Playing Stackelberg Opinion Optimization with Randomized Algorithms for Combinatorial Strategies

From a perspective of designing or engineering for opinion formation games in social networks, the "opinion maximization (or minimization)" problem has been studied mainly for designing subset selecting algorithms. We furthermore define a two-player zero-sum Stackelberg game of competitive opinion optimization by letting the player under study as the first-mover minimize the sum of expressed opinions by doing so-called "internal opinion design", knowing that the other adversarial player as the follower is to maximize the same objective by also conducting her own internal opinion design. We propose for the min player to play the "follow-the-perturbed-leader" algorithm in such Stackelberg game, obtaining losses depending on the other adversarial player's play. Since our strategy of subset selection is combinatorial in nature, the probabilities in a distribution over all the strategies would be too many to be enumerated one by one. Thus, we design a randomized algorithm to produce a (randomized) pure strategy. We show that the strategy output by the randomized algorithm for the min player is essentially an approximate equilibrium strategy against the other adversarial player

Flavor Structure of the Nucleon Sea

We review the current status and future prospects on the subject of flavor structure of the nucleon sea. The flavor structure of the nucleon sea provides unique information on the non-perturbative aspects of strong interactions allowing stringent tests of various models on the partonic structures of the nucleons as well as lattice QCD calculations. The scope of this review covers the unpolarized, polarized, and the transverse-momentum dependent sea-quark distributions of the nucleons. While the main focus of this review is on the physics motivation and recent progress on the subject of the nucleon sea, we also discuss future prospects of addressing some outstanding issues on the flavor structure of the nucleon sea.Comment: 61 pages and 36 figures; published versio