Standard quantum state tomography assumes sufficient control of a system to measure an informationally complete set of observables. Dynamical quantum state tomography (DQST) presents an alternative: given a system with known dynamics and a single fixed observable, it almost always suffices to control only the time at which each i.i.d. copy of the system is measured. This work presents an analogous scheme for tomography of multi-mode Bosonic Gaussian states undergoing Gaussian evolution, using a fixed single-mode homodyne measurement and only assuming control of the time of measurement. I prove that the scheme enables tomography for all discrete homogenous Gaussian evolutions and Gaussian quantum dynamical semigroups except for a null set which includes unitary evolution. When the state is known to be pure, a smaller number of measurement times is shown to be sufficient.

Accurate, real-time, yet non-destructive estimation of internal states in lithium-ion batteries is critical for predicting degradation, optimizing usage strategies, and extending operational lifespan. Here, we introduce PINEAPPLE (Physics-Informed Neuro-Evolution Algorithm for Prognostic Parameter inference in Lithium-ion battery Electrodes), a novel framework that integrates physics-informed neural networks (PINNs) with an evolutionary search algorithm to enable rapid, scalable, and interpretable parameter inference with potential for application to next-generation batteries. The meta-learned PINN utilizes fundamental physics principles to achieve accurate zero-shot prediction of electrode behavior with test errors below 0.1$\%$ while maintaining an order-of-magnitude speed-up over conventional solvers. PINEAPPLE demonstrates robust parameter inference solely from voltage-time discharge curves across multiple batteries from the open-source CALCE repository, recovering the evolution of key internal state parameters such as Li-ion diffusion coefficients across usage cycles. Notably, the inferred cycle-dependent evolution of these parameters exhibit consistent trends across different batteries without any customized degradation physics-embedded heuristic, highlighting the effective regularizing effect and robustness that can be conferred through incorporation of fundamental physics in PINEAPPLE. By enabling computationally efficient, real-time parameter estimation, PINEAPPLE offers a promising route towards the non-destructive, physics-based characterization of inter-cell and intra-cell variability of battery modules and battery packs, thereby unlocking new opportunities for downstream on-the-fly needs in next-generation battery management systems such as individual cell-scale state-of-health diagnostics.

We establish a new SU(N) symmetric model of interaction between the fields of four types: the multiplet of vector fields, which describes the so-called color aether, the multiplet of pseudoscalar fields, which is associated with the multi-component cosmic dark matter, the gauge and gravitational fields. The extended Lagrangian of the model contains a new constructive element, which is based on the covariant SU(N) symmetric divergence of the multiplet of vector fields; this new element, being the multiplet of scalars from the point of view of spacetime transformations and the color vector from the point of view of the SU(N) group space, gives us the possibility to formulate properly the multi-axionic extension of the Peccei-Quinn theory. The hypothesis of a spontaneous polarization of the multi-axionic color aether in the early Universe is presented. The set of self-consistent master equations of the model is derived. An application to cosmology is considered: the obtained master equations are solved for the truncated test model based on the Bianchi-I spacetime platform.

Tourism significantly affects the economies of many countries. Understanding the causal relationship between the length of overnight stay and traveller's expenditure is crucial for stakeholders to characterize spending profiles and to design marketing strategies. Causal mechanisms differ between personal and work-related travel because the decision-making processes have different drivers and constraints. We apply context-specific independence relations to model causal mechanisms in contexts specified by trip purpose and identify the causal effect of the length of stay on expenditure. Using the international visitor survey data on foreign travellers to Finland, we fit a hierarchical Bayesian model to estimate the posterior distribution of the counterfactual expenditure due to extending the length of stay by one night. We also perform a Bayesian sensitivity analysis of the estimated causal effect with respect to omitted variable bias.

