Counting monomials

This paper presents two enumeration techniques based on Hilbert functions. The paper illustrates these techniques by solving two chessboard problems

Optimal bounds for the colored Tverberg problem

We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Barany et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Barany & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.Comment: 17 pages, 3 figures; revised version (February 2013), to appear in J. European Math. Soc. (JEMS

Expertise in chess

This chapter provides an overview of research into chess expertise. After an historical background and a brief description of the game and the rating system, it discusses the information processes enabling players to choose good moves, and in particular the trade-offs between knowledge and search. Other topics include blindfold chess, talent, and the role of deliberate practice and tournament experience

Reflectance Intensity Assisted Automatic and Accurate Extrinsic Calibration of 3D LiDAR and Panoramic Camera Using a Printed Chessboard

This paper presents a novel method for fully automatic and convenient extrinsic calibration of a 3D LiDAR and a panoramic camera with a normally printed chessboard. The proposed method is based on the 3D corner estimation of the chessboard from the sparse point cloud generated by one frame scan of the LiDAR. To estimate the corners, we formulate a full-scale model of the chessboard and fit it to the segmented 3D points of the chessboard. The model is fitted by optimizing the cost function under constraints of correlation between the reflectance intensity of laser and the color of the chessboard's patterns. Powell's method is introduced for resolving the discontinuity problem in optimization. The corners of the fitted model are considered as the 3D corners of the chessboard. Once the corners of the chessboard in the 3D point cloud are estimated, the extrinsic calibration of the two sensors is converted to a 3D-2D matching problem. The corresponding 3D-2D points are used to calculate the absolute pose of the two sensors with Unified Perspective-n-Point (UPnP). Further, the calculated parameters are regarded as initial values and are refined using the Levenberg-Marquardt method. The performance of the proposed corner detection method from the 3D point cloud is evaluated using simulations. The results of experiments, conducted on a Velodyne HDL-32e LiDAR and a Ladybug3 camera under the proposed re-projection error metric, qualitatively and quantitatively demonstrate the accuracy and stability of the final extrinsic calibration parameters.Comment: 20 pages, submitted to the journal of Remote Sensin