Inferring three-dimensional structural information of biomacromolecules such as proteins from limited experimental data is an important and challenging task. Nuclear Overhauser effect measurements based on nucleic magnetic resonance, disulfide linking, and electron paramagnetic resonance labeling studies can all provide useful partial distance constraint characteristic of the conformations of p...

We construct 9-parameter and 13-parameter dynamical systems of the plane which map bi-quadratic curves to other bi-quadratic curves and return to the original curve after two iterations. These generalize the QRT maps which map each such curve to itself. The new families of maps include those that were found as reductions of integrable lattices by [11].

We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore, we show that no automorphism of a locally finite 2spherical twin building of rank at least 3 maps every residue of one fixed type to an opposite (a key step in the proof is showing that every duality of a thick finite projective plane admits an abs...

In this paper, we are concerned with protecting elliptic curve computation in a tamper proof device by protecting finite field computation against active side channel attacks, i.e., fault attacks. We propose residue representation of the field elements for fault tolerant Montgomery residue representation multiplication algorithm, by providing fault models for fault attacks, and countermeasures ...

Understanding the topological structure of phase space for dynamical systems in higher dimensions is critical numerous applications, including computation chemical reaction rates and transport objects solar system. Many techniques have been developed to study maps two-dimensional (2D) spaces, but extending these often a major challenge or even impossible. Previously, one such technique, homotop...

For a one-dimensional local domain CM constructed by Akizuki, we find residue maps which give rise to a local duality. The completion of CM is described using these residue maps. Injective hulls of a given module are all isomorphic. For this reason, people often speak of the injective hull to indicate its “uniqueness”. However, isomorphisms between these injective hulls are not canonical. In fa...

Recently, the first Abel map for a stable curve of genus g ≥ 2 has been constructed. Fix an integer d ≥ 1 and let C be a stable curve of compact type of genus g ≥ 2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-n...