Numerical simulation is used to model ion etching in trilayer lithography. The simulations are capable of capturing the evolution of the boundary between two materials as well as the physically observed phonemena reac...
Numerical simulation is used to model ion etching in trilayer lithography. The simulations are capable of capturing the evolution of the boundary between two materials as well as the physically observed phonemena reactive ion etching lag and undercutting. Numerical results are compared with experimental data and a good agreement is found except close to the material interface where the slope of the surface is large. This error is attributed to a purely energy dependent yield used in the simulations.
Single-particle electron cryomicroscopy is an essential tool for high-resolution 3D reconstruction of proteins and other biological macromolecules. An important challenge in cryo-EM is the reconstruction of non-rigid ...
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Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attai...
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Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep...
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An adaptive modeling method (AMM) that couples a deep neural network potential and a classical force field is introduced to address the accuracy-efficiency dilemma faced by the molecular simulation community. The AMM ...
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Dislocation motion governs the strength and ductility of metals, and the Peierls stress (σp) quantifies dislocation mobility. σp measurements carry substantial uncertainty in face-centered cubic (fcc) metals, and σ...
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Dislocation motion governs the strength and ductility of metals, and the Peierls stress (σp) quantifies dislocation mobility. σp measurements carry substantial uncertainty in face-centered cubic (fcc) metals, and σp values can differ by up to two orders of magnitude. We perform first-principles simulations based on orbital-free density functional theory (OFDFT) to calculate the most accurate currently possible σp for the motion of 12〈110〉111 dislocations in fcc Al. We predict the σps of screw and edge dislocations (dissociated in their equilibrium state) to be 1.9×10−4G and 4.9×10−5G, respectively (G is the shear modulus). These values fall within the range of measurements from mechanical deformation tests (10−4–10−5G). OFDFT also finds a new metastable structure for a screw dislocation not seen in earlier simulations, in which a dislocation core on the glide plane does not dissociate into partials. The corresponding σp for this undissociated dislocation is predicted to be 1.1×10−2G, which agrees with typical Bordoni peak measurements (10−2–10−3G). The calculated σps for dissociated and undissociated screw dislocations differ by two orders of magnitude. The presence of undissociated, as well as dissociated, screw dislocations may resolve the decades-long mystery in fcc metals regarding the two orders of magnitude discrepancy in σp measurements.
The generative adversarial network (GAN) is a well-known model for learning high-dimensional distributions, but the mechanism for its generalization ability is not understood. In particular, GAN is vulnerable to the m...
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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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A simple approach is proposed to obtain complexity controls for neural networks with general activation functions. The approach is motivated by approximating the general activation functions with one-dimensional ReLU ...
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Motivated by models of human decision making, we consider a heuristic solution for explore-exploit problems. In a numerical example we show that, with appropriate parameter values, the algorithm performs well. However...
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ISBN:
(纸本)9781467320658
Motivated by models of human decision making, we consider a heuristic solution for explore-exploit problems. In a numerical example we show that, with appropriate parameter values, the algorithm performs well. However, the parameters of the algorithm trade off exploration against exploitation in a complicated way so that finding the optimal parameter values is not obvious. We show that the optimal parameter values can be analytically computed in some cases and prove that suboptimal parameter tunings can provide robustness to modeling error. The analytic results suggest a feedback control law for dynamically optimizing parameters.
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