No abstract

How do we create content that will become viral in a whole network after we share it with friends or followers? Signi cant research activity has been dedicated to the problem of strategically selecting a seed set of initial adopters so as to maximize a meme's spread in a network. This line of work assumes that the success of such a campaign depends solely on the choice of a tunable seed set of adopters, while the way users perceive the propagated meme is xed. Yet, in many real-world settings, the opposite holds: a meme's propagation depends on users' perceptions of its tunable characteristics, while the set of initiators is xed. In this paper, we address the natural problem that arises in such circumstances: Suggest content, expressed as a limited set of attributes, for a creative promotion campaign that starts out from a given seed set of initiators, so as to maximize its expected spread over a social network. To our knowledge, no previous work addresses this problem. We nd that the problem is NP-hard and inapproximable. As a tight approximation guarantee is not admissible, we design an e cient heuristic, Explore-Update, as well as a conventional Greedy solution. Our experimental evaluation demonstrates that Explore-Update selects near-optimal attribute sets with real data, achieves 30% higher spread than baselines, and runs an order of magnitude faster than the Greedy solution.

The mathematical model of the mechanical system, which is a section of the pipeline with built-in motor pump system and damper for vibration damping, has been developed. The mathematical model is represented by a system of partial differential equations of hydrodynamics for moving fluid in the pipeline and a system of two ordinary differential equations for the damping device. Solution the system of equations is performed using analytical and numerical methods. The numerical solution of the equations of hydrodynamics carried out using the finite element method, implemented in the programming environment of mathematical package freeFEM ++.