We consider a semilinear Neumann problem with exponential nonlinearity in a smooth bounded domain $Ω\subset \mathbb{R}^2$. We prove that there exists a threshold $\bar{\varepsilon}>0$ such that for all $\varepsilon>\bar{\varepsilon}$, any classical solution must be constant. This result provides a positive answer to a conjecture recently posed by Calanchi, Ciraolo, and Messina (2026). Our proof relies on a combination of $L^1$-estimates, a Jensen-type argument via the Neumann Green's function to obtain uniform exponential integrability, and elliptic regularity.

Semantic communications (SCs) aim to transmit only the essential information required to perform given tasks, thereby improving communication efficiency. Deep learning-based joint source-channel coding (deep JSCC) has emerged as a promising approach for SC systems; however, its performance often degrades when the deployment channels differ from the training channel conditions, making robustness a critical requirement. This paper presents a structured overview of recent methodologies for enhancing the robustness of deep JSCC. Specifically, existing approaches are categorized into two classes: robust training approaches and adaptive approaches, with the latter further divided into adaptive semantic feature selection, physical-layer adaptation, and semantic feature adaptation. Finally, we discuss promising directions, including multi-task generalization and explainability in robust SC systems.

Shared mobility systems (e.g., shared cars and ride-hailing services) generate persistent spatial imbalances as vehicles concentrate at popular destinations, leaving trip origins depleted of supply. Operators incur substantial costs in repositioning empty vehicles, and quantifying the theoretical minimum rebalancing distance is practically important. Exact computation requires solving a transportation linear program that is challenging at the city scale. Closed-form approximation models are derived for the minimum rebalancing distance in rectangular service regions. Parallel derivations are presented for the Manhattan metric (grid road networks) and the Euclidean metric (unconstrained movement). A scalar spatial imbalance index condenses the full demand pattern into a single interpretable quantity. Both models share a unified structure: the per-vehicle rebalancing distance scales with the square root of service area, the imbalance index, and a shape factor that depends solely on the aspect ratio. Calibration and validation against 500 exact LP solutions per metric confirm the area-scaling exponent to within 2\% of the theoretical prediction, across three demand distribution families. An empirical case study using January 2026 New York City for-hire vehicle trip data across 263 traffic analysis zones confirms that the formula generalizes to real-world, network-constrained demand. The results equip operators and system designers with solver-free, theoretically grounded tools for benchmarking rebalancing performance and optimizing service, rebalancing frequency, and demand-management interventions.

Using $Λ$CDM and Padé-(2,1) cosmography, we study directional variations in the Hubble constant, $H_0$, using galaxy cluster and Type Ia Supernovae (from Pantheon Plus) by the hemisphere decomposition method. Since there is a degeneracy between $H_0$ and absolute magnitude $M_B$ for Supernovae, Cepheid host calibration is usually required to constrain $H_0$. Hence, in this work in order to complement the Cepheid host calibration in Supernovae, we also use calibrations based on galaxy cluster scaling relations. We find that there is a $\lesssim 1σ$ difference in $H_0$ variations when using galaxy clusters as calibrators compared to Cepheids highlighting that the variations in $H_0$ are robust across different calibration methods. Across all combinations of models and data sets used, we obtain a consistent deviation $\sim 2σ$ from isotropy. In nearly all cases, we notice that the maximum $ΔH_0$ aligns with the CMB dipole direction.

A seller investigates a buyer before setting prices, balancing the cost of acquiring information against the gain from tailoring the contract to the buyer's private type. The optimal signal is coarse: no matter how rich the type space, the seller never needs more than three outcomes per buyer. The bound equals the number of independent post-signal decisions plus one, a quantity we call the effective policy dimension. Screening involves two decisions, whether to allocate and what to charge, giving the ternary bound. Limited liability is the source: without it, the price is pinned by the envelope, only the allocation decision remains, and signals are binary as in monitoring. The Myerson exclusion rule is an artifact of not investigating. With investigation, every marginal buyer trades with positive probability, governed by a universal function that connects information design to rational inattention. The bound holds for any strictly convex information cost.

