We estimate unknown rotation matrices R_i from a set of measurements of relative rotations R_iR_j~T. Measurements are strongly affected by noise such that a small fraction of them are well concentrated around the true...
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ISBN:
(纸本)9781467357159
We estimate unknown rotation matrices R_i from a set of measurements of relative rotations R_iR_j~T. Measurements are strongly affected by noise such that a small fraction of them are well concentrated around the true relative rotations while the majority of measurements are outliers bearing little or no information. We propose a maximum likelihood estimator (MLE) that explicitly acknowledges this noise model, yielding a robust estimation algorithm. The MLE is computed via Riemannian trust-region optimization using the Manopt toolbox. Comparisons of the MLE with Cramer-Rao bounds suggest the estimator is asymptotically efficient.
We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observabl...
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We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of appropriately initialized detailed simulations, we circumvent the derivation of closures for the long-term dynamics of the assembly statistics.
Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the devel...
ISBN:
(纸本)9781713845393
Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.
We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the recent findings of [11], [10] in one space dimension it is nat...
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Cryo-electron microscopy (cryo-EM), the subject of the 2017 Nobel Prize in Chemistry, is a technology for determining the 3-D structure of macromolecules from many noisy 2-D projections of instances of these macromole...
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Magnesium-aluminum (Mg-Al) alloys are important metal alloys with a wide range of engineering applications. We investigate the elastic and thermodynamic properties of Mg, Al, and four stoichiometric Mg-Al compounds in...
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Magnesium-aluminum (Mg-Al) alloys are important metal alloys with a wide range of engineering applications. We investigate the elastic and thermodynamic properties of Mg, Al, and four stoichiometric Mg-Al compounds including Mg17Al12, Mg13Al14, and Mg23Al30, and MgAl2 with orbital-free density-functional theory (OFDFT). We first calculate the lattice constants, zero-temperature formation energy, and independent elastic constants of these six materials and compare the results to those computed via Kohn-Sham DFT (KSDFT) benchmarks. We obtain excellent agreement between these two methods. Our calculated elastic constants of hexagonal close-packed Mg and face-centered-cubic Al are also consistent with available experimental data. We next compute their phonon spectra using the force constants extracted from the very fast OFDFT calculations, because such calculations are computationally challenging using KSDFT. This is especially the case for the Mg23Al30 compound, whose 3×3×3 supercell consists of 1431 atoms. We finally employ the quasiharmonic approximation to investigate temperature-dependent thermodynamic properties, including formation energies, heat capacities, and thermal expansion of the four Mg-Al intermetallic compounds. The calculated heat capacity and thermal expansion of both Mg and Al agree well with experimental data. We additionally find that Mg13Al14 and MgAl2 are both unstable, consistent with their absence from the equilibrium Mg-Al phase diagram. Our work demonstrates that OFDFT is an efficient and accurate quantum-mechanical computational tool for predicting elastic and thermodynamic properties of complicated Mg-Al alloys and also should be applicable to many other engineering alloys.
With the increased availability of rich behavioral data sets, we present a novel combination of tools to analyze to analyze this information. Using criminal offense records as an example, we employ cross-correlation m...
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Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a p...
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We consider the multi-target detection problem of recovering a set of signals that appear multiple times at unknown locations in a noisy measurement. In the low noise regime, one can estimate the signals by first dete...
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