Papers

I estimate firm-level capital-, labor-, and material-augmenting productivity for Chinese manufacturing, 1998–2008, and the effect of state-owned enterprise (SOE) privatization on each. Results show technological change is strongly biased toward capital and labor. Private firms operate above SOEs on capital and labor, but below on materials. Privatization raises labor-augmenting productivity right after the transition, a front-loaded gain that fades on the full panel but persists among 1998 incumbents. It leaves capital-augmenting productivity no higher and modestly lowers materials. The SOE sector's catch-up runs through restructuring of the plants the state kept, with exit of overstaffed plants adding to the labor gain.

We test when compressed CMB likelihoods can be reliably used to constrain new physics beyond $\Lambda$CDM, formulating concrete criteria for when, why, and how CMB compression fails. We derive our conclusions by exploring a broad set of models that modify different aspects of the cosmological evolution, including late-time dark-energy dynamics, non-standard late-time dark-matter evolution through interactions or decay, and dark-matter models with persistently non-standard redshift evolution. For each case, we compare the results obtained from data combinations based on the full Planck-CMB likelihood with their counterparts based on a compressed CMB likelihood calibrated in $\Lambda$CDM. We find that the compression remains accurate for late-time dark-energy extensions that preserve the dark-matter background evolution and do not introduce significant additional perturbative effects. By contrast, modifying the dark-matter evolution breaks the mapping between the present-day matter density and the matter density at the epochs relevant to the CMB, causing the compressed constraints to fail even when the modification acts exclusively at late times. In these cases, the compressed likelihood can drastically alter the geometry of the multidimensional posterior distributions, shifting their centers, producing strongly anisotropic deformations, reordering principal modes, and generating genuine mixing and rotation of their eigendirections. These multidimensional distortions propagate into substantially incorrect marginalized constraints on cosmological parameters, with differences between the full and compressed analyses reaching nearly an order of magnitude in some of the cases studied here.

Physical many-body quantum systems typically interact locally, giving rise to ground states where entanglement grows with the area of the region being probed. Beyond entanglement, non-stabilizerness (or "magic") has been established as another crucial resource linked to quantum complexity and the properties of error-correcting states. Unlike entanglement, non-stabilizerness typically behaves with a volume-law scaling in ground states, indicating inherent computational complexity. In this work, we show that under a recent classification of quantum states, area-law states split into two distinct classes. Entanglement-dominated states obey an area-law for non-stabilizerness and admit efficient quantum algorithms for entanglement manipulation. Conversely, magic-dominated states exhibit a a faster-than-area growth of subsystem non-stabilizerness and require non-efficient algorithms for entanglement manipulation tasks. Within this context, we introduce the concept of the stabilizer regime, a restricted quantum phase that admits efficient entanglement manipulation and hosts area laws for both magic and entanglement.

Egocentric human data offer a path to scaling robot learning beyond costly robot demonstrations, yet the embodiment gap makes raw human trajectories a poor supervisory target for control. Our key insight is that, although low-level actions are embodiment-specific, their underlying motion intent can capture task-relevant structure that transfers across humans and robots. We introduce EgoLAP, a VLA pre-training framework that jointly learns from human and robot trajectories through a shared language-based action chain-of-thought. EgoLAP expresses motion intent as structured, temporally abstracted language actions and pairs them with motion-level reasoning grounded in scene geometry, physics, and object affordances. Across extensive real-world and simulated experiments, EgoLAP transfers human experience to robot control more effectively than alternative action representations and reaches 80.1% mean real-world task progress, a 2.3x performance gain over alternative action representations. Motion-level reasoning also outperforms a composite reasoning format that combines subtask, object-box, and visual-trace reasoning.

This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones separated by two external circles. We analyze how different geometric configurations of these zones influence the number of limit cycles. Moreover, we show the existence of at least sixteen limit cycles in fourth-degree piecewise polynomial holomorphic systems under certain configurations.

