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This paper describes the relationship between the first non-vanishing Milnor invariants of a classical link and the intersection invariant of a twisted Whitney tower. This is a certain 2-complex in the 4-ball, built from immersed disks bounded by the given link in the 3-sphere together with finitely many ‘layers’ of Whitney disks.The intersection invariant is a higher-order generalization of the intersection number between two immersed disks in the 4-ball, well known to give the linking number of the link on the boundary, which measures intersections among the Whitney disks and the disks bounding the given link, together with information that measures the twists (framing obstructions) of the Whitney disks.This interpretation of Milnor invariants as higher-order intersection invariants plays a key role in our classifications [J. Conant, R. Schneiderman and P. Teichner, ‘Higher-order intersections in low-dimensional topology’, Proc. Natl Acad. Sci. USA 108 (2011) 8131–8138; J. Conant, R. Schneiderman and P. Teichner, ‘Whitney tower concordance of classical links’, Geom. Topol. 16 (2012) 1419–1479] of both the framed and twisted Whitney tower filtrations on link concordance. Here, we show how to realize the higher-order Arf invariants, which also play a role in the classifications, and derive new geometric characterizations of links with vanishing length at most 2k Milnor invariants. [ABSTRACT FROM AUTHOR]

Image watermarking has become a popular technique for authentication and copyright protection. However, many proposed image watermarking techniques are sensitive to affine transforms, such as rotation, scaling and translation. Here, a local affine transform invariant watermarking is designed and tested against attacks performed by Stirmark using the Krawtchouk moment invariants. Watermark is inserted into the perceptually significant Krawtchouk moment invariants of the original image, and watermarking based on Krawtchouk moment invariants are local, that is, the embedded watermark affects only a selected portion of the original image, the position of which can be decided by the user. This, in effect, permits the watermark to be embedded at the portion of the image which is most significant information-wise. This also means that the watermark is especially robust to cropping. Independent component analysis (ICA) is utilised by detector to extract the perfect watermark blindly. The computational aspects of the proposed watermarking are also discussed in detail. Experimental results have demonstrated that the proposed watermarking technique has a good robustness against other attacks performed by Stirmark including affine transform, cropping, filtering, image compression and random geometric distortions. It is indicated that the proposed watermarking has superior advantages over the existing ones in many aspects. [ABSTRACT FROM AUTHOR]

Using the recent work of Hartelman, van der Maas, and Wagenmakers, we demonstrate the use of invariant stochastic catastrophe models in finance for modeling net flows (the difference between purchases and redemptions of fund shares) of U.S. mutual funds. We validate Goetzmann et al. and others' work concerning the importance of sentiment variables on stock fund flows. We also answer some of the questions Goetzmann et al. and Brown et al. pose at the end of their respective papers. We end with possible experiments for experimental economists and sociophysicists. [ABSTRACT FROM AUTHOR]

Presents the problem with subject-sensitive invariantism in the U.S. Implications of the first-person knowledge; Standards that govern first-person knowledge; Variation of the truth conditions for knowledge attributions.