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In practice, as opposed to a large set of finite-dimensional vectors approximated from discrete data, we often prefer to utilize functional data. In recent years, partially observable function data have frequently appeared in practical applications and are the objectofan increasing interest by the literature. In this thesis, we learn the concept of data integration depth of partially observable functions proposed by Elias et al. 2023, which can be used to measure the degree of data centralization. At the same time, we also studied the trimmed-mean estimator method and consistency proof proposed by Fraiman and Muniz 2001 for completely observable functions. This method refers to the process of removing some of the smallest and largest values before calculating the mean to enhance the robustness of the estimate. In this thesis, we introduce the concept of trimmed-mean estimator for partially observable functions. We discuss several theoretical and practical issues, including the proof that the proposed trimmed-mean estimator converges almost surely and provide a simulation study. The results show that our estimator performs better in terms of efficiency and robustness compared to the ordinary mean under partially observable functional data.

Diffusion models are promising for joint trajectory prediction and controllable generation in autonomous driving, but they face challenges of inefficient inference steps and high computational demands. To tackle these challenges, we introduce Optimal Gaussian Diffusion (OGD) and Estimated Clean Manifold (ECM) Guidance. OGD optimizes the prior distribution for a small diffusion time $T$ and starts the reverse diffusion process from it. ECM directly injects guidance gradients to the estimated clean manifold, eliminating extensive gradient backpropagation throughout the network. Our methodology streamlines the generative process, enabling practical applications with reduced computational overhead. Experimental validation on the large-scale Argoverse 2 dataset demonstrates our approach's superior performance, offering a viable solution for computationally efficient, high-quality joint trajectory prediction and controllable generation for autonomous driving. Our project webpage is at https://yixiaowang7.github.io/OptTrajDiff_Page/., Comment: 30 pages, 20 figures, Accepted to ECCV 2024

The increasing complexity of tasks in robotics demands efficient strategies for multitask and continual learning. Traditional models typically rely on a universal policy for all tasks, facing challenges such as high computational costs and catastrophic forgetting when learning new tasks. To address these issues, we introduce a sparse, reusable, and flexible policy, Sparse Diffusion Policy (SDP). By adopting Mixture of Experts (MoE) within a transformer-based diffusion policy, SDP selectively activates experts and skills, enabling efficient and task-specific learning without retraining the entire model. SDP not only reduces the burden of active parameters but also facilitates the seamless integration and reuse of experts across various tasks. Extensive experiments on diverse tasks in both simulations and real world show that SDP 1) excels in multitask scenarios with negligible increases in active parameters, 2) prevents forgetting in continual learning of new tasks, and 3) enables efficient task transfer, offering a promising solution for advanced robotic applications. Demos and codes can be found in https://forrest-110.github.io/sparse_diffusion_policy/.

This study presents a novel fault diagnosis model for urban rail transit systems based on Wavelet Transform Residual Neural Network (WT-ResNet). The model integrates the advantages of wavelet transform for feature extraction and ResNet for pattern recognition, offering enhanced diagnostic accuracy and robustness. Experimental results demonstrate the effectiveness of the proposed model in identifying faults in urban rail trains, paving the way for improved maintenance strategies and reduced downtime., Comment: 12 pages,10 figures

We introduce a pioneering unified library that leverages depth anything, segment anything models to augment neural comprehension in language-vision model zero-shot understanding. This library synergizes the capabilities of the Depth Anything Model (DAM), Segment Anything Model (SAM), and GPT-4V, enhancing multimodal tasks such as vision-question-answering (VQA) and composition reasoning. Through the fusion of segmentation and depth analysis at the symbolic instance level, our library provides nuanced inputs for language models, significantly advancing image interpretation. Validated across a spectrum of in-the-wild real-world images, our findings showcase progress in vision-language models through neural-symbolic integration. This novel approach melds visual and language analysis in an unprecedented manner. Overall, our library opens new directions for future research aimed at decoding the complexities of the real world through advanced multimodal technologies and our code is available at \url{https://github.com/AnthonyHuo/SAM-DAM-for-Compositional-Reasoning}.

