1,605 research outputs found
Applied Symmetry for Crystal Structure Prediction
This thesis presents an original open-source Python package called PyXtal (pronounced pi-crystal ) that generates random symmetric crystal structures for use in crystal structure prediction (CSP). The primary advantage of PyXtal over existing structure generation tools is its unique symmetrization method. For molecular structures, PyXtal uses an original algorithm to determine the compatibility of molecular point group symmetry with Wyckoff site symmetry. This allows the molecules in generated structures to occupy special Wyckoff positions without breaking the structure\u27s symmetry. This is a new feature which increases the space of search-able structures and in turn improves CSP performance.
It is shown that using already-symmetric initial structures results in a higher probability of finding the lowest-energy structure. Ultimately, this lowers the computational time needed for CSP. Structures can be generated for any symmetry group of 0, 1, 2, or 3 dimensions of periodicity. Either atoms or rigid molecules may be used as building blocks. The generated structures can be optimized with VASP, LAMMPS, or other computational tools. Additional options are provided for the lattice and inter-atomic distance constraints. Results for carbon and silicon crystals, water ice crystals, and molybdenum clusters are presented as usage examples
The Structure of Multigranular Rough Sets
We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given. We also consider the ordered sets of rough sets determined by these approximation pairs
Fidelity Bounds for Device-Independent Advantage Distillation
It is known that advantage distillation (that is, information reconciliation
using two-way communication) improves noise tolerances for quantum key
distribution (QKD) setups. Two-way communication is hence also of interest in
the device-independent case, where noise tolerance bounds for one-way error
correction are currently too low to be experimentally feasible. Existing
security proofs for the device-independent repetition-code protocol (the most
prominent form of advantage distillation) rely on fidelity-related security
conditions, but previous bounds on the fidelity were not tight. We improve on
those results by developing an algorithm that returns arbitrarily tight lower
bounds on the fidelity. Our results give new insight on how strong the
fidelity-related security conditions are, and could also be used to compute
some lower bounds on one-way protocol keyrates. Finally, we conjecture a
necessary security condition for the protocol studied in this work, that
naturally complements the existing sufficient conditions.Comment: 14 pages, 3 figures. Main changes: New observations regarding the
pretty-good fidelity and quantum Chernoff bound. Modification/Generalization
of Conjectured Necessary Conditio
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