arXiv subjects

Ye Liang

Publications and source records attributed to Ye Liang.

At least 19 recordsLinked to original sources

arXiv2026

DR-LabStack: Design and Implementation of a Clinician-Facing Web System for Diabetic Retinopathy Prediction

Pretrained diabetic retinopathy (DR) prediction models differ in their input fields, serialization formats, preprocessing requirements, and output semantics. Making these models accessible through a common clinical interface therefore requires explicit coordination between the user interface and the inference service. We designed and implemented DR-LabStack, a React-Flask web system integrating four externally developed pretrained models: RuleFit, Pruned RuleFit, Elaborative XGBoost, and Two-level Ensemble. A shared form retrieves ordered model features, renders model-specific numerical and categorical controls, and constructs a positional input vector. Backend adapters load heterogeneous artifacts and apply the ensemble's accompanying scaler, while a common JSON response supports binary classification display alongside method and source information. Functional evaluation on September 8, 2026 used copied application files and real model artifacts in a documented isolated environment. All four models loaded and exposed their 14-, 6-, 8-, and 25-field contracts. Sixty-two Flask test-client requests characterized service behavior; 12 limited-vector checks confirmed invocation-path and threshold consistency. Twenty-four browser-component scenarios with mocked transport verified input ordering and result rendering and characterized input-validation behavior. The resulting system demonstrates a reusable interaction and serving workflow for heterogeneous DR models. The contribution is web-system design, integration, and software functionality; clinical effectiveness and clinician usability require separate evaluation.

cs.LG↗

arXiv2026

RiVaT-Fuse: Reliability-Calibrated Variational Tensor Fusion for Multimodal Prediction under Modality Uncertainty

Image-metadata prediction requires fusing heterogeneous evidence whose reliability can vary across samples and latent factors. Existing representation-level fusion methods typically choose an aggregation architecture, such as concatenation, gating, conditional modulation, or attention, without explicitly defining what the fused representation should mean under modality uncertainty. We propose RiVaT-Fuse, a reliability-calibrated variational tensor fusion framework that defines fusion as sample-wise latent-state estimation. Rather than producing a fused vector by direct aggregation, RiVaT-Fuse estimates a consensus latent state through a variational objective that balances image evidence, metadata evidence, structured cross-modal interaction, and stability. The resulting framework replaces scalar modality confidence with matrix-valued trust geometry, decomposes interaction into additive, multiplicative, and relational components, and couples the latent state with conditional robustness and structured multi-task prediction. We provide well-posedness and stability interpretations of the latent solve and instantiate the framework with efficient low-rank-plus-diagonal trust operators. On an image-level image-metadata prediction benchmark, RiVaT-Fuse achieves the strongest overall predictive rank among direct representation-level baselines while improving probability and label stability under perturbation.

cs.LG↗

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

Multiplier Sensitivity in Isoperimetric Optimal Control

We study finite-horizon optimal control problems with scalar isoperimetric constraints from a function-space duality perspective. Controls are treated as elements of weakly compact subsets of $L^\infty(0,T;\mathbb R^m)$, while the state equation induces a control-to-state map into $W^{1,\infty}(0,T;\mathbb R^n)$. For linear dynamics, concave payoff, and an affine isoperimetric functional, we prove that the constrained value function has an interval domain, is concave, and admits a Fenchel--Moreau dual representation. This yields a superdifferential formula identifying the negative of the dual multiplier with the sensitivity of the value function with respect to the constraint level. A constraint qualification is then used to identify the dual multiplier with the normal Pontryagin multiplier of the augmented isoperimetric system. We also treat linear-quadratic problems with a single quadratic equality constraint by reducing them to quadratic forms on a Hilbert space. The resulting analysis separates the validity of the envelope formula from the regularity needed for Riccati synthesis, showing that sensitivity may persist even when the modified control-weight operator becomes singular.

math.AP↗

arXiv2026

Reflected Optimal Stopping with a Max-Type Payoff: Measure-Valued Stopping Gains and Killed Resolvent Representation

We study an infinite-horizon optimal stopping problem for a two-dimensional normally reflected diffusion in the quadrant with payoff $G(x_1,x_2)=x_1\vee \alpha x_2$. The problem combines three features that complicate the usual free-boundary analysis: reflection on the coordinate axes, a genuinely two-dimensional stopping region, and a nonsmooth max-type reward. We formulate the associated reflected obstacle problem, prove a verification theorem under explicit It\^o--Krylov--Tanaka admissibility and measure-superharmonicity assumptions, and derive a conditional epigraph structure for the stopping set. The main technical point is that the stopping-gain object $\Gamma=c+rG-\mathcal LG$ is a signed measure rather than a function. Its diagonal component is $\Gamma^\Delta(dx) = -\frac{n^\top a(x)n}{2\sqrt{1+\alpha^2}}\sigma_\Delta(dx)$, $n=(1,-\alpha)$, which shows that pointwise stopping-gain sign conditions must be interpreted with care. We also prove that the correct potential representation is the killed-resolvent formula $V(x)=G(x)-R_r^{\mathcal C}\Gamma(x)$, rather than the unrestricted reflected resolvent. A constant-coefficient reflected Brownian example illustrates the diagonal singular term explicitly.