The Runge--Kutta discontinuous Galerkin (RKDG) method is a high-order technique for addressing hyperbolic conservation laws, which has been refined over recent decades and is effective in handling shock discontinuities. Despite its advancements, the RKDG method faces challenges, such as stringent constraints on the explicit time-step size and reduced robustness when dealing with strong discontinuities. On the other hand, the Gas-Kinetic Scheme (GKS) based on a high-order gas evolution model also delivers significant accuracy and stability in solving hyperbolic conservation laws through refined spatial and temporal discretizations. Unlike RKDG, GKS allows for more flexible CFL number constraints and features an advanced flow evolution mechanism at cell interfaces. Additionally, GKS' compact spatial reconstruction enhances the accuracy of the method and its ability to capture stable strong discontinuities effectively. In this study, we conduct a thorough examination of the RKDG method using various numerical fluxes and the GKS method employing both compact and non-compact spatial reconstructions. Both methods are applied under the framework of explicit time discretization and are tested solely in inviscid scenarios. We will present numerous numerical tests and provide a comparative analysis of the outcomes derived from these two computational approaches.

Joint pedestrian trajectory prediction has long grappled with the inherent unpredictability of human behaviors. Recent investigations employing variants of conditional diffusion models in trajectory prediction have exhibited notable success. Nevertheless, the heavy dependence on accurate historical data results in their vulnerability to noise disturbances and data incompleteness. To improve the robustness and reliability, we introduce the Guided Full Trajectory Diffuser (GFTD), a novel diffusion model framework that captures the joint full (historical and future) trajectory distribution. By learning from the full trajectory, GFTD can recover the noisy and missing data, hence improving the robustness. In addition, GFTD can adapt to data imperfections without additional training requirements, leveraging posterior sampling for reliable prediction and controllable generation. Our approach not only simplifies the prediction process but also enhances generalizability in scenarios with noise and incomplete inputs. Through rigorous experimental evaluation, GFTD exhibits superior performance in both trajectory prediction and controllable generation.

Digital image correlation method is a non contact deformation measurement technique. Despite years of development, it is still difficult to solve the contradiction between calculation efficiency and seed point quantity.With the development of deep learning, the DIC algorithm based on deep learning provides a new solution for the problem of insufficient calculation efficiency in DIC.All supervised learning DIC methods requires a large set of high quality training set. However, obtaining such a dataset can be challenging and time consuming in generating ground truth. To fix the problem,we propose an unsupervised CNN Based DIC for 2D Displacement Measurement.The speckle image warp model is created to transform the target speckle image to the corresponding predicted reference speckle image by predicted 2D displacement map, the predicted reference speckle image is compared with the original reference speckle image to realize the unsupervised training of the CNN.The network's parameters are optimized using a composite loss function that incorporates both the Mean Squared Error and Pearson correlation coefficient.Our proposed method has a significant advantage of eliminating the need for extensive training data annotations. We conducted several experiments to demonstrate the validity and robustness of the proposed method. The experimental results demonstrate that our method can achieve can achieve accuracy comparable to previous supervised methods. The PyTorch code will be available at the following URL: https://github.com/fead1.

The quick and accurate retrieval of an object height from a single fringe pattern in Fringe Projection Profilometry has been a topic of ongoing research. While a single shot fringe to depth CNN based method can restore height map directly from a single pattern, its accuracy is currently inferior to the traditional phase shifting technique. To improve this method's accuracy, we propose using a U shaped High resolution Network (UHRNet). The network uses UNet encoding and decoding structure as backbone, with Multi-Level convolution Block and High resolution Fusion Block applied to extract local features and global features. We also designed a compound loss function by combining Structural Similarity Index Measure Loss (SSIMLoss) function and chunked L2 loss function to improve 3D reconstruction details.We conducted several experiments to demonstrate the validity and robustness of our proposed method. A few experiments have been conducted to demonstrate the validity and robustness of the proposed method, The average RMSE of 3D reconstruction by our method is only 0.443(mm). which is 41.13% of the UNet method and 33.31% of Wang et al hNet method. Our experimental results show that our proposed method can increase the accuracy of 3D reconstruction from a single fringe pattern.

Using two-frequency driving in two dimensions opens up new possibilites for Floquet engineering, which range from controlling specific symmetries to tuning the properties of resonant gaps. In this work, we study two-band lattice models subject to two-tone Floquet driving and analyse the resulting effective Floquet bandstructures both numerically and analytically. On the one hand, we extend the methodology of Sandholzer et al. [10.1103/PhysRevResearch.4.013056] from one to two dimensions and find competing topological phases in a simple Bravais lattice when the two resonant drives at $1\omega$ and $2\omega$ interfere. On the other hand, we explore driving-induced symmetry breaking in the hexagonal lattice, in which the breaking of either inversion or time-reversal symmetry can be tuned independently via the Floquet modulation. Possible applications of our work include a simpler generation of topological bands for ultracold atoms, and the realisation of non-linear Hall effects as well as Haldane's parity anomaly in inversion-symmetric parent lattices.

