Mixture-of-Experts (MoE) has been adopted by many leading large models to reduce computational requirements. However, frequent inter-GPU communication in MoE expert parallelism (EP) becomes a performance challenge. We observe substantial redundant inter-GPU data transfers in MoE that can be potentially addressed by in-switch computing. Unfortunately, the existing solution, NVLink SHARP (NVLS), can only support static collectives with regular patterns, incapable of dynamic communication with irregular patterns in MoE. To bridge the functionality gap, we propose DySHARP, an integral dynamic in-switch computing solution to accelerate MoE, encompassing both communication primitives and communication-aware scheduling: 1) Dynamic multimem addressing co-designs ISA, architecture, and runtime, as a dynamic extension to NVLS, reducing redundant traffic. However, the resulting traffic reduction is inherently asymmetric between two directions, preventing it from directly translating into speedup. 2) Token-centric kernel fusion deeply fuses the dispatch-computation-combine pipeline, resolving this asymmetry to translate traffic reduction into actual speedup. Compared with the state-of-the-art solution, DySHARP achieves up to 1.79$\times$ speedup.

Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into purely diffusive models, obscuring the microscopic interplay of pressure, spin current, and local friction. Furthermore, reconciling true irreversibility with strictly unitary evolution raises profound questions about the role of the observer's temporal resolution. In this paper, we introduce a fully data-driven framework based on generalized Extended Dynamic Mode Decomposition (gEDMD) integrated with the Mori-Zwanzig projection. By expanding the observable dictionary to explicitly include spin currents, we directly extract the Navier-Stokes hydrodynamic coefficients from a chaotic XXZ spin chain across varying temporal coarse-graining scales. Our unconstrained extraction reveals a profound physical dichotomy: the mechanical elasticity ($c^2$) is intrinsically derived from the exact unitary dynamics, preserving strict microscopic reversibility. In stark contrast, the macroscopic friction ($γ$) and kinematic viscosity ($ν$) exhibit zero net dissipation, oscillating rapidly around zero in the exact-derivative limit. We demonstrate that genuine macroscopic transport cannot be established without finite temporal coarse-graining. By introducing a finite observation timescale ($Δt_{\rm cg} > 0$), the system passes through a distinct crossover timescale where these reversible fluctuations average out, establishing an intermediate functional regime that yields strictly positive friction and viscosity. Our results clearly demonstrate that macroscopic friction in isolated quantum systems is not an absolute property, but fundamentally an emergent phenomenon dictated by the temporal resolution of the observer.

Solid-state batteries require electrolytes that sustain high ionic conductivity under the mechanical environment of a functioning cell. Lattice strain, arising from stack pressure, thermal cycling, or lattice mismatch at interfaces, can either enhance or suppress Li+ transport in solid electrolytes, yet how it couples to the underlying diffusion mechanism remains poorly understood. Using Li3YCl6 halide superionic conductor, we address this with large-scale molecular dynamics simulations driven by an Atomic Cluster Expansion (ACE) machine learning interatomic potential trained on first-principles data. The ACE model faithfully reproduces experimental and \textit{ab initio} structural, mechanical, and transport properties of Li3YCl6. We find that Li+ diffusion in Li3YCl6 follows a two-regime Arrhenius behavior, crossing over at a critical temperature $T_c$ from one-dimensional hopping at low temperature to three-dimensional cooperative diffusion at high temperature. Strain substantially modulates diffusivity: tensile strain enhances it while compressive strain suppresses it, yet leaves $T_c$ invariant, indicating that strain tunes diffusion efficiency without reshaping the underlying transport framework. In each regime, the mechanistic origin differs: altered activation barriers dominate at low temperature, while modified pre-exponential factors become critical at high temperature. These results establish lattice strain as a design lever for ionic conductivity in Li3YCl6 solid-state electrolytes.