In this paper I study a class of scenarios in which a scalar singlet dark matter candidate interacts with the Standard Model in such a way that the Higgs portal is strongly suppressed, even at loop level, through a specific mechanism involving scalar mediators. The mediator carries non-trivial gauge or internal quantum numbers that allow only a quartic coupling with the dark matter, and belongs to representations with no components that can mix with the Higgs boson, so that the dark matter interacts only with exotic states. I refer to this construction as $x$-channel because no single mediator is exchanged between the dark and visible sectors, to distinguish it from the standard $s$- and $t$-channel simplified scenarios. The suppression is due to a boundary condition on the running Higgs-portal coupling, which makes the tree-level and one-loop Higgs-mediated contributions vanish at zero momentum transfer, regardless of the internal quantum numbers of the mediator. I consider here a minimal realisation, in which the mediator is a singly- or doubly-charged colourless $SU(2)_L$-singlet scalar decaying to leptons, and study the complementarity between collider, Higgs, flavour, and astrophysical/cosmological constraints. Within the scanned ranges and benchmark assumptions, the surviving points are predominantly in the region where the dark matter is heavier than the charged scalar mediator. LHC limits determine the lower edge of this region, part of which can be probed by future colliders through the production of the charged scalars. Other realisations of the $x$-channel can open different phenomenological directions to explore.

We prove copy-optimal learning of the full Gaussian orbit of paired magic states on $n$ fermionic modes. The unknown evolution may be any parity-preserving quadratic circuit, including pair creation and annihilation, and each copy is measured once, in a fixed basis, on a single quartic Majorana observable. A nonadaptive learner returns a Gaussian preparation within trace distance $\epsilon$ from $\Theta(n^6/\epsilon^2)$ copies at fixed confidence, and no learner in this measurement model, adaptive or not, can do better. Measured quartic correlations certify the trace distance of the result. Our second result extends learning to a broader family: pure states whose unknown input blocks are superpositions of disjoint occupation patterns with bounded particle number, under the same evolution. Using single-copy Gaussian rotations and occupation readout, a batch-adaptive learner returns an input and a Gaussian circuit with infidelity $f$ from $\widetilde O(n^7/f)$ copies and polynomial classical processing. Connected quartic correlations reveal the hidden mode groups, and fresh local measurements restore the branches and their coherences. No particle-number conservation, minimum branch weight or spectral gap is assumed.

Many long-horizon agents compact their context on a global rule, usually a token budget, blind to what the agent was doing. We ask whether the agent's recent behaviour predicts when a compaction will hurt. TRACE's public corpus of 590 harness-triggered AppWorld compaction boundaries replays each boundary from a re-executed prefix state under the pre-compaction context and under the summary, and records the burden of the next actions: calls that error or repeat a call already made. We find that pre-boundary history predicts post-compaction harm only weakly. An internally prespecified contrast by prefix placement is a wide null, and the naive "has-written" label behind it turns out to measure trajectory phase. The best extension-protocol trigger reaches held-out AUROC 0.66 (0.64 on the replicate's own label) against a same-boundary replicate of 0.72; the best frozen, interpretable trigger avoids 21% of harmful (positive-burden) boundaries while keeping 84% of compaction opportunities, and exceeds the random-rule expectation on count but not on burden mass (a post hoc comparison). Whether the best trigger beats a token-budget rule at matched retention cannot be evaluated on the release. We state what corpora should ship to answer it.

The moving-coil meter provides a simple context in which to model deterministic electromechanical dynamics, thermal fluctuations, and electronic readout. The movement is a linear electromechanical system in which electrical resistance and intrinsic mechanical damping act as two independent dissipative channels, each accompanied by thermal fluctuations. The stored energy provides a Lyapunov function for stability, and the algebraic Lyapunov equation yields the stationary covariance in closed form. The result exhibits equipartition among the energy terms; damping is shown to reshape the temporal memory of the fluctuations without changing their steady-state variance, giving a thermal floor of a few picoamperes for a representative movement. Exact stochastic integration reproduces the stationary covariance and autocorrelation structure; the covariance is also recovered by spectral integration. Embedding the movement in an active current-drive readout shifts attention to the noise of the complete readout, which a design-stage estimate expresses as a few parts per million of full scale, growing as the input sensitivity increases. The example illustrates that measurement sensitivity and resolution cannot be considered independently. The treatment is aimed at master's-level students in physics with some background in statistical physics and stochastic processes, and basic familiarity with analog electronics.

