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Mathematical Innovation Advances Complex Simulations for Science’s Toughest Problems

A two-part diagram illustrating a mathematical framework for simplifying complex models. The top diagram shows a V-shaped path of blue arrows enclosing a horizontal line that extends from a point labeled '0' towards an infinity symbol. Small circles along the line represent key numbers describing a system's dynamics. The blue path illustrates a calculation where orange and green segments at the far right can be ignored, allowing scientists to focus on the system's essential features for faster results. The bottom diagram shows a horizontal line with colored tick marks representing a random process visiting different states over time. Above the line, red brackets group larger sets of states into repeating loops, or cycles. Below the line, blue brackets highlight more specific cycles. This illustrates how analyzing these cycles can simplify and speed up complex simulations.

Software Highlight: Caffeine Supercharges Fortran for the Exascale Era

A graphic representation of a coffee cup with layered components illustrating a software architecture. The layers from top to bottom include: 'Compiled Application,' 'PRIF,' 'Caffeine,' and 'GASNet-EX.' The base of the cup is labeled 'System Runtime & Memory Technologies,' indicating the foundational technologies that support the application.
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