arXiv subjects

Jiguang Yu

Publications and source records attributed to Jiguang Yu.

At least 19 recordsLinked to original sources

arXiv2026

FTU-Seek: Foundation Model-Guided Hard-Negative Learning for Sparse Functional Tissue Unit Segmentation

Functional tissue units (FTUs), including tertiary lymphoid structures (TLSs), blood vessels, and glands, encode localized immune, vascular, and epithelial organization in histopathology. Accurate quantification of these structures is important for studying tissue architecture and disease-associated tissue organization. However, FTUs are frequently sparse, heterogeneous, and surrounded by large amounts of morphologically similar background tissue, making automated segmentation in whole-slide images (WSIs) challenging. We therefore developed FTU-Seek, a pathology foundation model-guided framework that treats morphology-aware negative-patch selection as a key component of sparse FTU segmentation. FTU-Seek uses frozen multi-depth features from the UNI pathology foundation model to train a patch-level classifier that distinguishes FTU-containing from FTU-absent tissue. Target-absent patches are subsequently ranked according to their predicted target-containing probabilities, and the highest-scoring hard negatives are selected through a static Top$K$ strategy to construct compact segmentation training sets. The framework was evaluated using five-fold cross-validation and internal test cohorts across TLS, blood-vessel, and gland segmentation tasks, with an additional independent 30-WSI held-out cohort for TLS. Positive-only, all-tissue, random-negative, and matched random Top$K$ sampling strategies served as comparators. Segmentation-derived phenotypes were further explored in external TCGA cohorts.

cs.CV↗

arXiv2026

Rigorous Analysis of a Nonlocal Transport--Renewal System for Physiologically Structured Populations

We develop a rigorous analytical framework for a class of physiologically structured population models with two internal state variables, nonlocal ecological feedbacks, dynamic resources, inter-zone transfer, and selective harvesting. The full model is a coupled nonlinear PDE--ODE transport--renewal system with endogenous inflow at the recruitment boundary, a setting in which transport, nonlocal dependence, and boundary renewal interact at the same level. For this full nonautonomous multi-zone system, we prove finite-horizon well-posedness in a positive $L^{1}$-based state space, including global existence on arbitrary bounded time intervals, uniqueness, nonnegativity, and continuous dependence on initial data, environmental forcing, and harvesting effort. We then isolate an autonomous single-zone reduction at extinction and construct a positive compact next-generation operator on the recruit space. In a further nonlinear stationary reduction, we prove that supercriticality of the basic reproduction number $\mathcal R_{0}>1$ yields existence of a nontrivial stationary state under a parametrized compact-operator hypothesis encoding density-dependent renewal feedback. Finally, for a finite-horizon harvest objective over a compact Lipschitz-regular admissible class, we establish existence of an optimal control. The results separate what can be proved for the full climate-explicit system from what can be justified only after autonomous reduction, thereby clarifying the mathematical scope of threshold and control theory for structured populations.

math.AP↗

arXiv2026

Smooth expanding planar simple waves for Euler--Poisson--Boltzmann: uniform stability and quasineutral expansion

We study the warm-ion Euler--Poisson system with Maxwell--Boltzmann electrons on the cylinder $\R\times\T$ in the quasineutral regime. Taking a smooth expanding planar simple wave of the effective Euler system as the reference state, we construct an even Debye expansion through arbitrary finite order $M$ with a residual of $O(\eps^{2M+2})$. We rigorously establish nonlinear stability on every fixed interval $[t_0,T]$ ($t_0\ge0$), achieving a lifespan and energy constants strictly independent of the Debye length $0<\eps\le\eps_0$. To overcome the singular scaling of the electric field, we develop a novel compensated energy topology that couples the warm-ion symmetrizer to the time-differentiated nonlinear Poisson constraint. By integrating the top-order electric work directly into the time derivative of a weighted energy functional, this mechanism controls the potential in $H^s$ and its gradient in $\eps H^s$, completely eliminating the $\eps^{-1}$ loss typically encountered in the momentum equation. This framework successfully governs distinct neutral end states, captures genuinely two-dimensional rotational perturbations, and yields an arbitrary-order quasineutral asymptotic expansion for prepared data, providing a critical analytical foundation for the geometric theory of multidimensional quasineutral rarefactions.

math.AP↗

arXiv2026

A transport-only null model for apparent heterogeneity in diffusively dosed organoid arrays

