The advent of the X-ray Free Electron Laser (XFEL) has made it possible to record diffraction snapshots of biological entities injected into the X-ray beam before the onset of radiation damage. Algorithmic means must then be used to determine the sna
pshot orientations and thence the three-dimensional structure of the object. Existing Bayesian approaches are limited in reconstruction resolution typically to 1/10 of the object diameter, with the computational expense increasing as the eighth power of the ratio of diameter to resolution. We present an approach capable of exploiting object symmetries to recover three-dimensional structure to high resolution, and thus reconstruct the structure of the satellite tobacco necrosis virus to atomic level. Our approach offers the highest reconstruction resolution for XFEL snapshots to date, and provides a potentially powerful alternative route for analysis of data from crystalline and nanocrystalline objects.
The advent of the X-ray Free Electron Laser (XFEL) has made it possible to record snapshots of biological entities injected into the X-ray beam before the onset of radiation damage. Algorithmic means must then be used to determine the snapshot orient
ations and reconstruct the three-dimensional structure of the object. Existing approaches are limited in reconstruction resolution to at best 1/30th of the object diameter, with the computational expense increasing as the eighth power of the ratio of diameter to resolution. We present an approach capable of exploiting object symmetries to recover three-dimensional structure to 1/100th of the object diameter, and thus reconstruct the structure of the satellite tobacco necrosis virus to atomic resolution. Combined with the previously demonstrated capability to operate at ultralow signal, our approach offers the highest reconstruction resolution for XFEL snapshots to date, and provides a potentially powerful alternative route for analysis of data from crystalline and nanocrystalline objects.
We suggest a new method to compute the spectrum and wave functions of excited states. We construct a stochastic basis of Bargmann link states, drawn from a physical probability density distribution and compute transition amplitudes between stochastic
basis states. From such transition matrix we extract wave functions and the energy spectrum. We apply this method to $U(1)_{2+1}$ lattice gauge theory. As a test we compute the energy spectrum, wave functions and thermodynamical functions of the electric Hamiltonian and compare it with analytical results. We find excellent agreement. We observe scaling of energies and wave functions in the variable of time. We also present first results on a small lattice for the full Hamiltonian including the magnetic term.