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

Delay-Penalty Comparison for Sequential Testing and Quickest Detection in State-Dependent Diffusion Models

We study sequential testing and Bayesian quickest detection for diffusion observations whose drift changes between two alternatives while the signal-to-noise ratio may depend on the current observation. In this setting the posterior probability is generally not a closed one-dimensional Markov statistic: the natural sufficient state is the augmented process consisting of the posterior (or likelihood ratio) and the observed diffusion. We formulate both testing and quickest detection within this common filtering framework and identify the corresponding degenerate free-boundary problems. The main contribution is a delay-penalty comparison principle. For a common terminal false-alarm or terminal decision cost, a pointwise larger running delay penalty increases the value of continuation, shrinks the continuation region, and yields earlier stopping. When the stopping set has a one-sided posterior representation, this gives an order relation for the optimal alarm boundaries. The result applies to linear delay costs and to nonlinear marginal delay penalties after the appropriate Markovian augmentation, and is illustrated by a constant signal-to-noise Shiryaev example in which the alarm threshold is computed numerically and shown to be monotone in the delay cost. The framework clarifies how state-dependent information and nonlinear delay costs jointly affect the geometry of sequential testing and quickest-detection rules.

math.AP↗

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

Time and Killed Resolvents in Reflected Optimal Stopping with a Max Payoff

We study infinite-horizon optimal stopping for normally reflected two-dimensional diffusions in the positive quadrant with max payoff $G(x_1,x_2)=x_1\vee\alpha x_2$. The non-smooth payoff produces a singular stopping-gain measure on the kink set $\Delta=\{x_1=\alpha x_2\}$. We prove $\displaystyle \Gamma^\Delta(dx) = -\frac{n^\top a(x)n}{2\sqrt{1+\alpha^2}}\,\sigma_\Delta(dx)$, with $n=(1,-\alpha)$, so the diagonal component is non-positive and strictly negative under local ellipticity. This implies that every interior kink point lies in the continuation region. We further show that the correct value representation uses the resolvent killed at first entry into the stopping set, $\displaystyle V=G-R_r^{\mathcal C}\Gamma$, and give a closed-form reflected Brownian counter-example showing that the unrestricted reflected resolvent is generally wrong. A reflected Brownian benchmark and numerical experiments illustrate the local-time, resolvent-gap, and diagonal-avoidance mechanisms.

math.AP↗

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

Mountain Muography for China Jinping Underground Laboratory

The China Jinping Underground Laboratory (CJPL), located $\sim 2,400$~m beneath Jinping Mountain, is one of the world's deepest and largest ($\sim 300{,}000~\mathrm{m}^3$) underground facilities, hosting dark matter, nuclear astrophysics, and neutrino experiments. We report the first muon radiography (muography) conducted at this extraordinary depth. Cosmic muons detected by a one-ton prototype developed for the Jinping Neutrino Experiment were used to perform non-invasive subsurface density mapping over a 3~km lateral range. The 1.3~m diameter detector provides nearly isotropic acceptance and an angular resolution of $\sim 4.5^\circ$. By correlating the predicted surface muon flux distributions with the underground measurements, we reconstruct a directional opacity map that constrains the density structure of the overburden and shows excellent agreement with satellite-derived terrain models. This work demonstrates the feasibility of muography at extreme depths with kilometer-scale overburden and establishes a robust methodology for future geophysical applications and large-scale facilities, such as the full Jinping Neutrino Experiment. Based on this validated overburden model, we further predict the total muon fluxes for the eight experimental halls in CJPL-II, providing essential input for their physics programs.

hep-ex↗

arXiv2026

Synthetic Heterogeneous-Effects LASSO: A Fixed-effects Estimation Approach for High-dimensional Mixed-effects Models

This paper studies variable selection and post-selection inference for high-dimensional clustered data using marginal-model-based procedures. We show that, when covariates are heterogeneously distributed across clusters, marginal-model LASSO may use them as sparse proxies for latent cluster effects, shifting the estimation target away from the structural fixed effects and inducing false selections. To address this problem, we propose Synthetic Heterogeneous-Effects LASSO (SHEL), a fixed-effects penalized framework that incorporates cluster-level synthetic approximations to the latent heterogeneity. We establish theoretical properties of SHEL in high-dimensional settings and develop procedures for valid post-selection inference. The finite sample performance of the proposed method is investigated through extensive simulation studies. A longitudinal bulk RNA-seq dataset of enriched blood neutrophils from hospitalized COVID-19 patients is analyzed to demonstrate the method in a real application.