Spatial transport can create apparent biological heterogeneity even when organoids are intrinsically identical. We develop a transport-to-phenotype null model for diffusively dosed liver-cancer organoid arrays. The model couples bulk diffusion and clearance to partially accessible adsorption, reversible surface residence, productive internalization, and intracellular state dynamics. Matched asymptotics reduce the perforated-domain problem to a Green-function system, while renewal resolvents describe desorption, re-adsorption, and residence-time effects. Across $2000$ random ten-organoid arrays with localized dosing, the predicted transport-only maturation coefficient of variation has median $0.623$; one-factor design changes move this median between $0.27$ and $0.86$. After matching array-mean exposure, distributed dosing reduces the baseline spread approximately fivefold. The analysis also shows that, in a conservative reflecting chamber, desorption changes uptake timing and allocation but not total eventual uptake; reductions in total uptake require a competing loss channel. Residence laws with equal means can nevertheless produce different transient phenotypes. The spatial reduction is verified against finite-element solutions of the full PDE, and the time reconstruction against numerical Laplace inversion. Finally, a large-batch theorem shows that increasing batch size averages independent process variation but not shared line or batch effects. The framework provides a geometry-specific null against which measured organoid heterogeneity can be assessed.

math.AP↗

arXiv2026

From Flows to Maps: Sampling Laws for Attractor Intensity and Bounded-Noise Escape

Intensity of attraction quantifies the largest amplitude of a persistent bounded disturbance that an attractor can withstand without loss of controlled confinement in its basin. Although intensity has been formulated separately for flows and maps, its behavior under temporal sampling has remained unresolved. We establish an explicit correspondence between the intensity $\mu(A)$ of a continuous-time attractor and the intensity $\mu_h(A)$ of its exact time-$h$ map. For an $L$-Lipschitz vector field, \[ \frac{\mu(A)}{1+Lh} \leq \frac{\mu_h(A)}{h} \leq \mu(A)\frac{e^{Lh}-1}{Lh}, \] and hence $\mu_h(A)/h\to\mu(A)$. The resulting first-order rate is sharp in general, while smooth scalar escape geometries can exhibit second-order convergence. We extend the framework to one-step numerical methods through a stability theory for block intensity and to attracting invariant graphs over compact invertible nonautonomous bases, obtaining uniform sampling convergence over the forcing phase. For bounded-support random perturbations, normalized discrete intensity is identified with the pathwise safety threshold; above it, finite escape follows under an explicit finite-exit condition, while escape probabilities require additional assumptions on the noise law. We also show that the discrete state--normal boundary map converges to the normalized Pontryagin boundary system governing extremal reachable-set boundaries. Exact scalar benchmarks, a grazing resilience model, planar Duffing escape, anisotropic disturbances, periodic and quasiperiodic forcing, and transfer-operator computations illustrate the theory. These results give intensity estimated from discrete observations or simulations a sampling-independent continuous-time meaning.

math.DS↗

arXiv2026

Optimal Harvesting of Size-Structured Populations with Environmental Feedback and Fixed Recruitment Flux

We study a nonlinear size-structured transport model with distributed harvesting and prescribed recruitment flux, where environmental feedback is determined by a scalar population functional. After establishing global well-posedness on $L^1$, we reduce stationary equilibria to a scalar closure equation. This reduction reveals that loss of equilibrium uniqueness occurs through a generic fold, mathematically characterizing critical population transitions. On uniformly nonresonant equilibrium branches, we prove the existence of optimal stationary harvesting policies via the direct method of the calculus of variations. We then derive a boundary-corrected adjoint equation and establish an identity equating equilibrium sensitivity with the adjoint loop gain. This relation yields explicit criteria for the persistence and creation of optimal harvesting thresholds. Collectively, these results provide a unified analytical framework connecting environmental feedback, equilibrium structure, and optimal harvesting.

math.AP↗

arXiv2026

Computational Oncology of Chemotaxis-Driven Tumour--Immune Spatial Patterning and Stability

We develop a reaction--diffusion--chemotaxis model for spatial tumour--immune--chemokine dynamics that couples logistic tumour growth, immune-mediated killing, chemokine-dependent immune recruitment, chemotactic migration, and signal production. For the nondimensional system, we establish local classical solvability, nonnegativity, a uniform tumour-density bound, and global mass estimates for the immune and chemokine components. The tumour-free equilibrium is stable precisely when the baseline immune-control index satisfies $\sigma_0/\delta>1$, whereas positive homogeneous coexistence is characterized by a scalar nonlinear equation. Linearization in the Neumann Laplacian eigenbasis yields a mode-dependent cubic dispersion relation, showing that chemotaxis does not alter the tumour-invasion threshold but can destabilize homogeneous coexistence through a finite-wavelength oscillatory instability above a critical sensitivity $\xi_c$. A conservative finite-volume discretization with upwind chemotactic fluxes and implicit backward differentiation formula time integration is used to test these predictions. Numerical experiments recover the analytical equilibria and growth rates, identify the dominant unstable mode, reproduce the transition to spatial heterogeneity, and quantify the effects of immune recruitment, decay, and diffusion on the stability boundary. Grid-refinement, mass-balance, residual, and nonnegativity diagnostics support the computational reliability of the results.

