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In this paper, we extend the $L^\infty$ estimates of Guo-Phong for fully non-linear equations on compact hermitian manifolds to a possibly indefinite reference form satisfying a uniform admissibility criterion. Furthermore, we also establish one-sided stability estimates. Neither result requires homogeneity or concavity of the nonlinear operator.
Synthetic single-cell RNA-seq data generation offers a promising route for privacy-aware biomedical data sharing, but donor-linked datasets require careful balancing of biological utility and privacy risk. In this work, we benchmark synthetic generation methods for the CAMDA 2026 ELSA Health Privacy Challenge using the donor-split OneK1K dataset, comparing scGFT, scLDM, and Cell2Sentence across statistical fidelity, downstream biological preservation, and membership inference vulnerability. Because full-transcriptome generation is computationally demanding, we focus generative modeling on highly variable genes and evaluate alternative strategies for reconstructing non-HVG expression. Our results show that non-HVG handling is a central determinant of privacy: directly copying non-HVG values leads to severe leakage, whereas Poisson-based reconstruction substantially reduces membership inference risk. We further find that scGFT and scLDM better preserve biological structure than an independent Poisson baseline, while maintaining near-random privacy profiles under appropriate configurations. These findings highlight the importance of evaluating synthetic single-cell data beyond marginal similarity alone, emphasizing robustness, interpretability, and privacy-conscious design choices throughout preprocessing, generation, and post-processing.
Point cloud transformers aim to capture detailed local geometry and relationships across a scene at a manageable computational cost. Two common approaches are window attention and global attention. They differ in how they enable scene-wide interaction, which refers to information exchange among tokens across a scene. Window attention reduces computational cost by restricting self-attention to groups of tokens called windows; in serialized designs, each window contains a fixed number of consecutive tokens from a spatially ordered sequence. Because each block only directly connects tokens within the same window, information exchange across windows relies on changes in window membership across blocks and hierarchical pooling. Global attention, in contrast, directly connects all tokens within a scene, but computing attention over all token pairs can be costly when the number of tokens is large. To balance computational cost and scene-wide interaction, we introduce MixPT, a point transformer that uses a mix of window and global attention blocks in an interleaved schedule, while retaining a single fixed serialization pattern for its window blocks. For scenes with a large number of tokens, MixPT applies global attention to spatially pooled tokens and returns residual updates to the original-resolution stream. Across indoor and outdoor benchmarks, MixPT achieves competitive accuracy with lower latency than representative window and global attention baselines. We further demonstrate the feasibility of scaling the attention stage in depth by repeating the interleaved pattern of window and global attention blocks.
We determine the global minimizers of the three-dimensional Yukawa lattice energy at every fixed density. At unit covolume, BCC is the unique minimizer below a transition parameter $κ_*\approx1.7179218684699$, FCC is the unique minimizer above it, and exactly these two lattice classes minimize at the transition. Mathematically, denote the Yukawa potential and the energy per particle under this potential by \[ v_κ(r)=\frac{e^{-κr}}r,\qquad E_κ(L)=\frac12\sum_{v\in L\setminus\{0\}} \frac{e^{-κ|v|}}{|v|}. \] Then, \[ \arg\min_{|L|=1}E_κ(L)= \begin{cases} \hbox{BCC lattice},&0<κ<κ_*, \hbox{BCC or FCC lattice},&κ=κ_*, \hbox{FCC lattice},&κ>κ_*. \end{cases} \] As a consequence, the zero-screening comparison recovers the unique BCC minimum for the renormalized Coulomb energy.
Solar eruptions often drive shock waves. When propagating in the solar corona, strong shock waves would leave imprints on the solar surface in the chromosphere, which are called Moreton waves. Moreton waves generally decay as they move away. However, to our knowledge, for the first time we report that a Moreton wave is significantly enhanced midway during propagation, as revealed by the spectroscopic observations from China's first solar satellite, the Chinese H$α$ Solar Explorer. Combining magnetic measurements from the Solar Dynamics Observatory, we found that the location of the Moreton wave enhancement corresponds to a magnetic null point at an altitude of $\sim$70 Mm in the corona. It is demonstrated that the unexpected local enhancement of the Moreton wave is due to mode conversion around the magnetic null point, i.e., fast-mode waves are converted to slow-mode waves which are trapped locally. It is further revealed that, even for ordinary Moreton wave fronts, the H$α$ Doppler redshift velocity is positively correlated with the height of widespread low-altitude magnetic null points, implying that these low-lying null points, $\sim$1--7 Mm above the solar surface, facilitate mode conversion with different efficiency, thereby accounting for the spatially inhomogeneous Dopplergram of Moreton wave fronts.
