The recently developed rerandomized inverse variance weighted (RIVW) estimator provides a simple and efficient framework to break the winner's curse in two-sample Mendelian randomization (MR). However, this method has ignored the possible presence of sample structure (e.g., residual population stratification and sample overlap), a common confounding factor in MR studies. Sample structure can not only distort SNP-exposure and SNP-outcome association estimates but also induce correlation between them, leading exposure-side instrument selection to propagate bias to the outcome side. To address this challenge, we propose the bivariate RIVW (BRIVW) estimator that can simultaneously account for the winner's curse and sample structure. The BRIVW estimator extends the RIVW framework by modeling the joint distribution of SNP-exposure and SNP-outcome associations, first adjusting their covariance matrix via linkage disequilibrium score regression to account for sample structure, and then applying randomized instrument selection and Rao-Blackwellization to obtain unbiased post-selection association estimates as well as their covariance matrix. Under appropriate conditions, we show that the BRIVW estimator is consistent and asymptotically normal. Extensive simulations and real data analyses demonstrate that the BRIVW estimator provides more accurate causal effect estimates than existing methods.

Semantic communication acts as a key enabler for effective task execution in AI-driven systems, prioritizing the extraction of the underlying meaning before transmission. However, when devices rely on different logic and internal representations, semantic mismatches may arise, potentially hindering mutual understanding and effectiveness of communication. Furthermore, in interference channel environments, the coexistence of multiple devices introduce a significant degradation due to the presence of multi-user-interference. To address these challenges, in this paper we formulate the joint optimization of linear Multiple-Input-Multiple-Output (MIMO) transceivers as a distributed non-cooperative game, enabling a closed-form solution that effectively addresses semantic coexistence and latent space misalignment. We derive sufficient conditions for the existence of a Nash Equilibrium (NE), considering multiple point-to-point MIMO channels, with corresponding users modeled as selfish players optimizing their transmission and semantic alignment strategies. Numerical results substantiate the proposed approach in goal-oriented semantic communication by highlighting crucial trade-offs between information compression, interference mitigation, semantic alignment, and task performance.

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for the functional equation in some class of functions and establish a result on the existence of an absolutely continuous invariant measure under a multidimensional transformation that can be viewed as a generalization of classical $p$-adic maps to higher dimensions.

Quantum many-body scar (QMBS) in kinetically constrained quantum systems challenges the conventional eigenstate thermalization hypothesis (ETH). We develop an effective open-system description for constrained dynamics and introduce the definition of quasiparticle number in the system. Based on this, we formulate a revised ETH that accounts for both diagonal and off-diagonal structures of local observables. By introducing the cross coherence purity (CCP), we obtain a unified characterization of off-diagonal matrix elements and show that the relevant density of states (DOS) is determined by the distribution of eigenstates on the energy--quasiparticle-number plane. We numerically verify an inverse relation between the CCP and this generalized DOS. Applied to the quantum many-body scar model, the revised ETH accurately predicts long-time averages and temporal fluctuations of local observables and explains their dependence on initial states. Our framework shows that the anomalous fluctuations and quasi-periodic dynamics of scar states arise naturally from low-DOS regions. These results provide a unified understanding of thermalization and QMBS in kinetically constrained systems.

Neutron and X-ray reflectometry are important methods for studying thin multilayer systems. The Parratt method and the method of characteristic matrices, also referred to as transfer matrices, are used for simulation, evaluation of experimental results, and designing optical systems, like mirrors. The Parratt method had been derived for isotropic systems. The method of characteristic matrices can also handle anisotropic problems, but it is burdened with numerical instabilities, which may arise in the case of thick samples at grazing angle incidence. In this paper, we derive a generalized Parratt method applicable to anisotropic systems. Furthermore, as we show, this is devoid of the numerical instabilities arising in the method of characteristic matrices. We derive formulae for both reflectivity and transmissivity. The stability of the new approach is demonstrated by comparing calculated results obtained via different methods. The problem of rough interfaces is also addressed, and the results gained by different approximations for some systems are compared.

