Upcoming Doctoral Dissertations

"Real-world data exhibit hierarchical and compositional structure, where high-level semantics interact with fine-grained details. A central goal of modern generative modeling is to build models that capture this structure, not only synthesizing high-quality samples but also learning meaningful representations across multi-level abstraction. Hierarchical generative model and energy-based model (EBM) are two fundamental generative models factorized by distinct formulations, featuring unique properties and driving active research exploration." Read more

"Mucosal healing is strongly linked to improved clinical outcomes in patients with inflammatory bowel disease; however, the specific role of the epithelium in driving this process in vivo remains poorly defined. To address this, we examined mucosal repair in an acute dextran sulfate sodium–induced colitis model in which epithelial-specific deletion of Smad4 results in an attenuated colitis response. We find that enhanced epithelial wound healing alleviates the fibrotic response." Read more

"This research investigates computational complexity aspects of word problems in HNN extensions. The study builds upon Miller’s classical result demonstrating the existence of HNN extensions with decidable word problems but undecidable conjugacy problems." Read more

"We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over $L_2$ remains open, we prove that the Diophantine problem for single equations in one variable is decidable. Our approach reduces the problem to a divisibility question for families of parametric Laurent polynomials over $\MZ_2$, whose coefficients depend linearly on an integer parameter." Read more