We present Graph Neural ODEs (GNODEs) for modeling tumor microenvironment dynamics with mathematically guaranteed stability and conservation properties. Unlike bulk ODEs that miss spatial heterogeneity or discrete GNNs that inadequately capture continuous biological processes, GNODEs provide continuous-time evolution with explicit adjacency-aware dynamics while maintaining provable trajectory bounds. Our framework ensures: (1) existence and uniqueness of solutions under dynamic graph topology, (2) Lyapunov stability preventing unphysical states like negative cell counts, and (3) exact conservation of biological invariants through architectural constraints. Benchmarking on synthetic tumor data demonstrates that GNODE accurately captures the dynamics of the resistant cell fraction (0.282 predicted vs 0.242 true), whereas graph-free alternatives fail completely (0.000), underscoring the importance of stability-constrained local interactions for modeling emergent resistance.

Mai Phan Quoc Hung, Khanh Nguyen Quoc, Đoàn Minh Luong, Duong Thu Ngan, Duong Thi Phuong Thao, Tuan Do. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. In cognitive radio networks, secondary users equipped with frequency-agile cognitive radios communicate with one another via spectrum that is not being used by the primary, licensed users of the spectrum. We consider a multichannel cognitive radio network scenario in which a secondary transmitter can switch to different channels for opportunistic communications. Multichannel diversity can be achieved by dynamically switching to different channels during transmission. Our numerical results show that even a simple randomized channel switching scheme can significantly reduce the average symbol error probability. We also propose a scheduling algorithm based on maximizing signal-to-noise ratio to further improve the performance of cognitive transmission.