We study prior-independent pricing for selling a single item to a single buyer when the seller observes only a single sample from the valuation distribution, while the buyer knows the distribution. Classical robust pricing approaches either rely on distributional statistics, which typically require many samples to estimate, or directly use revealed samples to determine prices and allocations. We show that these two regimes can be bridged by leveraging the buyer's informational advantage: pricing policies that conventionally require the seller to know statistics such as the mean, $L^η$-norm, or superquantile can, in our framework, be implemented using only a single hidden sample. We introduce hidden pricing mechanisms, in which the seller commits ex ante to a pricing rule based on a single sample that is revealed only after the buyer's participation decision. We show that every concave pricing policy can be implemented in this way. To evaluate performance guarantees, we develop a general reduction for analyzing monotone pricing policies over $α$-regular distributions, enabling a tractable characterization of worst-case instances. Using this reduction, we characterize the optimal monotone hidden pricing mechanisms and compute their approximation ratios; in particular, we obtain an approximation ratio of approximately $0.79$ for monotone hazard rate (MHR) distributions. We further establish impossibility results for general concave pricing policies and for all prior-independent mechanisms. Finally, we show that our framework also applies to statistic-based robust pricing, thereby unifying sample-based and statistic-based approaches.

Atrial fibrillation (AF) is a common cardiac arrhythmia and a major risk factor for ischemic stroke. Early detection of AF using non-invasive signals can enable timely intervention. In this work, we present a comprehensive machine learning framework for AF detection from simultaneous photoplethysmogram (PPG) and electrocardiogram (ECG) signals. We partitioned continuous recordings from 35 subjects into 525 segments (15 segments of 10,000 samples each at 125Hz per subject). After data cleaning to remove segments with missing samples, 481 segments remained (263 AF, 218 normal). We extracted 22 features per segment, including time-domain statistics (mean, standard deviation, skewness, etc.), bandpower, and heart-rate variability metrics from both PPG and ECG signals. Three classifiers -- ensemble of bagged decision trees, cubic-kernel support vector machine (SVM), and subspace k-nearest neighbors (KNN) -- were trained and evaluated using 10-fold cross-validation and hold-out testing. The subspace KNN achieved the highest test accuracy (98.7\%), slightly outperforming bagged trees (97.9\%) and cubic SVM (97.1\%). Sensitivity (AF detection) and specificity (normal rhythm detection) were all above 95\% for the top-performing models. The results indicate that ensemble-based machine learning models using combined PPG and ECG features can effectively detect atrial fibrillation. A comparative analysis of model performance along with strengths and limitations of the proposed framework is presented.

We study the spectral theory of mixed local and nonlocal operators with lower-order terms in the right-hand side of the equation. This kind of problems is motivated by the analysis of superposition operators of mixed order and with the "wrong sign" of the lower-order terms with respect to the classical elliptic theory. Our results include: -convergence to classical cases when the right-hand side of the eigenvalye equations "localizes", recovering the simplicity and sign-definiteness of eigenfunctions in the limit; -a detailed analysis of disconnected domains, showing that, unlike the classical case, any eigenfunction associated with the first eigenvalue must change sign, and that the first eigenvalue of a union of disconnected domains is strictly smaller than that of its individual components; -examples in which the first eigenvalue is either simple or non-simple in disconnected domains; -a regularity theory that underpins these results.

Mahadev [SIAM J. Comput. 2022] introduced the first protocol for classical verification of quantum computation based on the Learning-with-Errors (LWE) assumption, achieving a 4-message interactive scheme. This breakthrough naturally raised the question of whether fewer messages are possible in the plain model. Despite its importance, this question has remained unresolved. In this work, we prove that there is no quantum black-box reduction of non-interactive classical verification of quantum computation of $\textsf{QMA}$ to any falsifiable assumption. Here, "non-interactive" means that after an instance-independent setup, the protocol consists of a single message. This constitutes a strong negative result given that falsifiable assumptions cover almost all standard assumptions used in cryptography, including LWE. Our separation holds under the existence of a $\textsf{QMA} \text{-} \textsf{QCMA}$ gap problem. Essentially, these problems require a slightly stronger assumption than $\textsf{QMA}\neq \textsf{QCMA}$. To support the existence of such problems, we present a construction relative to a quantum unitary oracle.

