We introduce the problem of PAC rank elicitation, which consists of sorting a given set of options based on adaptive sampling of stochastic pairwise preferences. More specifically, we assume the existence of a ranking procedure, such as Copeland’s method, that determines an underlying target order of the options. The goal is to predict a ranking that is sufficiently close to this target order w...

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we aim to approximate the unknown rank based on the location of sampled entries and some given completion. We consider a number of data models, including singl...

Ships play the major role in bulk transportation and they need their special energy system. This paper proposes a stochastic programing method for optimal sizing of a hybrid ship power system with energy storage system (ESS), photovoltaic power (PV) and diesel generator. To account for uncertainties, in this study a two-stage stochastic mixed-integer non-linear programing is used to model the o...

We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham and Wilson [5] in the case of unoriented graphs, and by Chung and Graham [3] in the case of tournaments. Indeed, our main theorem extends to the case of a general underlying graph G th...

Satellite orographic precipitation estimates exhibit large errors with space-time structure tied to landform. Observations in the Southern Appalachian Mountains (SAM) suggest that low-level clouds and fog (LLCF) amplify mid-day rainfall via seeder-feeder interactions (SFI) at both high and low elevations. Here, a rainfall microphysics model constrained by fog observations was used first to reve...

The optimal policy response to a low-probability extreme event is examined. A simple policy problem is solved for a sequence of different loss functions: quadratic, combined quadratic/absolute-deviation, absolute-deviation, combined quadratic/constant, and perfectionist. The paper shows that, under some simplifying assumptions, each of these loss functions puts less weight on a low-probability ...

This paper describes the use of polynomial chaos expansions to approximate the probability of a collision between two satellites after at least one performs a translation maneuver. Polynomial chaos provides a computationally efficient means to generate an approximate solution to a stochastic differential equation without introducing any assumptions on the a posteriori distribution. The stochast...