A koan is an enigmatic, and often senseless, question posed as an aid to meditation in Zen Buddhism. By “chi-square”, we mean Pearson’s general scheme of a p-value, or tail, statistic that is constructed as a sum of independent random variables, each of which is the square of a normal deviate N(0, 1) (or at least approximately so). Such a statistic is distributed according to the familiar χ2I d...

We consider a special case of the generalized Pólya’s urn model introduced in [3]. Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. A question of essential inter...

We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P ≠ NP. 2000 Mathematics Subject Classification: 68W25, 68W4

We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P 6= NP.

software tool that bins genomic fragments that have first undergone limited preassembly into contigs. Their strategy uses a variational Bayesian approach combining sequence composition and correlated abundance across multiple samples to produce sequence assignments. CONCOCT bins genomes with high precision and recall in simulated and real data, providing higher coverage than can typically be re...

We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles have to be packed nonoverlapping and orthogonal, i.e., axis-parallel. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P 6= NP.

We consider the problem of resource allocation in a parallel environment where new incoming resources are arriving online in groups or batches. We study this scenario in an abstract framework of allocating balls into bins. We revisit the allocation algorithm GREEDY[2] due to Azar, Broder, Karlin, and Upfal (SIAM J. Comput. 1999), in which, for sequentially arriving balls, each ball chooses two ...

Metabolite identifications are most frequently achieved in untargeted metabolomics by matching precursor mass and full, high-resolution MS(2) spectra to metabolite databases and standards. Here we considered an alternative approach for establishing metabolite identifications that does not rely on full, high-resolution MS(2) spectra. First, we select mass-to-charge regions containing the most in...