We prove a category-theoretic independence theorem for four fundamental notions: meaning, object, name, and existence. Working in a Lawvere-style categorical semantics and in particular in toposes, we show that these notions occupy distinct structural levels (object, morphism, element, and internal logical level) and are not uniformly recoverable from one another. The key separation arises between internal existence and global naming. Using a concrete example in the topos $\mathbf{Sh}(S^1)$-the sheaf of local sections of a nontrivial covering-we exhibit an object that is internally inhabited but admits no global element. These results provide a precise structural basis for treating geometric universes as foundational frameworks for information networks.

We investigate the utility of meta-optical encoders for generalizable image compression by leveraging their intrinsic shift-invariant point spread functions (PSFs). Compared with purely digital approaches, such optical encoders offer parallel and energy-efficient compression, enabling early data reduction prior to electronic processing and transmission, which is particularly attractive for resource-constrained and compact imaging systems. Although the operations realizable by a single passive optical layer remain fundamentally constrained, we systematically study several PSF encoding strategies combined with a total-variation (TV) digital reconstruction backend. Specifically, under identical compression ratios, we compare spatial binning, multi-channel random, and multi-channel orthogonal PSF based designs. Our results show that, at the same compression ratios, spatial binning achieves the highest reconstruction quality among all encoding strategies; however, it exhibits limited robustness to noise compared with multi-channel methods.

In many data-driven online decision systems, actions determine not only operational costs but also the data availability for future learning -- a phenomenon termed Prediction-Induced Censoring (PIC). This challenge is particularly acute in large-scale resource allocation for generative AI (GenAI) serving: insufficient capacity triggers shortages but hides the true demand, leaving the system with only a "greater-than" constraint. Standard decision-making approaches that rely on uncensored data suffer from selection bias, often locking the system into a self-reinforcing low-provisioning trap. To break this loop, this paper proposes an adaptive approach named PIC-Reinforcement Learning (PIC-RL), a closed-loop framework that transforms censoring from a data quality problem into a decision signal. PIC-RL integrates (1) Uncertainty-Aware Demand Prediction to manage the information-cost trade-off, (2) Pessimistic Surrogate Inference to construct decision-aligned conservative feedback from shortage events, and (3) Dual-Timescale Adaptation to stabilize online learning against distribution drift. The analysis provides theoretical guarantees that the feedback design corrects the selection bias inherent in naive learning. Experiments on production Alibaba GenAI traces demonstrate that PIC-RL consistently outperforms state-of-the-art baselines, reducing service degradation by up to 50% while maintaining cost efficiency.

Accurate simulation of wind turbulence over fast-propagating waves requires interface-capturing methods that suppress numerical artifacts while accurately resolving momentum transfer across the interface. In high wave-age regimes, numerical errors at the air-water interface can reach magnitudes comparable to the physical flow, directly affecting predicted turbulence statistics. This study examines widely used interface-capturing techniques to evaluate how spurious currents and interface regularization influence wind-wave simulations through curvature estimation and flux discretization. A systematic assessment is performed using static and translating droplet benchmarks, together with solitary and monochromatic wave cases, to identify and quantify the dominant numerical error mechanisms. In addition, comparison with experimental measurements reveals how these primary error sources manifest in coupled wind-wave simulations. These findings clarify the numerical origin of the observed discrepancies and underscore the importance of accurate curvature and flux treatment in high wave-age regimes.

The dynamics of magnetisation in a bounded ferromagnet in $\mathbb{R}^d$ ($d=1,2$) at high temperatures can be described by the stochastic Landau--Lifshitz--Bloch (sLLB) equation, which is a vector-valued quasilinear stochastic partial differential equation. In this paper, assuming adequate regularity of the initial data, we establish strong convergence in $L^2(Ω)$ of several semi-implicit and implicit fully discrete finite element schemes for the sLLB equation, together with explicit convergence rates. The analysis relies on localised error estimates and new exponential moment bounds for the exact solution. As a by-product, these moment bounds yield mean-square exponential stability of solutions and uniqueness of the invariant measure in one spatial dimension under a small noise assumption. We also sharpen existing convergence-in-probability results for the numerical schemes. Numerical experiments are presented to illustrate and support the theoretical findings.