Gross, Mansour and Tucker introduced the partial-dual polynomial of a ribbon graph and asked under what conditions such a polynomial is even-interpolating, odd-interpolating, or both. In this paper, we provide an answer to this open problem.Using the framework of delta-matroids, we prove that the twist polynomial of any binary delta-matroid is either an even polynomial, an odd polynomial, or both even-interpolating and odd-interpolating. Applying this to ribbon graphs, we deduce that the partial-dual polynomial of any ribbon graph satisfies the same conclusion.

The rapid proliferation of artificial intelligence (AI) in consumer-facing digital products has disrupted the assumptions underlying classical user experience (UX) evaluation frameworks. Legacy metrics such as the System Usability Scale (SUS), Net Promoter Score (NPS), and task completion rate were engineered for deterministic, rule-based interfaces where identical inputs yield identical outputs. In AI-mediated systems -- spanning conversational agents, generative interfaces, and recommendation engines -- outputs are stochastic, context-sensitive, and temporally variable, rendering these metrics structurally insufficient. This paper introduces the Adaptive Dynamic UX Statistical Framework (ADUX-Stat), a novel evaluation model that reconceptualises usability as a probabilistic signal distribution rather than a static scalar score. ADUX-Stat integrates three original constructs: (1) Interaction Entropy Index (IEI), quantifying the unpredictability of AI responses from a user perception standpoint; (2) Temporal Drift Coefficient (TDC), measuring longitudinal degradation or improvement of perceived usability over interaction sessions; and (3) Bayesian Usability Confidence Score (BUCS), producing credible interval estimates of usability quality under uncertainty. The framework is validated conceptually against five established AI product categories. ADUX-Stat addresses a critical gap at the intersection of HCI research, statistical modelling, and AI product evaluation, offering a reproducible, field-deployable methodology for UX practitioners and researchers alike.

In this note, we want to establish several formulas about functionals along harmonic Ricci flow on surface with boundary

The concept of "thermal inductance" expands the options of thermal circuit design. However, the inductive component is the only missing components in thermal circuits, unlike their electromagnetic counterparts. Herein, we report an electrically controllable reverse heat flow, in which heat flows from a low-temperature side to a high-temperature side locally and temporarily in a single material by imposing thermal inertia and an ac current. This effect can be regarded as an equivalent of the "thermoinductive" effect induced by the Peltier effect. We derive an exact solution indicating that this reverse heat flow occurs universally in solid-state systems and that it is considerably enhanced by thermoelectric properties. A local cooling of 25 mK is demonstrated in (Bi,Sb)2Te3, which is explained by our exact solution. This effect can be directly applied to the potential fabrication of a "thermoinductor" in thermal circuits.

We address questions posed by Gérard Laumon and Jean-Loup Waldspurger concerning the cohomological purity of affine Springer fibers. More precisely, we show that an affine Springer fiber is cohomologically pure if and only if its $ξ$-stable quotient is cohomologically pure, and that this is further equivalent to the cohomological purity of a certain sequence of truncated affine Springer fibers. We deduce from this a sheaf-theoretic reformulation of cohomological purity for affine Springer fibers. We then compare this new criterion with a previously known one via a microlocal analysis of the relevant intersection complexes. As a corollary, we show that both the primitive part of the cohomology of an affine Springer fiber and the cohomology of its $ξ$-stable quotient depend only on the root valuation datum of the defining element.

Express transportation network design is uncertain because origin--destination demand, travel time, operating cost, hub congestion, and realized sorting productivity vary over time. Existing multi-topology express network models usually optimize cost and maximum arrival time under fixed input data, which may produce designs that are efficient nominally but fragile under demand surges, route disruptions, and hub productivity losses. This paper develops a Bayesian posterior-predictive framework for multi-topology express transportation network design. The model learns demand, travel-time, cost, and hub-reliability uncertainty from historical or benchmark-calibrated data and propagates them through posterior predictive scenarios. For fully connected, hub-and-spoke, restricted-allocation, and direct-link hybrid topologies, candidate designs are evaluated using posterior expected cost, conditional value-at-risk of maximum arrival time, service reliability, hub hold-time reliability, and emission-aware penalties. A Bayesian multi-structure design methodology is proposed using posterior simulation, sample-average approximation, topology-wise optimization, and Bayes-risk selection. Theoretical results establish existence of a Bayes-optimal design, convergence of posterior scenario risks, and stability of topology selection. Simulation and CAB benchmark experiments show that the Bayesian design can trade modest additional cost for substantial reductions in tail delivery risk and improved hub reliability.

