We present the first potential function for pairing heaps with linear range. This implies that the runtime of a short sequence of operations is faster than previously known. It is also simpler than the only other potential function known to give amortized constant amortized time

One of the most difficult problems in computational chemistry is the prediction of the three-dimensional structure of a protein molecule given only its amino acid sequence. Although there are several programs for calculating the empirical or quantum mechanical energies, and there are more programs for either minimizing the energy as a function of conformation or for simulating the dynamics of a...

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Groucho (Gro)/Transducin-like enhancer of split (TLE) family proteins act as co-repressors of many transcription factors, and are involved in key signaling pathways. TLE1 negatively regulates inflammation and has potential roles in various diseases, including cancer. Previous studies suggest TLE1 could be used as a diagnostic marker and is a possible therapeutic target in various malignancies. ...

This note discusses proofs for convergence of first-order methods based on simple potentialfunction arguments. We cover methods like gradient descent (for both smooth and non-smooth settings), mirror descent, and some accelerated variants.