This paper investigates the cell-free multi-user integrated sensing and communication (ISAC) system, where multiple base stations collaboratively track the users and detect their signals. Moreover, reconfigurable intelligent surfaces (RISs) are deployed to serve as additional reference nodes to overcome the line-of-sight blockage issue of mobile users for accomplishing seamless sensing. Due to the high-speed user mobility, the multi-user tracking and signal detection performance can be significantly deteriorated without elaborated online user kinematic state updating principles. To tackle this challenge, we first manage to establish a probabilistic signal model to comprehensively characterize the interdependencies among user states, transmit signals, and received signals during the tracking procedure. Based on the Bayesian problem formulation, we further propose a novel hybrid variational message passing (HVMP) algorithm to realize computationally efficient joint estimation of user states and transmit signals in an online manner, which integrates VMP and standard MP to derive the posterior probabilities of estimated variables. Furthermore, the Bayesian Cramer-Rao bound is provided to characterize the performance limit of the multi-user tracking problem, which is also utilized to optimize RIS phase profiles for tracking performance enhancement. Numerical results demonstrate that the proposed algorithm can significantly improve both tracking and signal detection performance over the representative Bayesian estimation counterparts.

The purpose of this paper is to describe explicitly the modules of (Siegel-)Jacobi forms of degree two of index one of any scalar valued weight with respect to some congruence subgroups of small levels $N\leq 4$. Such a structure for the full Siegel modular group as a module over scalar valued Siegel modular forms of even weight has been explicitly given by T.~Ibukiyama. There we used an explicit structure theorem of rings of scalar valued Siegel modular forms by Igusa and that of vector valued Siegel modular forms of weight $\det^k\, \Sym^2$ by T. Satoh and T. Ibukiyama. On the other hand, for levels $N=2$, $3$, $4$, ring structures of scalar valued case have been also known by H. Aoki and T. Ibukiyama and $\det^k \Sym^2$-valued case by H. Aoki. In this paper, by merging these results, we give the same sort of simple structure theorems on modules of Jacobi forms of degree of two of index one for level $2$, $3$ and $4$.

We discuss the possibility of a simultaneous cosmic variation of two fundamental entities: the Newtonian gravitational coupling $G$ and the electron mass $m_e$. We show that this variation can account for the late-time cosmic acceleration without invoking a cosmological constant or an explicit dark-energy fluid. We compare the derived $m_e$ variation with laboratory bounds found from Quasar absorption Spectra. Our results indicate that late-time cosmic acceleration could be a manifestation of evolving fundamental couplings, establishing a direct bridge between precision tests of gravity, particle physics and the origin of cosmic acceleration.

The increasing use of language models in automated software testing raises concerns about their environmental impact, yet existing sustainability analyses focus almost exclusively on large language models. As a result, the energy and carbon characteristics of small language models (SLMs) during test generation remain largely unexplored. To address this gap, this work introduces the DeCEAT framework, which systematically evaluates the environmental and performance trade-offs of SLMs using the HumanEval benchmark and adaptive prompt variants (based on the Anthropic template). The framework quantifies emission and time-aware behavior under controlled conditions, with CodeCarbon measuring energy consumption and carbon emissions, and unit test coverage assessing the quality of generated tests. Our results show that different SLMs exhibit distinct sustainability strengths: some prioritize lower energy use and faster execution, while others maintain higher stability or accuracy under carbon constraints. These findings demonstrate that sustainability in the generation of SLM-driven tests is multidimensional and strongly shaped by prompt design. This work provides a focused sustainability evaluation framework specifically tailored to automated SLM-based test generation, clarifying how prompt structure and model choice jointly influence environmental and performance outcomes.