We develop a hierarchical Bayesian dynamic game for competitive inventory and pricing under incomplete information. Two firms repeatedly choose order quantities and prices while facing two layers of uncertainty: unknown market demand and private rival characteristics. The framework combines Bayesian learning about demand and substitution with strategic belief updating about rival types. To make decisions robust to posterior uncertainty, we introduce a credible-risk criterion that rewards expected future profit while penalizing posterior predictive dispersion. This yields a conservative equilibrium concept in which firms learn, compete, and adapt simultaneously. The paper provides the model formulation, information structure, posterior updating mechanism, equilibrium definition, and a computational strategy based on belief-state dynamic programming. A simulation study shows that Bayesian learning is crucial for strong performance and that the credible-risk rule is especially effective as an operational regularizer under uncertainty. A real-data illustration on a high-dimensional protein-expression dataset demonstrates that the same uncertainty-aware Bayesian principle can produce biologically interpretable subgroup and latent-state findings. The proposed framework offers a unified bridge between Bayesian game theory and operations research, with practical relevance for competitive decision-making in uncertain and information-limited environments.

Absolute negative mobility (ANM) is one of the most paradoxical transport phenomena in which a setup moves on average in a direction opposite to the applied force. According to the state of the art a minimal system exhibiting this effect in a one-dimensional dynamics involves an inertial particle subjected to a constant bias when dwelling in a nonlinear symmetric periodic potential in a nonequilibrium} and nonstationary state generated by an external driving. In this work we remarkably reduce its complexity and show that it may occur in a system composed of an overdamped particle in piecewise linear symmetric periodic potential in an equilibrium state provided that it is driven by active fluctuations in the form of white Poisson shot noise. Our result may help to explain exotic transport behavior emerging in biological cells where dynamics is typically overdamped and assisted by active fluctuations derived from various metabolic activities. It can be also exploited for effective separation strategies in a microscopic world thus transforming fluctuations from a nuisance into a functional resource.

In this paper, we define the topological pressure of continuous functions with respect to the holomorphic correspondences using the open covers of the Riemann sphere. Further, we show that this method coincides with the existing definition of pressure that uses the notion of separated and spanning family of orbits.

We discuss an incompleteness result proven by Bezboruah and Shepherdson. This result tells us that the weak theory ${\sf PA}^-$ does not prove the consistency of any theory (under certain assumptions explained in the paper). Kreisel argued that such a result is not meaningful. We discuss Kreisel's objection and conclude that his argument does not hold water. We compare Pudlák's extension of the Second Incompleteness Theorem with the Bezboruah-Sheperdson Theorem. Finally, we reprove the Bezboruah-Sheperdson Theorem for a sequence coding based on an insight of Nielsen and Markov.

Conversational shopping agents represent a critical consumer-facing application of Large Language Model (LLM)-powered agents, yet how to effectively apply post-training Reinforcement Learning (RL) to optimize such agents remains underexplored. This work investigates RL-based optimization for shopping agents in real-world scenarios, where agents must simultaneously satisfy multiple interdependent objectives spanning objective metrics (product correctness), subjective qualities (persuasiveness), outcome rewards (final response quality), and process rewards (tool efficiency). We present a complete methodology to address this challenge. Specifically, we first construct SmartShopBench, a benchmark that captures diverse shopping intents with a hierarchical evaluation that decomposes complex quality requirements into measurable levels. Building on this evaluation framework, we design Hierarchical Reward Modeling (HRM) to structure mixed reward types through conditional gating that reflects their logical dependencies. To enable efficient training, we further propose Dynamic Contrastive Policy Optimization (DCPO), which balances response quality with operational efficiency through dynamic trajectory selection based on reward and reasoning length. Extensive experiments demonstrate that our RL-trained agent, namely ChatShopBuddy, consistently outperforms larger models relying on generic reasoning, achieving superior stability rather than merely higher peaks. Our work provides valuable guidance for applying RL to real-world conversational agents.

In the reference Phys. Rev. Lett. 132, 233801 (2024), the authors claim to have introduced a ''real-space spin Chern number'' as well as a ''Spin Berry connection'' and a ''Spin Berry curvature''. The main finding of their letter is the statement that the integral of the ''Spin Berry curvature'' over the surface is equal to the ''Spin Chern number'' which is the Euler characteristic of the surface. What the authors show is that, given a vector field tangent to a surface, there is a connection whose curvature gives the Euler characteristic when it is integrated over the surface. The point of this comment is to explain that no new invariant has been defined and that the result shown is the exact statement of the Chern-Gauss-Bonnet theorem, in the particular case of a surface. Since the ''real-space spin Chern number'' is equal to the Euler characteristic, it is not a new invariant but just another name for the same thing. Moreover, the Euler number characterizes the surface and not the polarization state of the field.

