An international team of researchers shows through a concrete theoretical experiment that the prediction by standard complex quantum theory cannot be expressed by its real counterpart and ratifies its ...

Tutorials contains the code accompanying the HIP Tutorials that can be found in the HIP documentation. For a full overview over the examples see the section repository contents. Alternatively, instead ...

In this tutorial, we walk through advanced usage of Einops to express complex tensor transformations in a clear, readable, and mathematically precise way. We demonstrate how rearrange, reduce, repeat, ...

Many Americans are watching in amazement and horror at the serious allegations of government fraud and waste. These are not small clerical errors or isolated mistakes. It’s about taxpayer dollars — on ...

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The Nature Index 2025 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

Ask the publishers to restore access to 500,000+ books. An icon used to represent a menu that can be toggled by interacting with this icon. A line drawing of the Internet Archive headquarters building ...

It is a fact that imaginary numbers do not have practical significance. But the role of imaginary numbers is very broad and enormous, due to the existence of Euler’s formula. Due to Euler’s formula, ...