We present a method to conduct both quantum state reconstruction and entanglement purification simultaneously that is advantageous in several respects over previous work in this direction, showing that the number of Bell pairs necessary to boot a quantum network can be significantly reduced compared to an existing method. The existing method requires at least $10^5$ Bell pairs for the state reconstruction phase to estimate that the state is of fidelity $0.99$ within the error range of $10^{-2}$, whereas our approach only requires around $2,841$ to be certain with $99.7\%$ of confidence that the estimated fidelity lies within $[0.99-0.01, 0.99+0.01]$. In addition, in our approach we can start with a lower fidelity Bell pair and purify it multiple times, estimating at the same time the resultant fidelity with guarantee of $99.7\%$ that the fidelity estimate lies within a certain range. Moreover, the existing method cannot correct both bit-flip and phase-flip errors at the same time and can only correct one of these, whereas our approach can correct both bit-flip and phase-flip errors simultaneously. This research produces numerical estimates for the number of Bell pairs actually needed to guarantee a certain threshold fidelity $F$. The research can support the functioning real-world quantum networking by providing the information of the time needed for the bootstrapping of a quantum network to finish.

We modify Pogorelov's classic construction to demonstrate the absence of a priori $C^2$ estimates for the equations $\det(D^2 u \pm Du \otimes Du) = f(x)$ in dimension $n \ge 3$. We construct a sequence of solutions $z_\varepsilon$ with second derivatives blowing up at the origin as $\varepsilon \rightarrow 0$, while the corresponding right-hand sides $f_\varepsilon$ admit uniform $C^2$ estimates. Specifically, the counterexamples are given by $z_\varepsilon(x_1, \dots, x_n) = (1+x_1^2)(1+x_2^2)(\varepsilon^2 + η^2)^{α/2},$ where $η= \sqrt{x_3^2 + \dots + x_n^2}$ and $α= 2 - \frac{2}{n}$.

As large language models continue to scale, training demands on compute and system capacity grow rapidly, making single-vendor homogeneous clusters insufficient. This paper presents a technical solution for heterogeneous mixed training in AMD-NVIDIA environments. We first adopt a compatibility-oriented approach based on CPU-Forwarding Communication, with differentiated communication back-end selection across parallel groups and multi-NIC parallel data transfer. To achieve higher performance, we further propose another Device-Direct Communication approach, integrating a CPU-offloading P2P mechanism to enable direct cross-vendor GPU data transfer without host-memory staging. Experiments on LLaMA-8B and Qwen2-7B demonstrate that the proposed Device-Direct Communication approach achieves up to 98% of the throughput of an NVIDIA homogeneous system, while preserving training stability and correctness.

To support sixth-generation (6G)-enabled intelligent transportation systems (ITSs), a multi-modal sensing residual-corrected graph neural network (MM-ResGNN) framework is proposed for millimeter-wave (mmWave) path loss prediction in vehicular communications for the first time. The propagation environment is formulated as an environment sensing path loss graph (ESPL-Graph), where nodes represent the transmitter (Tx) and receiver (Rx) entities and edges jointly describe Tx--Rx transmission links and Rx--Rx spatial correlation links. Meanwhile, a geometry-driven physical baseline is introduced to decouple deterministic attenuation trends from stochastic residual variations. A vehicular multi-modal path loss dataset (VMMPL) is constructed, which covers three representative scenarios, including the urban wide lane, urban crossroad, and suburban forking road environments, and achieves precise alignment between RGB images and global semantic information in the physical space, and link-level ray-tracing (RT)-based path loss data in the electromagnetic space. In MM-ResGNN, topology-aware graph representations and fine-grained visual semantics are synergistically integrated through a gated fusion mechanism to estimate the path loss residual relative to the physical baseline. Experimental results demonstrate that MM-ResGNN achieves significant improvements over empirical models and conventional data-driven baselines, with a normalized mean squared error (NMSE) of 0.0098, a mean absolute error (MAE) of 5.7991~dB, and a mean absolute percentage error (MAPE) of 5.0498\%. Furthermore, MM-ResGNN exhibits robust cross-scenario generalization through a few-shot fine-tuning strategy, enabling accurate path loss prediction in unseen vehicular environments with limited labeled data.

