This paper proposes a collision avoidance method for ellipsoidal rigid bodies, which utilizes a control barrier function (CBF) designed from a supporting hyperplane. We formulate the problem in the Special Euclidean Group SE(2) and SE(3), where the dynamics are described as rigid body motion (RBM). Then, we consider the condition for separating two ellipsoidal rigid bodies by employing a signed distance from a supporting hyperplane of a rigid body to the other rigid body. Although the positive value of this signed distance implies that two rigid bodies are collision-free, a naively prepared supporting hyperplane yields a smaller value than the actual distance. To avoid such a conservative evaluation, the supporting hyperplane is rotated so that the signed distance from the supporting hyperplane to the other rigid body is maximized. We prove that the maximum value of this optimization problem is equal to the actual distance between two ellipsoidal rigid bodies, hence eliminating excessive conservativeness. We leverage this signed distance as a CBF to prevent collision while the supporting hyperplane is rotated via a gradient-based input. The designed CBF is integrated into a quadratic programming (QP) problem, where each rigid body calculates its collision-free input in a distributed manner, given communication among rigid bodies. The proposed method is demonstrated with simulations. Finally, we exemplify our method can be extended to a vehicle having nonholonomic dynamics.
相關內容
Digital Twins (DT) are a promising concept in cyber-physical systems research due to their advanced features including monitoring and automated reasoning. Semantic technologies such as Knowledge Graphs (KG) are recently being utilized in DTs especially for information modelling. Building on this move, this paper proposes a pipeline for semantic association rule learning in DTs using KGs and time series data. In addition to this initial pipeline, we also propose new semantic association rule criterion. The approach is evaluated on an industrial water network scenario. Initial evaluation shows that the proposed approach is able to learn a high number of association rules with semantic information which are more generalizable. The paper aims to set a foundation for further work on using semantic association rule learning especially in the context of industrial applications.
This study presents a novel multimodal fusion model for three-dimensional mineral prospectivity mapping (3D MPM), effectively integrating structural and fluid information through a deep network architecture. Leveraging Convolutional Neural Networks (CNN) and Multilayer Perceptrons (MLP), the model employs canonical correlation analysis (CCA) to align and fuse multimodal features. Rigorous evaluation on the Jiaojia gold deposit dataset demonstrates the model's superior performance in distinguishing ore-bearing instances and predicting mineral prospectivity, outperforming other models in result analyses. Ablation studies further reveal the benefits of joint feature utilization and CCA incorporation. This research not only advances mineral prospectivity modeling but also highlights the pivotal role of data integration and feature alignment for enhanced exploration decision-making.
We present a generalized FDTD scheme to simulate moving electromagnetic structures with arbitrary space-time configurations. This scheme is a local adaptation and 2+1-dimensional extension of the uniform and 1+1-dimensional scheme recently reported in [1]. The local adaptation, which is allowed by the inherently matched nature of the generalized Yee cell to the conventional Yee cell, extends the range of applicability of the scheme in [1] to moving structures that involve multiple and arbitrary velocity profiles while being fully compatible with conventional absorbing boundary conditions and standard treatments of medium dispersion. We show that a direct application of the conventional FDTD scheme predicts qualitatively correct spectral transitions but quantitatively erroneous scattering amplitudes, we infer from this observation generalized, hybrid-physical and auxiliary (non-physical) - fields that automatically satisfy moving boundary conditions in the laboratory frame, and accordingly establish local update equations based on the related Maxwell's equations and constitutive relations. We subsequently provide a detailed stability analysis with a generalization of the Courant criterion to the dynamic regime. We finally validate and illustrate the proposed method by several representative examples. The proposed scheme fills an important gap in the open literature on computational electromagnetics and offers an unprecedented, direct solution for moving structures in commercial software platforms.
This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem or pre-trained models. By utilising a continuous and periodic representation of the translation at each intermediate step, appropriate length-scale and thicknesses can be obtained. Numerical tests verifies the performance of the proposed methodology compared to state-of-the-art alternatives, and the dehomogenised designs achieve structural performance within a few percentages of the optimised homogenised solution. The nature of the phasor-based dehomogenisation is inherently mesh-independent and highly parallelisable, allowing for further efficient implementations and future extensions to 3D problems on unstructured meshes.
