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

Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, differential dynamic programming (DDP) provides an efficient approach to transcribe the optimal control problem into a finite-dimensional problem while optimally exploiting the sparsity induced by time. On the other hand, augmented Lagrangian methods make it possible to formulate efficient algorithms with advanced constraint-satisfaction strategies. In this paper, we propose to combine these two approaches into an efficient optimal control algorithm accepting both equality and inequality constraints. Based on the augmented Lagrangian literature, we first derive a generic primal-dual augmented Lagrangian strategy for nonlinear problems with equality and inequality constraints. We then apply it to the dynamic programming principle to solve the value-greedy optimization problems inherent to the backward pass of DDP, which we combine with a dedicated globalization strategy, resulting in a Newton-like algorithm for solving constrained trajectory optimization problems. Contrary to previous attempts of formulating an augmented Lagrangian version of DDP, our approach exhibits adequate convergence properties without any switch in strategies. We empirically demonstrate its interest with several case-studies from the robotics literature.

The area under the ROC curve (AUC) is one of the most widely used performance measures for classification models in machine learning. However, it summarizes the true positive rates (TPRs) over all false positive rates (FPRs) in the ROC space, which may include the FPRs with no practical relevance in some applications. The partial AUC, as a generalization of the AUC, summarizes only the TPRs over a specific range of the FPRs and is thus a more suitable performance measure in many real-world situations. Although partial AUC optimization in a range of FPRs had been studied, existing algorithms are not scalable to big data and not applicable to deep learning. To address this challenge, we cast the problem into a non-smooth difference-of-convex (DC) program for any smooth predictive functions (e.g., deep neural networks), which allowed us to develop an efficient approximated gradient descent method based on the Moreau envelope smoothing technique, inspired by recent advances in non-smooth DC optimization. To increase the efficiency of large data processing, we used an efficient stochastic block coordinate update in our algorithm. Our proposed algorithm can also be used to minimize the sum of ranked range loss, which also lacks efficient solvers. We established a complexity of $\tilde O(1/\epsilon^6)$ for finding a nearly $\epsilon$-critical solution. Finally, we numerically demonstrated the effectiveness of our proposed algorithms for both partial AUC maximization and sum of ranked range loss minimization.

GitHub Copilot is an artificial intelligence model for automatically generating source code from natural language problem descriptions. Since June 2022, Copilot has officially been available for free to all students as a plug-in to development environments like Visual Studio Code. Prior work exploring OpenAI Codex, the underlying model that powers Copilot, has shown it performs well on typical CS1 problems thus raising concerns about the impact it will have on how introductory programming courses are taught. However, little is known about the types of problems for which Copilot does not perform well, or about the natural language interactions that a student might have with Copilot when resolving errors. We explore these questions by evaluating the performance of Copilot on a publicly available dataset of 166 programming problems. We find that it successfully solves around half of these problems on its very first attempt, and that it solves 60\% of the remaining problems using only natural language changes to the problem description. We argue that this type of prompt engineering, which we believe will become a standard interaction between human and Copilot when it initially fails, is a potentially useful learning activity that promotes computational thinking skills, and is likely to change the nature of code writing skill development.

Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not), and for identifying strategies for regularization or efficiency improvements. Despite recent progress, e.g., comparing vision transformers to CNNs, systematic comparison of function, especially across different networks, remains difficult and is often carried out layer by layer. Approaches such as canonical correlation analysis (CCA) are applicable in principle, but have been sparingly used so far. In this paper, we revisit a (less widely known) from statistics, called distance correlation (and its partial variant), designed to evaluate correlation between feature spaces of different dimensions. We describe the steps necessary to carry out its deployment for large scale models -- this opens the door to a surprising array of applications ranging from conditioning one deep model w.r.t. another, learning disentangled representations as well as optimizing diverse models that would directly be more robust to adversarial attacks. Our experiments suggest a versatile regularizer (or constraint) with many advantages, which avoids some of the common difficulties one faces in such analyses. Code is at //github.com/zhenxingjian/Partial_Distance_Correlation.

The work is devoted to the construction of a new type of intervals -- functional intervals. These intervals are built on the idea of expanding boundaries from numbers to functions. Functional intervals have shown themselves to be promising for further study and use, since they have more rich algebraic properties compared to classical intervals lamy. In the work, linear functional arithmetic was constructed from one variable. This arithmetic was applied to solve such problems of interval analysis, as minimization of a function on an interval and finding zeros of a function on an interval. Results of numerical experiments for linear functional arithmetic showed a high order of convergence and a higher speed the growth of algorithms when using intervals of a new type, despite the fact that the calculations did not use information about derivative function. Also in the work, a modification of the minimization algorithms functions of several variables, based on the use of the function rational intervals of several variables. As a result, it was Improved speedup of algorithms, but only up to a certain number of unknowns.

Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the underlying symmetry and conservation laws of physics. However, so far, every descriptor newly proposed for an ML model has required a cumbersome and mathematically tedious remodeling. We therefore propose using modern techniques from algorithmic differentiation within the ML modeling process -- effectively enabling the usage of novel descriptors or models fully automatically at an order of magnitude higher computational efficiency. This paradigmatic approach enables not only a versatile usage of novel representations and the efficient computation of larger systems -- all of high value to the FF community -- but also the simple inclusion of further physical knowledge such as higher-order information (e.g. Hessians, more complex partial differential equations constraints etc.), even beyond the presented FF domain.

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, their application for clustering has some limitations. Miller and Harrison (2014) proved posterior inconsistency in the number of clusters when the true number of clusters is finite for Dirichlet process and Pitman--Yor process mixture models. In this work, we extend this result to additional Bayesian nonparametric priors such as Gibbs-type processes and finite-dimensional representations of them. The latter include the Dirichlet multinomial process and the recently proposed Pitman--Yor and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a post-processing algorithm introduced by Guha et al. (2021) for the Dirichlet process extends to more general models and provides a consistent method to estimate the number of components.

In this study we consider unconditionally non-oscillatory, high order implicit time marching based on time-limiters. The first aspect of our work is to propose the high resolution Limited-DIRK3 (L-DIRK3) scheme for conservation laws and convection-diffusion equations in the method-of-lines framework. The scheme can be used in conjunction with an arbitrary high order spatial discretization scheme such as 5th order WENO scheme. It can be shown that the strongly S-stable DIRK3 scheme is not SSP and may introduce strong oscillations under large time step. To overcome the oscillatory nature of DIRK3, the key idea of L-DIRK3 scheme is to apply local time-limiters (K.Duraisamy, J.D.Baeder, J-G Liu), with which the order of accuracy in time is locally dropped to first order in the regions where the evolution of solution is not smooth. In this way, the monotonicity condition is locally satisfied, while a high order of accuracy is still maintained in most of the solution domain. For convenience of applications to systems of equations, we propose a new and simple construction of time-limiters which allows flexible choice of reference quantity with minimal computation cost. Another key aspect of our work is to extend the application of time-limiter schemes to multidimensional problems and convection-diffusion equations. Numerical experiments for scalar/systems of equations in one- and two-dimensions confirm the high resolution and the improved stability of L-DIRK3 under large time steps. Moreover, the results indicate the potential of time-limiter schemes to serve as a generic and convenient methodology to improve the stability of arbitrary DIRK methods.

Current treatment planning of patients diagnosed with a brain tumor, such as glioma, could significantly benefit by accessing the spatial distribution of tumor cell concentration. Existing diagnostic modalities, e.g. magnetic resonance imaging (MRI), contrast sufficiently well areas of high cell density. In gliomas, however, they do not portray areas of low cell concentration, which can often serve as a source for the secondary appearance of the tumor after treatment. To estimate tumor cell densities beyond the visible boundaries of the lesion, numerical simulations of tumor growth could complement imaging information by providing estimates of full spatial distributions of tumor cells. Over recent years a corpus of literature on medical image-based tumor modeling was published. It includes different mathematical formalisms describing the forward tumor growth model. Alongside, various parametric inference schemes were developed to perform an efficient tumor model personalization, i.e. solving the inverse problem. However, the unifying drawback of all existing approaches is the time complexity of the model personalization which prohibits a potential integration of the modeling into clinical settings. In this work, we introduce a deep learning based methodology for inferring the patient-specific spatial distribution of brain tumors from T1Gd and FLAIR MRI medical scans. Coined as Learn-Morph-Infer the method achieves real-time performance in the order of minutes on widely available hardware and the compute time is stable across tumor models of different complexity, such as reaction-diffusion and reaction-advection-diffusion models. We believe the proposed inverse solution approach not only bridges the way for clinical translation of brain tumor personalization but can also be adopted to other scientific and engineering domains.

As one of the challenging NLP tasks, designing math word problem (MWP) solvers has attracted increasing research attention for the past few years. In previous work, models designed by taking into account the properties of the binary tree structure of mathematical expressions at the output side have achieved better performance. However, the expressions corresponding to a MWP are often diverse (e.g., $n_1+n_2 \times n_3-n_4$, $n_3\times n_2-n_4+n_1$, etc.), and so are the corresponding binary trees, which creates difficulties in model learning due to the non-deterministic output space. In this paper, we propose the Structure-Unified M-Tree Coding Solver (SUMC-Solver), which applies a tree with any M branches (M-tree) to unify the output structures. To learn the M-tree, we use a mapping to convert the M-tree into the M-tree codes, where codes store the information of the paths from tree root to leaf nodes and the information of leaf nodes themselves, and then devise a Sequence-to-Code (seq2code) model to generate the codes. Experimental results on the widely used MAWPS and Math23K datasets have demonstrated that SUMC-Solver not only outperforms several state-of-the-art models under similar experimental settings but also performs much better under low-resource conditions.