Simulation-based inference (SBI) enables parameter estimation for complex stochastic models with intractable likelihoods when model simulation is feasible. Neural posterior estimation (NPE) is a popular SBI approach that often achieves accurate inference with far fewer simulations than classical approaches. But in practice, neural approaches can be unreliable for two reasons: incompatible data summaries arising from model misspecification yield unreliable posteriors due to extrapolation, and prior-predictive draws can produce extreme summaries that lead to difficulties in obtaining an accurate posterior for the observed data of interest. Existing preconditioning schemes target well-specified settings, and their behaviour under misspecification remains unexplored. We study preconditioning under misspecification and propose preconditioned robust neural posterior estimation, which computes data-dependent weights that focus training near the observed summaries and fits a robust neural posterior approximation. We also introduce a forest-proximity preconditioning approach that uses tree-based proximity scores to down-weight outlying simulations and concentrate computation around the observed dataset. Across two synthetic examples and one real example with incompatible summaries and extreme prior-predictive behaviour, we demonstrate that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.

While there is an extensive body of research analyzing policy gradient methods for discounted cumulative-reward MDPs, prior work on policy gradient methods for average-reward MDPs has been limited, with most existing results restricted to ergodic or unichain settings. In this work, we first establish a policy gradient theorem for average-reward multichain MDPs based on the invariance of the classification of recurrent and transient states. Building on this foundation, we develop refined analyses and obtain a collection of convergence and sample-complexity results that advance the understanding of this setting. In particular, we show that the proposed $α$-clipped policy mirror ascent algorithm attains an $ε$-optimal policy with respect to positive policies.

In this paper, a new semi-discrete version of the Carleman estimate-based convexification globally convergent numerical method is developed. It is used for the delivery of the starting point for the training procedure of deep learning. An important feature of the continuous version of the convexification method is that its convergence to the true solution is independent on the availability of a good first guess about this solution. A new concept of the h-strong convexity is introduced, where h is the grid step size in the semi-discrete version of the convexification method. The h -strong convexity allows to obtain an a priori accuracy estimate of the starting point for the training step of the deep learning procedure. This approach is demonstrated for a highly nonlinear problem of Electrical Impedance Tomography. Results of numerical experiments for complicated media structures demonstrate the computational feasibility of this procedure.

Strontium titanate ($\mathrm{SrTiO_3, STO}$) dome-shaped superconducting transition temperature as a function of chemical potential, consistent with STO experiments, and shows that tunable s-wave and d-wave symmetries are modulated by doping. Superconducting fluctuations validate the mean-field approximation at low temperatures but destroy pairing at higher temperatures. The charge-density-wave order competes with superconductivity, enhances the effective electron mass inversely with the chemical potential, and increases with the interaction strength $U$ and the temperature $T$. SDW order is rare and fragile, while an additional magnetic term induces subtle band splitting. These findings suggest e-e contributions to STO's transport anomalies and provide criteria to distinguish e-e from e-ph origins, offering insights for engineering higher $T_c$ in dilute systems.

In oncology phase I trials, model-assisted designs have been increasingly adopted because they enable adaptive yet operationally simple dose adjustment based on accumulating safety data, leading to a paradigm shift in dose-escalation methodology. In practice, a single mid-trial dose insertion may be considered to examine safer doses and/or to collect more informative efficacy data. In this study, we investigate methods to improve dose assignment and the selection of the maximum tolerated dose (MTD) or the optimal biological dose (OBD) when a new dose level is added during an ongoing trial under a model-assisted framework, by assigning informative prior information to the inserted dose. We propose a hybrid design that uses a non-informative model-assisted design at trial initiation and, upon dose insertion, applies an informative-prior extension only to the newly added dose. In addition, to address potential skeleton misspecification, we propose two adaptive extensions: (i) an online-weighting approach that updates the skeleton over time, and (ii) a Bayesian-mixture approach that robustly combines multiple candidate skeletons. We evaluate the proposed methods through simulation studies.