LLM-based agents are increasingly advancing scientific and engineering problem solving, with physics simulation emerging as a challenging yet practical testbed for reproducing complex physical phenomena with application in embodied AI, games and films. As the workhorse of such simulation, a solver computes how the state of a dynamic system evolves over time. Building such solvers requires physical understanding to identify appropriate models, mathematical reasoning to formulate the underlying dynamics, and software engineering to implement them as executable code, yet this capability of LLM agents remains underexplored. To this end, we introduce WorldSolver, a benchmark of 168 simulation tasks derived from physical phenomena in 61 classic computer graphics papers, spanning 7 physical domains. Each task contains a code scaffold that provides a fixed simulation environment for the scene, with the solver implementation left for the agent to complete. Specifically, we evaluate them along three dimensions: Execution Checks for successful execution, Visual Fidelity for reproducing the intended dynamic behavior in the rendered simulation, and Physical Plausibility for physics-grounded verification of the generated dynamics. Experiments on frontier agents reveal that producing executable solvers is difficult itself, and satisfying visual and physical correctness is even harder. GPT-5.6-Sol and Claude-Opus-5 perform comparatively better than the other evaluated agents, yet achieve overall scores of only 48.7% and 46.7%, respectively. WorldSolver is an early step toward agentic solver generation, and we hope it helps drive progress toward agents that can faithfully simulate the dynamic physical world. Code is available at https://github.com/sirujiang/WorldSolver.

Reusing the scores that select a Best-of-$N$ winner can overstate its expected reward. We study evaluation from a fixed matrix of $K$ independent scores per candidate for a policy that selects using $J$ fresh scores. A single estimator based only on this matrix is exactly unbiased for expected judge reward under every independent, stable collection of candidate-specific score laws if and only if $J<K$, for every pool size $M\ge N\ge2$. At $J=K-1$, the selector deepens as $K$ grows. For independent Gaussian scores with common variance and fixed $M\ge N\ge2$, the unbiased minimax risk in this regime is of order $\sigma^2/\sqrt K$, attained by Holdout; allowing bias improves the rate to $\sigma^2/K$. For two candidates, we derive the minimum-variance unbiased estimator at known variance and the sharp asymptotic unbiased minimax constant $1/(\pi\sqrt2)$, which Holdout attains without knowing the variance. The cyclic average over subsets and ties can be computed in $O(MK\log M)$ operations. At fixed selector depth, cyclic evaluation of bounded scores has $O(K^{-1})$ risk uniformly in pool size. The impossibility result concerns the fixed matrix: one additional fresh winner score permits unbiased evaluation of the all-$K$ policy.

Knowledge that a language model appears to forget during finetuning often remains stored and can be recovered, a phenomenon called spurious forgetting. Finetuning on new facts can even produce forgetting that undoes itself: recall of the old facts collapses, recovers as training continues on new facts alone, and only then erodes for good. We seek to understand when such forgetting is not catastrophic. A minimal associative memory reproduces these dynamics with three ingredients: keys with shared structure, concentrated new values, and normalization in the network. Finetuning moves all old representations along a common direction, hiding the old facts while preserving their relative geometry; normalization withdraws this shift once the new facts are learned, whereas fact-specific changes accumulate and cause the erosion. Moreover, subtracting the common shift eliminates the collapse in a Transformer trained on synthetic data, and removing a single direction from each weight update restores old facts in a pretrained language model. Forgetting thus combines a shared, reversible loss of access with a slow erosion of individual facts, and only the second is catastrophic. Which one dominates depends on whether the new data move old memories together or apart.

We study path-flow alignment as a unified training objective for flow matching. Instead of fixing the interpolation path and learning only the velocity field, we jointly train an endpoint-preserving path network and a flow network using the same alignment loss: the flow learns to match the path velocity, and the path learns to align its velocity to the current flow. Although every fixed learned path defines a valid flow-matching objective, the alignment loss alone is not a reliable criterion for path learning. We identify path overfitting, a failure mode in which the alignment loss decreases while sample quality worsens. We find that this failure is associated with low-entropy bottlenecks in the induced probability path, where the learned path routes samples through overly concentrated intermediate marginals. Motivated by this diagnosis, we introduce a stochastic path regularizer that hides part of the source information from the path network while preserving exact endpoints. The resulting regularization gives an explicit entropy floor for the stochastic training-path marginals and empirically suppresses the bottleneck in the learned sampler, making joint path-flow training effective. On ImageNet-256x256 with SiT backbones, our method consistently improves FID across model scales, extends to model-guidance training, and leaves the inference-time architecture and sampler unchanged. Code is available at https://github.com/lizeyu090312/traj_opt_paper

