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The Independence Postulate (IP) is a finitary Church-Turing Thesis, saying mathematical sequences are independent from physical ones. Modelling observations as infinite sequences of real numbers, IP implies the existence of anomalies.

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Evaluating the performance of Simultaneous Localization and Mapping (SLAM) algorithms is essential for scientists and users of robotic systems alike. But there are a multitude different permutations of possible options of hardware setups and algorithm configurations, as well as different datasets and algorithms, such that it is infeasible to thoroughly compare SLAM systems against the full state of the art. To solve that we present the SLAM Hive Benchmarking Suite, which is able to analyze SLAM algorithms in thousands of mapping runs, through its utilization of container technology and deployment in the cloud. This paper presents the architecture and open source implementation of SLAM Hive and compares it to existing efforts on SLAM evaluation. We perform mapping runs of many of the most popular visual and LiDAR based SLAM algorithms against commonly used datasets and show how SLAM Hive and then be used to conveniently analyze the results against various aspects. Through this we envision that SLAM Hive can become an essential tool for proper comparisons and evaluations of SLAM algorithms and thus drive the scientific development in the research on SLAM. The open source software as well as a demo to show the live analysis of 100s of mapping runs can be found on our SLAM Hive website.

Q-learning is one of the most well-known Reinforcement Learning algorithms. There have been tremendous efforts to develop this algorithm using neural networks. Bootstrapped Deep Q-Learning Network is amongst them. It utilizes multiple neural network heads to introduce diversity into Q-learning. Diversity can sometimes be viewed as the amount of reasonable moves an agent can take at a given state, analogous to the definition of the exploration ratio in RL. Thus, the performance of Bootstrapped Deep Q-Learning Network is deeply connected with the level of diversity within the algorithm. In the original research, it was pointed out that a random prior could improve the performance of the model. In this article, we further explore the possibility of replacing priors with noise and sample the noise from a Gaussian distribution to introduce more diversity into this algorithm. We conduct our experiment on the Atari benchmark and compare our algorithm to both the original and other related algorithms. The results show that our modification of the Bootstrapped Deep Q-Learning algorithm achieves significantly higher evaluation scores across different types of Atari games. Thus, we conclude that replacing priors with noise can improve Bootstrapped Deep Q-Learning's performance by ensuring the integrity of diversities.

Purpose:Generative Artificial Intelligence (GAI) models, such as ChatGPT, may inherit or amplify societal biases due to their training on extensive datasets. With the increasing usage of GAI by students, faculty, and staff in higher education institutions (HEIs), it is urgent to examine the ethical issues and potential biases associated with these technologies. Design/Approach/Methods:This scoping review aims to elucidate how biases related to GAI in HEIs have been researched and discussed in recent academic publications. We categorized the potential societal biases that GAI might cause in the field of higher education. Our review includes articles written in English, Chinese, and Japanese across four main databases, focusing on GAI usage in higher education and bias. Findings:Our findings reveal that while there is meaningful scholarly discussion around bias and discrimination concerning LLMs in the AI field, most articles addressing higher education approach the issue superficially. Few articles identify specific types of bias under different circumstances, and there is a notable lack of empirical research. Most papers in our review focus primarily on educational and research fields related to medicine and engineering, with some addressing English education. However, there is almost no discussion regarding the humanities and social sciences. Additionally, a significant portion of the current discourse is in English and primarily addresses English-speaking contexts. Originality/Value:To the best of our knowledge, our study is the first to summarize the potential societal biases in higher education. This review highlights the need for more in-depth studies and empirical work to understand the specific biases that GAI might introduce or amplify in educational settings, guiding the development of more ethical AI applications in higher education.

Diffusion models (DMs) have gained attention in Missing Data Imputation (MDI), but there remain two long-neglected issues to be addressed: (1). Inaccurate Imputation, which arises from inherently sample-diversification-pursuing generative process of DMs. (2). Difficult Training, which stems from intricate design required for the mask matrix in model training stage. To address these concerns within the realm of numerical tabular datasets, we introduce a novel principled approach termed Kernelized Negative Entropy-regularized Wasserstein gradient flow Imputation (KnewImp). Specifically, based on Wasserstein gradient flow (WGF) framework, we first prove that issue (1) stems from the cost functionals implicitly maximized in DM-based MDI are equivalent to the MDI's objective plus diversification-promoting non-negative terms. Based on this, we then design a novel cost functional with diversification-discouraging negative entropy and derive our KnewImp approach within WGF framework and reproducing kernel Hilbert space. After that, we prove that the imputation procedure of KnewImp can be derived from another cost functional related to the joint distribution, eliminating the need for the mask matrix and hence naturally addressing issue (2). Extensive experiments demonstrate that our proposed KnewImp approach significantly outperforms existing state-of-the-art methods.