Agile flights of autonomous quadrotors in cluttered environments require constrained motion planning and control subject to translational and rotational dynamics. Traditional model-based methods typically demand complicated design and heavy computation. In this paper, we develop a novel deep reinforcement learning-based method that tackles the challenging task of flying through a dynamic narrow gate. We design a model predictive controller with its adaptive tracking references parameterized by a deep neural network (DNN). These references include the traversal time and the quadrotor SE(3) traversal pose that encourage the robot to fly through the gate with maximum safety margins from various initial conditions. To cope with the difficulty of training in highly dynamic environments, we develop a reinforce-imitate learning framework to train the DNN efficiently that generalizes well to diverse settings. Furthermore, we propose a binary search algorithm that allows online adaption of the SE(3) references to dynamic gates in real-time. Finally, through extensive high-fidelity simulations, we show that our approach is robust to the gate's velocity uncertainties and adaptive to different gate trajectories and orientations.

The stair phase coding patterns have been widely used to determine the fringe order for phase unwrapping of the wrapped phase in 3D shape measurement. Although the special coding sequence algorithm can achieve with a large number of codewords, it needs current codeword and its adjacent codewords to jointly determine the fringe order. If any codeword of the grouped adjacent codewords is incorrectly recognized, it will result in false fringe order.Therefore, it is challenging to significantly increase the number of codewords. When it is necessary to simultaneously measure more than two isolated objects with large size differences, if the fringe frequency is high, the number of fringes on the smaller objects is too few to determine the fringe orders. On the other hand, if the fringe frequency is low, the image can not contain all isolated objects at the same time. To solve this problem, we propose an absolute phase measurement method based on bidirectional coding patterns. The wrapped phase of the object is obtained by fou step phase shifting patterns, and the fringe orders is obtained by two bidirectional coded patterns. When coding the bidirectional patterns, we code two groups of stair phase with different frequency along horizontal direction, which respectively represent local fringe order information and partition information, then, we alternately repeated the two groups of stair phase along the vertical direction to obtain the bidirectional coding patterns in the whole pattern. Each local fringe order information and the corresponding partition information in small region jointly determine the fringe order of each position in the wrapped phase. To verify the effectiveness of our method, we did simulations and three experiments. Simulation and experimental results show that our method is effective for complex surfaces and isolated objects with different sizes.

The temporal analysis of products reactor provides a vast amount of transient kinetic information that may be used to describe a variety of chemical features including the residence time distribution, kinetic coefficients, number of active sites, and the reaction mechanism. However, as with any measurement device, the TAP reactor signal is convoluted with noise. To reduce the uncertainty of the kinetic measurement and any derived parameters or mechanisms, proper preprocessing must be performed prior to any advanced analysis. This preprocessing consists of baseline correction, i.e., a shift in the voltage response, and calibration, i.e., a scaling of the flux response based on prior experiments. The current methodology of preprocessing requires significant user discretion and reliance on previous experiments that may drift over time. Herein we use machine learning techniques combined with physical constraints to convert the raw instrument signal to chemical information. As such, the proposed methodology demonstrates clear benefits over the traditional preprocessing in the calibration of the inert and feed mixture products without need of prior calibration experiments or heuristic input from the user.

One of the long-standing challenges in lexical semantics consists in learning representations of words which reflect their semantic properties. The remarkable success of word embeddings for this purpose suggests that high-quality representations can be obtained by summarizing the sentence contexts of word mentions. In this paper, we propose a method for learning word representations that follows this basic strategy, but differs from standard word embeddings in two important ways. First, we take advantage of contextualized language models (CLMs) rather than bags of word vectors to encode contexts. Second, rather than learning a word vector directly, we use a topic model to partition the contexts in which words appear, and then learn different topic-specific vectors for each word. Finally, we use a task-specific supervision signal to make a soft selection of the resulting vectors. We show that this simple strategy leads to high-quality word vectors, which are more predictive of semantic properties than word embeddings and existing CLM-based strategies.