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

Inverse Problems for the Heat Equation Using Conjugate Gradient Methods

In many engineering systems, e.g., in heat exchanges, reflux condensers, combustion chambers, nuclear vessels, etc. concerned with high temperatures/pressures/loads and/or hostile environments, certain properties of the physical medium, geometry, boundary and initial conditions are not known and their direct measurement can be very inaccurate or even inaccessible. In such a situation, one can adopt an inverse approach and try to infer the unknowns from some extra accessible measurements of other quantities that may be available. The purpose of this thesis is to determine the unknown space-dependent coefficients and/or initial temperature in inverse problems of heat transfer, especially to simultaneously reconstruct several unknown quantities. These inverse problems are investigated from additional pieces of information, such as internal temperature observations, final measured temperature and time-integral temperature measurement. The main difficulty involved in the solution of these inverse problems is that they are typically ill-posed. Thus, their solutions are unstable under small perturbations of the input data and classical numerical techniques fail to provide accurate and stable numerical results. Throughout this thesis, the inverse problems are transformed into optimization problems, and their minimizers are shown to exist. A variational method is employed to obtain their Fréchet gradients with respect to the unknown quantities. Based on this gradient, the conjugate gradient method (CGM) is established together with the adjoint and sensitivity problems. The stability of the numerical solution is investigated by introducing Gaussian random noise into the input measured data. Accurate and stable numerical solutions are obtained when using the CGM regularized by the discrepancy principle