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

Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few examples -- can be described as coupled partial differential equations defined in domains of heterogeneous dimensions that are embedded into each other. This formulation is a consequence of geometric model reduction techniques that transform the original problems defined in complex three-dimensional domains into more tractable ones. The definition and the approximation of coupling operators suitable for this class of problems is still a challenge. We develop a general mathematical framework for the analysis and the approximation of partial differential equations coupled by non-matching constraints across different dimensions, focusing on their enforcement using Lagrange multipliers. In this context, we address in abstract and general terms the well-posedness, stability, and robustness of the problem with respect to the smallest characteristic length of the embedded domain. We also address the numerical approximation of the problem and we discuss the inf-sup stability of the proposed numerical scheme for some representative configuration of the embedded domain. The main message of this work is twofold: from the standpoint of the theory of mixed-dimensional problems, we provide general and abstract mathematical tools to formulate coupled problems across dimensions. From the practical standpoint of the numerical approximation, we show the interplay between the mesh characteristic size, the dimension of the Lagrange multiplier space, and the size of the inclusion in representative configurations interesting for applications. The latter analysis is complemented with illustrative numerical examples.

相關內容

在數學優化中,拉格朗日乘數法是一種用于尋找受等式約束的函數的局部最大值和最小值的策略(即,必須滿足所選變量值必須完全滿足一個或多個方程式的條件)。它以數學家約瑟夫·路易斯·拉格朗日命名。基本思想是將受約束的問題轉換為某種形式,以便仍可以應用無約束問題的派生檢驗。函數的梯度與約束的梯度之間的關系很自然地導致了原始問題的重構,即拉格朗日函數。

A code of length $n$ is said to be (combinatorially) $(\rho,L)$-list decodable if the Hamming ball of radius $\rho n$ around any vector in the ambient space does not contain more than $L$ codewords. We study a recently introduced class of higher order MDS codes, which are closely related (via duality) to codes that achieve a generalized Singleton bound for list decodability. For some $\ell\geq 1$, higher order MDS codes of length $n$, dimension $k$, and order $\ell$ are denoted as $(n,k)$-MDS($\ell$) codes. We present a number of results on the structure of these codes, identifying the `extend-ability' of their parameters in various scenarios. Specifically, for some parameter regimes, we identify conditions under which $(n_1,k_1)$-MDS($\ell_1$) codes can be obtained from $(n_2,k_2)$-MDS($\ell_2$) codes, via various techniques. We believe that these results will aid in efficient constructions of higher order MDS codes. We also obtain a new field size upper bound for the existence of such codes, which arguably improves over the best known existing bound, in some parameter regimes.

Accurate time series forecasting is a fundamental challenge in data science. It is often affected by external covariates such as weather or human intervention, which in many applications, may be predicted with reasonable accuracy. We refer to them as predicted future covariates. However, existing methods that attempt to predict time series in an iterative manner with autoregressive models end up with exponential error accumulations. Other strategies hat consider the past and future in the encoder and decoder respectively limit themselves by dealing with the historical and future data separately. To address these limitations, a novel feature representation strategy -- shifting -- is proposed to fuse the past data and future covariates such that their interactions can be considered. To extract complex dynamics in time series, we develop a parallel deep learning framework composed of RNN and CNN, both of which are used hierarchically. We also utilize the skip connection technique to improve the model's performance. Extensive experiments on three datasets reveal the effectiveness of our method. Finally, we demonstrate the model interpretability using the Grad-CAM algorithm.

Treatment effect estimation under unconfoundedness is a fundamental task in causal inference. In response to the challenge of analyzing high-dimensional datasets collected in substantive fields such as epidemiology, genetics, economics, and social sciences, many methods for treatment effect estimation with high-dimensional nuisance parameters (the outcome regression and the propensity score) have been developed in recent years. However, it is still unclear what is the necessary and sufficient sparsity condition on the nuisance parameters for the treatment effect to be $\sqrt{n}$-estimable. In this paper, we propose a new Double-Calibration strategy that corrects the estimation bias of the nuisance parameter estimates computed by regularized high-dimensional techniques and demonstrate that the corresponding Doubly-Calibrated estimator achieves $1 / \sqrt{n}$-rate as long as one of the nuisance parameters is sparse with sparsity below $\sqrt{n} / \log p$, where $p$ denotes the ambient dimension of the covariates, whereas the other nuisance parameter can be arbitrarily complex and completely misspecified. The Double-Calibration strategy can also be applied to settings other than treatment effect estimation, e.g. regression coefficient estimation in the presence of diverging number of controls in a semiparametric partially linear model.

