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We discuss the Nckel model of an open quantum dot, i.e. a straight hard-wall channel with a potential well. If this potential depends on the longitudinal variable only, there are embedded eigenvalues which turn into resonances if the symmetry is violated, either by applying a magnetic field or by deformation of the well. For a weak symmetry breaking we derive the perturbative expansion of these resonances. We also deduce a sufficient condition under which the discrete spectrum of such a system (without any symmetry) survives the presence of a strong magnetic field. It is satisfied, in particular, if the dot potential is purely attractive.

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum 2 -divergence for some 2 . We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

We propose and analyze a multivariate encryption scheme that uses odd characteristic and an embedding in its construction. This system has a very simple core map F(X) = X^2, allowing for efficient decryption. We also discuss ways to make this decryption faster with specific parameter choices. We give heuristic arguments along with experimental data to show that this scheme resists all known attacks.

In this paper, we address the problem of constraint detection for layout regularization. The layout we consider is a set of two-dimensional elements where each element is represented by its bounding box. Layout regularization is important in digitizing plans or images, such as floor plans and facade images, and in the improvement of user-created contents, such as architectural drawings and slide layouts. To regularize a layout, we aim to improve the input by detecting and subsequently enforcing alignment, size, and distance constraints between layout elements. Similar to previous work, we formulate layout regularization as a quadratic programming problem. In addition, we propose a novel optimization algorithm that automatically detects constraints. We evaluate the proposed framework using a variety of input layouts from different applications. Our results demonstrate that our method has superior performance to