We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and correlation functions. We show that any finite width of the natural-frequency distribution suppresses the finite-temperature spin-glass transition, because the resulting low-frequency singularity of the correlation function is incompatible with the spherical constraint. At zero temperature, however, a spin-glass phase persists for arbitrary frequency dispersion. This residual zero-temperature glassiness is likely a special feature of the spherical dynamics and would be destroyed by local nonlinearities. The model thus provides a solvable oscillator framework for studying how nonequilibrium perturbations suppress finite-temperature glassy freezing.

Carbon-aware grid optimization relies on accurate locational emission metrics to effectively guide demand-side decarbonization tasks such as spatial load shifting. However, existing metrics are only valid around limited operating regions and unfortunately cannot generalize the emission patterns beyond these regions. When these metrics are used to signal carbon-sensitive resources, they could paradoxically increase system-wide emissions. This work seeks to develop a sensitivity-consistent metric for locational average carbon emissions (LACE-S) using a neural representation approach. To ensure physical validity, the neural model enforces total emission balance through an explicit projection layer while matching marginal emission sensitivities across the entire loading region. Jacobian-based regularization is further introduced to capture the underlying partition of load buses with closely aligned generator responses. Moreover, we present a scalable zonal aggregation strategy, ZACE-S, to reduce the model complexity by mapping nodal inputs to predefined market zones. Numerical tests on the IEEE 30-bus system have verified the performance improvements of LACE-S in matching total emissions and their sensitivities over the non-regularized design. Crucially, while spatial load shifting driven by existing metrics often increases the post-shift emissions, the proposed LACE-S metric has led to a reliable reduction of system-wide emissions, demonstrating its excellent consistency with the global emission patterns.

We define possibly unsaturated, upper semicontinuous Fell bundles over Hausdorff, locally compact groupoids and establish a universal property for representations of their full section C*-algebras on Hilbert modules over arbitrary C*-algebras. Based on this, we prove that the full section C*-algebra is functorial and exact, and we define a quasi-orbit space and a quasi-orbit map. We deduce and extend Renault's Integration and Disintegration Theorems to general Fell bundles using our universal property.

We introduce quantum Borcherds-Bozec superalgebras. We present and prove various results of the quantum superalgebras including a bilinear form, higher Serre relation, quasi-R-matrix, character formula for the irreducible highest weight modules. We also prove the category of integrable representations is semi-simple.

We study anomalies in family unification models within the framework of the bordism classification of invertible field theories. These models are based on four-dimensional $\mathcal{N}=1$ supersymmetric nonlinear sigma models, in which the three generations of quarks and leptons arise as superpartners of the sigma model fields. We focus on models whose target spaces are constructed from the exceptional group $E_{7}$ and its subgroups. For the consistency of the theory, sigma model anomalies must be cancelled. We show the absence of global sigma model anomalies, which are encoded in the torsion part of the relevant bordism groups, by explicitly computing these groups using the Atiyah-Hirzebruch spectral sequence. In constructing family unification models, symmetries acting on the coset spaces are gauged, which may introduce additional anomalies. We identify the relevant bordism groups in this setting and demonstrate that no global anomalies arise when the isotropy subgroup of the coset space is gauged.

Free-space-addressable optical resonators that combine long photon lifetimes (high $Q$ factors) with strong spatial localization of optical fields (small mode volumes, $V_m$) enhance light-matter interactions with facile far-field excitation. The Purcell factor governing spontaneous emission enhancement scales as $Q\,V_m^{-1}$. Periodically asymmetric resonators, in which perturbations convert bound modes into radiating modes, offer a route to free-space resonances, with the radiative $Q$ factor tuned by the geometric and optical strength of the asymmetry-inducing perturbations. However, free-space resonators that simultaneously achieve high $Q$ and small $V_m$ have remained rare. This limitation arises in part because existing designs do not tailor geometric and optical asymmetries concurrently, thus limiting access to high-$Q$ regimes. Here, we show that jointly tuning geometric and optical asymmetries unlocks a biaxial radiative landscape with iso-$Q$ contours that connect disparate perturbations with equivalent $Q$ factors. We demonstrate this framework with very-large-scale-integrated single-crystalline Si nanoantenna pixels (VINPix) with out-of-plane perturbations of 35-150 nm amorphous Si, SiN$_x$, and SiO$_2$. We experimentally establish biaxial $Q$ factor control in air and achieve $Q$ factors up to $76,000$ at wavelength-scale mode volumes ($V_m \sim 1.7\,λ_0^3\,n_{\mathrm{eff}}^{-3}$) in simultaneously imaged arrays of $>80$ resonators in water. Furthermore, we computationally demonstrate 50-nm-wide slotted VINPix that reach $Q$ factors of $10^6$ at subwavelength mode volumes ($V_m \sim 0.2\,λ_0^3\,n_{\mathrm{eff}}^{-3}$) with 20 nm SiO$_2$ perturbations, yielding Purcell factors as high as $5 \times 10^5$ in an all-dielectric free-space resonator.

