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Mass spectrometry proteomics is the method of choice for large-scale quantitation of proteins in biological samples, allowing rapid measurement of the concentrations of thousands of proteins in various modified forms. However, this technique still faces fundamental challenges in terms of reproducibility, bias, and comprehensiveness of proteome coverage. Next-generation mass spectrometry, also known as data-independent acquisition, is a promising new approach with the potential to measure the proteome in a far more comprehensive and reproducible fashion than existing methods, but it has lacked a computational framework suited to the highly convoluted spectra it inherently produces. I will discuss Specter, an algorithm that employs linear unmixing to disambiguate the signals of individual proteins and peptides in next-generation mass spectra. In addition to describing the linear algebra underlying Specter, we'll discuss its implementation in Spark with Python, and see several real datasets to which it's been applied.