The spin-1/2 Heisenberg antiferromagnetic chain is the canonical example of an integrable quantum many-body model. Despite its exact solvability, explicit finite-size solutions are typically only accessible via numerical evaluation of the Bethe ansatz equations. Here, we analyse the algebraic structure of the exact, symbolic ground states for chains up to ten sites using the coordinate Bethe ansatz. We show that both the ground state wavefunction and the Bethe-roots rapidly develop algebraic complexity with respect to system size, but at different rates. The Bethe-roots appear to become Galois unsolvable for chains of eight or more sites, whereas the ground state wavefunction coefficients and energy appear to become unsolvable for ten or more sites. This demonstrates a lack of explicit analytic tractability in a quantum integrable model due to algebraic complexity.

Dark matter may play an important role in galaxy formation through its non-trivial properties. For example, self-interacting dark matter may contribute to the formation of the widely observed core structures in galaxies. However, galaxy formation is a complex process, and such core structures can also arise from baryonic effects within the cold dark matter framework. To clarify the role of dark matter self-interactions, it is necessary to study systems that evolve without significant baryonic disturbances. Low-surface-brightness galaxies in the field, which are gravitationally isolated and have evolved with minimal external influence, are suitable candidates for this purpose. Since these galaxies typically contain only a small amount of baryonic matter, strong baryonic effects are not expected in their evolutionary history. In this study, we assume that these galaxies decoupled from proto-clusters at high redshift. Based on this assumption, we set initial conditions and estimate the time required for core formation, which we compare with the time corresponding to the redshift of proto-clusters. We examine five low-surface-brightness galaxies in the field and three observed proto-clusters at redshifts z=2.45, 7.66 and 7.88. Our analyses, based on order-of-magnitude estimates without numerical simulations, excludes a self-interaction cross section of sigma/m = 1 cm^2/g, while sigma/m = 0.1 cm^2/g is favored. This result is consistent with constraints derived from the shapes of present-day cluster cores.

Collective quantum states are often associated with extended systems, where spatially extensive degrees of freedom enable emergent many-body behavior; whether such strongly correlated states survive at atomic dimensions remains a fundamental question. Tomonaga-Luttinger liquids provide a paradigmatic example of one-dimensional collective quantum matter characterized by spin-charge separation. Using low-temperature scanning tunneling microscopy and spectroscopy, we directly visualize quantized collective modes in atomically confined mirror twin boundary segments of monolayer WSe2. Distinct standing-wave branches associated with fractionalized spin and charge excitations persist in segments as short as one nanometer, establishing the atomic-scale confinement limit of Luttinger-liquid behavior. These ultrashort segments form a new class of many-body quantum dots whose discrete spectra arise from confined collective bosonic modes rather than single-particle electron states. When assembled into ordered chains, inter-dot coupling reshapes electron-like fundamental states while collective spin/charge excitations remain largely intact, revealing distinct coupling responses of emergent many-body modes. Our results demonstrate that collective quantum matter can persist and exhibit fundamentally distinct coupling behavior at atomic length scales, establishing a novel platform for engineering strongly correlated quantum phases from atomically confined building blocks.