Gaia two-parameter (G2P) stars have cumulative errors in parallax and proper motion so great that only their mean positions were reported in DR3. One potential cause of these high errors is another star as indicated by two intensity peaks in the scans. Speckle interferometry astrometric measurements of 25 G2P stars with high multi-peak percentages were obtained with the 1.5m telescope at Mt. Wilson Observatory. Of the 25 observed G2P stars, seven had no reported Gaia companions within 5.0". We found nearby companions for all seven. The 18 other G2P stars had known Gaia companions within 2.0". Of these, 13 had separations that agreed closely with the speckle measurements but with some discrepancy in position angles, three stars did not agree in either separation or position angle and no companion was detected for the remaining two. Although some of these issues may be resolved in DR4 or DR5, others may be inherent limitations of Gaia capabilities that speckle interferometry observations may be able to fill.

Integrated optoelectronic systems strive to combine the logic/memory density of electronics with the bandwidth of photonics, but monolithic realization is impeded by the inefficient electronic-to-photonic interface. Current architectures rely on separate readout circuitry and modulators, creating bottlenecks in energy and latency, while existing direct transduction methods often compromise on switching speed or non-volatility. Here, we report an ultrafast, non-volatile optoelectronic memory, named LuminoMem, that integrates electrical storage and mid-infrared light emission in a single device. The device utilizes a floating-gate architecture, in which the Weyl semiconductor tellurium serves simultaneously as a charge-trapping storage layer and an emissive medium. This design enables nanosecond-scale electrical programming of non-volatile photoluminescence at 3.4 um, allowing direct optical access to stored states without external modulation. We demonstrate 4-bit (16-level) optical storage capacity and validate the device's performance through neural network simulations that achieve high accuracy on the Fashion-MNIST dataset. By effectively bridging the gap between electronic storage and mid-infrared photonics, the demonstrated mid-infrared LuminoMem provides a hardware foundation for promoting current computation efficiency and potential intelligent platforms that co-integrate computing, memory, and sensing capabilities.

Piezoelectric actuators are critical for achieving high accelerating gradients and preventing RF trips in narrow-bandwidth superconducting radio-frequency (SRF) cavities by compensating for detuning caused by Lorentz force detuning. Depending on the maximum acceleration gradient an appropriate piezo stroke requirement has to be fulfilled. Since the stroke of piezo actuators decreases at cryogenic temperatures, evaluating their performance under such conditions is essential. Common characterization methods either use the SRF cavity itself as a sensor or rely on capacitance measurements during cool-down. Both these approaches do not measure the stroke directly and involve a trade-off between measurement precision and experimental simplicity, as well as cost and time. We developed a new method for the direct and precise measurement of piezo stroke at cryogenic temperature inside a cryocooler-cooled cryostat using a laser displacement sensor. The setup was used to characterize and evaluate two piezo actuators for cavity frequency tuners of the ILC prototype cryomodule, which is currently being built at KEK. In this article we are reporting on the development, setup, test, and application of this novel method, allowing the direct stroke measurement of piezos in vacuum and at cryogenic temperatures.

