亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

This paper aims to provide a machine learning framework to simulate two-phase flow in porous media. The proposed algorithm is based on Physics-informed neural networks (PINN). A novel residual-based adaptive PINN is developed and compared with the residual-based adaptive refinement (RAR) method and with PINN with fixed collocation points. The proposed algorithm is expected to have great potential to be applied to different fields where adaptivity is needed. In this paper, we focus on the two-phase flow in porous media problem. We provide two numerical examples to show the effectiveness of the new algorithm. It is found that adaptivity is essential to capture moving flow fronts. We show how the results obtained through this approach are more accurate than using RAR method or PINN with fixed collocation points, while having a comparable computational cost.

Endoscopic Mayo score and Ulcerative Colitis Endoscopic Index of Severity are commonly used scoring systems for the assessment of endoscopic severity of ulcerative colitis. They are based on assigning a score in relation to the disease activity, which creates a rank among the levels, making it an ordinal regression problem. On the other hand, most studies use categorical cross-entropy loss function, which is not optimal for the ordinal regression problem, to train the deep learning models. In this study, we propose a novel loss function called class distance weighted cross-entropy (CDW-CE) that respects the order of the classes and takes the distance of the classes into account in calculation of cost. Experimental evaluations show that CDW-CE outperforms the conventional categorical cross-entropy and CORN framework, which is designed for the ordinal regression problems. In addition, CDW-CE does not require any modifications at the output layer and is compatible with the class activation map visualization techniques.

Attention networks such as transformers have been shown powerful in many applications ranging from natural language processing to object recognition. This paper further considers their robustness properties from both theoretical and empirical perspectives. Theoretically, we formulate a variant of attention networks containing linearized layer normalization and sparsemax activation, and reduce its robustness verification to a Mixed Integer Programming problem. Apart from a na\"ive encoding, we derive tight intervals from admissible perturbation regions and examine several heuristics to speed up the verification process. More specifically, we find a novel bounding technique for sparsemax activation, which is also applicable to softmax activation in general neural networks. Empirically, we evaluate our proposed techniques with a case study on lane departure warning and demonstrate a performance gain of approximately an order of magnitude. Furthermore, although attention networks typically deliver higher accuracy than general neural networks, contrasting its robustness against a similar-sized multi-layer perceptron surprisingly shows that they are not necessarily more robust.

This paper studies the minimum weight set cover (MinWSC) problem with a {\em small neighborhood cover} (SNC) property proposed by Agarwal {\it et al.} in \cite{Agarwal.}. A parallel algorithm for MinWSC with $\tau$-SNC property is presented, obtaining approximation ratio $\tau(1+3\varepsilon)$ in $O(L\log_{1+\varepsilon}\frac{n^3}{\varepsilon^2}+ 4\tau^{3}2^\tau L^2\log n)$ rounds, where $0< \varepsilon <\frac{1}{2}$ is a constant, $n$ is the number of elements, and $L$ is a parameter related to SNC property. Our results not only improve the approximation ratio obtained in \cite{Agarwal.}, but also answer two questions proposed in \cite{Agarwal.}.

The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling conditions on the energy and the geometric properties of the folding arc in dependence on the small sheet thickness. The resulting two-dimensional model is a piecewise nonlinear Kirchhoff plate bending model with a continuity condition at the folding arc. A discontinuous Galerkin method and an iterative scheme are devised for the accurate numerical approximation of large deformations.

In the present work we tackle the problem of finding the optimal price tariff to be set by a risk-averse electric retailer participating in the pool and whose customers are price-sensitive. We assume that the retailer has access to a sufficiently large smart-meter dataset from which it can statistically characterize the relationship between the tariff price and the demand load of its clients. Three different models are analyzed to predict the aggregated load as a function of the electricity prices and other parameters, as humidity or temperature. More specifically, we train linear regression (predictive) models to forecast the resulting demand load as a function of the retail price. Then we will insert this model in a quadratic optimization problem which evaluates the optimal price to be offered. This optimization problem accounts for different sources of uncertainty including consumer's response, pool prices and renewable source availability, and relies on a stochastic and risk-averse formulation. In particular, one important contribution of this work is to base the scenario generation and reduction procedure on the statistical properties of the resulting predictive model. This allows us to properly quantify (data-driven) not only the expected value but the level of uncertainty associated with the main problem parameters. Moreover, we consider both standard forward based contracts and the recently introduced power purchase agreement contracts as risk-hedging tools for the retailer. The results are promising as profits are found for the retailer with highly competitive prices and some possible improvements are shown if richer datasets could be available in the future. A realistic case study and multiple sensitivity analyses have been performed to characterize the risk-aversion behavior of the retailer considering price-sensitive consumers.

Experimental aeroacoustics is concerned with the estimation of acoustic source power distributions, which are for instance caused by fluid structure interactions on scaled aircraft models inside a wind tunnel, from microphone array measurements of associated sound pressure fluctuations. In the frequency domain aeroacoustic sound propagation can be modelled as a random source problem for a convected Helmholtz equation. This article is concerned with the inverse random source problem to recover the support of an uncorrelated aeroacoustic source from correlations of observed pressure signals. We show a variant of the factorization method from inverse scattering theory can be used for this purpose. We also discuss a surprising relation between the factorization method and a commonly used beamforming algorithm from experimental aeroacoustics, which is known as Capon's method or as the minimum variance method. Numerical examples illustrate our theoretical findings.

We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the objective function on sets of size two. We begin with a negative result that no algorithm using only $k$-wise information can guarantee performance better than $k/n$. We present two algorithms that utilize only pairwise information about the function and characterize their performance relative to the optimal, which depends on the curvature of the submodular function. Additionally, if the submodular function possess a property called supermodularity of conditioning, then we can provide a method to bound the performance based purely on pairwise information. The proposed algorithms offer significant computational speedups over a traditional greedy strategy. A by-product of our study is the introduction of two new notions of curvature, the $k$-Marginal Curvature and the $k$-Cardinality Curvature. Finally, we present experiments highlighting the performance of our proposed algorithms in terms of approximation and time complexity.

Adversarial attacks to image classification systems present challenges to convolutional networks and opportunities for understanding them. This study suggests that adversarial perturbations on images lead to noise in the features constructed by these networks. Motivated by this observation, we develop new network architectures that increase adversarial robustness by performing feature denoising. Specifically, our networks contain blocks that denoise the features using non-local means or other filters; the entire networks are trained end-to-end. When combined with adversarial training, our feature denoising networks substantially improve the state-of-the-art in adversarial robustness in both white-box and black-box attack settings. On ImageNet, under 10-iteration PGD white-box attacks where prior art has 27.9% accuracy, our method achieves 55.7%; even under extreme 2000-iteration PGD white-box attacks, our method secures 42.6% accuracy. A network based on our method was ranked first in Competition on Adversarial Attacks and Defenses (CAAD) 2018 --- it achieved 50.6% classification accuracy on a secret, ImageNet-like test dataset against 48 unknown attackers, surpassing the runner-up approach by ~10%. Code and models will be made publicly available.

In this paper we introduce a covariance framework for the analysis of EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. We perform a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. Apart from that, we illustrate our method on real EEG and MEG data sets. The proposed covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed for accurate dipole localization, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, such as in combined EEG/fMRI experiments in which the correlation between EEG and fMRI signals is investigated.