Major depressive disorder (MDD) is a heterogeneous mental disorder. International guidelines present overall symptom severity as the key dimension for clinical characterisation. However, additional layers of heterogeneity may reside within severity levels related to how symptoms interact with one-another in a patient, called symptom dynamics. We investigate these individual differences by estimating the proportion of patients that display differences in their symptom dynamics while sharing the same diagnosis and overall symptom severity. We show that examining symptom dynamics provides information about the person-specific psychopathological expression of patients beyond severity levels by revealing how symptoms aggravate each other over time. These results suggest that symptom dynamics may serve as a promising new dimension for clinical characterisation. Areas of opportunity are outlined for the field of precision psychiatry in uncovering disorder evolution patterns (e.g., spontaneous recovery; critical worsening) and the identification of granular treatment effects by moving toward investigations that leverage symptom dynamics as their foundation. Future work aimed at investigating the cascading dynamics underlying depression onset and maintenance using the large-scale (N > 5.5 million) CIPA Study are outlined. 

A 1977 conjecture of Erdős and Hajnal asserts that for every hereditary class of graphs not containing all graphs, every graph in the class has a polynomial-sized clique or stable set. Fox, Pach, and Suk and independently Chernikov, Starchenko, and Thomas asked whether this conjecture holds for every class of graphs of bounded VC-dimension. In joint work with Alex Scott and Paul Seymour, we resolved this question in the affirmative. The talk will introduce the Erdős–Hajnal conjecture and discuss some ideas behind the proof of the bounded VC-dimension case.