Image courtesy of UWM/Allie Kilmer
A new algorithm reduces timing uncertainty by a factor of 300, revealing ultrafast dynamics on timescales as short as a quadrillionth of a second.

The Science

A clear understanding of ultrafast phenomena underlies the ultimate control of reactions ranging from vision to photosynthesis. A major breakthrough towards this understanding hinges on the ability to generate movies of such ultrafast dynamics by correctly ordering experimental "snapshots" taken during reactions. Exactly when a snapshot was recorded in the evolution of a reaction, however, is often uncertain. A team of physicists developed a mathematical technique that accurately orders collections of noisy snapshots that were recorded with extreme timing uncertainty.

The Impact

Determining the temporal evolution – the dynamics – of a system in the past or into the future is a paramount goal of science. But imperfect knowledge of the time-points at which experimental snapshots of an evolving system were recorded often degrades the ability to recover accurate dynamical information. Examples of this problem exist in physics, chemistry, and biology, where reaction initiation can be non-uniform; astronomy, climate science, and geology, where timing of past events can be uncertain; and signal processing, where noise and timing jitter are prevalent. The new computer algorithm is thus expected to have a broad impact in many areas of science and technology.


A team of scientists from the University of Wisconsin-Milwaukee, Northwestern University, and the University of Hamburg have demonstrated a powerful algorithm that retrieves accurate temporal information from data with timing uncertainty. The fundamental premise is simple. A sufficiently long series of snapshots ordered according to their inaccurate timestamps still contains some time-evolutionary information ("a weak arrow of time"). This information allows the course of events to be accurately reconstructed by powerful mathematical techniques that extract signal, in this case the arrow of time, from noise. Using data recorded at the Linac Coherent Light Source with 300-femtosecond timing uncertainty, the team compiled a spectral movie of the rupture of chemical bonds on the one-femtosecond scale (light travels ~1% of the width of human hair in one femtosecond).


Abbas Ourmazd
University of Wisconsin Milwaukee


The research conducted by Fung and Ourmazd was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under award DE-SC0002164 (algorithm design & development, and data analysis), and by the U.S. National Science Foundation under awards STC 1231306 (numerical trial models) and 1551489 (underlying analytical models).  The research conducted by Ramakrishna and Seideman was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under award DE-FG02-04ER15612. The Linac Coherent Light Source is an Office of Science User Facility operated by SLAC National Accelerator Laboratory for the Office of Basic Energy Sciences.


R. Fung, A.M. Hanna, O. Vendrell, S. Ramakrishna, T. Seideman, R. Santra, and A. Ourmazd, "Dynamics from noisy data with extreme timing uncertainty." Nature 532, 471 (2016). [DOI: 10.1038/nature17627External link]

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