arXiv subjects

Elizabeth Y. Huang

Publications and source records attributed to Elizabeth Y. Huang.

5 recordsLinked to original sources

arXiv2025

Expertise and confidence explain how social influence evolves along intellective tasks

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.

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arXiv2020

Flow and Elastic Networks on the $n$-torus: Geometry, Analysis, and Computation

Networks with phase-valued nodal variables are central in modeling several important societal and physical systems, including power grids, biological systems, and coupled oscillator networks. One of the distinctive features of phase-valued networks is the existence of multiple operating conditions corresponding to critical points of an energy function or feasible flows of a balance equation. For networks with phase-valued states, it is not yet fully understood how many operating conditions exist, how to characterize them, and how to compute them efficiently. A deeper understanding of feasible operating conditions, including their dependence upon network structures, may lead to more reliable and efficient network systems. This paper introduces flow and elastic network problems on the $n$-torus and provides a rigorous and comprehensive framework for their study. Based on a monotonicity assumption, this framework localizes the solutions, bounds their number, and leads to an algorithm to compute them. Our analysis is based on a novel winding partition of the $n$-torus into winding cells, induced by Kirchhoff's angle law for undirected graphs. The winding partition has several useful properties, including notably that, each winding cell contains at most one solution. The proposed algorithm is based on a novel contraction mapping and is guaranteed to compute all solutions. Finally, we apply our results to numerically study the active power flow equations in several test cases and estimate power capacity and congestion of a power network.

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arXiv2020

Assign and Appraise: Achieving Optimal Performance in Collaborative Teams

Tackling complex team problems requires understanding each team member's skills in order to devise a task assignment maximizing the team performance. This paper proposes a novel quantitative model describing the decentralized process by which individuals in a team learn who has what abilities, while concurrently assigning tasks to each of the team members. In the model, the appraisal network represents team member's evaluations of one another and each team member chooses their own workload. The appraisals and workload assignment change simultaneously: each member builds their own local appraisal of neighboring members based on the performance exhibited on previous tasks, while the workload is redistributed based on the current appraisal estimates. We show that the appraisal states can be reduced to a lower dimension due to the presence of conserved quantities associated to the cycles of the appraisal network. Building on this, we provide rigorous results characterizing the ability, or inability, of the team to learn each other's skill and thus converge to an allocation maximizing the team performance. We complement our analysis with extensive numerical experiments.

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arXiv2018

Synchronization of Kuramoto Oscillators: Inverse Taylor Expansions

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.

math.OC↗

arXiv2018

Synchronization of Coupled Oscillators: The Taylor Expansion of the Inverse Kuramoto Map

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.

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