Generative retrieval trains a language model to generate the identifier of a relevant document. Recent work replaces the autoregressive decoder with diffusion, but changes identifiers, training recipe and decoding at once, so differences cannot be credited to the paradigm. On NQ320K and MS300K, we train autoregressive, masked-diffusion and block-diffusion models with residual-quantised, product-quantised and random identifiers. With identifier length and training budget fixed, we decode each model in several ways. Decoding alone moves a diffusion model's Hit@1 by 6.6 to 13.7 points. Our reference diffusion decoding, generate-and-match, generates an identifier, then retrieves the closest corpus identifiers. The generated identifier is right for 14-21% of NQ320K queries. We test one-pass scoring to decode diffusion retrievers: the model reads a fully masked identifier once, and each document is scored by its codes' probabilities. It matches or beats generate-and-match in 11 of 12 settings. Autoregressive models still lead in Hit@1; on NQ320K, the lead comes from the model, not beam search. Starting from one sampled identifier, one-pass scoring removes 46-83% of masked diffusion's deficit to beam search; from generate-and-match, at most a quarter. On NQ320K, every paradigm largely memorises which identifier answers which query: random identifiers keep 83-90% of the Hit@1 of residual-quantised ones. There, product-quantised identifiers lead residual-quantised ones by 3.4 points in the autoregressive model and by -0.7 to +3.6 in diffusion models; across decodings, AR's gap exceeds diffusion's by 1.5-2.3 points, around our 2-point threshold. Paradigm comparisons must report each paradigm at its own recipe and best decoding.

The following motif is common in spatiotemporal settings: we have a sequence of covariate and label pairs observed for a relatively short, recent time period. We have access to unlabeled covariates over a longer time period. Data is observed over many spatial locations. For instance, crop yield might be observed over a large geographical area for recent years, but weather data (which is informative about crop yield) is available for a much longer period. The goal is to estimate, at each spatial location, the expected label (e.g., crop yield) in the future and provide a valid confidence interval for this value. The observed time period alone is too short for reliable estimates. Imputing missing labels with machine learning can cause substantial bias. Prediction-powered inference (PPI) can correct for this bias, but it relies on an i.i.d. assumption that breaks under our expected temporal dependencies. Heteroskedasticity and autocorrelation consistent (HAC) procedures account for temporal correlation, but have not been adapted to cases where some labels are imputed. We provide reliable point estimates and confidence intervals given: short labeled time series (across spatial locations), a longer unlabeled time series, and an imperfect predictor of labels given covariates. We show our method outperforms natural alternatives.

Polynomial transformations are basic primitives in quantum algorithms: quantum signal processing and singular value transformation compile univariate polynomials into circuits with query complexity essentially set by degree. Multivariable transformations of noncommuting matrices, however, lack a comparable synthesis theory. We develop a complete constructive theory under joint block access for all polynomials contractive on the prescribed matrix domain. Given a compact finite-state description of a degree-$D$ polynomial $P$ and $0<\tau<1$, we synthesize $P$ with $(1+\tau)$-optimal normalization using $O(D/\sqrt{\tau})$ queries, and exactly $D$ under row-block access, matching a degree lower bound. The complete circuit realization is classically computable in polynomial time with polylogarithmic dependence on accuracy. The key to our construction is a finite algorithmic Schur–Agler theorem: the coefficient recurrence defines a polynomial-dimensional continuation space supporting a complete semidefinite certificate for contractivity on the prescribed domain. Factoring this certificate yields the contractive realization underlying the query algorithm. Beyond matrix transformations, our framework lifts multivariable polynomial synthesis to quantum channel transformations. Given coherent Kraus access $K=\{K_a\}_a$, we synthesize any finite jointly contractive family of noncommutative polynomial maps $K\mapsto\{F_b(K)\}_b$ as completely positive operations, allowing coherent interference among Kraus histories. Furthermore, channel-level transformations specified by causal Choi data can be synthesized explicitly as fixed-order quantum combs. Collectively, these results point to a broader program: multivariable approximation as a language for multi-operator quantum algorithms and higher-order quantum information processing.

