Dynamic arrays have brought significant flexibility to Excel, allowing formulas to automatically expand or contract across cells. However, this functionality introduces a common issue: formatting ...

Python threading and subprocesses explained Learn how to choose between threads or processes for parallel operations in Python, and find out what the free-threaded build in Python 3.13 brings to the ...

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...

Move over karyotypes—genetic disorder detection has vastly improved. Researchers are now using array CGH (aCGH), to quickly scan through an entire genome for imbalances. Because aCGH facilitates ...

Triton kernels for causal depthwise separable convolutions with per-token (dynamic) convolution weights. The following example shows how to add low-rank dynamic short convolutions to the queries, keys ...