Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable Instances

This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families of CNF formulas hard for resolution, which is a central task of Proof-Complexity theory, but also propose models with both many hard instances and exact phase transitions. Then, the implications of such models are addressed. It is shown both theoretically and experimentally that an application of Model RB/RD might be in the generation of hard satisfiable instances, which is not only of practical importance but also related to some open problems in cryptography such as generating one-way functions. Subsequently, a further theoretical support for the generation method is shown by establishing exponential lower bounds on the complexity of solving random satisfiable and forced satisfiable instances of RB/RD near the threshold. Finally, conclusions are presented, as well as a detailed comparison of Model RB/RD with the Hamiltonian cycle problem and random 3-SAT, which, respectively, exhibit three different kinds of phase transition behavior in NP-complete problems.Comment: 19 pages, corrected mistakes in Theorems 5 and

Extroverts Tweet Differently from Introverts in Weibo

Being dominant factors driving the human actions, personalities can be excellent indicators in predicting the offline and online behavior of different individuals. However, because of the great expense and inevitable subjectivity in questionnaires and surveys, it is challenging for conventional studies to explore the connection between personality and behavior and gain insights in the context of large amount individuals. Considering the more and more important role of the online social media in daily communications, we argue that the footprint of massive individuals, like tweets in Weibo, can be the inspiring proxy to infer the personality and further understand its functions in shaping the online human behavior. In this study, a map from self-reports of personalities to online profiles of 293 active users in Weibo is established to train a competent machine learning model, which then successfully identifies over 7,000 users as extroverts or introverts. Systematical comparisons from perspectives of tempo-spatial patterns, online activities, emotion expressions and attitudes to virtual honor surprisingly disclose that the extrovert indeed behaves differently from the introvert in Weibo. Our findings provide solid evidence to justify the methodology of employing machine learning to objectively study personalities of massive individuals and shed lights on applications of probing personalities and corresponding behaviors solely through online profiles.Comment: Datasets of this study can be freely downloaded through: https://doi.org/10.6084/m9.figshare.4765150.v