The numerical modeling of hydraulic jumps remains challenging due to complex interactions among free-surface deformation, air entrainment and detrainment, and turbulent bubble transport. Whereas accurate prediction of these flows is essential for the design of hydraulic structures, existing high-fidelity tools require prohibitive computational resources for engineering applications. This study implements a three-phase mixture model based on an Unsteady Reynolds-Averaged Navier Stokes (URANS) framework, to numerically simulate flow and air entrainment across twelve hydraulic jumps with Froude numbers ranging from $1.98$ to $8.48$, representing the first systematic analysis for such a comprehensive range of Froude numbers. The model accurately represents time-averaged velocity fields and air concentration profiles, as well as dynamic features including jump toe oscillation and free-surface deformation, showing good agreement with experimental data from seven facilities. Compared to Improved Delayed Detached Eddy Simulations (IDDES), the proposed approach achieves similar accuracy with approximately 400-fold fewer cells and a 300-fold reduction in computational cost. The investigation shows that the selection of turbulence closure affects the accuracy of the prediction of air entrainment. These findings establish the three-phase mixture approach as a practical engineering tool for hydraulic jump simulation, offering an effective balance of accuracy and computational cost.

As AI coding agents become embedded in software development workflows, developers are beginning to operationalize ethical principles by encoding behavioral rules into repository-level context files for AI agents, such as AGENTS.md files. Rather than examining the ethics of AI agents in the abstract, this vision paper investigates how ethics and values are already being translated for AI agents into actionable instructions that shape agent behavior. Through a preliminary investigation, we find that developers are already embedding guidance related to fairness, accessibility, sustainability, tone, and privacy. These artifacts function as a developer-authored governance layer, translating abstract principles into situated, natural-language directives within development workflows. We outline a research agenda for studying this emerging practice, including how encoded values vary across communities, what governance dynamics emerge when multiple contributors negotiate these files, and whether agents reliably adhere to the constraints specified. Understanding how ethics and values are operationalized for AI agents is essential to ground AI governance in modern software engineering practice.

We provide a partial answer to Burns' 1982 conjecture on the affineness of entire Grauert tubes: the complement of a codimension-one subset of an entire Grauert tube is affine. This result is obtained by establishing a generalized version of Demailly's criterion for affineness of Stein manifolds, which may be of independent interest.

In this work, we propose an easy-to-implement fixed-point algorithm for reconstructing a space-time dependent source in a subdiffusion model from lateral boundary measurements. The numerical scheme combines a Galerkin finite element method for spatial discretization with a finite difference method for temporal discretization. We establish the linear convergence of the fixed-point iteration and derive an error bound that depends explicitly on the discretization parameters and the noise level. The error analysis relies on stability properties of the continuous inverse problem and technical estimates for the associated direct problem with limited-regularity data. Numerical experiments are presented to support and complement the theoretical analysis.

Aesthetic qualities command measurable premiums in traditional goods markets. However, it remains unclear whether users are willing to pay for such qualities in AI-generated text. This paper estimates the willingness to pay for aesthetic attributes in large language model outputs using an online experiment with N = 117 participants. Participants evaluated responses from four anonymized models across academic, professional, and personal contexts, rated outputs along multiple dimensions, and submitted bids for access using a Becker-DeGroot-Marschak (BDM) mechanism. We find no statistically significant relationship between perceived aesthetic quality and willingness to pay. While participants systematically distinguish between outputs and exhibit consistent preferences over stylistic features, these differences do not translate into higher monetary valuation. Further analysis shows that aesthetic and functional attributes load onto a single latent factor, suggesting that users perceive quality as a unified construct rather than a separable aesthetic dimension. These results imply that, in current large language model (LLM) markets, aesthetic improvements function as baseline expectations rather than sources of price differentiation.

Floquet engineering of cavity magnon-polaritons by periodically modulating the magnon frequency has recently attracted much interest as a way to manipulate the energy spectrum of magnon-photon hybrid systems. However, modulating the frequency of magnons by a time-varying bias magnetic field can be challenging. We demonstrate cavity magnon-polariton Floquet engineering by modulating the microwave cavity frequency, allowing large modulation depth and bandwidth. We apply commensurate two-frequency Floquet modulations with the higher frequency at twice and three times the lower frequency, and demonstrate that the resulting spectrum depends on the relative amplitude and phase of the two drive tones. In comparison with single-frequency Floquet modulations, the spectrum has qualitatively different features; in particular, new anticrossings appear between previously uncoupled sidebands. Our platform offers an alternative way to manipulate Floquet quasi-energy levels in hybrid systems.