Continuous-time autoregressive and moving average (CARMA) models are extensively used to model high-frequency and irregularly sampled data. We study Whittle estimation for the model parameters when the process is observed at renewal times. The driving noise is assumed to be a Lévy process allowing for more flexibility including heavy-tailed marginal distributions and jumps in the sample paths. We show that the Whittle estimator based on the integrated periodogram is consistent and asymptotically normal under very mild conditions. To obtain these results, we establish the asymptotic normality of the integrated periodogram.

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard modes, like round-to-nearest (RN), which grows as $n$. For this reason, the former is increasingly employed in large-scale, low-precision computations as an RN alternative. Additionally, SR alleviates stagnation, whereby relatively small summands are completely rounded off and do not contribute to the sum. We provide an update to [Croci et al., Roy. Soc. Open Sci. 9.3 (2022), pp. 1-25], a survey which discusses the development and use of SR between 1949 and 2022, citing over 100 references. Since then, there has been a surge of new research, and this update covers almost four years of further progress in applying, analysing, and implementing SR. Our main focus is limited-precision stochastic rounding, a new variant that fixes the precision of the random numbers used. We provide insights into industrial and numerical analysis activities surrounding SR, highlighting the next possible steps in making this rounding mode more widely available in hardware.

Assessment literacy (AL) is essential for personalized education, yet difficult to cultivate in pre-service teachers. Conventional teacher preparation programs focus on theoretical knowledge, while digital assessment tools commonly provide opaque scores or parameters. These limitations hinder reflection and transfer, leaving AL underdeveloped. We propose XIA, an eXplainable Intelligent Assessment platform that extends statistics-informed support with visualized cognitive diagnostic reasoning, including contrastive and counterfactual explanations. In a pre-post controlled study with 21 pre-service teachers, we combined quantitative tasks and questionnaires with qualitative interviews. The findings offer preliminary evidence that XIA supported reflection, self-regulation, and assessment awareness, and helped reduce assessment errors. Interviews further showed a shift from score-based judgments toward evidence-based reasoning. This work contributes insights into the design of intelligent assessment tools, showing how explanatory scaffolding can bridge assessment theory and classroom practice and support the cultivation of AL in teacher education.

Tidal disruption events (TDEs) are unique tools for investigating quiescent supermassive black hole (SMBH), accretion physics, and circumnuclear medium (CNM) environments. The CNM density profile is of great astrophysical significance, since it provides key diagnostics for the accretion history of dormant SMBH. TDEs can launch outflows that produce radio emission when propagating into the CNM. The closure relation (CR), i.e., the relation between the temporal indices and the spectral indices, are therefore monitoring the CNM density profile. In this work, we first collect 53 TDEs with radio observations to date. We then obtain the predicted CR for arbitrary CNM and different dynamical phases of the outflow, and apply to the radio TDE sample. We constrain the CNM density profile for 26 radio TDEs with good data quality. The results are generally consistent with those estimated with equipatition method, suggesting that CR analysis is efficient in the study of CNM profile for a quiescent SMBH.

Very recently, a lattice QCD collaboration has explored threshold pion electroproduction near the physical pion mass and has simulated the relevant multipole amplitudes. Different multipole amplitudes are usually entangled in experimental data, and thus extracting each of them independently from first principles provides additional essential constraints on phenomenological theories. We use nonperturbative Hamiltonian theory to investigate the electroproduction process, providing an advanced approach with additional two-particle coupled channels to acquire the physical electric dipole amplitudes from the original lattice QCD data. We note that future lattice QCD simulations of the electric dipole amplitudes at higher energies will be much closer to their physical counterparts than the current ones near threshold. In addition, we obtain a new expression which, like that of Lellouch-Lüscher, depends only on the final-state interactions but provides both the real and imaginary parts of the transition amplitudes.

We construct analytic symplectomorphisms on the sphere, the disk and the cylinder which are minimally ergodic (only 3 ergodic measures). To achieve this, we apply and generalize a principle introduced by Berger, based on the Approximation by Conjugacy method of Anosov-Katok.

