arXiv subjects

Ruihan Zhou

Publications and source records attributed to Ruihan Zhou.

9 recordsLinked to original sources

arXiv2026

Dynamic Cloud Service-Capacity Deployment with Costly Response Readiness

AI product launches require service-capacity decisions before sufficient product-specific workload histories are available. Early service observations update beliefs about remaining workload, but workload does not physically deplete capacity as inventory demand does. Preserving rapid-response capability may also require costly capacity-access and operational arrangements. We study how a firm should jointly decide current capacity deployment and future response readiness. We formulate a finite-horizon dynamic program with workload beliefs, serviceable capacity, and an absorbing response-channel state. A preservation-deployment decomposition solves one deployment problem for each continuation choice and compares the resulting optimized values. This structure identifies when response readiness should be preserved and how much capacity should be deployed. We operationalize the framework through the Cold-Start Belief Actionability Policy (CBAP), which estimates side-specific values using workload scenarios drawn from predictive beliefs. We also establish bounds on its decision and lifecycle performance losses. Numerical experiments and a BurstGPT-based evaluation show that CBAP reduces lifecycle cost relative to benchmark policies by avoiding premature deployment and unnecessary readiness spending. The results distinguish forecast informativeness from operational actionability and show that current deployment and future response readiness are separate decision margins. Zero deployment may represent Standby rather than Exit, while positive deployment need not imply preserving the response channel.

math.OC↗

arXiv2026

Beyond Skepticism: Evaluating LLMs Pedagogical Intent Reasoning with the Adaptive Pedagogical Vigilance Framework

The capacity of Large Language Models (LLMs) to reason about pedagogical intent within instructional communication remains underexplored, particularly in educational domains such as translation pedagogy. To address this, we propose the \textbf{Adaptive Pedagogical Vigilance (APV)} framework, a novel computational formalism that reframes communicative vigilance as an adaptive mechanism for optimizing learning through intent inference. APV formalizes the problem via a Bayesian Pedagogical Intent Inference Engine (PIIE), which models how instructors select content to maximize pedagogical utility and how vigilant learners should inversely reason about latent instructional configurations -- encompassing genre, stance, and incentives. We evaluate APV through a three-tier hierarchy: distinguishing instructional genre, reasoning about structured pedagogical setups, and generalizing to authentic educational discourse. Experiments on leading LLMs (e.g., GPT-4o, Claude 3.5) show that APV substantially improves model vigilance. It achieves the strongest discrimination between pedagogical and exposure-based content, correlates highly with human judgments ($r=0.958$), and maintains robust performance on naturalistic data where baseline methods degrade. This work establishes a unified framework for assessing and enhancing LLMs' understanding of pedagogical motives, advancing the development of more reliable AI-assisted learning systems.

cs.CL↗

arXiv2026

Geometric uncertainty principles for Schr\"odinger evolutions on negatively curved manifolds

In this paper, we study the uncertainty principle for Schr\"odinger equations with a bounded time-independent potentials on certain Cartan-Hadamard manifolds endowed with an asymptotic hyperbolic metric in dimensions $n\geq2$. The classical Hardy uncertainty principle in Euclidean space, as developed in the works of Escauriaza-Kenig-Ponce-Vega (JEMS, 2008; Duke Math. J., 2010), reveals a rigidity phenomenon for solution $u$ to Schr\"odinger equations: sufficiently strong Gaussian decay at two distinct times yields $u\equiv0$. In this work, we show that a similar rigidity persists in the setting of hyperbolic geometry, despite the absence of translation invariance and Fourier representation. Our approach follows a general strategy of Escauriaza-Kenig-Ponce-Vega, where the underlying geometry brings an essential change. This enables us to establish new Carleman estimates and logarithmic convexity. Unlike the Euclidean setting, the hyperbolic geometry exhibits exponential volume growth and nontrivial geodesic escape at infinity, which fundamentally alters the propagation mechanism of Schr\"odinger evolutions. Based on the newly-built virial identities and an approximation argument, we derive the logarithmic convexity. The main difficulty in proving the logarithmic convexity is the lack of convolution structure on general manifolds. By making use of the exponential map and Jacobi field, we define a new mollifier on curved geometry. Meanwhile, to establish the Carleman estimate adapted to hyperbolic space, we introduce a new weight function adapted to the curved manifold. Our results highlight the role of curvature in shaping quantitative uniqueness properties for dispersive equations.

math.AP↗

arXiv2026

Cold-Start Forecasting of New Product Life-Cycles via Conditional Diffusion Models

Forecasting the life-cycle trajectory of a newly launched product is important for launch planning, resource allocation, and early risk assessment. This task is especially difficult in the pre-launch and early post-launch phases, when product-specific outcome history is limited or unavailable, creating a cold-start problem. In these phases, firms must make decisions before demand patterns become reliably observable, while early signals are often sparse, noisy, and unstable We propose the Conditional Diffusion Life-cycle Forecaster (CDLF), a conditional generative framework for forecasting new-product life-cycle trajectories under cold start. CDLF combines three sources of information: static descriptors, reference trajectories from similar products, and newly arriving observations when available. Here, static descriptors refer to structured pre-launch characteristics of the product, such as category, price tier, brand or organization identity, scale, and access conditions. This structure allows the model to condition forecasts on relevant product context and to update them adaptively over time without retraining, yielding flexible multi-modal predictive distributions under extreme data scarcity. The method satisfies consistency with a horizon-uniform distributional error bound for recursive generation. Across studies on Intel microprocessor stock keeping unit (SKU) life cycles and the platform-mediated adoption of open large language model repositories, CDLF delivers more accurate point forecasts and higher-quality probabilistic forecasts than classical diffusion models, Bayesian updating approaches, and other state-of-the-art machine-learning baselines.