Rapidly rotating Rayleigh-Bénard convection admits a class of exact steady single-mode solutions describing high-amplitude convection cells. Using a matched asymptotic analysis in the high-Rayleigh-number limit, we obtain a rigorous characterization of their bulk and boundary-layer structure, yielding explicit scaling laws for the Nusselt and Reynolds numbers, including their dependence on the horizontal wavenumber. We show that, for suitable wavenumbers, these solutions attain the diffusivity-free ultimate scalings frequently assumed for geophysical and astrophysical convection, with additional enhancing logarithmic corrections. This reveals a specific mechanism through which rapidly rotating convection can approach ultimate heat transport via coherent columnar structures with well-defined horizontal scales.

Moiré superlattices formed by transition metal dichalcogenide (TMD) heterobilayers provide a versatile platform for studying strongly correlated electronic, excitonic, and topological phenomena in solids. In particular, angle-aligned MoSe$_2$/WS$_2$ heterobilayers, which have a Type-I band alignment at zero vertical electric field, host rich correlated spin and charge physics. Here, combining large-scale first-principles calculations and optical reflection spectroscopy, we report a thorough study of the emergent moiré excitonic states and interlayer charge-transfer states in angle-aligned electron-doped MoSe$_2$/WS$_2$ moiré superlattices. The moiré excitonic states serve as sensitive optical probes to the localization profile of doped electrons. We observe a series of interlayer charge-transfer transitions from n/n$_0$ = 1 to 4 (where n$_0$ denotes the moiré density) when the vertical electric field switches the heterostructure band alignment from Type-I to Type-II. By tuning the vertical electric field, we can precisely control the interlayer electron localization, realizing a Fermi-Hubbard model with a tunable charge-transfer band on an effective honeycomb lattice. Furthermore, Monte Carlo simulation of the doping dependence of the electric-field susceptibility predicts that multiple correlated charge-ordered states appear at both integer and fractional fillings. Our results provide a holistic understanding of the emergent optical excitations and the correlated charge-transfer states in electron-doped MoSe$_2$/WS$_2$ moiré superlattices.

We analyzed the distribution of spin parity in spiral galaxies using the HSC DR2 data. The spiral winding parity of disk galaxies, observed as S-spiral or Z-spiral projected onto the sky plane, provides robust information on the sign of the line-of-sight component of their spin vectors, specifically whether the spin vector points toward or away from us. The distribution of 49,494 S/Z annotated spirals with spectroscopic redshift (0.05 $\le z$) was analyzed for 46,247 fiducial cubic search volumes of various sizes, 20--200 Mpc, deployed in the 3D supergalactic coordinates. We counted the number of S-spirals and Z-spirals in each cube, evaluated the binomial probability of the observed S/Z imbalance, and identified statistically anomalous cube candidates. The observed cumulative distribution functions for the 256 sets of cubes are in good agreement with the theoretical binomial distribution and with those obtained from 1000 Monte Carlo realizations assuming random S/Z spin assignments. The number of statistically anomalous cubes is also comparable to that expected from the random assignments. These results indicate that the spin-vector distribution of spiral galaxies is consistent with statistical randomness expected from the standard cosmological model of structure formation.

