Monodromy action on unknotting tunnels in fiber surfaces

The second author showed that a tunnel of tunnel number one, fibered link in S³ can be isotoped to lie as a properly embedded arc in the fiber surface of the link. In this paper, we observe that this is true for fibered links in any 3-manifold, we analyze how the arc behaves under the monodromy action, and we show that the tunnel arc is nearly clean, with the possible exception of twisting around the boundary of the fiber

Network Flow Optimization for Restoration of Images

The network flow optimization approach is offered for restoration of grayscale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. The new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori estimates of corrupted images, is presented. The algorithm is able to compute the MAP estimates of large size images and can be used in a concurrent mode. We also describe the efficient solutions of the problem of integer minimization of two energy functions for the Ising models of gray-scale and color images

Neighbors of knots in the Gordian graph

We show that every knot is one crossing change away from a knot of arbitrarily high bridge number and arbitrarily high bridge distance.Comment: Accepted by American Mathematical Monthly. New version incorporates referee comment