Advanced reactor concepts based on the thorium fuel cycle offer several advantages over conventional uranium-fueled systems, but they also stress-test the existing NDA toolbox for international safeguards. In particular, the presence of 232U and its ~MeV gamma-emitting daughters in thorium-based spent fuel creates a harsh radiological environment that complicates gamma-based active interrogation safeguard techniques. NRTA has emerged as a promising safeguards technique due to its isotopic specificity in the epithermal range and its robustness against non-resonant shielding. However, deploying NRTA in thorium safeguards requires neutron detectors that maintain timing performance and quantitative accuracy in intense gamma fields. This paper reports a comparative characterization of two candidate detectors for portable NRTA: GS20 and CLYC. GS20 has already been demonstrated as an effective epithermal detector in portable NRTA systems but offers limited neutron--gamma discrimination. CLYC, by contrast, provides strong pulse-shape discrimination (PSD) but has a much longer scintillation decay time and includes 133Cs, whose resonances partially overlap with key actinide resonances in the epithermal region. Using a DT-driven NRTA setup with a 2 m flight path, we compare GS20 and CLYC in measurements of a 1.50 mm tungsten target under both ``clean'' conditions and in an artificially constructed high gamma-radiation environment produced by an auxiliary source as a way of emulating a highly radioactive 233U target. The results indicate that CLYC, despite its long decay time, provides significantly more precise NRTA measurements in high radiation environments than GS20. For thorium-based safeguards scenarios where 233U must be identified and quantified in the presence of intense gamma backgrounds, CLYC-like detectors with strong PSD appear to be the more reliable choice.

A common view in monitored quantum dynamics is that local measurements suppress entanglement growth. We show that this intuition can fail in a one-dimensional spinful fermionic chain governed by a BCS Hamiltonian with pairing strength $Δ$ and subject to continuous, on-site, spin-resolved charge measurements at rate $γ$. Using free-fermion simulations and quasiparticle analysis, we show that pairing suppresses entanglement growth, while measurements suppress pairing. Their competition yields measurement-enhanced entanglement: for $Δ>0$, the steady-state entanglement $S_s$ increases with $γ$ over a finite interval $0<γ<γ_{\rm peak}$. This occurs because stronger measurements suppress pairing correlations, which would otherwise suppress entanglement growth. Using a nonlinear sigma-model calculation and free-fermion simulations, we provide evidence that for $Δ>0$ and small but finite $γ$, the steady-state entanglement scales as $S_s\sim \ln^2 L$. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.

Uplink performance remains a critical limitation in modern 5G networks, where UEs have to balance limited transmission power against propagation challenges. We conducted extensive measurements in the University of Notre Dame's football stadium, which has a seating capacity of 80,000 spectators, evaluating network behavior under both unloaded (pregame) and severely congested (game day) conditions, with a focus on uplink performance. Analyzing PHY-layer metrics captured via the Rohde & Schwarz QualiPoc, we show that high-frequency TDD bands in the uplink are severely bottlenecked in both the spectral and temporal domains. Despite transmitting near maximum 3GPP power limits, propagation loss inherent to high-frequency bands restricts UEs to low MCS indices and low PRB allocations, even in unloaded networks. This inability to achieve wideband allocation is further compounded by the significantly smaller number of uplink slots compared to downlink slots in TDD frames. Consequently, we observe a severe disparity between uplink and downlink: while high-frequency TDD bands carry the majority of downlink throughput, the network relies heavily on lower-frequency FDD bands for uplink. Additional measurements under favorable propagation conditions around a Verizon COW deployment located in the stadium parking lot also show that this limitation is not solely propagation-driven; rather, the duplexing scheme itself also plays a significant role. Even when TDD bands achieve higher or comparable MCS, FDD bands have a performance edge in the uplink due to the restrictive, downlink-heavy TDD architecture. These findings emphasize the indispensable role of low-frequency FDD spectrum in sustaining uplink capacity, providing insights that will help guide the design of next-generation wireless networks.

