Exploring the generalizability of visual search strategies

When searching our visual environment, we often have multiple strategies available. For example, when looking for apples on a supermarket shelf, you can look for red things, round things, or you can just search serially through all items. How do we choose a strategy? Recent research on this question has revealed substantial variation across individuals in attentional control strategies when approaching visual search tasks, and the strategies have been found to be reliable within subjects. However, strategies on one visual search task have failed to generalize across different paradigms that assess various components of strategy use (Clarke et al., 2018). Thus, evidence for whether strategies generalize beyond a single paradigm remains scarce. While previous tests of generalizability used paradigms that vary in many ways, we focused on a single strategy component that could be preserved across tasks, with several other changes. In two experiments, we assessed the correlation between individuals' strategies in the Standard Adaptive Choice Visual Search (Standard ACVS; Irons & Leber, 2018) and a modified novel visual search task, Spatial ACVS. In the Standard ACVS, participants seeking to perform optimally have to enumerate subsets of different colored squares and identify the smaller subset to choose a target from. Similarly, in the Spatial ACVS, participants seeking optimal performance have to enumerate spatially separate subsets of squares (one on the left and one on the right side of the display), choosing the target in the smaller subset. Participants finished both tasks in the same order in one experimental session. Results showed a positive correlation in optimal target choices between the two tasks (r = .38), indicating similar strategy usage. Future studies can focus on what strategy components tend more to be generalized across tasks and whether an individual's strategy can generalize to tasks with a combination of several strategy components. The ultimate goal is to fully understand how people choose their attentional control strategies in unconstrained, real-life environments.NSF BCS-1632296No embargoAcademic Major: Psycholog

Structure theorem of square complex orthogonal design

Square COD (complex orthogonal design) with size $[n, n, k]$ is an $n \times n$ matrix $\mathcal{O}_z$, where each entry is a complex linear combination of $z_i$ and their conjugations $z_i^*$, $i=1,\ldots, k$, such that $\mathcal{O}_z^H \mathcal{O}_z = (|z_1|^2 + \ldots + |z_k|^2)I_n$. Closely following the work of Hottinen and Tirkkonen, which proved an upper bound of $k/n$ by making a crucial observation between square COD and group representation, we prove the structure theorem of square COD