Megahertz pulse trains enable multi-hit serial femtosecond crystallography experiments at X-ray free electron lasers

The European X-ray Free Electron Laser (XFEL) and Linac Coherent Light Source (LCLS) II are extremely intense sources of X-rays capable of generating Serial Femtosecond Crystallography (SFX) data at megahertz (MHz) repetition rates. Previous work has shown that it is possible to use consecutive X-ray pulses to collect diffraction patterns from individual crystals. Here, we exploit the MHz pulse structure of the European XFEL to obtain two complete datasets from the same lysozyme crystal, first hit and the second hit, before it exits the beam. The two datasets, separated by <1 µs, yield up to 2.1 Å resolution structures. Comparisons between the two structures reveal no indications of radiation damage or significant changes within the active site, consistent with the calculated dose estimates. This demonstrates MHz SFX can be used as a tool for tracking sub-microsecond structural changes in individual single crystals, a technique we refer to as multi-hit SFX

Motivic fundamental groups and integral points

We give a motivic proof of finiteness of S-integral points on punctured projective line. We do this by studying torsors over different notions of unipotent fundamental groups attached to an open curve defined over a number field and the algebraic spaces which parametrize these torsors. This reduces finiteness of integral points of such curves to a strict inequality between some global and local Galois cohomology groups. When the curve is a punctured projective line, we use abelian categories of mixed Tate motives over the base number field and localizations of its ring of integers to replace the global cohomology groups by algebraic K-groups of the base number field. Finally for totally real number fields, we use Borel's explicit calculations to conclude finiteness of S-integral points

Analytical analysis of motion separability

Motion segmentation is an important task in computer vision and several practical approaches have already been developed. A common approach to motion segmentation is to use the optical flow and formulate the segmentation problem using a linear approximation of the brightness constancy constraints. Although there are numerous solutions to solve this problem and their accuracies and reliabilities have been studied, the exact definition of the segmentation problem, its theoretical feasibility and the conditions for successful motion segmentation are yet to be derived. This paper presents a simplified theoretical framework for the prediction of feasibility, of segmentation of a two-dimensional linear equation system. A statistical definition of a separablemotion (structure) is presented and a relatively straightforward criterion for predicting the separability of two different motions in this framework is derived. The applicability of the proposed criterion for prediction of the existence of multiple motions in practice is examined using both synthetic and real image sequences.The prescribed separability criterion is useful in designing computer vision applications as it is solely based on the amount of relative motion and the scale of measurement noise

Theoretical analysis of Hough Transform optimal cell size: Segmentation of nearby lines

Hough Transform (HT) is commonly used to solve the line extraction problem. Although images are discretized at the onset, the Hough domain is continuous and in practice it has to be partitioned into cells. It has been suggested that the optimality of the size (resolution) of those cells would depend on the amount noise in the image. In this paper, we study the effect of discretization on the success of line detection where there are nearby lines and develop a theoretical foundation for the optimality of the Hough domain discretization for segmentation purposes. Experiments with real images show that our results are useful in practice for line detection application

Statistical separability of local motions in volumetric images

Measurement of local differences in the 3D motions of dynamic body organs (captured by volumetric scanners) is of increasing interest in biomedicai imaging applications. Estimation methods of 3D optical flow in those images have been studied in recent years. However, theoretical limits of 3D optical flow-based motion estimation and segmentation are yet to be analysed. In this paper, a novel criterion is proposed to statistically predict the separability of local 3D motions. Simulation results demonstrate how the proposed approach works in principle to predict separability of two motions in terms of the amount of relative motion and the scale of noise

Statistical separability of local motions in volumetric images

Measurement of local differences in the 3D motions of dynamic body organs (captured by volumetric scanners) is of increasing interest in biomedicai imaging applications. Estimation methods of 3D optical flow in those images have been studied in recent years. However, theoretical limits of 3D optical flow-based motion estimation and segmentation are yet to be analysed. In this paper, a novel criterion is proposed to statistically predict the separability of local 3D motions. Simulation results demonstrate how the proposed approach works in principle to predict separability of two motions in terms of the amount of relative motion and the scale of noise

Theoretical analysis of hough transform optimal cell size: Segmentation of nearby lines

Hough Transform (HT) is commonly used to solve the line extraction problem. Although images are discretized at the onset, the Hough domain is continuous and in practice it has to be partitioned into cells. It has been suggested that the optimality of the size (resolution) of those cells would depend on the amount noise in the image. In this paper, we study the effect of discretization on the success of line detection where there are nearby lines and develop a theoretical foundation for the optimality of the Hough domain discretization for segmentation purposes. Experiments with real images show that our results are useful in practice for line detection applications.Marjan Hadian-Jazi, Alireza Bab-Hadiashar, Reza Hoseinnezhad, and David Sute

The serial millisecond crystallography instrument at the Australian Synchrotron incorporating the "lipidico" injector

A serial millisecond crystallography (SMX) facility has recently been implemented at the macromolecular crystallography beamline, MX2 at the Australian Synchrotron. The setup utilizes a combination of an EIGER X 16M detector system and an in-house developed high-viscosity injector, "Lipidico." Lipidico uses a syringe needle to extrude the microcrystal-containing viscous media and it is compatible with commercially available syringes. The combination of sample delivery via protein crystals suspended in a viscous mixture and a millisecond frame rate detector enables high-Throughput serial crystallography at the Australian Synchrotron. A hit-finding algorithm, based on the principles of "robust-statistics," is employed to rapidly process the data. Here we present the first SMX experimental results with a detector frame rate of 100 Hz (10 ms exposures) and the Lipidico injector using a mixture of lysozyme microcrystals embedded in high vacuum silicon grease. Details of the experimental setup, sample injector, and data analysis pipeline are designed and developed as part of the Australian Synchrotron SMX instrument and are reviewed here

Megahertz pulse trains enable multi-hit serial femtosecond crystallography experiments at X-ray free electron lasers

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.The European X-ray Free Electron Laser (XFEL) and Linac Coherent Light Source (LCLS) II are extremely intense sources of X-rays capable of generating Serial Femtosecond Crystallography (SFX) data at megahertz (MHz) repetition rates. Previous work has shown that it is possible to use consecutive X-ray pulses to collect diffraction patterns from individual crystals. Here, we exploit the MHz pulse structure ofthe European XFEL to obtain two complete datasets from the same lysozyme crystal, first hit and the second hit, before it exits the beam. The two datasets, separated by <1 µs, yield up to 2.1 Å resolution structures. Comparisons between the two structures reveal no indications of radiation damage or significant changes within the active site, consistent with the calculated dose estimates. This demonstrates MHz SFX can be used as a tool for tracking sub-microsecond structural changes in individual single crystals, a technique we refer to as multi-hit SFX