Noting that there is very little literature on the topic, a first analytical approach is proposed in this work for estimating the viscosity-like parameter of three-phase viscoplastic materials. In a first part, the conditions of application and the consequences of the three classical averaging equations involving the strain rates, the stresses and the power are reviewed for 2-phase mixtures and extended to three phases. The classical static and Taylor bounds as well as the heuristic ''Iso-strain rate'' assumption are analyzed. An extension of the Mori-Tanaka estimation to the three-phase case is then proposed for viscoplastic linear constituents. If the volume fraction of one of the phases (inclusions) is very low, in particular when its viscosity tends towards zero or infinity, fully analytical results are presented, which provides an extension of the classical dilute model.

As generative AI (GenAI) systems become increasingly prevalent across various technological stacks, the question of how such systems handle sensitive and personal data flows becomes increasingly important. Specifically, both the ability to harness and process large swaths of information as well as their stochastic nature raise key concerns related to both security and privacy. Unfortunately, while some of the traditional security threat modeling can effectively identify certain violations, privacy-related issues are often overlooked. To respond to these challenges, we introduce a novel domain-specific privacy threat modeling framework to support the privacy threat analysis of GenAI-based applications. This framework is constructed through a two-pronged approach: (1) a systematic review of the emerging literature on GenAI privacy threats, and (2) a case-driven application to a representative Chatbot system. These efforts yield a foundational GenAI privacy threat modeling framework built on LINDDUN. The new framework affects three out of the seven privacy threat types of LINDDUN and introduces 100 new GenAI examples to the knowledge base. Its effectiveness is validated on an AI Agent system, which demonstrates that a comprehensive privacy analysis can be supported by the new framework.

To quantify the impact of AI on software development, the community requires a robust pre-AI baseline. This study analyzes valid satisfaction data from 1,155 software developers collected in July 2022, immediately preceding the mainstream adoption of generative AI tools. We report a high-satisfaction ecosystem (Mean = 8.14 [95% CI 8.01-8.25]), dominated by Visual Studio Code (79% usage). Multivariable regression confirms that autonomy in tool choice is the strongest predictor of IDE satisfaction (beta = 0.51), significantly outweighing demographic or role-based factors. Conversely, cloud IDE adoption was negligible (4.3% regular usage), with 40.1% citing network dependency as the primary barrier, a constraint that remains relevant for modern cloud-reliant AI agents. Additionally, we identify an "experimenter" segment (29.9%) characterized by high tool churn but no significant satisfaction difference (t = 0.43, p = 0.67), and demonstrate significant variation in IDE retention rates (VS Code: 68.5%, traditional IDEs: 3.9-25%), suggesting underlying dissatisfaction despite high overall satisfaction. By providing a quantitative snapshot of developer sentiment and workflows on the eve of the AI revolution, this study establishes a verifiable baseline for longitudinal research into the productivity-satisfaction misalignment observed in the post-AI era.

Fourth-generation storage-ring light sources have achieved transverse emittances approaching the diffraction limit at x-ray wavelengths, while their longitudinal coherence remains limited. Existing laser-modulation schemes can induce strong microbunching but modulate each bunch only once per revolution, thereby restricting coherent radiation to a single beamline and underutilizing the intrinsic multi-user capability of storage rings. We propose a multiple-echo-enabled harmonic generation (multi-EEHG) scheme that applies successive excitation-echo cycles to the same stored bunch within one revolution, enabling coherent radiation delivery to multiple beamlines at different wavelengths. A general formulation of the n-stage EEHG bunching factor and a corresponding optimization procedure are derived. As an example, a triple-EEHG configuration is designed for the SAPS storage ring. Simulations demonstrate coherent radiation at multiple wavelengths with single-pulse photon numbers up to $10^9$, corresponding to an enhancement of approximately three orders of magnitude over synchrotron radiation for the same spectral bandwidth, while achieving few-meV bandwidth without a monochromator. The proposed scheme offers a scalable approach for multi-beamline coherent operation in next-generation storage-ring light sources.