Embodied agents must reason about 3D space while the video is still arriving, answering questions as soon as they have observed enough of the scene. VLMs that incorporate 3D geometric priors achieve strong spatial reasoning, but they operate offline, i.e., the full video must be available before they produce an answer. Streaming VLMs process frames causally and decide for themselves when to respond, yet they lack explicit 3D representations. We present SpaTime, a streaming VLM that fuses causal geometry tokens into the language model at every frame, using only the frames observed so far. To supervise when the model answers, we propose a response-time loss that maps per-frame response probabilities to a differentiable expected response time and penalizes the distance from the ground-truth frame. For evaluation, we construct StreamVSTI-Bench and StreamVSI-Bench, streaming adaptations of VSTI-Bench and VSI-Bench. On StreamVSTI-Bench, SpaTime reaches 49.2% overall accuracy and reduces the mean response-time error by 66% relative to the strongest streaming baseline.

Peixoto et al. (arXiv:2602.16937v2) stress that graph-based formulations can express any interaction model, a point the literature on higher-order networks (HONs) has often overlooked. We agree with much of their critique. We argue that expressiveness, however, might not be the main reason hypergraphs are often preferred. A network is read from a model rather than assumed, and to properly study the role of structure-one of the most basic questions in complex systems research-one needs a representation that keeps that structure separate from the functional form of the interactions. We show that such representation is in general a directed hypergraph (equivalently, a directed factor graph), with one hyperarc per interaction term, recovering a (directed) graph for pairwise interactions, and an undirected hypergraph for symmetric, higher-order ones. Most of the HONs literature has focused so far on symmetric interactions, which, in light of what established here, might explain why there (undirected) hypergraphs are regularly presented as the natural representation for systems with higher-order interactions.

This study investigates the asymptotic behavior of two dependence measures defined on networks, Moran's $I$ statistic and Newman's assortativity, under the null hypothesis that a Gaussian node attribute $Y$ is independent of the network structure. We demonstrate that the structure of the network directly affects the convergence rate to normality of these measures as the size of the network increases. We further establish that, in some instances, the mean values of these dependence measures under the null hypothesis remain non-negligible asymptotically and must therefore be explicitly accounted for when calculating the test statistics. Applications to a variety of simulated and real networks also reveal that the normal approximation performs well only when the network is not strongly heterogeneous. Network topology determines both the convergence rate to normality and whether the limiting distribution is Gaussian. In dense networks whose degree heterogeneity does not vanish, we further show that assortativity can fail to be a valid test statistic even though Moran's $I$ remains well behaved, whereas a dominating node invalidates both.

Entanglement sudden death (ESD), explored through a series of works by Yu and Eberly, supports the notion of entanglement vanishing abruptly and completely at a finite time, even when the underlying open-system dynamics remain smooth. In this article, we revisit the development of ESD from bipartite origins to genuine multipartite entanglement. We first illustrate the canonical mechanism of ESD with two independently damped qubits, for which the concurrence vanishes at a finite time while populations and coherences remain nonzero. We next present our results on multipartite entanglement for generalized GHZ states under depolarization. Global and independent local depolarizing dynamics can be chosen to produce identical reduced evolution for every individual qubit, yet they yield different genuine-multipartite-entanglement sudden death times, whose ordering can reverse with the initial state. For N-qubit GHZ states, this distinction becomes asymptotically stronger since the ESD time scales as 1/N under independent local depolarization, whereas under global depolarization it approaches a finite value in the thermodynamic limit. Echoing a central lesson of Prof. Eberly's work, we report the lifetime of multipartite entanglement is not fixed by the local dynamics, but rather depends on the evolution of the joint quantum state.