This study constrains the range of in-medium mass modification through a comparison of theoretical calculations with experimental transverse momentum spectra and the yield ratio {\bar{p}}/p of protons and antiprotons. Based on the constrained range and a Gaussian source model with radial ow, the theoretical predictions for the fermion back-to-back correlation (fBBC) of p{\bar{p}} pairs at RHIC energies are presented. The results reveal a strong sensitivity of the fBBC signal to the assumed source time distribution: a Lorentzian form generates a pronounced high-momentum signal, whereas an α-stable Lévy form leads to a marked low-momentum signal. Moreover, the in-medium mass modification is shown to enhance the yield ratio {\bar{p}}/p. Therefore, events characterized by a larger {\bar{p}}/p ratio are predicted to have a significantly higher probability of exhibiting a detectable fBBC signal. This study may propose a promising new direction for the experimental observation of this phenomenon

Continuous Integration (CI) systems often run many builds concurrently. In this setting, a legitimate build failure may not be caused by the code push that triggered it. Such unrelated build failures can waste developer effort because developers must determine whether the failure is actionable for their current change. We study 77,354 CI build failures from seven open source Apache projects to understand and predict unrelated build failures. We find that developers spend a median of 4 hours identifying whether a failure is related or unrelated to their push. We also perform a document analysis of 371 confirmed unrelated build failures sampled from 10,316 potentially unrelated failures. The analysis shows that unrelated test failures account for 20% of the cases in which developers classify build failures as unrelated. To predict unrelated build failures, we extract 33 features from issue reports, issue comments, and commits associated with the triggering push. We build semi-supervised Positive and Unlabeled (PU) learning models for seven Apache projects. The models achieve precision from 0.70 to 0.88, recall from 0.30 to 1.00, F1-score from 0.44 to 0.91, and AUC from 0.63 to 0.97. Feature importance analysis shows that CI latency, repeated error messages, and the number of preceding comments are useful indicators of unrelated build failures. These results show that PU learning can help developers identify build failures that are unlikely to be caused by their current push.

Machine-learning systems used in survey-based social measurement require uncertainty estimates that are reliable across population subgroups, not merely valid in aggregate. We study ordinal conformal prediction for five-level AI-attitude forecasting on the Pew American Trends Panel (Wave 152; n=4,591; 12 race x education subgroups), comparing standard split conformal, Mondrian (group-specific) conformal, and a regularized Mondrian comparator across 100 respondent-disjoint splits with survey-weighted evaluation. Standard conformal achieves nominal marginal coverage for all four base predictors but leaves weighted subgroup gaps of ~13 percentage points. For the strongest predictor (XGBoost), Mondrian worsens the fairness-efficiency trade-off: weighted set size rises by +0.036 (dz =1.66) while the weighted subgroup gap grows by +0.013 (dz =0.30). A regularized comparator that shrinks group thresholds toward the global quantile mitigates this instability (Delta gap = -0.001, Delta size = +0.012) but does not yield a decisive fairness gain. Failure analysis traces the mechanism to calibration-cell fragmentation interacting with group-specific confidence mismatch. The negative result persists across alternate outcome codings and subgroup granularities, demonstrating that nominal marginal validity is insufficient for subgroup reliability and that naive group-specific calibration is not a dependable fairness remedy in complex survey settings.

In recursive state estimation, numerical error can play a major role in an algorithm's overall performance and reliability. Roundoff errors due to finite precision arithmetic can violate theoretical guarantees, leading to asymmetric and non-positive-semidefinite covariance matrices. In algorithms employing first-order covariance mappings, such as the extended Kalman filter, these issues have been mitigated by employing square root factorizations of the covariance matrix. However, existing techniques do not directly extend to higher-order moment mappings, which show great value in highly nonlinear settings. This paper presents the first known square root computation of the second-order covariance mapping. The square root computation is not only more accurate, as is shown in two distinct numerical experiments, but generally requires fewer floating point operations compared to the full covariance matrix computation.

An emerging blockchain protocol design pattern leverages the asymmetry between the computational effort in performing versus verifying tasks. For example, cryptographic validity proofs (e.g., SNARKS) require the prover to expend significant effort demonstrating the correctness of their claim, while the verifiers benefit from extremely easy validation. The operationalization of this paradigm requires efficiently soliciting the performance of expensive tasks in pseudonymous, adversarial environments. We formalize this as a mechanism design question. The protocol balances the economic cost of a liveness fault, where the work is not completed, with the payments required to incentivize specific behavior from candidate suppliers. We show that the loss of the optimal protocol scales logarithmically in the cost of a liveness fault, scaled up by the adversarial fraction of the network. Further, we find that the optimal equilibria have an intuitive structure, allowing us to provide concrete advice to practitioners. Specifically, in many regimes, the optimum designates a single, random node as the primary worker and a committee as a fallback, which is reminiscent of leader-based consensus mechanisms. We also characterize the asymptotic regimes where having negative payments (i.e., slashing in blockchain parlance) is especially helpful.

