We consider the canonical generalization of the well-studied Longest Increasing Subsequence problem to multiple sequences, called k-LCIS: Given k integer sequences X1, . . . , Xk of length at most n, the task is to determine the length of the longest common subsequence of X1, . . . , Xk that is also strictly increasing. Especially for the case of k = 2 (called LCIS for short), several algorithm...

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process, A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy–Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has...

Because people forget much of what they learn, students could benefit from learning strategies that yield long-lasting knowledge. Yet surprisingly little is known about how long-term retention is most efficiently achieved. Here we examine how retention is affected by two variables: the duration of a study session and the temporal distribution of study time across multiple sessions. Our results ...

We define and study various properties of lateral increasing for mappings defined between two ordered spaces. After introducing some particular classes of ordered spaces, we formulate unilateral characterizations of the property of increasing. The main theorem characterizes the increasing of a map defined on a complete totally ordered space with bilateral conditions which generalize the classic...