Following our paper showing evidence for a sequence of Kaluza-Klein gravitons, we interpret the massive 4 jet excesses observed by CMS in RUN2 and RUN3 data. They could come from the decay of two heavy KK gluons gkk(3.6TeV) and gkk(8.6TeV) into pairs of KK quarks qkk(1TeV) and qkk(2.1TeV). Present limits on gkk seem to exclude gkk(3.6TeV) but these limits assume a dominant decay into top pairs, which can be questioned as was the case in our study of KK graviton decays. The cross section predicted for gkk(8.6) requires a BR into a pair of qkk(2.1TeV) or order 10% which is not unlikely. Prospect for reaching a 6 s.d. level local evidence with RUN3 data are promising for 3 channels.
Systems that aim to help a user engage with viewpoints other than their own have to decide how different those viewpoints should be. Viewpoints are mainly represented on a scalar scale, too coarse to distinguish viewpoints that disagree with the user about different things. We introduce a selection policy in which a bandit sets how far viewpoints may sit from the user, and the policy selects the most novel viewpoint within that bound. We vary only its stance encoder, comparing a scalar score with Perspectivized Stance Vectors, which break a position into separate stances on concepts. We integrate it inside a dialog system and run a between-subjects study (N=63). Concept-level stance produces more varied exposure sequences and broader coverage of the topic's positions, but does not change how deeply users justify viewpoints or how accurately they reconstruct them. Finally, we analyze user--viewpoint relations at the concept level, showing that users reconstruct a viewpoint least accurately on concepts that one side took no position on, rather than on concepts where the two disagreed. Our findings open up opportunities for dialog systems that support engagement with alternative viewpoints by acting on which concepts a user and a viewpoint disagree on, rather than on distance alone.
Let $u$ be a received word for the full-length Reed--Solomon code $\operatorname{RS}_q(k)$, with interpolation polynomial $f_u$ of degree $k+m$. For each $m\in\{3,4,5,6,7\}$, we classify all such deep holes over every finite field, without a field-size hypothesis. None occur for odd $m$ in this range. At $m=4$ and $m=6$, the only exceptions are, respectively, the Segre sextic and Frobenius-power families; these occur only in dimension two over fields of characteristic two. For arbitrary $m\geqslant3$, we also establish two uniform bounds. If $\sqrt q\geqslant12(m+1)\log(2m+2)$, no word of interpolation degree $k+m$ is a deep hole when $q$ is odd, $k\geqslant3$, or $m$ is odd. If $q>16(m+2)^4$, we obtain the corresponding complete classification at every admissible $k$, including the explicit dimension-two exceptions. Our proofs use an agreement criterion expressed in complete homogeneous symmetric functions, agreement-count estimates, finite geometry, permutation-polynomial restrictions, and subset constructions for solving the resulting symmetric-function equations. The remaining finite cases are settled by finite computations with supplied certificates and deterministic verification programs.
Reusable skills allow large language model agents to package task-specific procedures, tool affordances, and execution guidance into modular units. Prior work has largely studied how agents retrieve, compose, or synthesize skills before execution. In coding agents, however, execution poses an additional runtime control problem: the same task may be solved through primitive tool calls, macro skills, or hybrid execution that starts with a macro and falls back to micro-level recovery. We introduce Adaptive Skill Granularity, a framework that treats skill granularity as an action-abstraction policy conditioned on task structure, execution state, and macro-skill failures. The system combines a feature-based granularity controller and a finite-state recovery executor. We evaluate the framework with a deterministic coding-agent protocol using verifier-defined success, total cost, and process metrics such as macro adoption, failure recovery, route match, and transition correctness. Results show that fixed macro execution is efficient when applicable but brittle under mismatch, while runtime routing and explicit macro-to-micro recovery improve robustness and recover controlled macro failures that fixed-granularity execution leaves unresolved. Our findings suggest that skill libraries for coding agents should be treated not only as retrievable resources, but also as controllable, verifiable, and recoverable execution abstractions.
Coherent synchrotron radiation generated in a bending magnet can propagate far downstream and heat the beam pipe. We investigate a beam-free side outlet that diverts part of this radiation into a separate guide. We use a paraxial equation to calculate radiation generation in the bend and its division between the two guides. Modal and finite-difference solutions are used in the bend, and quadratic finite elements on a changing transverse mesh in the branching region. We check the paraxial approximation against full-wave solutions at selected frequencies. Separately, we calculate radiation attenuation in a conducting pipe without an outlet using complex modes that satisfy impedance boundary conditions. For this example, independently damped perfectly conducting modes underestimate the high-frequency transmitted power. For a $70\times25$ mm rectangular chamber with a $30^\circ$ bend of radius 2.2 m and Gaussian bunches of rms length $10\,μ$m, the selected outlet diverts about 53\% of the total outgoing radiation power into the beam-free channel.
