Elizabeth Y. Huang

Omid Askarisichani, Elizabeth Y. Huang, Abed K. Musaffar et al.

Discovering the antecedents of individuals' influence in collaborative environments is an important, practical, and challenging problem. In this paper, we study interpersonal influence in small groups of individuals who collectively execute a sequence of intellective tasks. We observe that along an issue sequence with feedback, individuals with higher expertise and social confidence are accorded higher interpersonal influence. We also observe that low-performing individuals tend to underestimate their high-performing teammate's expertise. Based on these observations, we introduce three hypotheses and present empirical and theoretical support for their validity. We report empirical evidence on longstanding theories of transactive memory systems, social comparison, and confidence heuristics on the origins of social influence. We propose a cognitive dynamical model inspired by these theories to describe the process by which individuals adjust interpersonal influences over time. We demonstrate the model's accuracy in predicting individuals' influence and provide analytical results on its asymptotic behavior for the case with identically performing individuals. Lastly, we propose a novel approach using deep neural networks on a pre-trained text embedding model for predicting the influence of individuals. Using message contents, message times, and individual correctness collected during tasks, we are able to accurately predict individuals' self-reported influence over time. Extensive experiments verify the accuracy of the proposed models compared to baselines such as structural balance and reflected appraisal model. While the neural networks model is the most accurate, the dynamical model is the most interpretable for influence prediction.

Saber Jafarpour, Elizabeth Y. Huang, Francesco Bullo

Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with arbitrary topology and heterogeneous edge weights. We propose a novel equivalent transcription for the equilibrium synchronization equation. Using this transcription, we develop a power series expansion to compute the synchronized solution of the Kuramoto model as well as a sufficient condition for the strong convergence of this series expansion. Truncating the power series provides (i) an efficient approximation scheme for computing the synchronized solution, and (ii) a simple-to-check, statistically-correct hierarchy of increasingly accurate synchronization tests. This hierarchy of tests provides a theoretical foundation for and generalizes the best-known approximate synchronization test in the literature. Our numerical experiments illustrate the accuracy and the computational efficiency of the truncated series approximation compared to existing iterative methods and existing synchronization tests.

Elizabeth Y. Huang, Saber Jafarpour, Francesco Bullo

Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite extensive study on this topic, the quest for sharp closed-form synchronization tests is still in vain. In this paper, we present an algorithm for finding the Taylor expansion of the inverse Kuramoto map. We show that this Taylor series can be used to obtain a hierarchy of increasingly accurate approximate tests with low computational complexity. These approximate tests are then used to estimate the threshold of synchronization as well as the position of the synchronization manifold of the network.