Finite type invariants of integral homology 3-spheres: A survey

This is a survey on the current status of the study of finite type invariants of integral homology 3-spheres based on lectures given in the workshop on knot theory at Banach International Center of Mathematics, Warsaw, July 1995. As a new result, we show that the space of finite type invariants of integral homology 3-spheres is a graded polynomial algebra generated by invariants additive under the connected sum. We also discuss some open questions on this subject.Comment: 27 pages, amslatex. A new section was added surveying recent developments of the subject. To appear in the proceedings of Warsaw knot theory workshop, July-August 199

Face Spoofing Detection by Fusing Binocular Depth and Spatial Pyramid Coding Micro-Texture Features

Robust features are of vital importance to face spoofing detection, because various situations make feature space extremely complicated to partition. Thus in this paper, two novel and robust features for anti-spoofing are proposed. The first one is a binocular camera based depth feature called Template Face Matched Binocular Depth (TFBD) feature. The second one is a high-level micro-texture based feature called Spatial Pyramid Coding Micro-Texture (SPMT) feature. Novel template face registration algorithm and spatial pyramid coding algorithm are also introduced along with the two novel features. Multi-modal face spoofing detection is implemented based on these two robust features. Experiments are conducted on a widely used dataset and a comprehensive dataset constructed by ourselves. The results reveal that face spoofing detection with the fusion of our proposed features is of strong robustness and time efficiency, meanwhile outperforming other state-of-the-art traditional methods.Comment: 5 pages, 2 figures, accepted by 2017 IEEE International Conference on Image Processing (ICIP

On the Head and the Tail of the Colored Jones Polynomial

The colored Jones polynomial is a series of one variable Laurent polynomials J(K,n) associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of J(K,n) are independent of n when n is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a Volume-ish Theorem for the colored Jones Polynomial.Comment: 14 pages, 6 figure