Educational dialogue is critical for decoding student learning processes, yet manual annotation remains time-consuming. This study evaluates the efficacy of GPT-5.2 and Gemini-3 using three prompting strategies (few-shot, single-agent, and multi-agent reflection) across diverse subjects, educational levels, and four coding dimensions. Results indicate that while multi-agent prompting achieved the highest accuracy, the results did not reach statistical significance. Accuracy proved highly context-dependent, with significantly higher performance in K-12 datasets compared to university-level data, alongside disciplinary variations within the same educational level. Performance peaked in the affective dimension but remained lowest in the cognitive dimension. Furthermore, analysis revealed four bias patterns: (1) Gemini-3 exhibited a consistent optimistic bias in the affective dimension across all subjects; (2) the cognitive dimension displayed domain-specific directional bias, characterized by systematic underestimation in Mathematics versus overestimation in Psychology; (3) both models are more prone to overestimation than underestimation within the meta-cognitive dimension; and (4) behavioral categories such as question, negotiation, and statements were frequently misclassified. These results underscore the need for context-sensitive deployment and targeted mitigation of directional biases in automated annotation.

We discuss the problem of defining a tensor product of profinitely many copies of a vector space $V$, and propose a definition $\bigotimes_X^{\mathrm{mcc}} V$ in the special situation that (1) $V$ is finite-dimensional over $\mathbf{F}_2$, and (2) the profinite $X$ indexing the tensor factors is acted on with finitely many orbits by a pro-$2$-group. The "mcc" on the tensor sign stands for "magnetized and conditionally convergent." A variant construction makes sense when $V$ is a bimodule over a ring of the form $\mathbf{F}_2 \times \cdots \times \mathbf{F}_2$, and the index set $X$ has the profinite version of a cyclic order. The definition organizes some computations in Heegaard Floer homology: it can be pitched as a computation of the Heegaard Floer theory of some pro-$3$-manifolds, though we do not know how to define such a thing.

A Cayley graph $\Cay(G,S)$ is said to be inner-automorphic if $S$ is a union of conjugacy classes of a group $G$, and arc-transitive if its full automorphism group acts transitively on the set of arcs. In this paper, we characterize four well-known families of arc-transitive graphs that arise as connected inner-automorphic Cayley graphs on dihedral groups, and we provide a necessary condition for other connected arc-transitive Cayley graphs on dihedral groups to be inner-automorphic. We further construct an infinite family of examples satisfying this condition, thereby demonstrating the existence of such graphs. Finally, we complete the classification of all 2-distance-transitive connected inner-automorphic Cayley graphs on dihedral groups.

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge information, many real-world applications provide informative node features in addition to graph topology. To capture this setting, we introduce the featured correlated Gaussian Wigner model, where two graphs are coupled through an unknown vertex permutation, and the node features are correlated under the same permutation. We characterize the optimal information-theoretic thresholds for exact recovery and partial recovery of the latent mapping. On the algorithmic side, we propose QPAlign, an algorithm based on a quadratic programming relaxation, and demonstrate its strong empirical performance on both synthetic and real datasets. Moreover, we also derive theoretical guarantees for the proposed procedure, supporting its reliability and providing convergence guarantees.

We examine the impact of input neodymium (Nd) atomic data on the light curves and spectra of kilonovae, probing the sensitivity of kilonova observables to the atomic physics of this important lanthanide element. We use the SuperNu Monte Carlo radiative transfer code, simulating a simple semi-analytic 1D kilonova with a pure Nd atmosphere, fixing the radiative transfer method while using input atomic data generated by three different codes: the LANL suite of atomic physics codes, HULLAC, and Autostructure. We see that the choice of atomic data significantly shapes the resulting light curves and spectra. Peak bolometric luminosities differ by a ratio of nearly 1.5 between HULLAC/Autostructure and LANL data sets. Moreover, we observe significant near- to mid-IR differences in the structure of the spectra. We specifically attribute these differences to the choice of atomic data for neutral Nd I. Many of the results here have been adapted from a presentation at "Radiative Transfer and Atomic Physics of Kilonovae" in Stockholm, 2023. We additionally present a LANL data set with energies calibrated to available values in the NIST Atomic Spectra Database, and demonstrate that this calibration also significantly affects IR spectral structure at late time. The substantial differences in kilonova observables that arise from tuning the atomic data of just one lanthanide element highlight the special attention that must be paid to atomic physics uncertainties when modeling kilonovae, from AT2017gfo to beyond.

