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

Achieving accurate approximations to solutions of large linear systems is crucial, especially when those systems utilize real-world data. A consequence of using real-world data is that there will inevitably be missingness. Current approaches for dealing with missing data, such as deletion and imputation, can introduce bias. Recent studies proposed an adaptation of stochastic gradient descent (SGD) in specific missing-data models. In this work, we propose a new algorithm, $\ell$-tuple mSGD, for the setting in which data is missing in a block-wise, tuple pattern. We prove that our proposed method uses unbiased estimates of the gradient of the least squares objective in the presence of tuple missing data. We also draw connections between $\ell$-tuple mSGD and previously established SGD-type methods for missing data. Furthermore, we prove our algorithm converges when using updating step sizes and empirically demonstrate the convergence of $\ell$-tuple mSGD on synthetic data. Lastly, we evaluate $\ell$-tuple mSGD applied to real-world continuous glucose monitoring (CGM) device data.

We introduce time-ordered multibody interactions to describe complex systems manifesting temporal as well as multibody dependencies. First, we show how the dynamics of multivariate Markov chains can be decomposed in ensembles of time-ordered multibody interactions. Then, we present an algorithm to extract those interactions from data capturing the system-level dynamics of node states and a measure to characterize the complexity of interaction ensembles. Finally, we experimentally validate the robustness of our algorithm against statistical errors and its efficiency at inferring parsimonious interaction ensembles.

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method. In particular, we consider the framework of multi-level Monte Carlo for parametric expectations and propose modifications of the MLMC estimator, error estimation procedure, and adaptive MLMC parameter selection to ensure the estimation of the CVaR and sensitivities for a given design with a prescribed accuracy. We then propose combining the MLMC framework with an alternating inexact minimisation-gradient descent algorithm, for which we prove exponential convergence in the optimisation iterations under the assumptions of strong convexity and Lipschitz continuity of the gradient of the objective function. We demonstrate the performance of our approach on two numerical examples of practical relevance, which evidence the same optimal asymptotic cost-tolerance behaviour as standard MLMC methods for fixed design computations of output expectations.

We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. Building on the findings of the work \cite{gotoh2018robust}, we study the connections between a class of DRO and the Taguchi method in the context of robust design optimization. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

Since the tension instability was discovered in updated Lagrangian smoothed particle hydrodynamics (ULSPH) at the end of the 20th century, researchers have made considerable efforts to suppress its occurrence. However, up to the present day, this problem has not been fundamentally resolved. In this paper, the concept of hourglass modes is firstly introduced into ULSPH, and the inherent causes of tension instability in elastic dynamics are clarified based on this brand-new perspective. Specifically, we present an essentially non-hourglass formulation by decomposing the shear acceleration with the Laplacian operator, and a comprehensive set of challenging benchmark cases for elastic dynamics is used to showcase that our method can completely eliminate tensile instability by resolving hourglass modes. The present results reveal the true origin of tension instability and challenge the traditional understanding of its sources, i.e., hourglass modes are the real culprit behind inducing this instability in tension zones rather that the tension itself. Furthermore, a time integration scheme known as dual-criteria time stepping is adopted into the simulation of solids for the first time, to significantly enhance computational efficiency.

We propose a novel surrogate modelling approach to efficiently and accurately approximate the response of complex dynamical systems driven by time-varying exogenous excitations over extended time periods. Our approach, namely manifold nonlinear autoregressive modelling with exogenous input (mNARX), involves constructing a problem-specific exogenous input manifold that is optimal for constructing autoregressive surrogates. The manifold, which forms the core of mNARX, is constructed incrementally by incorporating the physics of the system, as well as prior expert- and domain- knowledge. Because mNARX decomposes the full problem into a series of smaller sub-problems, each with a lower complexity than the original, it scales well with the complexity of the problem, both in terms of training and evaluation costs of the final surrogate. Furthermore, mNARX synergizes well with traditional dimensionality reduction techniques, making it highly suitable for modelling dynamical systems with high-dimensional exogenous inputs, a class of problems that is typically challenging to solve. Since domain knowledge is particularly abundant in physical systems, such as those found in civil and mechanical engineering, mNARX is well suited for these applications. We demonstrate that mNARX outperforms traditional autoregressive surrogates in predicting the response of a classical coupled spring-mass system excited by a one-dimensional random excitation. Additionally, we show that mNARX is well suited for emulating very high-dimensional time- and state-dependent systems, even when affected by active controllers, by surrogating the dynamics of a realistic aero-servo-elastic onshore wind turbine simulator. In general, our results demonstrate that mNARX offers promising prospects for modelling complex dynamical systems, in terms of accuracy and efficiency.

Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been many attempts to prove this link, especially in evolutionary game theory, yielding both negative and positive results. This paper presents a universal and intuitive approach to this link. We prove that static stability assures dynamic stability if agents' choices of switching strategies are rationalizable by introducing costs and constraints in those switching decisions. This idea guides us to define \textit{net }gains from switches as the payoff improvement after deducting the costs. Under rationalizable dynamics, an agent maximizes the expected net gain subject to the constraints. We prove that the aggregate maximized expected net gain works as a Lyapunov function. It also explains reasons behind the known negative results. While our analysis here is confined to myopic evolutionary dynamics in population games, our approach is applicable to more complex situations.

Recurrent neural networks (RNNs) have yielded promising results for both recognizing objects in challenging conditions and modeling aspects of primate vision. However, the representational dynamics of recurrent computations remain poorly understood, especially in large-scale visual models. Here, we studied such dynamics in RNNs trained for object classification on MiniEcoset, a novel subset of ecoset. We report two main insights. First, upon inference, representations continued to evolve after correct classification, suggesting a lack of the notion of being ``done with classification''. Second, focusing on ``readout zones'' as a way to characterize the activation trajectories, we observe that misclassified representations exhibit activation patterns with lower L2 norm, and are positioned more peripherally in the readout zones. Such arrangements help the misclassified representations move into the correct zones as time progresses. Our findings generalize to networks with lateral and top-down connections, and include both additive and multiplicative interactions with the bottom-up sweep. The results therefore contribute to a general understanding of RNN dynamics in naturalistic tasks. We hope that the analysis framework will aid future investigations of other types of RNNs, including understanding of representational dynamics in primate vision.

In this work, we consider the problem of building distribution-free prediction intervals with finite-sample conditional coverage guarantees. Conformal prediction (CP) is an increasingly popular framework for building prediction intervals with distribution-free guarantees, but these guarantees only ensure marginal coverage: the probability of coverage is averaged over a random draw of both the training and test data, meaning that there might be substantial undercoverage within certain subpopulations. Instead, ideally, we would want to have local coverage guarantees that hold for each possible value of the test point's features. While the impossibility of achieving pointwise local coverage is well established in the literature, many variants of conformal prediction algorithm show favorable local coverage properties empirically. Relaxing the definition of local coverage can allow for a theoretical understanding of this empirical phenomenon. We aim to bridge this gap between theoretical validation and empirical performance by proving achievable and interpretable guarantees for a relaxed notion of local coverage. Building on the localized CP method of Guan (2023) and the weighted CP framework of Tibshirani et al. (2019), we propose a new method, randomly-localized conformal prediction (RLCP), which returns prediction intervals that are not only marginally valid but also achieve a relaxed local coverage guarantee and guarantees under covariate shift. Through a series of simulations and real data experiments, we validate these coverage guarantees of RLCP while comparing it with the other local conformal prediction methods.