Attention Deficit Hyperactivity Disorder (ADHD) is a neurodevelopmental condition characterized by inattention, hyperactivity, and impulsivity, which can significantly impact an individual's daily functioning and quality of life. Occupational therapy plays a crucial role in managing ADHD by fostering the development of skills needed for daily living and enhancing an individual's ability to participate fully in school, home, and social situations. Recent studies highlight the potential of integrating Large Language Models (LLMs) like ChatGPT and Socially Assistive Robots (SAR) to improve psychological treatments. This integration aims to overcome existing limitations in mental health therapy by providing tailored support and adapting to the unique needs of this sensitive group. However, there remains a significant gap in research exploring the combined use of these advanced technologies in ADHD therapy, suggesting an opportunity for novel therapeutic approaches. Thus, we integrated two advanced language models, ChatGPT-4 Turbo and Claude-3 Opus, into a robotic assistant to explore how well each model performs in robot-assisted interactions. Additionally, we have compared their performance in a simulated therapy scenario to gauge their effectiveness against a clinically validated customized model. The results of this study show that ChatGPT-4 Turbo excelled in performance and responsiveness, making it suitable for time-sensitive applications. Claude-3 Opus, on the other hand, showed strengths in understanding, coherence, and ethical considerations, prioritizing safe and engaging interactions. Both models demonstrated innovation and adaptability, but ChatGPT-4 Turbo offered greater ease of integration and broader language support. The selection between them hinges on the specific demands of ADHD therapy.

Kolmogorov-Arnold Networks (KANs) have very recently been introduced into the world of machine learning, quickly capturing the attention of the entire community. However, KANs have mostly been tested for approximating complex functions or processing synthetic data, while a test on real-world tabular datasets is currently lacking. In this paper, we present a benchmarking study comparing KANs and Multi-Layer Perceptrons (MLPs) on tabular datasets. The study evaluates task performance and training times. From the results obtained on the various datasets, KANs demonstrate superior or comparable accuracy and F1 scores, excelling particularly in datasets with numerous instances, suggesting robust handling of complex data. We also highlight that this performance improvement of KANs comes with a higher computational cost when compared to MLPs of comparable sizes.

Physics-Informed Neural Networks (PINNs) have gained popularity in scientific computing in recent years. However, they often fail to achieve the same level of accuracy as classical methods in solving differential equations. In this paper, we identify two sources of this issue in the case of Cauchy problems: the use of $L^2$ residuals as objective functions and the approximation gap of neural networks. We show that minimizing the sum of $L^2$ residual and initial condition error is not sufficient to guarantee the true solution, as this loss function does not capture the underlying dynamics. Additionally, neural networks are not capable of capturing singularities in the solutions due to the non-compactness of their image sets. This, in turn, influences the existence of global minima and the regularity of the network. We demonstrate that when the global minimum does not exist, machine precision becomes the predominant source of achievable error in practice. We also present numerical experiments in support of our theoretical claims.

We provide both a theoretical and empirical analysis of the Mean-Median Difference (MM) and Partisan Bias (PB), which are both symmetry metrics intended to detect gerrymandering. We consider vote-share, seat-share pairs $(V, S)$ for which one can construct election data having vote share $V$ and seat share $S$, and turnout is equal in each district. We calculate the range of values that MM and PB can achieve on that constructed election data. In the process, we find the range of vote-share, seat share pairs $(V, S)$ for which there is constructed election data with vote share $V$, seat share $S$, and $MM=0$, and see that the corresponding range for PB is the same set of $(V,S)$ pairs. We show how the set of such $(V,S)$ pairs allowing for $MM=0$ (and $PB=0$) changes when turnout in each district is allowed to be different. Although the set of $(V,S)$ pairs for which there is election data with $MM=0$ is the same as the set of $(V,S)$ pairs for which there is election data with $PB=0$, the range of possible values for MM and PB on a fixed $(V, S)$ is different. Additionally, for a fixed constructed election outcome, the values of the Mean-Median Difference and Partisan Bias can theoretically be as large as 0.5. We show empirically that these two metric values can differ by as much as 0.33 in US congressional map data. We use both neutral ensemble analysis and the short-burst method to show that neither the Mean-Median Difference nor the Partisan Bias can reliably detect when a districting map has an extreme number of districts won by a particular party. Finally, we give additional empirical and logical arguments in an attempt to explain why other metrics are better at detecting when a districting map has an extreme number of districts won by a particular party.

Comprehensive evaluation is one of the basis of experimental science. In High-Performance Graph Processing, a thorough evaluation of contributions becomes more achievable by supporting common input formats over different frameworks. However, each framework creates its specific format, which may not support reading large-scale real-world graph datasets. This shows a demand for high-performance libraries capable of loading graphs to (i) accelerate designing new graph algorithms, (ii) to evaluate the contributions on a wide range of graph algorithms, and (iii) to facilitate easy and fast comparison over different graph frameworks. To that end, we present ParaGrapher, a high-performance API and library for loading large-scale and compressed graphs. ParaGrapher supports different types of requests for accessing graphs in shared- and distributed-memory and out-of-core graph processing. We explain the design of ParaGrapher and present a performance model of graph decompression, which is used for evaluation of ParaGrapher over three storage types. Our evaluation shows that by decompressing compressed graphs in WebGraph format, ParaGrapher delivers up to 3.2 times speedup in loading and up to 5.2 times speedup in end-to-end execution in comparison to the binary and textual formats. ParaGrapher is available online on //blogs.qub.ac.uk/DIPSA/ParaGrapher/.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

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