Prophet inequalities compare the expected performance of an online algorithm for a stochastic optimization problem to optimal solution in hindsight. They are major alternative classic worst-case competitive analysis, particular importance design and analysis simple (posted-price) incentive compatible mechanisms with provable approximation guarantees. A central open this area concerns subadditiv...

Let fb k (n)g 1 n=0 be the Bell numbers of order k. It is proved that the sequence fb k (n)=n!g 1 n=0 is log-concave and the sequence fb k (n)g 1 n=0 is log-convex, or equivalently, the following inequalities hold for all n 0, 1 b k (n + 2)b k (n) b k (n + 1) 2 n + 2 n + 1 : Let f(n)g 1 n=0 be a sequence of positive numbers with (0) = 1. We show that if f(n)g 1 n=0 is log-convex, then (n)(m) (n...

Much of the research in software engineering focuses on understanding the dynamic nature of software systems. Such research typically uses automated instrumentation or profiling techniques on the code. In this thesis, we examine logs as another source of dynamic information. Such information is generated from statements inserted into the code during development to draw the attention of system o...

We present LTLS, a technique for multiclass and multilabel prediction that can perform training and inference in logarithmic time and space. LTLS embeds large classification problems into simple structured prediction problems and relies on efficient dynamic programming algorithms for inference. We train LTLS with stochastic gradient descent on a number of multiclass and multilabel datasets and ...

Weconsider noisy optimization problems,without the assumption of variance vanishing in the neighborhood of the optimum. We show mathematically that simple rules with exponential number of resamplings lead to a log-log convergence rate. In particular, in this case the log of the distance to the optimum is linear on the log of the number of resamplings. As well as with number of resamplings polyn...