Caroline N. Cappetto | Searcharxiv

arXiv2026

Adaptive High-Level Tight Control of Prostate Cancer: A Path from From Terminal Disease to Chronic Condition

Metastatic prostate cancer is one of the leading causes of cancer-related morbidity and mortality worldwide. It is characterized by a high mortality rate and a poor prognosis. In this work, we explore how a clinical oncologist can apply a Stackelberg game-theoretic framework to prolong metastatic prostate cancer survival, or even make it chronic in duration. We utilize a Bayesian optimization approach to identify the optimal adaptive chemotherapeutic treatment policy for a single drug (Abiraterone) to maximize the time before the patient begins to show symptoms. We show that, with precise adaptive optimization of drug delivery, it is possible to significantly prolong the cancer suppression period, potentially converting metastatic prostate cancer from a terminal disease to a chronic disease for most patients, as supported by clinical and analytical evidence. We suggest that clinicians might explore the possibility of implementing a high-level tight control (HLTC) treatment, in which the trigger signals (i.e. biomarker levels) for drug administration and cessation are both high and close together, typically yield the best outcomes, as demonstrated through both computation and theoretical analysis. This simple insight could serve as a valuable guide for improving current adaptive chemotherapy treatments in other hormone-sensitive cancers.

q-bio.QM↗

arXiv2025

Digitization Can Stall Swarm Transport: Commensurability Locking in Quantized-Sensing Chains

We present a minimal model for autonomous robotic swarms in one- and higher-dimensional spaces, where identical, field-driven agents interact pairwise to self-organize spacing and independently follow local gradients sensed through quantized digital sensors. We show that the collective response of a multi-agent train amplifies sensitivity to weak gradients beyond what is achievable by a single agent. We discover a fractional transport phenomenon in which, under a uniform gradient, collective motion freezes abruptly whenever the ratio of intra-agent sensor separation to inter-agent spacing satisfies a number-theoretic commensurability condition. This commensurability locking persists even as the number of agents tends to infinity. We find that this condition is exactly solvable on the rationals -- a dense subset of real numbers -- providing analytic, testable predictions for when transport stalls. Our findings establish a surprising bridge between number theory and emergent transport in swarm robotics, informing design principles with implications for collective migration, analog computation, and even the exploration of number-theoretic structure via physical experimentation.

cond-mat.soft↗