Papers

Let $\TP_k$ denote the triangular pyramid with $k$ layers. For a graph family $\mathcal F$, let $\ex(n,\mathcal F)$ be the maximum number of edges in an $n$-vertex graph containing no member of $\mathcal F$ as a subgraph. For a graph $H$, let $\cJ(H)$ be the family of subgraph-minimal graphs among all such graphs $H-I$, where $I\subseteq V(H)$ is an independent set. For every integer $k\ge4$ and all sufficiently large $n$, we prove that \[ \ex(n,\TP_k)=\max_{0\le m\le n}\{m(n-m)+\ex(m,\cJ(\TP_k))\}+O_k(n)=\left\lfloor n^2/4\right\rfloor+\Theta_k(n^{4/3}). \] Moreover, for $k=4$, we characterize all extremal graphs and show that \[ \ex(n,\TP_4)=\max_{0\le m\le n}\bigl\{m(n-m)+\ex\big(m,\cJ(\TP_4)\big)\bigr\} \] for sufficiently large $n$.

Analogous to quasi-Frobenius rings, dual rings, and Johns rings, the classes of $p$-quasi-Frobenius rings, $p$-dual rings, $p$-Johns rings are introduced and used to discuss and settle principal analogues of the Faith-Menal, Faith, and FGF conjectures. A chain symmetry theorem establishes that for quasi-injective semi-projective modules with semiprime endomorphism ring, endonoetherianity and endoartinianity are equivalent and force the endomorphism ring to be semisimple artinian. Within this unified setting, it is shown that (1) two-sided $p$-Johns rings are $p$-quasi-Frobenius, giving a principal Faith-Menal analogue, with a counterexample showing that the one-sided hypothesis is insufficient; (2) semiprimary principal right ideal rings that are right principally injective and right Kasch are $p$-quasi-Frobenius-this affirmatively answers a question of Faith (Q2) in the principal two-sided ideal ring case and settles the principal Faith conjecture, with a counterexample showing the hypotheses to be indispensable; and (3) right $p$-Johns rings that are left CF and left perfect are $p$-quasi-Frobenius, yielding a principal FGF analogue, with a counterexample demonstrating that the hypotheses are essential. Wherever needed, examples are provided to show that various classes introduced are different from the existing classes in the literature.

We prove an effective version of the Chebotarev density theorem, conditional on the quasi-Riemann hypothesis for the Dedekind zeta function. Drawing on recent breakthroughs of OpenAI and Cureton–Thorner, we make unconditional the Ellenberg–Venkatesh bounds on $\ell$-torsion in class groups of number fields and extend an averaged result of Lemke Oliver–Smith to arbitrary families of degree-$d$-fields. Further applications are given to the least prime splitting and to small generators in number fields.

Understanding why 2D materials remain suspended in solutions is essential to understanding the mechanisms of aggregation and exfoliation. These dynamics have been difficult to model because of the long timescales and large activation energies involved in these simulations. Here we describe an improved strategy for modelling the solvation and stability of 2D materials that uses the Gibbs free energy of solvation to accurately calibrate two disconnected potential energy surfaces for the fully desolvated and fully solvated 2D materials. By joining these surfaces using solvation energy, we obtain predictions for 2D material stability in various solvents that are qualitatively different than prior simulations and that have excellent agreement with experimental results. Our approach predicts a much higher barrier to full desolvation of the material, suggesting that materials that appear to be aggregated in fact still retain monolayers of solvent between adjacent layers of 2D materials. This work provides much needed understanding on the interactions between the solvent and 2D material that can guide future experimental work.

We study the irrationality of smooth Fano complete intersection fourfolds in weighted projective spaces, using an atom theoretic approach based solely on Gromov–Witten invariants. We prove symplectic irrationality, and hence irrationality for every smooth member, in a wide range of families for which irrationality was previously known only for very general members.