We study symmetric divergence form elliptic equations with measurable coefficients that may be degenerate and unbounded, under a uniform bound on the coarse ellipticity ratio over all ambient cubes and scales. We prove that uniform coarse ellipticity and classical $A_2$ weighted ellipticity define incomparable coefficient classes. For every admissible choice of coarse parameters, we construct a scalar weight with a logarithmically corrected, locally integrable singularity along a product Cantor set. Its codimension is chosen according to the upper coarse discount exponent, and the resulting coefficient satisfies the uniform coarse condition but is comparable to no $A_2$ weight. Conversely, an explicit $A_2$ weight fails the coarse condition for every admissible parameter choice. Under uniform coarse ellipticity we give a direct PDE treatment of boundary regularity in the approximable energy realization. Using coarse interior estimates, we prove boundary decay and solvability of the continuous Dirichlet problem in bounded NTA domains. An almost-positivity argument, with energy approximation and boundary testing justified, yields boundary Harnack and Hölder continuity of quotients of positive solutions with common zero boundary values. The argument requires no additional energy Sobolev inequality and avoids the construction of Green functions. Further examples distinguish uniform coarse control from finite coefficient moments and from coercivity on $\mathrm L^2(\mathrm{d} x)$. We also record interior Hölder estimates and continuity criteria under nonuniform control along nested scales.
We prove the strict Pólya inequality for Neumann eigenvalues of spherical shells in every dimension $d\ge2$, for every radius ratio and every positive energy. The proof also covers balls. For shells, the excess over the leading Weyl term has a positive lower bound depending only on dimension. Above explicit frequency thresholds independent of the radius ratio, we obtain a surplus of boundary order. These estimates remain uniform as the hole shrinks or the shell becomes thin. We compare weighted sampling errors for inverse radial actions while retaining the removed volume exactly. The proof is entirely analytic and requires no computer-assisted verification.
Despite advances in numerical methods, non-Newtonian flow simulations remain computationally expensive because velocity and stress must be advanced together through rate- and history-dependent constitutive dynamics. Neural-operator surrogates reduce inference cost after training, but their training data require the same expensive simulations they aim to replace, making data-efficient learning essential when only a few non-Newtonian simulations can be afforded. Here, we introduce the Rheological Operator Pretrained Transformer (RheOPT), which pretrains a transformer-based neural operator on inexpensive Newtonian simulations and fine-tunes it on a small number of non-Newtonian samples. Rather than transferring the Newtonian constitutive response itself, RheOPT reuses geometry-conditioned transport structure that remains useful after the stress model changes. We evaluate RheOPT in two geometry-matched settings: a $4{:}1$ contraction channel for Giesekus, Oldroyd-B, and Bingham fluids, and the oscillatory wake behind a triangular obstacle for Oldroyd-B flow. In the contraction, Newtonian pretraining substantially improves few-shot prediction, and a model fine-tuned on four target samples can match or exceed a from-scratch model trained on four times as many. This benefit is reliable under reversible instance normalization (RevIN) but dataset dependent under Global normalization, a difference we trace to the dynamic range of each fluid's velocity and stress fields. In the wake, where relative $L_2$ error alone cannot verify that vortex shedding is recovered, phase-insensitive diagnostics show that pretraining recovers the shedding frequency and wake fluctuation amplitude that are suppressed by the from-scratch model in the few-shot regime. Overall, RheOPT establishes Newtonian simulation as a physically grounded pretraining source for data-efficient non-Newtonian operator learning.
AI coding agents can now build small playable games in minutes, but the results usually look like programmer art: gray blockouts, colored geometric primitives, and flat semantic blobs. We present AnyGameRenderer, a video-to-video generative renderer that turns such footage into high-quality visuals with characters, motion detail, and effects. Throughout, it keeps the layout, camera, and every entity's position and timing intact. Our AnyGameRenderer generalizes across a wide range of genres that agents build, such as tower defense, auto-battlers, top-down survivors, turn-based battles, kart racing, and crowd runners. AnyGameRenderer takes plain video as its game-state input, with no complex representations such as engine G-buffers, per-object class labels, or low-poly proxies. Gray blockouts, colored primitives, semantic maps, and wireframes all work as input. It also preserves entity correspondence: group counts stay correct, and entities appear and disappear on the right frame. We implement AnyGameRenderer by LoRA fine-tuning MiniMax-H3 ref2va, a 33B reference-video-conditioned video generation model. Training uses $\sim$10k paired clips from three sources: (i) multi-stream rendering data from 38 agent-made games exported from GEAR, an AI game-creation tool; (ii) two-stream rendering data from Unreal Engine, with programmatically controlled crowds, count changes, and entity scales; and (iii) real gameplay recordings, with pairs reconstructed via 3D-box detection. To evaluate the entity correspondence, we propose an entity-level benchmark of 59 held-out cases with 753 entities, scored against ground-truth boxes. Compared with the base model, AnyGameRenderer better preserves entity correspondence: temporal match rises from 50.9\% to 62.9\%, missed count changes fall from 34.7\% to 21.3\%, and fewer entities are hallucinated or left unrendered.