cs.LG↗

arXiv2026

Magnetic uncertainty in variable geometry

In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable smallness assumptions on the leading coefficients, we prove that any solution exhibiting super-quadratic exponential decay at two distinct times must vanish identically. Under an additional structural assumption on the coefficient matrix $G$, we further establish a Hardy-type result at the quadratic exponential scale. We also obtain an analogous uniqueness result for the heat equation with variable-coefficient magnetic perturbations. Our results unify and extend previous works in two directions: they recover the constant-coefficient covariant case treated by Barcelo-Fanelli-Gutierrez-Ruiz-Vilela when $G=I$, and the variable-coefficient non-magnetic case considered by Federico-Li-Yu when $A=0$. The proofs combine logarithmic convexity arguments with Carleman estimates adapted to variable-coefficient covariant Schr\"odinger and parabolic flows. Although our approach follows the general strategy introduced by Escauriaza-Kenig-Ponce-Vega, substantial new difficulties arise from the interaction between the variable metric and the magnetic structure, which requires new weight functions and refined commutator estimates.

math.AP↗

arXiv2026

A Paley-Wiener type uniqueness result for the electromagnetic Schr\"odinger equation

In this paper, we establish a Paley-Wiener type uncertainty principle for Schr\"odinger equations with bounded electric and magnetic potentials, \begin{align*} i\partial_tu+\Delta_Au+V(t,x)u=0,\,\,u(0,x)=u_0(x), \end{align*} where $\Delta_A=(\nabla-iA)^2$ denotes the magnetic Schr\"odinger operator. Specifically, under suitable assumptions on $A$ and $V$, we show that if a solution $u$ exhibits linear exponential decay and support property in one spatial direction at times $t=0$ and $t=1$ respectively, then $u$ must vanish identically. This result extends the theorem of Kenig-Ponce-Vega [Ann. Sci. \'Ec. Norm. Sup\'er. (4) 47 (2014), 539-557] to the case $A\neq0$. We overcome the difficulty brought by the magnetic potential which breaks the translation invariance in the leading term of Hamiltonian $H=\Delta_A+V$. As a direct consequence, we also obtain a uniqueness result for a class of semi-linear Schr\"odinger equation with electromagnetic potentials.

math.AP↗

arXiv2025

Control and stabilization problem for a class of fourth-order nonlinear Schr\"odinger equation on boundaryless compact manifold

In this paper, we study the stabilization property and large time controllability for a class of fourth-order Schr\"odinger equations on a compact manifold without boundary in dimensions $1\leq d\leq5$: \begin{align} i\partial_tu+(\Delta_g^2-\beta\Delta_g)u=-|u|^{2k}u, \,\,x\in M\tag{4NLS}\label{4NLS1} \end{align} where $k\in\mathbb{N}$ and $\beta\in\mathbb{R}_{+}$ when $1\leq d\leq 4$ but $\beta\in\mathbb{Q}_{+}$ for $d=5$. We adapt the strategy in Macia [Vietnam J. Math. (2021)] to establish observability and the propagation of singularities. Moreover, we use these propagation estimates to deduce the unique continuation property for $\eqref{4NLS1}$. By the classical Hilbert Uniqueness Method (HUM) and the Picard iteration, the stabilization and large time controllability hold under the Geometric Control Condition (GCC) and the Unique Continuation Property (UCP) for the linearized equation. To obtain the controllability and stabilization at the $H^2$ level with $d=5$, we will focus on $M=\Bbb S^5$ with $k=1$. Our results extend those of Laurent [SIAM J. Math. Anal. (2009)] and Capistrano Filho-Pampu [Math. Z., 2022].

math.AP↗

arXiv2024

RiskMiner: Discovering Formulaic Alphas via Risk Seeking Monte Carlo Tree Search

The formulaic alphas are mathematical formulas that transform raw stock data into indicated signals. In the industry, a collection of formulaic alphas is combined to enhance modeling accuracy. Existing alpha mining only employs the neural network agent, unable to utilize the structural information of the solution space. Moreover, they didn't consider the correlation between alphas in the collection, which limits the synergistic performance. To address these problems, we propose a novel alpha mining framework, which formulates the alpha mining problems as a reward-dense Markov Decision Process (MDP) and solves the MDP by the risk-seeking Monte Carlo Tree Search (MCTS). The MCTS-based agent fully exploits the structural information of discrete solution space and the risk-seeking policy explicitly optimizes the best-case performance rather than average outcomes. Comprehensive experiments are conducted to demonstrate the efficiency of our framework. Our method outperforms all state-of-the-art benchmarks on two real-world stock sets under various metrics. Backtest experiments show that our alphas achieve the most profitable results under a realistic trading setting.

q-fin.CP↗

arXiv2024

AlphaRank: An Artificial Intelligence Approach for Ranking and Selection Problems

We introduce AlphaRank, an artificial intelligence approach to address the fixed-budget ranking and selection (R&S) problems. We formulate the sequential sampling decision as a Markov decision process and propose a Monte Carlo simulation-based rollout policy that utilizes classic R&S procedures as base policies for efficiently learning the value function of stochastic dynamic programming. We accelerate online sample-allocation by using deep reinforcement learning to pre-train a neural network model offline based on a given prior. We also propose a parallelizable computing framework for large-scale problems, effectively combining "divide and conquer" and "recursion" for enhanced scalability and efficiency. Numerical experiments demonstrate that the performance of AlphaRank is significantly improved over the base policies, which could be attributed to AlphaRank's superior capability on the trade-off among mean, variance, and induced correlation overlooked by many existing policies.

cs.LG↗