We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.
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Mapping out reaction pathways and their corresponding activation barriers is a significant aspect of molecular simulation. Given their inherent complexity and nonlinearity, even generating a initial guess of these paths remains a challenging problem. Presented in this paper is an innovative approach that utilizes neural networks to generate initial guess for these reaction pathways. The proposed method is initiated by inputting the coordinates of the initial state, followed by progressive alterations to its structure. This iterative process culminates in the generation of the approximate representation of the reaction path and the coordinates of the final state. The application of this method extends to complex reaction pathways illustrated by organic reactions. Training was executed on the Transition1x dataset, an organic reaction pathway dataset. The results revealed generation of reactions that bore substantial similarities with the corresponding test data. The method's flexibility allows for reactions to be generated either to conform to predetermined conditions or in a randomized manner.
We provide a novel approach to achieving a desired outcome in a coordination game: the original 2x2 game is embedded in a 2x3 game where one of the players may use a third action. For a large set of payoff values only one of the Nash equilibria of the original 2x2 game is stable under replicator dynamics. We show that this Nash equilibrium is the {\omega}-limit of all initial conditions in the interior of the state space for the modified 2x3 game. Thus, the existence of a third action for one of the players, although not used, allows both players to coordinate on one Nash equilibrium. This Nash equilibrium is the one preferred by, at least, the player with access to the new action. This approach deals with both coordination failure (players choose the payoff-dominant Nash equilibrium, if such a Nash equilibrium exists) and miscoordination (players do not use mixed strategies).
We use invariant theory of finite groups to study shape enumerators of self-dual linear codes in a finite NRT metric space. We provide a new approach that avoids applying Molien's formula to compute all possible shape enumerators. Enhancing existing methods, we describe the shape enumerators of all self-dual NRT codes over an arbitrary finite field.
Slot labelling is an essential component of any dialogue system, aiming to find important arguments in every user turn. Common approaches involve large pre-trained language models (PLMs) like BERT or RoBERTa, but they face challenges such as high computational requirements and dependence on pre-training data. In this work, we propose a lightweight method which performs on par or better than the state-of-the-art PLM-based methods, while having almost 10x less trainable parameters. This makes it especially applicable for real-life industry scenarios.
We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high-dimensional expansion, which coincides with the earlier definition in terms of two-sided link expanders. Using this definition, we describe an analog of the Fourier expansion and the Fourier levels of the Boolean hypercube for simplicial complexes. Our analog is a decomposition into approximate eigenspaces of random walks associated with the simplicial complexes. Our random-walk definition and the decomposition have the additional advantage that they extend to the more general setting of posets, encompassing both high-dimensional expanders and the Grassmann poset, which appears in recent work on the unique games conjecture. We then use this decomposition to extend the Friedgut-Kalai-Naor theorem to high-dimensional expanders. Our results demonstrate that a constant-degree high-dimensional expander can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing only $|X(k-1)|=O(n)$ points in contrast to $\binom{n}{k}$ points in the $(k)$-slice (which consists of all $n$-bit strings with exactly $k$ ones).
Ubiquitous extended reality environments such as the Metaverse will have a significant impact on the Internet, which will evolve to interconnect a large number of mixed reality spaces. Currently, Metaverse development is related to the creation of mixed reality environments, not tackling the required networking functionalities. This article analyzes suitable networking design choices to support the Metaverse, proposing a new service-centric networking approach capable of incorporating low-latency data fetching, distributed computing, and fusion of heterogeneous data types over the Cloud-to-Thing continuum.
The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants interpolating boundary points is assumed. However, the study of approximants, which additionally interpolate corresponding tangent directions and curvatures at the boundary of an arc, is also considered. Several low-degree polynomial approximants are studied in detail. When several solutions fulfilling the interpolation conditions exist, the optimal one is characterized, and a numerical algorithm for its construction is suggested. Theoretical results are demonstrated with several numerical examples and a comparison with general (i.e. non-one-sided) approximants are provided.
Pairwise comparison models are used for quantitatively evaluating utility and ranking in various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the number of subjects diverges, which is currently lacking in the literature except in a few special instances. This paper addresses this gap by establishing an asymptotic normality result for the maximum likelihood estimator in a broad class of pairwise comparison models. The key idea lies in identifying the Fisher information matrix as a weighted graph Laplacian matrix which can be studied via a meticulous spectral analysis. Our findings provide the first unified theory for performing statistical inference in a wide range of pairwise comparison models beyond the Bradley--Terry model, benefiting practitioners with a solid theoretical guarantee for their use. Simulations utilizing synthetic data are conducted to validate the asymptotic normality result, followed by a hypothesis test using a tennis competition dataset.
Human-in-the-loop aims to train an accurate prediction model with minimum cost by integrating human knowledge and experience. Humans can provide training data for machine learning applications and directly accomplish some tasks that are hard for computers in the pipeline with the help of machine-based approaches. In this paper, we survey existing works on human-in-the-loop from a data perspective and classify them into three categories with a progressive relationship: (1) the work of improving model performance from data processing, (2) the work of improving model performance through interventional model training, and (3) the design of the system independent human-in-the-loop. Using the above categorization, we summarize major approaches in the field, along with their technical strengths/ weaknesses, we have simple classification and discussion in natural language processing, computer vision, and others. Besides, we provide some open challenges and opportunities. This survey intends to provide a high-level summarization for human-in-the-loop and motivates interested readers to consider approaches for designing effective human-in-the-loop solutions.
Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.
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