Here’s my third and final set of lecture notes for a 4 1 2 \frac{1}{2}-hour minicourse at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. Part 1 is ...

$$I_{m,n}(a,b,c,d):=\int_{-\infty}^{\infty} \frac{1}{(a^2(x-b)^2 + c^2)^m} \frac{1}{(x^2+d^2)^n} \mathrm{d}x$$ where $$m,n\in\mathbb{N}, \hspace{1em} a\in\mathbb{R ...

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The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg, and Haudenosaunee peoples. Our main campus is situated on the ...

Sequencing by synthesis is the underlying technology for many next- generation DNA sequencing platforms. We developed a new model, the fixed flow cycle model, to derive the distributions of sequence ...

Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled ...

A key problem in computational proteomics is distinguishing between correct and false peptide identifications. We argue that evaluating the error rates of peptide ...

In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among ...