Galaxy mergers can drive gas toward galactic nuclei, enhancing both star formation and black hole accretion in post-merger galaxies. Here we use the IllustrisTNG-50 simulation and two boxes from the BRAHMA simulation suite, all of which adopt different black hole formation models, to characterize merger-associated signatures in candidate massive black hole (MBH)-pair hosts. In all three simulations, we select post-merger galaxies whose progenitors both host MBHs and quantify their enhancements in star formation and black hole accretion relative to matched non-merging controls. In TNG50, we find substantial merger-triggered enhancements in both specific star formation rate (sSFR) and specific black hole accretion rate (sBHAR) at $0 \leq z < 3.3$, reaching $\sim 1.4\times$ and $\sim 1.5-1.7\times$ the controls, respectively. The BRAHMA runs employ more physically motivated seed formation models, seeding BHs in lower-mass galaxies and at higher redshifts than TNG50. In BRAHMA, merger-driven enhancements in sSFR and gas fractions are comparable to those in TNG50 at $z \lesssim 3.3$ and persist to the highest redshifts probed by BRAHMA ($z \sim 6$). Despite this, BRAHMA shows no significant merger-driven enhancement in sBHAR across its entire redshift range. In a similar vein, TNG50 pair hosts show an enhanced AGN fraction relative to matched controls, whereas BRAHMA shows only a weak excess among the most rapidly accreting MBHs.

We present an exposition of an argument, discovered by GPT-6 Pro, that gives an optimal bound for the polynomial Littlewood-Offord problem. Namely, let $F$ be a degree-$d$ multilinear polynomial that contains $r$ degree-$d$ monomials involving disjoint sets of variables. Then, for i.i.d. Rademacher random variables $\xi_1, \ldots, \xi_n$, we have $\mathbb{P}[F(\xi_1, \ldots, \xi_n) = 0] = O_d(r^{-1/2})$. This improves upon the previous bound of $(\log r)^{O_d(1)} r^{-1/2}$ due to Meka, O. Nguyen, and Vu, and resolves a conjecture attributed to H. Nguyen and Vu. The key part of the proof is an estimate for the total influence of bounded-degree rational functions, which resolves a recent conjecture of Kothari, Kovacs-Deak, Wang, and Yang.

Given any fixed integer $k \ge 2$ and sufficiently large $d$, we show that the largest possible fractional chromatic number of a $k$-uniform $d$-degenerate uncrowded hypergraph $H$ (i.e., with girth at least $5$) satisfies \[ \chi_f(H) = (1 + o_d(1)) \left((k-1)\,\frac{d}{\log d}\right)^{\frac{1}{k-1}}. \] In fact, we prove that this holds for $k$-uniform $d$-degenerate hypergraphs of girth at least $g$, for any given $g \ge 5$. As a corollary, we obtain improved bounds on the fractional chromatic number of $d$-degenerate linear hypergraphs. This work builds upon a recent result by Allen, Dhawan, and Noel, extending it from graphs to hypergraphs. In addition to overcoming the new difficulties that arise in the hypergraph setting, our approach yields a simpler proof even in the original graph case. Our proof of the upper bound uses a simpler iterative procedure for sampling independent sets. We also establish bounds for fractional colorings with local demands, a framework introduced by Kelly and Postle, verifying a recent conjecture of Yu and Zhang. As a consequence, we obtain a degree-sequence bound on the independence number of uncrowded hypergraphs with a leading constant matching the shattering threshold. For the matching lower bound, we use a hypergraph variant of the uniform attachment model and harmonic vertex weights to bound the fractional chromatic number via linear programming duality, then remove all short cycles by deleting vertices of negligible total weight. We also replace the Catalan-number argument used in the graph case with a matrix-norm estimate, simplifying the analysis.

Motivated by recent results on the order of connected graphs with positive Lin–Lu–Yau Ricci curvature under forbidden minor or forbidden subgraph conditions and minimum degree assumptions, we prove that, for every integer $t\ge 5$, every locally finite graph $G$ with no $K_t$ minor, minimum degree at least $t-1$ and positive Lin–Lu–Yau Ricci curvature on every edge satisfies \[ \Delta(G)=O(t^5\log^{3/2}t). \] The minimum degree condition $t-1$ is best possible. Moreover, if $G$ is connected, then $G$ is finite and \[|V(G)|<2t\Delta(G)^6=O(t^{31}\log^9 t). \]

We study a discrete Lagrangian model for a one-dimensional chain of rigid rods coupled by elastic springs. We characterize the geometry of its zero-energy constraint and distinguish the spinner and flipper regimes. Under graph-type hypotheses, selected zero-energy chains converge, after rescaling, to trajectories of an autonomous ordinary differential equation. For the physical linkage, we identify a simple alternating selection criterion under which chains form a unique monotone heteroclinic family in the spinner regime. In the flipper regime, we determine the topology of the constraint set and the number of successors, but leave global branch selection open. We also derive one- and two-component continuum residual expansions, distinguishing consistency from convergence of time-dependent solutions. Reproducible numerical experiments test the selected spinner recurrence and its asymptotic multiplier; for a simplified one-component model with smooth periodic data, they recover first- and second-order discrepancies for the leading and corrected continuum equations, respectively.

