Control strategies for vector systems typically depend on the controller's ability to plan out future control actions. However, in the case where model parameters are random and time-varying, this planning might not be possible. This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental tension in the control of underactuated vector systems - the need to balance the growth of the system in different dimensions. We characterize the stabilizability of d-dimensional systems with symmetric gain matrices by providing tight necessary and sufficient conditions that depend on the eigenvalues of the system. The proof technique is slightly different from the standard dynamic programming approach and relies on the fact that the second moment stability of the system can also be understood by examining any arbitrary weighted two-norm of the state.

The major types of non-small-cell lung cancer (NSCLC)-squamous cell carcinoma and adenocarcinoma-have distinct immune microenvironments. We developed a genetic model of squamous NSCLC on the basis of overexpression of the transcription factor Sox2, which specifies lung basal cell fate, and loss of the tumor suppressor Lkb1 (SL mice). SL tumors recapitulated gene-expression and immune-infiltrate features of human squamous NSCLC; such features included enrichment of tumor-associated neutrophils (TANs) and decreased expression of NKX2-1, a transcriptional regulator that specifies alveolar cell fate. In Kras-driven adenocarcinomas, mis-expression of Sox2 or loss of Nkx2-1 led to TAN recruitment. TAN recruitment involved SOX2-mediated production of the chemokine CXCL5. Deletion of Nkx2-1 in SL mice (SNL) revealed that NKX2-1 suppresses SOX2-driven squamous tumorigenesis by repressing adeno-to-squamous transdifferentiation. Depletion of TANs in SNL mice reduced squamous tumors, suggesting that TANs foster squamous cell fate. Thus, lineage-defining transcription factors determine the tumor immune microenvironment, which in turn might impact the nature of the tumor.