In recent years, multiparameter persistent homology (MPH) has been developed to address the limitations of traditional single-parameter persistence. While much progress has been made on the theoretical aspects of MPH, practical applications have mostly been limited to the special case of two parameters. Building on recent developments in the computation of MPH in more than two parameters, we propose and implement a new algorithm for the computation of multiparameter persistence landscapes in this setting. We apply this work to compute landscapes of three-parameter persistence modules built on spatiotemporal data arising in biology.
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Many species live in groups and coordinate behavior with conspecifics, but the sensory computations that allow individuals to detect, evaluate, and respond to others remain difficult to study. A major challenge is that social interactions are reciprocal: animals continuously change each other’s sensory experience, making it hard to separate stimulus, perception, internal state, and behavioral response.
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\r\nIn my lab, we use juvenile zebrafish shoaling as an experimentally accessible model for vertebrate social behavior. Using virtual reality, we previously identified self-like biological motion as a visual trigger of shoaling and traced this signal into a tecto-thalamic pathway that contributes to social attraction. We now build on this framework to ask how elementary visual cues are combined into richer social representations.
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\r\nI will discuss two examples. In one project, behavioral experiments and neural recordings suggest that zebrafish evaluate group size through an integrated visual variable that combines object number and motion, so that faster small groups can become behaviorally equivalent to slower larger groups. In another, we study social buffering: the reduction of fear-related behavior by conspecific cues. Here, social information can either transmit immediate alarm or provide persistent safety, depending on context. Whole-brain activity mapping reveals neural correlates of fear state and its suppression by social cues.
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\r\nTogether, these projects show how controlled visual stimuli, quantitative behavior, whole-brain activity mapping, and cellular-resolution imaging can reveal how animals transform simple sensory features into social decisions. More broadly, this work aims to understand how nervous systems extract meaning from the motion and presence of others — from detecting social cues to finding safety in numbers.
Thesis Director: Prof. Z. Patakfalvi,
\r\nMathematics doctoral program
\r\nThesis Nr. 12192
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\r\nTo take part in the public defense, please contact directly the speaker
Thesis Director: Prof. S. C. Olhede,
\r\nMathematics doctoral program
\r\nThesis Nr. 11276
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\r\nTo take part in the public defense, please contact directly the speaker