math.AP↗

arXiv2026

Endogenous Feedback in Size-Structured Transport Equations

We study a nonlinear size-structured transport equation where the endogenous scalar output $E(t)=\int_{l_0}^{l_m}\chi(l)x(t,l)\,dl$ feeds back into velocity and mortality. This principal-coefficient feedback precludes a semilinear perturbation framework. Freezing the feedback path yields a non-autonomous linear evolution, reducing the closed-loop problem to a scalar Volterra fixed point $E=\mathcal K(E)$. Mass balance provides an intrinsic feedback interval, while a Bielecki-norm contraction ensures unique nonnegative weak solutions. Stationary equilibria satisfy a scalar closure equation $E=\Phi(E)$. We prove uniqueness below the sharp margin $1-\Phi'(E)>0$ and identify $\Phi'(E)=1$ as a nondegenerate fold threshold. Linearization yields a finite-memory renewal equation with characteristic equation $\mathcal E(\lambda)=1$, whose root set determines the feedback spectrum and stability. Finally, the stationary harvesting adjoint reduces to a rank-one perturbation formula. At zero discount, we establish the identity $\mathcal E(0)=\Phi'(E^*)=B(0)$, linking closure resonance, spectral crossing, and adjoint loop gain.

math.AP↗

arXiv2026

Bilinear control of age--space structured populations

We study constrained bilinear optimal control for nonlocal age--space structured population equations with renewal boundary conditions and endogenous surveillance feedback. The control acts as a coefficient in a mixed transport--diffusion equation, while a scalar observable generated by the state enters both the interior dynamics and the renewal law. This produces a nonlinear closed-loop control-to-state map and a feedback-dependent adjoint system. Using a characteristic mild formulation rather than a standard Lions--Magenes argument, we establish closed-loop well-posedness and Fr\'echet differentiability. We then derive the reduced and feedback-corrected adjoint equations. The feedback derivative is identified as a low-rank perturbation $\ell_{\bar y,\bar u}(p)(t)\chi(a,x)$; in the Volterra-kernel regime, the associated transfer operator is quasinilpotent, yielding an explicit resolvent representation of the adjoint. Finally, we prove first-order optimality conditions and decompose the switching function into reduced and feedback-induced components.

math.OC↗

arXiv2026

Fredholm--residue selection of the unsteady Kutta amplitude

We give an operator-theoretic interpretation of unsteady Kutta selection in trailing-edge acoustic receptivity. The inviscid acoustic--wake problem leaves one outgoing wake amplitude undetermined. We show that, under explicit structural hypotheses, this amplitude is the same scalar obtained from three representations: cancellation of the inverse-square-root edge singularity, Fredholm compatibility of the viscous lower-deck problem, and the residue of the Kutta-normalized transform solution at the downstream wake pole: $\displaystyle A = -\frac{C_-^{(0)}}{C_-^{(KH)}} = -\frac{\langle \mathbf F_{\rm inc},\Psi^\ast\rangle}{\langle \mathbf F_{KH},\Psi^\ast\rangle} = i\operatorname*{Res}_{\alpha=\alpha_{KH}}\mathcal M(\alpha)$. The inner Fredholm--edge mechanism is verified exactly in a linear-shear lower-deck model, where the primal shear and adjoint velocity are Airy fields and the edge concomitant is nonzero outside a discrete resonance set.

math.NA↗

arXiv2026

Random Walk on B\'ezier Curves for Global Optimization

Balancing exploration and exploitation remains a central challenge in metaheuristic optimization. To address this issue, this paper proposes B\'ezier Walk Evolution (BWE), a geometry-driven optimization framework that reformulates evolutionary search as adaptive trajectory construction in the decision space. BWE integrates B\'ezier curve modeling with a distance-aware random walk mechanism to generate topology-guided search trajectories. By adaptively varying the curve order during evolution, the proposed method enables a smooth transition from diversified global exploration to refined local exploitation. Higher-order B\'ezier curves leverage multiple population-derived control points to enhance search diversity, while lower-order curves generate near-linear trajectories to improve convergence efficiency. This adaptive geometric search mechanism provides an interpretable alternative to conventional nature-inspired designs. Extensive experiments on 41 benchmark functions from the CEC2017 and CEC2022 suites, spanning dimensions from 10 to 100, show that BWE achieves strong overall performance and favorable scalability compared with 7 classical and 6 state-of-the-art optimizers, including L-SHADE and CMA-ES. Additional evaluations on five constrained engineering design problems further demonstrate the practical applicability and robustness of BWE.

