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Steven Hao

Publications and source records attributed to Steven Hao.

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PandaSet: Advanced Sensor Suite Dataset for Autonomous Driving

The accelerating development of autonomous driving technology has placed greater demands on obtaining large amounts of high-quality data. Representative, labeled, real world data serves as the fuel for training deep learning networks, critical for improving self-driving perception algorithms. In this paper, we introduce PandaSet, the first dataset produced by a complete, high-precision autonomous vehicle sensor kit with a no-cost commercial license. The dataset was collected using one 360{\deg} mechanical spinning LiDAR, one forward-facing, long-range LiDAR, and 6 cameras. The dataset contains more than 100 scenes, each of which is 8 seconds long, and provides 28 types of labels for object classification and 37 types of labels for semantic segmentation. We provide baselines for LiDAR-only 3D object detection, LiDAR-camera fusion 3D object detection and LiDAR point cloud segmentation. For more details about PandaSet and the development kit, see https://scale.com/open-datasets/pandaset.

cs.CV

An Elementary Proof of the Cayley Formula Using Random Maps

Cayley's formula states that the number of labelled trees on $n$ vertices is $n^{n-2}$, and many of the current proofs involve complex structures or rigorous computation. We present a bijective proof of the formula by providing an elementary calculation of the probability that a cycle occurs in a random map from an $n$-element set to an $n+1$-element set.

math.CO

A Simple Proof of the Cayley Formula using Random Graphs

We present a nice result on the probability of a cycle occurring in a randomly generated graph. We then provide some extensions and applications, including the proof of the famous Cayley formula, which states that the number of labeled trees on $n$ vertices is $n^{n-2}.$

math.CO