As wearable and digital health systems increasingly generate longitudinal physiological records, communicating these observations in patient-accessible language remains a significant challenge. Large Language Models (LLMs) offer a promising mechanism for translating structured clinical information into readable narratives, but this process may introduce semantic drift, where clinically precise meaning is distorted during simplification. We investigate evidence-grounded health summarization for menstrual health monitoring using a constrained generation framework that combines structured evidence conditioning with Retrieval-Augmented Generation (RAG) using a prompt-based constrained generation framework. We evaluate semantic alignment using Natural Language Inference (NLI), atomic factuality metrics, and readability measures. Across three LLMs and 4,500 generated summaries, explicit grounding constraints consistently improve clinical alignment, particularly by improving uncertainty preservation and, once faithfulness is evaluated against retrieved evidence, generally preserving or improving faithfulness, while effects on omission remain model-dependent. We also find that improved clinical alignment comes at the cost of increased reading difficulty and medical terminology. These findings highlight the need to jointly evaluate faithfulness, uncertainty preservation, and readability when developing patient-facing medical LLM systems.
Let $\mathcal H=\ell^2(\mathbb Z)$ and let $\mathbb Z$ act by bilateral shifts. We prove that the quotient $\mathbb S(\mathcal H)/\mathbb Z$ of the unit sphere, equipped with its quotient metric, has infinite Hilbert distortion. Consequently, $\mathcal H/\mathbb Z$ does not admit a bilipschitz embedding into Hilbert space, answering a question of Cahill, Iverson, and Mixon. The proof first embeds every flat torus $\mathbb R^n/L$, after rescaling, into the quotient $\mathbb S\big(\ell^2(\mathbb Z^n)\big)/\mathbb Z^n$ with distortion arbitrarily close to $1$, where $\mathbb Z^n$ acts by translations. We then show that every finite subset of this quotient embeds into $\mathbb S(\mathcal H)/\mathbb Z$ with distortion arbitrarily close to $1$. The lower bounds of Khot and Naor for the Hilbert distortion of flat tori then imply the result.
We present an analysis of the polarized synchrotron emission at the power-spectrum level in the multipole range $30 < \ell < 130$, using the recent QUIJOTE-MFI wide survey (10-20GHz) in combination with Planck and WMAP data. The EE and BB power spectra are well described by a simple power-law model, with no evidence for the need of additional parameters. The best-fit slopes are $α_{EE} = -3.24 \pm 0.12$ and $α_{BB} = -3.81 \pm 0.34$ for $|b|>20^\circ$, hinting toward a steepening of the BB spectrum relative to EE at the $\sim 1.6σ$ level. The synchrotron frequency spectral indices are found to be $β_s^{EE} = -3.26 \pm 0.05$ and $β_s^{BB} = -3.25 \pm 0.10$ for the same cut, in agreement with earlier real-space analyses. We find no evidence for spatial variations of $β_s$ across different Galactic latitude cuts, within current uncertainties. The synchrotron BB/EE power ratio is approximately 0.2 over the considered multipole range, lower than typical values for thermal dust, and consistent with previous measurements. We also measure a dust-synchrotron spatial correlation in the range 0.1-0.25 over $30 < \ell < 130$. Using these results, we estimate the level of synchrotron contamination in future CMB B-mode measurements, finding an average power in the considered sky masks equivalent to $r \sim 0.003$ at 90GHz and $r \sim 0.0002$ at 150GHz for the relevant angular scales.
Text-to-speech (TTS) is usually evaluated by transcribing its output with an automatic speech recognition (ASR) system, so the word error rate also counts recognizer errors. We measure these errors on human recordings of the test sentences. On LibriSpeech and FLEURS, the evaluation recognizer misses 33-67% of very rare words even in human speech, and all three recognizers miss 22-42%. Checking every word with two more recognizer families lowers the apparent TTS error on words that at least one recognizer hears two- to three-fold (very rare LibriSpeech words: from 10-13% to 3-5%), yet very rare words remain the hardest. Ignoring words the recognizer misses in human speech is biased: the other recognizers find TTS errors far more often on these words (4-6% vs. 0.2-0.3%) and overturn about half of the errors this mask keeps. As half of the remaining adjudicated errors may be spelling variants, a listening test is needed.