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Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, such schemes cannot accurately represent relativistic dynamics in the laboratory because of the dominance of dissipation and external gravitational fields. Here we demonstrate that an ``active" object (a wheeled robot), which moves in a straight line on level ground and can alter its speed depending on the curvature of the deformable terrain it moves on, can exactly capture dynamics in curved relativistic spacetimes. Via the systematic study of the robot's dynamics in the radial and orbital directions, we develop a mapping of the emergent trajectories of a wheeled vehicle on a spandex membrane to the motion in a curved spacetime. Our mapping demonstrates how the driven robot's dynamics mix space and time in a metric, and shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow the programming of a desired spacetime, such as the Schwarzschild metric near a non-rotating blackhole. Our mapping and framework facilitate creation of a robophysical analog to a general relativistic system in the laboratory at low cost that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

Intelligent reflecting surfaces (IRSs) are a promising low-cost solution for achieving high spectral and energy efficiency in future communication systems by enabling the customization of wireless propagation environments. Despite the plethora of research on resource allocation design for IRS-assisted multiuser communication systems, the optimal design and the corresponding performance upper bound are still not fully understood. To bridge this gap in knowledge, in this paper, we investigate the optimal resource allocation design for IRS-assisted multiuser systems employing practical discrete IRS phase shifters. In particular, we jointly optimize the beamforming vector at the base station (BS) and the discrete IRS phase shifts to minimize the total transmit power for the cases of perfect and imperfect channel state information (CSI) knowledge. To this end, two novel algorithms based on the generalized Benders decomposition (GBD) method are developed to obtain the globally optimal solution for perfect and imperfect CSI, respectively. Moreover, to facilitate practical implementation, we propose two corresponding low-complexity suboptimal algorithms with guaranteed convergence by capitalizing on successive convex approximation (SCA). In particular, for imperfect CSI, we adopt a bounded error model to characterize the CSI uncertainty and propose a new transformation to convexify the robust quality-of-service (QoS) constraints. Our numerical results confirm the optimality of the proposed GBD-based algorithms for the considered system for both perfect and imperfect CSI. Furthermore, we unveil that both proposed SCA-based algorithms can achieve a close-to-optimal performance within a few iterations. Moreover, compared with the state-of-the-art solution based on the alternating optimization (AO) method, the proposed SCA-based scheme achieves a significant performance gain with low complexity.

We present a multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty. The algorithm is based on a collective smoother that at each iteration sweeps over the nodes of the computational mesh, and solves a reduced saddle-point system whose size depends on the number $N$ of samples used to discretized the probability space. We show that this reduced system can be solved with optimal $O(N)$ complexity. We test the multigrid method on three problems: a linear-quadratic problem, possibly with a local or a boundary control, for which the multigrid method is used to solve directly the linear optimality system; a nonsmooth problem with box constraints and $L^1$-norm penalization on the control, in which the multigrid scheme is used within a semismooth Newton iteration; a risk-adverse problem with the smoothed CVaR risk measure where the multigrid method is called within a preconditioned Newton iteration. In all cases, the multigrid algorithm exhibits excellent performances and robustness with respect to the parameters of interest.

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameters estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is $O_{p}(1)$, exact recovery of true change-points can be achieved in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the number and locations of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method.

About: We propose an incremental LOD generation approach for point clouds that allows us to simultaneously load points from disk, update an octree-based level-of-detail representation, and render the intermediate results in real time while additional points are still being loaded from disk. LOD construction and rendering are both implemented in CUDA and share the GPU's processing power, but each incremental update is lightweight enough to leave enough time to maintain real-time frame rates. Background: LOD construction is typically implemented as a preprocessing step that requires users to wait before they are able to view the results in real time. This approach allows users to view intermediate results right away. Results: Our approach is able to stream points from an SSD and update the octree on the GPU at rates of up to 580 million points per second (~9.3GB/s from a PCIe 5.0 SSD) on an RTX 4090. Depending on the data set, our approach spends an average of about 1 to 2 ms to incrementally insert 1 million points into the octree, allowing us to insert several million points per frame into the LOD structure and render the intermediate results within the same frame. Discussion/Limitations: We aim to provide near-instant, real-time visualization of large data sets without preprocessing. Out-of-core processing of arbitrarily large data sets and color-filtering for higher-quality LODs are subject to future work.