cs.NE↗

arXiv2026

Nonsmooth Obstacles and Killed Resolvents in Reflected Stochastic Control

We study an infinite-horizon optimal stopping problem for a normally reflected two-dimensional diffusion in the quadrant with nonsmooth max-type payoff $G(x_1,x_2)=x_1\vee\alpha x_2$. The main novelty is a measure-valued variational formulation: the stopping gain $\Gamma=c+rG-\mathcal LG$ is shown to be a signed Radon measure whose singular component is supported on the kink diagonal $\{x_1=\alpha x_2\}$, and this component is computed explicitly. We prove that the value admits the killed-resolvent representation \[ V=G-R_r^{\mathcal C}\Gamma, \] where the reflected diffusion is killed upon entry into the stopping set. This corrects the generally invalid unrestricted-resolvent formula. Under explicit monotonicity hypotheses, the stopping set has epigraph form, and the free boundary is characterized by a killed-potential trace condition. A verification theorem certifies locally Lipschitz candidate boundaries as optimal.

math.OC↗

arXiv2026

A Measure-Valued Obstacle Problem for an Obliquely Reflected Diffusion with a Max-Type Payoff

We study an obliquely reflected optimal stopping problem in the nonnegative quadrant with nonsmooth max-type payoff $G(x)=x_1\vee\alpha x_2$, and we develop a measure-valued potential-theoretic formulation of the associated obstacle problem. The kink of $G$ on the diagonal $x_1=\alpha x_2$ produces a singular surface measure in the distributional generator, while the oblique reflection directions generate boundary local-time contributions on the coordinate faces. Together with the absolutely continuous stopping gain, these terms define a total signed stopping measure $\Gtot$. We derive the corresponding reflected It\^{o}--Tanaka identity, prove a killed-resolvent representation of the value function in the continuation region, and show that the unrestricted reflected resolvent is generally incorrect because the process is not absorbed on the stopping set. The free boundary is formulated through a continuation-side trace condition for the killed potential. Under a vertical monotonicity hypothesis on $V-G$, the stopping set is shown to have an epigraph form. We finally prove a verification theorem: any admissible epigraph candidate satisfying contact, strict continuation, reflected Neumann compatibility, growth, the trace condition, and measure-superharmonicity coincides with the value function, and its first entry time is optimal.

math.AP↗

arXiv2026

Killed resolvents and measure-valued stopping gains for reflected optimal stopping with max-type rewards

We study an infinite-horizon optimal stopping problem for a normally reflected two-dimensional diffusion in the positive quadrant with nonsmooth max-type reward $G(x_1,x_2)=x_1\vee \alpha x_2$. The paper develops a conditional measure-theoretic framework for the associated reflected obstacle problem. The main innovation is to show that the stopping gain $\Gamma=c+rG-\mathcal LG$ is a signed measure, not a function: the kink of $G$ generates an explicit negative surface measure on $\Delta=\{x_1=\alpha x_2\}$. We then prove that the correct potential representation uses the resolvent of the reflected diffusion killed on first entry into the stopping set, rather than the unrestricted reflected resolvent. Under explicit monotonicity, regularity, and measure-superharmonicity assumptions, we derive an epigraph representation, a continuation-side boundary-trace condition, and a candidate verification theorem. The framework clarifies hidden regularity and uniqueness assumptions in multidimensional nonsmooth optimal stopping.

math.PR↗

arXiv2026

Spectral perturbation theory for wall-admittance effects on compressible boundary-layer instability

Thin wall treatments modify high-speed boundary-layer instability through the pressure they admit or absorb at the wall. This paper develops a unified admittance formulation for such effects on trapped compressible Rayleigh modes. For a simple rigid-wall eigenpair, we prove the spectral sensitivity law \[ c(A)=c_0+KA+\mathcal O(|A|^2), \qquad \delta\sigma=\alpha\Imag(KA)+\mathcal O(|A|^2), \] where $A$ is the wall admittance and $K$ is an explicit functional of the rigid-wall eigenfunction. The formula separates wall physics from outer-mode physics and yields a phase criterion for stabilisation. Matched asymptotics show that viscous and thermal wall layers, blind-pore coatings and shallow non-separating roughness all reduce to this same boundary condition, with additive leading admittances. Mach-4.5 computations validate the sensitivity coefficient and demonstrate porous damping, viscous-wall damping and sign-changing reactive roughness effects.