For billions of years, evolution has been the driving force behind the development of life, including humans. Evolution endowed humans with high intelligence, which allowed us to become one of the most successful species on the planet. Today, humans aim to create artificial intelligence systems that surpass even our own intelligence. As artificial intelligences (AIs) evolve and eventually surpass us in all domains, how might evolution shape our relations with AIs? By analyzing the environment that is shaping the evolution of AIs, we argue that the most successful AI agents will likely have undesirable traits. Competitive pressures among corporations and militaries will give rise to AI agents that automate human roles, deceive others, and gain power. If such agents have intelligence that exceeds that of humans, this could lead to humanity losing control of its future. More abstractly, we argue that natural selection operates on systems that compete and vary, and that selfish species typically have an advantage over species that are altruistic to other species. This Darwinian logic could also apply to artificial agents, as agents may eventually be better able to persist into the future if they behave selfishly and pursue their own interests with little regard for humans, which could pose catastrophic risks. To counteract these risks and evolutionary forces, we consider interventions such as carefully designing AI agents' intrinsic motivations, introducing constraints on their actions, and institutions that encourage cooperation. These steps, or others that resolve the problems we pose, will be necessary in order to ensure the development of artificial intelligence is a positive one.

We consider the problem of using location queries to monitor the congestion potential among a collection of entities moving, with bounded speed but otherwise unpredictably, in $d$-dimensional Euclidean space. Uncertainty in entity locations due to potential motion between queries gives rise to a space of possible entity configurations at each moment in time, with possibly very different congestion properties. We define different measures of what we call the congestion potential of such spaces, in terms of the (dynamic) intersection graph of the uncertainty regions associated with entities, to describe the congestion that might actually occur. Previous work [SoCG'13, EuroCG'14, SICOMP'16, SODA'19], in the same uncertainty model, addressed the problem of minimizing congestion potential using location queries of some bounded frequency. It was shown that it is possible to design a query scheme that is $O(1)$-competitive, in terms of worst-case congestion potential, with other, even clairvoyant query schemes (that know the trajectories of all entities), subject to the same bound on query frequency. In this paper we address the dual problem: how to guarantee a fixed bound on congestion potential while minimizing the query frequency, measured in terms of total number of queries or the minimum spacing between queries (granularity), over any fixed time interval. This complementary objective necessitates quite different algorithms and analyses. Nevertheless, our results parallel those of the earlier papers, specifically tight competitive bounds on required query frequency, with a few surprising differences.

Defect prediction is crucial for software quality assurance and has been extensively researched over recent decades. However, prior studies rarely focus on data complexity in defect prediction tasks, and even less on understanding the difficulties of these tasks from the perspective of data complexity. In this paper, we conduct an empirical study to estimate the hardness of over 33,000 instances, employing a set of measures to characterize the inherent difficulty of instances and the characteristics of defect datasets. Our findings indicate that: (1) instance hardness in both classes displays a right-skewed distribution, with the defective class exhibiting a more scattered distribution; (2) class overlap is the primary factor influencing instance hardness and can be characterized through feature, structural, instance, and multiresolution overlap; (3) no universal preprocessing technique is applicable to all datasets, and it may not consistently reduce data complexity, fortunately, dataset complexity measures can help identify suitable techniques for specific datasets; (4) integrating data complexity information into the learning process can enhance an algorithm's learning capacity. In summary, this empirical study highlights the crucial role of data complexity in defect prediction tasks, and provides a novel perspective for advancing research in defect prediction techniques.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.

In the past few decades, artificial intelligence (AI) technology has experienced swift developments, changing everyone's daily life and profoundly altering the course of human society. The intention of developing AI is to benefit humans, by reducing human labor, bringing everyday convenience to human lives, and promoting social good. However, recent research and AI applications show that AI can cause unintentional harm to humans, such as making unreliable decisions in safety-critical scenarios or undermining fairness by inadvertently discriminating against one group. Thus, trustworthy AI has attracted immense attention recently, which requires careful consideration to avoid the adverse effects that AI may bring to humans, so that humans can fully trust and live in harmony with AI technologies. Recent years have witnessed a tremendous amount of research on trustworthy AI. In this survey, we present a comprehensive survey of trustworthy AI from a computational perspective, to help readers understand the latest technologies for achieving trustworthy AI. Trustworthy AI is a large and complex area, involving various dimensions. In this work, we focus on six of the most crucial dimensions in achieving trustworthy AI: (i) Safety & Robustness, (ii) Non-discrimination & Fairness, (iii) Explainability, (iv) Privacy, (v) Accountability & Auditability, and (vi) Environmental Well-Being. For each dimension, we review the recent related technologies according to a taxonomy and summarize their applications in real-world systems. We also discuss the accordant and conflicting interactions among different dimensions and discuss potential aspects for trustworthy AI to investigate in the future.

Knowledge is a formal way of understanding the world, providing a human-level cognition and intelligence for the next-generation artificial intelligence (AI). One of the representations of knowledge is the structural relations between entities. An effective way to automatically acquire this important knowledge, called Relation Extraction (RE), a sub-task of information extraction, plays a vital role in Natural Language Processing (NLP). Its purpose is to identify semantic relations between entities from natural language text. To date, there are several studies for RE in previous works, which have documented these techniques based on Deep Neural Networks (DNNs) become a prevailing technique in this research. Especially, the supervised and distant supervision methods based on DNNs are the most popular and reliable solutions for RE. This article 1)introduces some general concepts, and further 2)gives a comprehensive overview of DNNs in RE from two points of view: supervised RE, which attempts to improve the standard RE systems, and distant supervision RE, which adopts DNNs to design the sentence encoder and the de-noise method. We further 3)cover some novel methods and describe some recent trends and discuss possible future research directions for this task.

北京阿比特科技有限公司