Image stylization with latent-diffusion models entangles two independently refined axes: what a region depicts and how it is depicted. Such pipelines expose only global controls, yet professional retouching demands deliberate, region-specific control. We lift two conditioning weights already present in a ControlNet + IP-Adapter stylization pipeline from global scalars to per-location spatial maps, yielding local, per-axis control of content and style in a single generative pass. Because the two weights act on disjoint pathways, adjusting them independently spans a 2x2 retouching vocabulary, from free regeneration to identity preservation. We validate that edits stay confined to the retouched region and that each weight predominantly steers its own axis. Our approach requires no retraining and drops unchanged into any such pipeline.

In K-12 mathematics tutoring, student-tutor dialogue provides rich evidence of learners' problem-solving processes and sources of difficulty. Learning analytics research increasingly relies on large language models (LLMs) to extract such information from dialogue for a variety of downstream tasks, including knowledge tracing, behavioral modeling, and diagnosis of student reasoning errors. However, the validity of these model-generated interpretations remains insufficiently understood. In this exploratory study, we examine the validity of LLM classifications of five student failure modes in mathematics tutoring dialogue using an operational diagnostic codebook: uncertainty, misattribution, operator selection, conceptual gap, and procedural slip. Across models, human-LLM agreement was moderate (kappa = .524-.597), while cross-model agreement was substantially higher (kappa = .755-.781; alpha = .769). These findings show that cross-model agreement can create a misleading appearance of correctness, challenging the assumption that consensus among LLMs constitutes evidence of valid learner interpretation. For learning analytics, the implication is clear: scalable labeling is useful only if the inferred constructs are valid, and model consensus cannot substitute for independent evidence of that validity.

Battery energy storage systems must respect strict state-of-charge (SOC) limits to prevent overcharge and deep discharge, a task complicated by measurement noise and costly-to-model nonlinear dynamics. Data-enabled predictive control (DeePC) resolves the costly modeling issue by predicting future behavior directly from data. However, its regularization robustifies only the prediction and not the constraints. Scenario-based DeePC (Scenario-DeePC) extends DeePC with the scenario approach, building constraint robustness fully data-driven from observed prediction errors rather than an assumed disturbance distribution. This paper presents the first real-world deployment of Scenario-DeePC, on a grid-connected battery system at the NEST research facility, whose SOC estimate exhibits abrupt, irregular recalibration jumps in addition to ordinary noise. Compared to standard DeePC, Scenario-DeePC achieves comparable tracking performance with substantially fewer constraint violations. Its adaptive scenario buffer further tightens constraint handling automatically, improving robustness to unpredictable recalibration events.

We prove that the probability that Gaussian elimination with partial pivoting on $n \times n$ random matrices has growth $\rho$ is at least inverse quasi-polynomial: $\Omega(\exp(-c \log^2 (\rho)\log(n)))$ for some constant $c > 0$. This lower bound breaks standard conjectures in the smoothed and average-case analysis of Gaussian elimination. To the best of our knowledge, it is the first non-trivial lower bound on the probability of large growth for Gaussian random matrices.

Extended reality (XR) is increasingly a setting for empirical visualization research, where study-relevant state is distributed across headset and controller pose, scene configuration, selections, spatial layouts, and AR anchors. Existing XR tools support parts of the workflow, such as scene authoring, interaction, or session analysis, yet seldom treat an XR stimulus as a reusable component of a complete study lifecycle. We present reVISit-XR, an extension of reVISit that makes customizable WebXR stimuli embeddable, trackable, and replayable within empirical visualization studies. reVISit-XR sequences XR scenes alongside standard study components, collects reactive task responses, captures scene-authored semantic state together with generic XR traces, and rehydrates participant sessions for later desktop and headset analysis. Organized as a reusable stimulus build package and a study integration package, it lets XR stimuli act as first-class study components. We demonstrate its scope and feasibility through seven integrated, reusable examples and a deployed study, and discuss its current capabilities and future extensions.