Fix a nonzero level $\mathfrak{n} \in \mathbb{F}_q[T]$. In this paper, we first establish a function field analogue of Ligozat's theorem, which serves as our main result and provides a criterion for Drinfeld modular units on the Drinfeld modular curve $X_0(\mathfrak{n})$. We further conjecture that this criterion characterizes all Drinfeld modular units; we verify the conjecture in the cases of prime power level and of level equal to the product of two primes. Second, as an application of Drinfeld modular units, we investigate the rational cuspidal divisor class group $\mathcal{C}(\mathfrak{n})$ of $X_0(\mathfrak{n})$. We construct an injective map $g$ from the group of degree $0$ rational cuspidal divisors on $X_0(\mathfrak{n})$ to the group of Drinfeld modular units on $X_0(\mathfrak{n})$ tensored with $\mathbb{Q}$ over $\mathbb{Z}$. As a result, we establish an explicit upper bound for the exponent of $\mathcal{C}(\mathfrak{n})$ for general level $\mathfrak{n}$.

In this note, we prove convergence of the half-space exponential last passage percolation (LPP) model, away from the boundary, to the directed landscape. Our approach couples the half-space and full-space LPP models and constructs two barrier events based on the monotonicity of last passage paths. Combining this coupling with moderate deviation estimates for both models and the known convergence of full-space LPP to the directed landscape, we establish the desired convergence.

Adiabatic quantum computation with Rydberg atoms provides a natural route for solving combinatorial optimization problems such as the maximum independent set (MIS). However, its performance is fundamentally limited by the reduction of the spectral gap with increasing system size and connectivity, which induces population leakage from the ground state during finite-time evolution. Here we introduce the Adjusted Detuning for Ground-Energy Leakage Blockade (ADGLB), a spectral-gap-guided schedule engineering method that modifies the laser detuning profile to suppress leakage without introducing additional Hamiltonian terms or iterative optimization loops. We experimentally benchmark ADGLB on a quasi-one-dimensional chain of $N=10$ atoms, and the MIS preparation probability increases substantially compared with the standard adiabatic schedule. Furthermore, we show that the schedule optimized for smaller instances can be directly applied to larger two-dimensional triangular lattices with $N=25$ and $N=37$. With a small heuristic offset, the method also remains effective for instances with higher hardness parameters. These findings demonstrate that spectral-gap-guided schedule engineering offers a scalable and hardware-efficient strategy for enhancing adiabatic quantum optimization on neutral-atom platforms.

Tungsten (W) is the leading candidate material for plasma-facing components in fusion reactors, yet its upper operational temperature is limited by premature grain growth and recrystallization processes. Irradiation adds further complications by generating defect clusters and transmutation products that alter both the driving forces and kinetics of grain boundary motion. In this work, we develop a physics-based, multiscale framework that couples crystal plasticity, stochastic cluster dynamics, and discrete grain boundary dynamics to model the co-evolution of plastic deformation, irradiation damage, and grain growth in fusion-grade tungsten polycrystals. The approach enables simulations on realistic microstructures with arbitrary grain size and misorientation distributions, without recourse to mean-field simplifications. The model captures (i) the spatial heterogeneity of dislocation density distribution during hot working; (ii) irradiation-induced defect accumulation under fusion conditions, and (iii) the buildup of chemical and elastic driving forces for grain boundary migration and microstructural evolution. Parametric studies demonstrate the dominant influence that temperature has on thermally activated grain-boundary mobility, a weaker dependence on prior strain, and a pronounced retardation of recrystallization by rhenium segregation arising from neutron transmutation. Under fusion energy irradiation conditions, our framework predicts a substantial reduction of the effective recrystallization temperature relative to unirradiated microstructures, while Re production restores and even elevates this limit. By providing quantitative projections of recrystallization kinetics and in-service recrystallization temperatures, this work establishes a predictive tool for assessing the lifetime and operational envelope of W-based plasma-facing materials under fusion conditions.