This paper explores secure communication in an underwater energy-harvesting (EH) relay network that supports hybrid optical-acoustic transmission. The optical hop is modeled using a Gamma-Gamma turbulence channel with pointing errors and may occasionally be blocked by underwater obstacles. At the same time, an eavesdropper is assumed to monitor the acoustic hop, creating a secrecy concern. To address this, we formulate the relay power allocation problem as an infinite-horizon Markov decision process (MDP). A model-based reinforcement learning (RL) driven optimal power allocation (OPA) strategy is proposed to maximize long-term cumulative secrecy performance until the network stops functioning. To offer lower-complexity alternatives, we also develop a Greedy Algorithm (GA) and a Naive Algorithm (NA). Simulation results show that the RL based OPA adapts effectively to battery dynamics, varying channel conditions, and optical link availability, achieving the highest secure data transmission, while GA performs reasonably and NA performs poorly due to its short-sighted decisions.

In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schrödinger (DNLS) equations are often employed to model these dynamics, particularly in the context of Bose-Einstein condensates and optical waveguide arrays. While the classical DNLS with cubic nonlinearity admits well-known solitonic solutions, the introduction of competing nonlinearities, such as quadratic-cubic and cubic-quintic terms, gives rise to new behaviors, including multistability and front formation. One such emergent structure, the Maxwell front, is characterized by stationary interfaces between two energetically equivalent steady states, occurring at a critical parameter known as the Maxwell point. This paper investigates the existence and stability of Maxwell fronts in DNLS models with competing nonlinearities. Specifically, we examine the quadratic-cubic nonlinearity, as found in the discrete quantum droplets equation, and the cubic-quintic nonlinearity, both of which exhibit multistability. We explore the persistence of Maxwell fronts in both the anticontinuum limit (where the coupling between lattice sites is weak) and the continuum limit (where the coupling is strong). The stability of these fronts is analyzed through linear stability analysis, utilizing eigenvalue counting arguments and exponential asymptotic techniques. Our results provide new insights into multistability, front dynamics, and the role of competing nonlinearities in discrete wave systems. The main contributions of this work include the characterization of Maxwell fronts in DNLS equations with competing nonlinearities, the analysis of their stability across different coupling regimes, and the application of novel asymptotic methods to investigate their behavior in the continuum limit.

We extract cubic interactions from the covariant equations of motion of Chiral Higher Spin Gravity and compute the corresponding amplitudes. These amplitudes are found to agree with earlier results obtained in the light-cone gauge. We also classify all possible cubic amplitudes that can be constructed from chiral fields arising in twistor theory. In addition, we derive propagators for arbitrary spin in the Feynman/Lorenz gauges. These propagators are then used to solve Berends--Giele recursion relations for a truncation of Chiral Higher Spin Gravity, which is a higher-spin extension of self-dual Yang--Mills theory. We confirm that all tree-level amplitudes vanish.

In Internet of Things (IoTs), the freshness of system status information is crucial for real-time monitoring and decision-making. This paper studies the transmission scheduling problem in wireless monitoring systems, where information freshness -- typically quantified by the Age of Information (AoI) -- is heavily constrained by limited channel resources and influenced by factors such as the randomness of data arrivals and unreliable wireless channel. Such randomness leads to asynchronous AoI evolution at local sensors and the monitoring center, rendering conventional scheduling policies that rely solely on the monitoring center's AoI inefficient. To this end, we propose a dual-AoI model that captures asynchronous AoI dynamics and formulate the problem as minimizing a long-term time-average AoI function. We develop a scheduling policy based on Markov decision process (MDP) to solve the problem, and analyze the existence and monotonicity of a deterministic stationary optimal policy. Moreover, we derive a low-complexity scheduling policy which exhibits a channel-state-dependent threshold structure. In addition, we establish a necessary and sufficient condition for the stability of the AoI objective. Simulation results demonstrate that the proposed policy outperforms existing approaches.

We introduce LegalEdge, an edge intelligence-driven framework that integrates Federated Learning (FL) and Deep Q-Networks (DQN) to optimize electric vehicle (EV) charging infrastructure. LegalEdge contracts are novel smart contracts deployed on the blockchain to manage dynamic pricing and incentive mechanisms transparently and autonomously. By leveraging FL, multiple edge devices such as EV charging stations collaboratively train DQN agents without sharing raw data, preserving user privacy while reducing communication costs. These edge-deployed agents learn optimal charging strategies in real time based on local conditions and global policy updates. LegalEdge ensures low-latency decisions, high contract integrity, and efficient energy allocation. Our experimental results demonstrate significant improvements in learning convergence, transaction speed, and operational transparency, establishing LegalEdge as a scalable, intelligent, and accountable solution for next-generation EV charging networks.