stat.ME↗

arXiv2026

Size-Selective Threshold Harvesting under Nonlocal Crowding and Exogenous Recruitment

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.

math.OC↗

arXiv2026

Age-Structured Harvesting Models: A Structural Comparison of Rate-Control and Effort-Control Optimality Systems

We study optimal harvesting in continuous-time, age-structured population models of McKendrick--von Foerster type, and we compare two harvesting mechanisms. In the \emph{rate-control} formulation, harvesting enters the state equation as an additive removal term; in the \emph{effort-control} formulation, harvesting acts multiplicatively as an additional mortality intensity and the mortality coefficient depends on the aggregate stock. For the rate-control problem we first establish existence of an optimal control for the infinite-horizon discounted problem, and we then derive, \emph{under explicitly stated regularity and constraint-qualification assumptions}, a conditional Pontryagin-type necessary optimality system consisting of the adjoint equation, the terminal-age and transversality conditions, the switching relations for the distributed and boundary controls, and the complementary-slackness relation for the state constraint. For the effort-control problem we \emph{formally} derive the associated adjoint equation and identify the nonlocal coupling term generated by aggregate (density) dependence, with the sign of that term verified by a step-by-step variational computation; a rigorous infinite-horizon maximum principle for this nonlinear, nonlocally coupled problem is beyond the present scope and is stated as such. We complement the analysis with autonomous stationary reductions, with explicit representations of the state and adjoint, and with a reproducible numerical study. The central message is structural: the harvesting mechanism is not a cosmetic modelling choice. Rate-control produces an additive/affine/local optimality structure, whereas effort-control produces a multiplicative/nonlinear/nonlocal one, with direct consequences for persistence, stationary profiles, and bioeconomic interpretation.

math.OC↗

arXiv2026

The Geometry of Quasi-Cycles: How Stoichiometric Covariance Alters Pre-Bifurcation Signatures

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.

math.DS↗

arXiv2026

Full-Covariance Chemical Langevin Predator--Prey Diffusion with Absorbing Boundaries

Many stochastic Rosenzweig--MacArthur predator--prey models inject ad hoc independent (diagonal) noise and therefore cannot encode the event-level coupling created by predation and biomass conversion. We derive an absorbed, fully mechanistic diffusion approximation and its extinction structure from a continuous-time Markov chain on $\mathbb N_0^2$ with four reaction channels: prey birth, prey competition death, predator death, and a coupled predation--conversion event. Absorbing coordinate axes are imposed to represent the irreversibility of demographic extinction. Under Kurtz density-dependent scaling, the law-of-large-numbers limit recovers the classical RM ODE, while central-limit scaling yields a chemical-Langevin diffusion with explicit drift and full state-dependent covariance. A distinctive signature is the strictly negative cross-covariance $\Sigma_{12}(N,P)=-mNP/(1+N)$ induced solely by the predation--conversion increment $(-1,1)$. We define the absorbed It\^o SDE by freezing trajectories at the first boundary hit and prove strong well-posedness, non-explosion, and moment bounds up to absorption. Extinction has positive probability from every interior state, and predator extinction is almost sure when $m\le c$.

math.PR↗

arXiv2026

Dedifferentiation stabilizes stem cell lineages: From CTMC to diffusion theory and thresholds

We study stem-terminally differentiated (TD) lineages in small niches where demographic noise from discrete division and death events is non-negligible. Starting from a mechanistic five-channel, density-dependent CTMC (symmetric self-renewal, symmetric differentiation, asymmetric division, dedifferentiation, TD death), we derive its mean-field limit and a functional CLT, obtaining a chemical Langevin diffusion whose explicit state-dependent covariance exactly matches the CTMC's aggregated channel-wise infinitesimal covariances. Within this diffusion approximation we remove the dedifferentiation flux and obtain a sharp dichotomy: in subcritical regimes the stem coordinate becomes extinct asymptotically almost surely, whereas in supercritical regimes polynomial moments diverge exponentially. This identifies, at the diffusion level, a structural failure mode of strictly hierarchical lineages under demographic fluctuations and clarifies how a cyclic return flux can rescue homeostasis. For interpretation we also derive an exact totals ODE backbone from a damage-structured transport model and obtain two steady-state constraints (ratio and equalization laws) linking compartment ratios to turnover and balancing dedifferentiation against fate bias. Numerical experiments corroborate the $\Omega^{-1/2}$ fluctuation scaling, illustrate the pathology, and contrast theorem-regime global convergence with threshold (Allee-type) behaviour outside the theorem hypotheses.

physics.bio-ph↗