Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus

The notion of modulus is a striking feature of Rosenlicht-Serre's theory of generalized Jacobian varieties of curves. It was carried over to algebraic cycles on general varieties by Bloch-Esnault, Park, R\"ulling, Krishna-Levine. Recently, Kerz-Saito introduced a notion of Chow group of $0$-cycles with modulus in connection with geometric class field theory with wild ramification for varieties over finite fields. We study the non-homotopy invariant part of the Chow group of $0$-cycles with modulus and show their torsion and divisibility properties. Modulus is being brought to sheaf theory by Kahn-Saito-Yamazaki in their attempt to construct a generalization of Voevodsky-Suslin-Friedlander's theory of homotopy invariant presheaves with transfers. We prove parallel results about torsion and divisibility properties for them.Comment: 15 pages, exposition improve

Robust Minutiae Extractor: Integrating Deep Networks and Fingerprint Domain Knowledge

We propose a fully automatic minutiae extractor, called MinutiaeNet, based on deep neural networks with compact feature representation for fast comparison of minutiae sets. Specifically, first a network, called CoarseNet, estimates the minutiae score map and minutiae orientation based on convolutional neural network and fingerprint domain knowledge (enhanced image, orientation field, and segmentation map). Subsequently, another network, called FineNet, refines the candidate minutiae locations based on score map. We demonstrate the effectiveness of using the fingerprint domain knowledge together with the deep networks. Experimental results on both latent (NIST SD27) and plain (FVC 2004) public domain fingerprint datasets provide comprehensive empirical support for the merits of our method. Further, our method finds minutiae sets that are better in terms of precision and recall in comparison with state-of-the-art on these two datasets. Given the lack of annotated fingerprint datasets with minutiae ground truth, the proposed approach to robust minutiae detection will be useful to train network-based fingerprint matching algorithms as well as for evaluating fingerprint individuality at scale. MinutiaeNet is implemented in Tensorflow: https://github.com/luannd/MinutiaeNetComment: Accepted to International Conference on Biometrics (ICB 2018