Let $U$ be a smooth quasi-projective complex variety with a regular function $f$. The twisted de Rham cohomology groups $\mathrm{H}^k_{\mathrm{dR}}(U, f)$ carry the decreasing irregular Hodge filtration, whose graded pieces have dimensions known as the irregular Hodge numbers. In this paper, we prove that the irregular Hodge numbers admit an explicit characterization in terms of classical Hodge numbers, closely related to Hodge-theoretic numbers constructed by Katzarkov, Kontsevich, and Pantev for Landau--Ginzburg models. As direct applications, we show that irregular Hodge numbers of non-degenerate functions are independent of the choice of non-degenerate functions, and we give a concrete formula for irregular Hodge numbers for unipotent non-degenerate functions.

We consider the problem of forwarding packets arriving online with their destinations in a line network. In each time step, each router can forward one packet along the edge to its right. Each packet that is forwarded arrives at the next router one time step later. Packets are forwarded until they reach their destination. The flow time of a packet is the difference between its release time and the time of its arrival at its destination. The goal is to minimize the maximum flow time. This problem was introduced by Antoniadis et al.~in 2014. They propose a collection of natural algorithms and prove for one, and claim for others, that none of them are $O(1)$-competitive. It was posed as an open problem whether such an algorithm exists. We make the first progress on answering this question. We consider the special case where each packet needs to be forwarded by exactly one or two routers. We show that a greedy algorithm, which was not previously considered for this problem, achieves a competitive ratio of exactly $2-2^{1-k}$, where $k$ is the number of active routers in the network. We also give a general lower bound of $4/3$, even for randomized algorithms.

Context: Having domain models derived from textual specifications has proven to be very useful in the early phases of software engineering. However, creating correct domain models and establishing clear links with the textual specification is a challenging task, especially for novice modelers. Objectives: We propose an approach for determining the alignment between a partial domain model and a textual specification. Methods: To this aim, we use Natural Language Processing techniques to pre-process the text, generate an artificial natural language specification for each model element, and then use an LLM to compare the generated description with matched sentences from the original specification. Ultimately, our algorithm classifies each model element as either aligned (i.e., correct), misaligned (i.e., incorrect), or unclassified (i.e., insufficient evidence). Furthermore, it outputs the related sentences from the textual specification that provide the evidence for the determined class. Results: We have evaluated our approach on a set of examples from the literature containing diverse domains, each consisting of a textual specification and a reference domain model, as well as on models containing modeling errors that were systematically derived from the correct models through mutation. Our results show that we are able to identify alignments and misalignments with a precision close to 1 and a recall of approximately 78%, with execution times ranging from 18 seconds to 1 minute per model element. Conclusion: Since our algorithm almost never classifies model elements incorrectly, and is able to classify over 3/4 of the model elements, it could be integrated into a modeling tool to provide positive feedback or generate warnings, or employed for offline validation and quality assessment.

The impact of temperature-induced deformations and shape fluctuations on the particle stability and decay processes has been investigated across the isotopes of hot nuclear systems with $Z = 28$ to $50$, with focus on astrophysically crucial pathways at excitation energies relevant to stellar environments. We perform global finite-temperature analysis using the statistical theory of hot nuclei combined with the triaxially deformed Nilsson Hamiltonian and Strutinsky's prescription, and explore the interplay between deformation, shell quenching, separation energies, and $β$-decay characteristics at finite temperatures. Our results show that around critical temperatures $T_c \approx 1$--$2$ MeV, where the shell quenching effects become predominant, the nuclear deformation reduces and the shape undergoes a transition to the spherical configuration. Our computed neutron and proton separation energies, which usually decrease with increasing temperature, implying the reduced binding in hot nuclei, occasionally show an enhancement in some nuclei at reduced deformation around $T_c$ that shifts the last unbound nucleon to the bound, stabilizing the nucleus by shifting the drip-line boundaries. A few nuclei are found to show one- and two-neutron drip line expansion with temperature. Moreover, the temperature-induced changes in deformation strongly correlate with the marked variations in our calculated $Q_β$ values and lifetimes, underscoring their impact on weak interaction rates. These findings provide insight into the sensitivity of particle stability and weak-interaction observables to thermal effects and may serve as complementary inputs for modeling nuclear processes in hot astrophysical environments.