calculation speed and precision. We make recommendations for excellent performance. 

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5. Fundamental limits for rank-one matrix estimation with groupwise heteroskedasticity

   Behne, J. (January 2022, International Conference on Artificial Intelligence and Statistics)

   Low-rank matrix recovery problems involving high-dimensional and heterogeneous data appear in applications throughout statistics and machine learning. The contribution of this paper is to establish the fundamental limits of recovery for a broad class of these problems. In particular, we study the problem of estimating a rank-one matrix from Gaussian observations where different blocks of the matrix are observed under different noise levels. In the setting where the number of blocks is fixed while the number of variables tends to infinity, we prove asymptotically exact formulas for the minimum mean-squared error in estimating both the matrix and underlying factors. These results are based on a novel reduction from the low-rank matrix tensor product model (with homogeneous noise) to a rank-one model with heteroskedastic noise. As an application of our main result, we show that show recently proposed methods based on applying principal component analysis (PCA) to weighted combinations of the data are optimal in some settings but sub-optimal in others. We also provide numerical results comparing our asymptotic formulas with the performance of methods based weighted PCA, gradient descent, and approximate message passing. 

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