This paper develops an updatable inverse probability weighting (UIPW) estimation for the generalized linear models with response missing at random in streaming data sets. A two-step online updating algorithm is provided for the proposed method. In the first step we construct an updatable estimator for the parameter in propensity function and hence obtain an updatable estimator of the propensity function; in the second step we propose an UIPW estimator with the inverse of the updating propensity function value at each observation as the weight for estimating the parameter of interest. The UIPW estimation is universally applicable due to its relaxation on the constraint on the number of data batches. It is shown that the proposed estimator is consistent and asymptotically normal with the same asymptotic variance as that of the oracle estimator, and hence the oracle property is obtained. The finite sample performance of the proposed estimator is illustrated by the simulation and real data analysis. All numerical studies confirm that the UIPW estimator performs as well as the batch learner.
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated as a supervised learning task to solve a least-squares regression problem that imposes an algebraic equation approximating a PDE (and boundary conditions if applicable). This algebraic equation involves a graph-Laplacian type matrix obtained via DM asymptotic expansion, which is a consistent estimator of second-order elliptic differential operators. The resulting numerical method is to solve a highly non-convex empirical risk minimization problem subjected to a solution from a hypothesis space of neural networks (NNs). In a well-posed elliptic PDE setting, when the hypothesis space consists of neural networks with either infinite width or depth, we show that the global minimizer of the empirical loss function is a consistent solution in the limit of large training data. When the hypothesis space is a two-layer neural network, we show that for a sufficiently large width, gradient descent can identify a global minimizer of the empirical loss function. Supporting numerical examples demonstrate the convergence of the solutions, ranging from simple manifolds with low and high co-dimensions, to rough surfaces with and without boundaries. We also show that the proposed NN solver can robustly generalize the PDE solution on new data points with generalization errors that are almost identical to the training errors, superseding a Nystrom-based interpolation method.
We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.
This paper proposes a novel hue-like angular parameter to model the structure of deep convolutional neural network (CNN) activation space, referred to as the {\em activation hue}, for the purpose of regularizing models for more effective learning. The activation hue generalizes the notion of color hue angle in standard 3-channel RGB intensity space to $N$-channel activation space. A series of observations based on nearest neighbor indexing of activation vectors with pre-trained networks indicate that class-informative activations are concentrated about an angle $\theta$ in both the $(x,y)$ image plane and in multi-channel activation space. A regularization term in the form of hue-like angular $\theta$ labels is proposed to complement standard one-hot loss. Training from scratch using combined one-hot + activation hue loss improves classification performance modestly for a wide variety of classification tasks, including ImageNet.
Large Language Models (LLMs) have the ability to solve a variety of tasks, such as text summarization and mathematical questions, just out of the box, but they are often trained with a single task in mind. Due to high computational costs, the current trend is to use prompt instruction tuning to better adjust monolithic, pretrained LLMs for new -- but often individual -- downstream tasks. Thus, how one would expand prompt tuning to handle -- concomitantly -- heterogeneous tasks and data distributions is a widely open question. To address this gap, we suggest the use of \emph{Mixture of Prompts}, or MoPs, associated with smart gating functionality: the latter -- whose design is one of the contributions of this paper -- can identify relevant skills embedded in different groups of prompts and dynamically assign combined experts (i.e., collection of prompts), based on the target task. Additionally, MoPs are empirically agnostic to any model compression technique applied -- for efficiency reasons -- as well as instruction data source and task composition. In practice, MoPs can simultaneously mitigate prompt training "interference" in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources), as well as possible implications from model approximations. As a highlight, MoPs manage to decrease final perplexity from $\sim20\%$ up to $\sim70\%$, as compared to baselines, in the federated scenario, and from $\sim 3\%$ up to $\sim30\%$ in the centralized scenario.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191