physics.flu-dyn↗

arXiv2026

Structural dichotomy and mass criticality in indirect chemotaxis cascades: fourth-order ellipticity versus Volterra memory

We investigate the structural and operator-theoretic foundations of indirect signal-generation mechanisms in Keller--Segel-type chemotaxis models. By analyzing a physically motivated multi-stage signaling cascade, we establish a precise mathematical dichotomy between instantaneous equilibration and transient kinetic memory. Specifically, we prove that the fully equilibrating parabolic--elliptic--elliptic (PES) cascade reduces to a static fourth-order elliptic interaction. In dimension four, an exact algebraic cancellation of the leading Newtonian singularity yields a purely logarithmic kernel, shifting the mass-critical dimension from $N=2$ to $N=4$. Through an $L^2$-gradient flow formulation, we identify the corresponding concentration-scaling candidate critical mass $M_* = 64\pi^2\tau/\chi$. In sharp contrast, we demonstrate that the mixed elliptic--parabolic (MEP) cascade retains a genuine Volterra memory effect that defies static reduction. Its interaction drift acts as a singular perturbation in time-exhibiting classical two-dimensional Keller--Segel principal order near the time diagonal, yet providing fourth-order smoothing in its frozen-time average, necessitating a mixed space-time threshold theory. These results isolate the physical origin of mass-critical dimensional shifts in multiscale biological systems and formulate the specific adapted Adams/logarithmic Hardy--Littlewood--Sobolev (log-HLS) inequalities and mixed-norm criteria required to close the threshold problems.

math.AP↗

arXiv2026

A Diagnostic Framework for Implementation Risk in Bilevel Decision Problems: The Ambiguity Premium and the Robustness--Efficiency Frontier

Hierarchical decision problems are often modeled as bilevel programs in which a leader commits to a policy and a follower responds optimally. When the follower's optimal response is nonunique, or when only near-optimal follower behavior can be verified, the same leader decision may induce a range of upper-level outcomes. This paper develops a diagnostic framework for quantifying that exposure. For a leader decision $x$, we evaluate the optimistic and pessimistic upper-level values over the $\epsilon$-optimal follower response set $S_\epsilon(x)$ and use their difference, \[ \Delta_\epsilon(x):=\psi_\epsilon^p(x)-\psi_\epsilon^o(x), \] as an ambiguity premium. The premium itself is classical in the optimistic--pessimistic bilevel distinction; the contribution here is to make it operational as an implementation-risk diagnostic. We establish a diameter bound $\Delta_\epsilon(x)\le L_F(x)\,\mathrm{diam}(S_\epsilon(x))$ and an $\mathcal{O}(\sqrt{\epsilon})$ estimate under quadratic lower-level growth. We then organize existing bilevel--GNEP reformulations by their computational roles and propose a screening workflow that reports, for each candidate policy, nominal value, ambiguity exposure, and a first-order residual. Two stylized case studies -- a parallel-link Stackelberg pricing problem and a convex generation-planning model with diversification constraints -- show how the resulting robustness--efficiency frontier can identify policies that are nominally attractive but sensitive to near-optimal follower responses.

math.OC↗

arXiv2026

Controlling the Swarm: Sparse Actuation and Collision Avoidance under Stochastic Delay

Classical flocking models demonstrate how local interactions generate emergent order, but real-world multi-agent deployments are bound by severe constraints: limited actuator availability, heterogeneous communication latencies, and environmental noise. In this talk, we present a unified finite-N framework that tackles the interplay of these exact mechanisms. We study a delayed stochastic leader-follower particle system featuring topological communication, singular repulsion, and bounded sparse leader actuation. A central challenge in such systems is mathematical well-posedness, as discontinuous communication laws and singular repulsions clash with standard strong Ito frameworks. We resolve this by introducing an augmented Lyapunov functional that simultaneously enforces a strict collision barrier and closes a uniform Gronwall estimate. Building on this rigorous foundation, we formulate a free-terminal-time, chance-constrained optimal control problem. We show that temporally sparse, bang-off-bang leader actuation not only drastically reduces control effort compared to continuous baselines, but also reveals non-monotone sensitivities to leader density. Ultimately, we demonstrate that in delayed stochastic swarms, adding more direct actuation is not strictly optimal -- highlighting a highly non-trivial resource allocation paradox in cooperative control.

math.OC↗