We introduce swept-area pseudometrics on ropelength-filtered spaces of knot representatives. For a knot type \(K\) and a ropelength level \(Λ\), admissible isotopies are required to pass through curves of thickness at least one and length at most \(Λ\). The swept area is the parametrized area traced by the moving curve, and its infimum over admissible isotopies defines an extended pseudometric on each admissible component. We also define the admissible fundamental group of a based admissible component and equip it with a swept-area length function. The construction is separated from the rigidity questions it raises. The zero-distance quotient is always a metric space, while non-degeneracy before quotienting is treated separately. We prove non-degeneracy on uniformly non-collinear finite-dimensional polygonal strata. We also prove calibration lower bounds from projected signed area, including a rotation-invariant supremum over oriented planes, and use them to obtain exact distance formulas for concentric round unknots and homothetic planar ellipses. We further prove rigidity of the ideal unknot. The framework is related to static scale-free invariants such as density and compression radius, and to filtered-topological structures such as ideal strata and merge scales. We define swept-area weighted lifted Reidemeister graphs and prove that, for diagrammatically generic isotopies, the associated diagrammatic distance is bounded above by the geometric swept-area distance. We also record monotonicity in the ropelength parameter and formulate problems toward full non-degeneracy and approximation theory.

Older adults have increasingly turned to conversational AI as a source of emotional support. However, little is known about how emotionally supportive interactions are experienced in everyday use, particularly when AI systems limit, redirect, or intervene during these interactions. We interviewed 18 older adults about their experiences using conversational AI for emotional support, examining when they turn to AI, how they engage during emotionally vulnerable moments, and how they respond when support feels disrupted. Our findings show that older adults often rely on AI when other forms of social support feel inaccessible. However, current safety-related interventions can redirect interactions in ways that participants experience as interruptions to emotional engagement or as shifts in control away from them. Such disruptions can undermine older adults' ability to remain emotionally engaged and, in some cases, contribute to emotional distress. We discussed design implications for emotionally supportive conversational AI, emphasizing the need for safety interventions that are enacted within older adults' social contexts, align with users' emotional pacing, and preserve their sense of agency.

Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the single splitting of the coefficient matrix derived from the corresponding normal equation. In this work, we put forward an innovative iterative framework grounded in the double splitting of normal equations tailored for ILS problem. Specifically, we elaborate on a distinct implementations of the double splitting strategy, which offer constructive insights and methodological references for subsequent research on double splitting-based iterative methods. Two numerical experiments further corroborate that the proposed double splitting iterative paradigm outperforms conventional single splitting approaches in both computational efficiency and convergence robustness.

For a graph $G$ and an integer $d\geq 0$, the defective chromatic polynomial $χ_d(G;k)$ counts the $k$-colorings of $G$ in which each vertex has at most $d$ neighbors of its own color. We investigate which structural properties of $G$ are determined by the full family $\{χ_d(G;k)\}_{d\geq 0}$. We establish a contraction formula expressing $χ_d(G;k)$ as a sum of ordinary chromatic polynomials of the edge contractions of $G$. As a first application, we prove that for triangle-free graphs, the full family determines the degree sequence. For trees, we show further that the family $\{χ_d(T;k)\}_{d\geq 0}$ determines the path-subgraph counts $N(P_j,T)$ for $j=1,2,3,4$, but not for $j=5$. For each $n\geq 9$, we construct a pair of nonisomorphic trees of order $n$ that share the same defective chromatic polynomials for every $d\geq 0$.