Error bounds are derived for sampling and estimation using a discretization of an intrinsically defined Langevin diffusion with invariant measure $\text{d}\mu_\phi \propto e^{-\phi} \mathrm{dvol}_g $ on a compact Riemannian manifold. Two estimators of linear functionals of $\mu_\phi $ based on the discretized Markov process are considered: a time-averaging estimator based on a single trajectory and an ensemble-averaging estimator based on multiple independent trajectories. Imposing no restrictions beyond a nominal level of smoothness on $\phi$, first-order error bounds, in discretization step size, on the bias and variance/mean-square error of both estimators are derived. The order of error matches the optimal rate in Euclidean and flat spaces, and leads to a first-order bound on distance between the invariant measure $\mu_\phi$ and a stationary measure of the discretized Markov process. This order is preserved even upon using retractions when exponential maps are unavailable in closed form, thus enhancing practicality of the proposed algorithms. Generality of the proof techniques, which exploit links between two partial differential equations and the semigroup of operators corresponding to the Langevin diffusion, renders them amenable for the study of a more general class of sampling algorithms related to the Langevin diffusion. Conditions for extending analysis to the case of non-compact manifolds are discussed. Numerical illustrations with distributions, log-concave and otherwise, on the manifolds of positive and negative curvature elucidate on the derived bounds and demonstrate practical utility of the sampling algorithm.

We address outdoor Neural Radiance Fields (NeRF) [23] with real-world camera views and LiDAR maps. Existing methods usually require densely-sampled source views and do not perform well with the open source camera-LiDAR datasets. In this paper, our design leverages 1) LiDAR sensors for strong 3D geometry priors that significantly improve the ray sampling locality, and 2) Conditional Adversarial Networks (cGANs) [15] to recover image details since aggregating embeddings from imperfect LiDAR maps causes artifacts. Our experiments show that while NeRF baselines produce either noisy or blurry results on Argoverse 2 [42], our system not only outperforms baselines in image quality metrics under both clean and noisy conditions, but also obtains closer Detectron2 [43] results to the ground truth images. Furthermore, this system can be used in data augmentation for training a pose regression network [3] and multi-season view synthesis. We hope this work to serve as a new LiDAR-based NeRF baseline that pushes this research direction forward (released here).

Code clone detection is an important aspect of software development and maintenance. The extensive research in this domain has helped reduce the complexity and increase the robustness of source code, thereby assisting bug detection tools. However, the majority of the clone detection literature is confined to a single language. With the increasing prevalence of cross-platform applications, functionality replication across multiple languages is common, resulting in code fragments having similar functionality but belonging to different languages. Since such clones are syntactically unrelated, single language clone detection tools are not applicable in their case. In this article, we propose a semi-supervised deep learning-based toolRubhus, capable of detecting clones across different programming languages.Rubhususes the control and data flow enriched abstract syntax trees (ASTs) of code fragments to leverage their syntactic and structural information and then applies graph neural networks (GNNs) to extract this information for the task of clone detection. We demonstrate the effectiveness of our proposed system through experiments conducted over datasets consisting of Java, C, and Python programs and evaluate its performance in terms of precision, recall, and F1 score. Our results indicate thatRubhusoutperforms the state-of-the-art cross-language clone detection tools.

3D imaging radar offers robust perception capability through visually demanding environments due to the unique penetrative and reflective properties of millimeter waves (mmWave). Current approaches for 3D perception with imaging radar require knowledge of environment geometry, accumulation of data from multiple frames for perception, or access to between-frame motion. Imaging radar presents an additional difficulty due to the complexity of its data representation. To address these issues, and make imaging radar easier to use for downstream robotics tasks, we propose a learning-based method that regresses radar measurements into cylindrical depth maps using LiDAR supervision. Due to the limitation of the regression formulation, directions where the radar beam could not reach will still generate a valid depth. To address this issue, our method additionally learns a 3D filter to remove those pixels. Experiments show that our system generates visually accurate depth estimation. Furthermore, we confirm the overall ability to generalize in the indoor scene using the estimated depth for probabilistic occupancy mapping with ground truth trajectory. The code and model will be released11https://github.com/rpl-cmu/learned-depth-imaging-radar.

Hepatocellular carcinoma (HCC)is a common type of liver cancer and has a high mortality world-widely. The diagnosis, prognoses, and therapeutics are very poor due to the unclear molecular mechanism of progression of the disease. To unveil the molecular mechanism of progression of HCC, we extract a large sample of mRNA expression levels from the GEO database where a total of 167 samples were used for study, and out of them, 115 samples were from HCC tumor tissue. This study aims to investigate the module of differentially expressed genes (DEGs)which are co-expressed only in HCC sample data but not in normal tissue samples. Thereafter, we identified the highly significant module of significant co-expressed genes and formed a PPI network for these genes. There were only six genes (namely, MSH3, DMC1, ALPP, IL10, ZNF223, and HSD17B7)obtained after analysis of the PPI network. Out of six only MSH3, DMC1, HSD17B7, and IL10 were found enriched in GO Term & Pathway enrichment analysis and these candidate genes were mainly involved in cellular process, metabolic and catalytic activity, which promote the development & progression of HCC. Lastly, the composite 3-node FFL reveals the driver miRNAs and TFs associated with our key genes.

We present a fast, scalable, and accurate Simultaneous Localization and Mapping (SLAM) system that represents indoor scenes as a graph of objects. Leveraging the observation that artificial environments are structured and occupied by recognizable objects, we show that a compositional and scalable object mapping formulation is amenable to a robust SLAM solution for drift-free large-scale indoor reconstruction. To achieve this, we propose a novel semantically assisted data association strategy that results in unambiguous persistent object landmarks and a 2.5D compositional rendering method that enables reliable frame-to-model RGB-D tracking. Consequently, we deliver an optimized online implementation that can run at near frame rate with a single graphics card, and provide a comprehensive evaluation against state-of-the-art baselines. An open-source implementation will be provided at https://github.com/rpl-cmu/object-slam.