Development of a method for improving stability method of applying digital watermarks to digital images

A technique for increasing the stability of methods for applying digital watermark into digital images is presented. A technique for increasing the stability of methods for applying digital watermarks into digital images, based on pseudo-holographic coding and additional filtering of a digital watermark, has been developed. The technique described in this work using pseudo-holographic coding of digital watermarks is effective for all types of attacks that were considered, except for image rotation. The paper presents a statistical indicator for assessing the stability of methods for applying digital watermarks. The indicator makes it possible to comprehensively assess the resistance of the method to a certain number of attacks. An experimental study was carried out according to the proposed method. This technique is most effective when part of the image is lost. When pre-filtering a digital watermark, the most effective is the third filtering method, which is averaging over a cell with subsequent binarization. The least efficient is the first method, which is binarization and finding the statistical mode over the cell. For an affine type attack, which is an image rotation, this technique is effective only when the rotation is compensated. To estimate the rotation angle, an affine transformation matrix is found, which is obtained from a consistent set of corresponding ORB-descriptors. Using this method allows to accurately extract a digital watermark for the entire range of angles. A comprehensive assessment of the methodology for increasing the stability of the method of applying a digital watermark based on Wavelet transforms has shown that this method is 20 % better at counteracting various types of attacks

Stability conditions and braid group actions on affine An quivers

We study stability conditions on the Calabi–Yau-[Formula: see text] categories associated to an affine type [Formula: see text] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [Formula: see text]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [Formula: see text] based on the Khovanov–Seidel–Thomas method.

Two Maps on Affine Type $A$ Crystals and Hecke Algebras

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type $A$ and in the representation theory of Hecke algebras of type $G(l,l,n)$.

On quasiprimitive edge-transitive graphs of odd order and twice prime valency

A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let {\varGamma} be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of {\varGamma}. In the case where G acts transitively on the edge set and quasiprimitively on the vertex set of {\varGamma}, we prove that either G is almost simple, or G is a primitive group of affine type. If further G is an almost simple primitive group, then, with two exceptions, the socle of G acts transitively on the edge set of {\varGamma}.

A note on extremely primitive affine groups

Let G be a finite primitive permutation group on a set $$\Omega $$ Ω with non-trivial point stabilizer $$G_{\alpha }$$ G α . We say that G is extremely primitive if $$G_{\alpha }$$ G α acts primitively on each of its orbits in $$\Omega {\setminus } \{\alpha \}$$ Ω \ { α } . In earlier work, Mann, Praeger, and Seress have proved that every extremely primitive group is either almost simple or of affine type and they have classified the affine groups up to the possibility of at most finitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall’s conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of affine groups in order to complete the classification of the extremely primitive groups. Mann et al. have conjectured that none of these affine candidates are extremely primitive and our main result confirms this conjecture.