Sunday, February 5, 2023

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2023-02-10 / 14:00 ~ 16:00
IBS-KAIST 세미나 - 수리생물학: 인쇄
by ()
Mapping individual differences in behavior is fundamental to personalized neuroscience, but quantifying complex behavior in real world settings remains a challenge. While mobility patterns captured by smartphones have increasingly been linked to a range of psychiatric symptoms, existing research has not specifically examined whether individuals have person-specific mobility patterns. We collected over 3000 days of mobility data from a sample of 41 adolescents and young adults (age 17–30 years, 28 female) with affective instability. We extracted summary mobility metrics from GPS and accelerometer data and used their covariance structures to identify individuals and calculated the individual identification accuracy—i.e., their “footprint distinctiveness”. We found that statistical patterns of smartphone-based mobility features represented unique “footprints” that allow individual identification (p < 0.001). Critically, mobility footprints exhibited varying levels of person-specific distinctiveness (4–99%), which was associated with age and sex. Furthermore, reduced individual footprint distinctiveness was associated with instability in affect (p < 0.05) and circadian patterns (p < 0.05) as measured by environmental momentary assessment. Finally, brain functional connectivity, especially those in the somatomotor network, was linked to individual differences in mobility patterns (p < 0.05). Together, these results suggest that real-world mobility patterns may provide individual-specific signatures relevant for studies of development, sleep, and psychopathology.
2023-02-07 / 11:00 ~ 12:00
IBS-KAIST 세미나 - 대수기하학: The Martens-Mumford Theorem and the Green-Lazarsfeld Secant Conjecture 인쇄
by Daniele Agostini(Eberhard Karls Universität Tübingen)
The syzygies of a curve are the algebraic relation amongst the equation defining it. They are an algebraic concept but they have surprising applications to geometry. For example, the Green-Lazarsfeld secant conjecture predicts that the syzygies of a curve of sufficiently high degree are controlled by its special secants. We prove this conjecture for all curves of Clifford index at least two and not bielliptic and for all line bundles of a certain degree. Our proof is based on a classic result of Martens and Mumford on Brill-Noether varieties and on a simple vanishing criterion that comes from the interpretation of syzygies through symmetric products of curves.
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