In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simul...
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We present an alternative type of parity-time (PT)-symmetric generalized Scarf-II potentials, which makes possible for non-Hermitian Hamiltonians in the classical linear Schrödinger system to possess fully real s...
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We present an alternative type of parity-time (PT)-symmetric generalized Scarf-II potentials, which makes possible for non-Hermitian Hamiltonians in the classical linear Schrödinger system to possess fully real spectra with unique features such as the multiple PT-symmetric breaking behaviors and to support one-dimensional (1D) stable PT-symmetric solitons of power-law waveform, namely power-law solitons, in focusing Kerr-type nonlinear media. Moreover, PT-symmetric high-order solitons are also derived numerically in 1D and 2D settings. Around the exactly obtained nonlinear propagation constants, families of 1D and 2D localized nonlinear modes are also found numerically. The majority of fundamental nonlinear modes can still keep steady in general, whereas the 1D multipeak solitons and 2D vortex solitons are usually susceptible to suffering from instability. Likewise, similar results occur in the defocusing Kerr-nonlinear media. The obtained results will be useful for understanding the complex dynamics of nonlinear waves that form in PT-symmetric nonlinear media in other physical contexts.
Out-of-distribution (OOD) detection aims to identify OOD data based on representations extracted from well-trained deep models. However, existing methods largely ignore the reprogramming property of deep models and th...
ISBN:
(纸本)9781713871088
Out-of-distribution (OOD) detection aims to identify OOD data based on representations extracted from well-trained deep models. However, existing methods largely ignore the reprogramming property of deep models and thus may not fully unleash their intrinsic strength: without modifying parameters of a well-trained deep model, we can reprogram this model for a new purpose via data-level manipulation (e.g., adding a specific feature perturbation to the data). This property motivates us to reprogram a classification model to excel at OOD detection (a new task), and thus we propose a general methodology named watermarking in this paper. Specifically, we learn a unified pattern that is superimposed onto features of original data, and the model's detection capability is largely boosted after watermarking. Extensive experiments verify the effectiveness of watermarking, demonstrating the significance of the reprogramming property of deep models in OOD detection.
All matter is made up of fermions — one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state....
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A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major sur...
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Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning ...
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Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability. Methods: By hypothesizing that deep feature extraction can be modeled as a spatiotemporally continuous process, we designed a novel deep learning model, neural ODE, in which deep feature extraction was governed by an ODE without explicit expression. The dynamics of 1) MR images after interactions with the deep neural network and 2) segmentation formation can thus be visualized after solving ODE. An accumulative contribution curve (ACC) was designed to quantitatively evaluate each MR image's utilization by the deep neural network towards the final segmentation results. The proposed neural ODE model was demonstrated using 369 glioma patients with a 4-modality mp-MRI protocol: T1, contrast-enhanced T1 (T1-Ce), T2, and FLAIR. Three neural ODE models were trained to segment enhancing tumor (ET), tumor core (TC), and whole tumor (WT), respectively. The key MR modalities with significant utilization by deep neural network were identified based on ACC analysis. Segmentation results by deep neural networks using only the key MR modalities were compared to the ones using all 4 MR modalities in terms of Dice coefficient, accuracy, sensitivity, and specificity. Results: All neural ODE models successfully illustrated image dynamics as expected. ACC analysis identified T1-Ce as the only key modality in ET and TC segmentations, while both FLAIR and T2 were key modalities in WT segmentation. Compared to the U-Net results using all 4 MR modalities, Dice coefficient of ET (0.784→0.775), TC (0.760→0.758), and WT (0.841→0.837) using the key modalities only had minimal differences without significance. Accuracy, sensitivity, and specificity results demonstrated the same patterns. Conclusion: The neural ODE model offers a new tool for optimizing the deep lear
Refereeing in sports is about fairness. The referee's job is to balance what the player with the ball thinks is fair with what the player trying to take the ball thinks is fair. Referees are judges on those two op...
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While coursework provides undergraduate data science students with some relevant analytic skills, many are not given the rich experiences with data and computing they need to be successful in the workplace. Additional...
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The paper addresses the problem of fusing multiple data sources in freeway networks. The incremental Unscented Kalman Filter (UKF) and the Unscented Information Filter (UIF) are developed based on cell-transmission mo...
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