We aim to improve the Inverted Neural Radiance Fields (iNeRF) algorithm which defines the image pose estimation problem as a NeRF based iterative linear optimization. NeRFs are novel neural space representation models that can synthesize photorealistic novel views of real-world scenes or objects. Our contributions are as follows: we extend the localization optimization objective with a depth-based loss function, we introduce a multi-image based loss function where a sequence of images with known relative poses are used without increasing the computational complexity, we omit hierarchical sampling during volumetric rendering, meaning only the coarse model is used for pose estimation, and we how that by extending the sampling interval convergence can be achieved even or higher initial pose estimate errors. With the proposed modifications the convergence speed is significantly improved, and the basin of convergence is substantially extended.

Occupancy mapping is a fundamental component of robotic systems to reason about the unknown and known regions of the environment. This article presents an efficient occupancy mapping framework for high-resolution LiDAR sensors, termed D-Map. The framework introduces three main novelties to address the computational efficiency challenges of occupancy mapping. Firstly, we use a depth image to determine the occupancy state of regions instead of the traditional ray-casting method. Secondly, we introduce an efficient on-tree update strategy on a tree-based map structure. These two techniques avoid redundant visits to small cells, significantly reducing the number of cells to be updated. Thirdly, we remove known cells from the map at each update by leveraging the low false alarm rate of LiDAR sensors. This approach not only enhances our framework's update efficiency by reducing map size but also endows it with an interesting decremental property, which we have named D-Map. To support our design, we provide theoretical analyses of the accuracy of the depth image projection and time complexity of occupancy updates. Furthermore, we conduct extensive benchmark experiments on various LiDAR sensors in both public and private datasets. Our framework demonstrates superior efficiency in comparison with other state-of-the-art methods while maintaining comparable mapping accuracy and high memory efficiency. We demonstrate two real-world applications of D-Map for real-time occupancy mapping on a handle device and an aerial platform carrying a high-resolution LiDAR. In addition, we open-source the implementation of D-Map on GitHub to benefit society: github.com/hku-mars/D-Map.

The greedy and nearest-neighbor TSP heuristics can both have $\log n$ approximation factors from optimal in worst case, even just for $n$ points in Euclidean space. In this note, we show that this approximation factor is only realized when the optimal tour is unusually short. In particular, for points from any fixed $d$-Ahlfor's regular metric space (which includes any $d$-manifold like the $d$-cube $[0,1]^d$ in the case $d$ is an integer but also fractals of dimension $d$ when $d$ is real-valued), our results imply that the greedy and nearest-neighbor heuristics have \emph{additive} errors from optimal on the order of the \emph{optimal} tour length through \emph{random} points in the same space, for $d>1$.

Owing to effective and flexible data acquisition, unmanned aerial vehicle (UAV) has recently become a hotspot across the fields of computer vision (CV) and remote sensing (RS). Inspired by recent success of deep learning (DL), many advanced object detection and tracking approaches have been widely applied to various UAV-related tasks, such as environmental monitoring, precision agriculture, traffic management. This paper provides a comprehensive survey on the research progress and prospects of DL-based UAV object detection and tracking methods. More specifically, we first outline the challenges, statistics of existing methods, and provide solutions from the perspectives of DL-based models in three research topics: object detection from the image, object detection from the video, and object tracking from the video. Open datasets related to UAV-dominated object detection and tracking are exhausted, and four benchmark datasets are employed for performance evaluation using some state-of-the-art methods. Finally, prospects and considerations for the future work are discussed and summarized. It is expected that this survey can facilitate those researchers who come from remote sensing field with an overview of DL-based UAV object detection and tracking methods, along with some thoughts on their further developments.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.