Jiguang Yu

Jiguang Yu, Nicholas Brendle, Joel T. Johnson et al.

We propose a physics-grounded mechanism design for dynamic spectrum sharing that bridges the gap between radiometric retrieval constraints and economic incentives. We formulate the active and passive users coexistence problem as a Vickrey-Clarke-Groves (VCG) auctions mechanism, where the radiometer dynamically procures ``quiet'' time-frequency tiles from active users based on the marginal reduction in retrieval error variance. This approach ensures allocative efficiency and dominant-strategy incentive compatibility (DSIC). To overcome the computational intractability of exact VCG on large grids, we derive an approximation algorithm by using the monotone submodularity induced by the radiometer equation. AMSR-2-based simulations show that the approach avoids high-cost tiles by aggregating low-cost spectrum across time and frequency. In an interference-trap case study, the proposed framework reduces procurement costs by about 60% over a fixed-band baseline while satisfying accuracy targets.

Louis Shuo Wang, Jiguang Yu, Ye Liang et al.

Environmental enrichment can destabilize predator--prey coexistence through a Hopf bifurcation, yet real ecosystems are finite and intrinsically stochastic. We investigate how mechanistically derived demographic noise shapes near-Hopf dynamics in the Rosenzweig--MacArthur model by systematically comparing two diffusion closures that share identical deterministic drift but differ solely in predation-induced covariance structure. Starting from a continuous-time Markov chain description, we derive a full-covariance stochastic differential equation whose diffusion tensor inherits stoichiometric coupling, generating a negative prey--predator cross-covariance. This model is contrasted with a drift-matched diagonal-noise comparator. Using linear noise approximation, Lyapunov analysis, and matrix-valued power spectral density formulations, we propagate local covariance structure through the entire diagnostic chain, including stochastic sensitivity ellipses and a dimensionless noisy-precursor indicator. The results highlight that drift equivalence does not imply covariance equivalence and show how event-level noise geometry influences macroscopic behavior in nonlinear ecological systems. This work integrates bifurcation theory and stochastic analysis to advance multi-scale modeling of complex interacting systems.

Jiguang Yu, Louis Shuo Wang, Ye Liang

In this paper, we formulate and analyze an original infinite-horizon bioeconomic optimal control problem for a nonlinear, size-structured fish population. Departing from standard endogenous reproduction frameworks, we model population dynamics using a McKendrick--von Foerster partial differential equation characterized by strictly exogenous lower-boundary recruitment and a nonlocal crowding index. This nonlocal environment variable governs density-dependent individual growth and natural mortality, accurately reflecting the ecological pressures of enhancement fisheries or heavily subsidized stocks. We first establish the existence and uniqueness of the no-harvest stationary profile and introduce a novel intrinsic replacement index tailored to exogenously forced systems, which serves as a vital biological diagnostic rather than a classical persistence threshold. To maximize discounted economic revenue, we derive formal first-order necessary conditions via a Pontryagin-type maximum principle. By introducing a weak-coupling approximation to the adjoint system and applying a single-crossing assumption, we mathematically prove that the optimal size-selective harvesting strategy is a rigorous bang-bang threshold policy. A numerical case study calibrated to an Atlantic cod (\textit{Gadus morhua}) fishery bridges our theoretical framework with applied management. The simulations confirm that the economically optimal minimum harvest size threshold ($66.45$ cm) successfully maintains the intrinsic replacement index above unity, demonstrating that precisely targeted, size-structured harvesting can seamlessly align economic maximization with long-run biological viability.

Jiguang Yu, Louis Shuo Wang, Shihan Ban

Tissues must maintain macroscopic homeostasis despite the continuous microscopic accumulation of cellular damage. Theoretical models of this process often suffer from a disconnect between microscopic biophysics and macroscopic phenomenological games. Here, we bridge this gap by deriving an exact dimensionality reduction of a physiologically structured partial differential equation (PDE) into a low-dimensional dynamical system. Under the condition of uniform mortality, we mathematically demonstrate that tissue homeostasis operates as an induced Nash equilibrium, where the per-capita net growth rates of stem and differentiated phenotypes perfectly equalize. This reduction yields closed-form algebraic rules, the Ratio and Equalization Laws, that map continuous microscopic state dynamics to measurable macroscopic observables. To demonstrate the biological utility of this framework, we present a concrete, falsifiable case study of the murine intestinal crypt. By modeling crypt regeneration following irradiation-induced stem cell depletion, our framework successfully recovers the experimentally observed reliance on progenitor dedifferentiation. Furthermore, the model generates explicit, testable predictions, enabling the in vivo estimation of hard-to-measure lineage plasticity rates directly from aggregate static cell counts. This work provides a rigorous, predictive mathematical foundation for understanding how fast-renewing tissues filter microscopic noise to sustain macroscopic regenerative capacity.