Large Language Model (LLM) simulations, where LLMs act as students with varying approaches to learning tasks, can support teachers' noticing of student thinking. However, simulations using zero- or few-shot prompting often yield inauthentic knowledge and language, directing teachers to unrealistic reasoning. We evaluate three approaches (Fine-tuning, Multi-agent, and Direct Preference Optimization; DPO) to improve the authenticity and pedagogical utility of simulated students. All approaches improve cognitive and linguistic authenticity, compared with few-shot prompts. Interviews with elementary mathematics pre-service teachers and researchers (\textit{n} = 8) reveal distinct pedagogical affordances. The fine-tuned model produces realistic, brief responses but limits opportunities to extend students' thinking. Meanwhile, the multi-agent and DPO approaches generate explicit reasoning behind student strategies. We discuss implications for designing LLM simulations that balance authenticity with instructional utility for teacher learning.

We investigate the geometry of a certain space of meromorphic connections with irregular singularities, and prove in particular that it is a (real) symplectic Lie groupoid. The connections have a physical meaning: they correspond to certain solutions of the topological-antitopological fusion (tt*) equations of Cecotti and Vafa, and hence to deformations of supersymmetric quantum field theories. The groupoid structure arises because we restrict ourselves to the tt* equations of Toda type, whose monodromy data has a Lie theoretic description. To obtain these results, we show first that the universal centralizer of a Lie group is a holomorphic symplectic groupoid over the Steinberg cross section.

Let $pi:X\toΔ$ be a one-parameter degeneration whose central fiber $X_0$ has a single ordinary double point. The nearby- and vanishing-cycle formalism determines a canonical perverse sheaf on $X_0$, obtained from the variation morphism and fitting into an extension of the intersection complex by a point-supported rank-one contribution. We study this object from the perspective of limiting mixed Hodge theory and Saito's theory of mixed Hodge modules. In the ordinary double point case, we show that the corrected perverse object is the unique minimal Verdier self-dual perverse extension of the shifted constant sheaf across the node, and that its rank-one singular contribution and the corresponding rank-one vanishing contribution in the limiting mixed Hodge structure arise from the same nearby-cycle formalism. We also formulate the analogous structural statements for multi-node degenerations and for more general stratified singular loci. Finally, we explain how Saito's divisor-gluing formalism provides the natural framework for a fuller mixed-Hodge-module refinement of these constructions.

In this study, we present an analytical investigation of the superradiant scattering of a massive charged conformally coupled scalar field in rotating charged $de~Sitter$ black hole spacetimes within two gravitational theories: General Relativity (GR) and fourth-order Conformal (Weyl-squared) Gravity (CWG). For the massless charged conformally coupled scalar, we exploit a recently discovered correspondence between the Heun equation and the semiclassical limit of Belavin-Polyakov-Zamolodchikov (BPZ) equations in two-dimensional conformal field theory to solve for the superradiant amplification factors as controlled expansions in a small parameter scaling. For the massive charged conformally coupled scalar, we use WKB methods to derive an order of magnitude approximation for the amplification factors in the cosmological region in terms of those in the region $r_+\ll r \ll r_c$ where $r_+$ and $r_c$ are the outer and cosmological event horizons, respectively. For both the massless and massive sectors, suppression of superradiant amplification in CWG relative to that in GR is observed across the parameter regimes studied. Particularly, in the massive sector, we find strong exponential suppression of superradiant amplification on the order of $e^{-2μΛ^{-1/2}}$ in the cosmological region.

We present an LLM-powered social discovery platform that uses digital twins to autonomously evaluate interpersonal compatibility through behavioral simulation. The platform unifies three key pillars: (1) digital twins that engage in autonomous multi-turn conversations on behalf of users to estimate compatibility, (2) gamified territory conquest mechanics that incentivize real-world exploration and create organic settings for in-person encounters, and (3) AI companions that preserve persistent shared memory across devices. Built upon CogniPair's cognitive architecture (Ye et al., 2026), validated on the Columbia Speed Dating dataset (551 participants), our system extends prior simulation-only matching into a fully deployed social discovery environment. Through deployment, we derive empirical cost-quality baselines and identify fundamental scaling bottlenecks that remain hidden in component-level testing alone.

The uncertainties and covariance matrices of fission yield are important in the uncertainty analysis of decay heat. At present, there are no covariance matrixes of fission yield given in the evaluated nuclear data library, although they have provided the uncertainties with good estimates. In this work, the generalized least squares (GLS) updating approach was adopted to evaluate the fission yield covariances with the constraints from basic physical conservation equation and chain yield data, using the nuclear data files from ENDF/B-VIII.0, JENDL-5 and JEFF-3.3. Based on these original and updated data, summation calculation was performed for fission pulse decay heat of thermal neutron-induced fission of $^{235}$U. The uncertainties of decay heat were obtained through generalized perturbation theory, including the uncertainties propagated from fission yield, decay energy, decay constant and branching ratio. The original uncorrelated yield data contributes a $\sim 4 \%$ uncertainty at all times and dominates the decay heat uncertainty at cooling times longer than \SI{100}{s}. With the generated covariance matrixes, the uncertainty of calculated decay heat is strongly reduced and decay energy data makes a major contribution in general. The relative uncertainties at cooling time \SI{0.1}{\second} are $\sim$10$\%$ for ENDF/V-VIII.0 and JEFF-3.3 and $\sim$5$\%$ for JENDL-5 and those at cooling time 10$^{5}$ s are about 1$\%$ for three libraries. The influence of the GLS updating procedure on the contributions of important fission products to decay heat and their sensitive coefficients was also discussed.

We develop a self-contained theoretical framework that classifies the topological phases and critical phenomena of classical pyrochlore magnets with arbitrary spin $S$, subject to competing exchange and single-ion anisotropies. In the small-$w$ regime, where the single-ion term favors low spin amplitudes, exact dualities reveal a dichotomy: integer spins exhibit a continuous 3D $XY$ deconfinement transition, whereas half-integer spins remain in a $U(1)$ Coulomb liquid without any transition. In the large-$w$ regime, where the local spin amplitudes are maximized ($|S^z| = S$), the macroscopic flux is quantized to multiples of $2S$. By mapping the defect structure to topological loop gases, we prove that the compatibility between the physical ice rule and the emergent $\mathbb{Z}_{2S}$ flux conservation holds if and only if $S \le 3/2$. For $S=3/2$, this maps the system to the 3-state Potts model, whose symmetry-allowed cubic invariant drives a first-order transition. For $S \ge 2$, monopole contamination breaks the discrete clock mapping. Using an exact decomposition of the partition function, we show that the hierarchical string fusion cascade exponentially suppresses the discrete perturbations, which act as a dangerously irrelevant operator at the 3D $XY$ fixed point, protecting 3D $XY$ criticality. Finally, incorporating thermal monopoles, we show that they act as a symmetry-breaking effective magnetic field that severs defect strings. Consequently, the continuous transitions are rounded into crossovers, whereas the first-order $S=3/2$ transition is predicted to survive at finite temperatures, terminating at a critical endpoint. Classical Monte Carlo simulations for $S$ up to $7/2$ corroborate these analytical predictions.

Several recently proposed program logics have incorporated notions of underapproximation into their design, enabling them to reason about reachability rather than safety. In this paper, we explore how similar ideas can be integrated into an expressive type and effect system. We use the resulting underapproximate type specifications to guide the synthesis of test generators that probe the behavior of effectful black-box systems. A key novelty of our type language is its ability to capture underapproximate behaviors of effectful operations using symbolic traces that expose latent data and control dependencies, constraints that must be preserved by the test sequences the generator outputs. We implement this approach in a tool called Clouseau, and evaluate it on a diverse range of applications by integrating Clouseau's synthesized generators into property-based testing frameworks like QCheck and model-checking tools like P. In both settings, the generators synthesized by Clouseau are significantly more effective than the default testing strategy, and are competitive with state-of-the-art, handwritten solutions.