Many related prediction problems, which we call questions, come with few labels each. What information can be shared across them, and what is actually necessary for good decisions? We answer both for recalibration, motivated by decision models such as Jev (TypeSafe AI, 2026) that return a probability for any yes/no question a developer writes. A predictor reports a probability $P$ with output law $\mu$ on $m$ questions, each with $n$ labels and a nondecreasing map $g_j(p)=\mathbb{P}(Y=1\mid P=p)$; the compound risk is the excess Brier score over the true maps, averaged over questions. Over maps within sup-distance $\tau\le 1$ and total variation $V\le 2$ of one nondecreasing shape (fixed effects), the minimax compound risk is $(mn)^{-2/3}+\min\{\tau^2,1/n\}+\min\{\tau^2,V^2,(V/n)^{2/3}\}$ up to universal constants, for every non-atomic $\mu$. A pooled isotonic fit with a per-question correction sized once, on held-out labels of all questions, attains it without knowing $\tau$, $V$ or $\mu$ ($n\ge 2$, $m\ge 3$); tuning each question on its own labels loses a factor of order $\min\{n,\log(m^2/n)\}$ when the maps differ by constants and $m^2/n$ is large. When the maps are drawn from an unknown prior (random effects), other questions need not identify the Bayes rule. The loss, the identification regret, is at most $2^{-n}$ once the law of a question's data is known, extending a bound of Skibinsky (1968) for coins, and in the worst case at least $\beta_\star^{-n}/(72\sqrt{n})$ at every finite $m$, where $\beta_\star\approx 3.583$. Beyond a few labels per question, what cannot be learned is nearly unnecessary. For constant maps (an uninformative predictor) and constant-map priors, the exponential base is exactly $\beta_\star$, not the 4 suggested by the moment range; for monotone maps it lies in $[2,\beta_\star]$.

Cobimaximal mixing remains a viable approximate pattern since the predicted atmospheric angle ($\pi/4$) and Dirac CP phase ($-\pi/2$) are compatible with current experimental data at the $3\sigma$ level. In this work, we investigate how an additional sterile neutrino state breaks the cobimaximal mixing and the underlying $\mu-\tau$ reflection symmetry in a $3+1$ neutrino scenario. Given the strong constraints already imposed on active-sterile mixings, we examine the resulting restrictions on the model parameter space, assuming a small symmetry breaking induced by the sterile state. We derive predictions for the relevant model parameters, active-sterile mixing angles, and Dirac CP-violating phases, by considering small deviations from the symmetric limit. We also analyze the allowed combinations of Majorana phases through their impact on the effective Majorana mass governing neutrinoless double beta decay. Current experimental limits on this process impose severe constraints on the inverted ordering realization of the $3+1$ scenario, excluding the small breaking regime within the parameter ranges considered. In contrast, the normal ordering case remains viable and predicts values of the effective Majorana mass that lie within the sensitivity reach of upcoming neutrinoless double beta decay experiments.

Membership Inference Attacks (MIAs) are currently the dominant approach to evaluating privacy in machine learning applications. Despite their significance, several concerns remain unexplored, particularly with regard to tabular data. Existing evaluations focus predominantly on high-dimensional datasets, leaving the privacy behavior of small-to-medium datasets unexplored. In this paper, we present a new taxonomy for MIAs and conduct a comprehensive study of the factors influencing vulnerability. We evaluate four distinct state-of-the-art attacks across diverse tabular datasets and model architectures. Our results show that datasets with higher class granularity and majority class percentage are more susceptible to MIAs. We further demonstrate that advanced MIAs are highly dependent on adversarial knowledge of the target model, while reference model-free attacks often achieve statistically comparable results. Most importantly, we show that records with unique signatures (single-outs) remain highly vulnerable, even when common defenses are applied. These findings indicate that current defenses reduce average leakage, but fail to adequately protect the most sensitive individuals.

Recent progress in generative models has made talking-head deepfakes highly realistic and easy to create, jeopardizing public trust. However, most audio-visual deepfake detectors rely on lip-speech synchronization and are designed for static, frontal videos, limiting their reliability in dynamic, in-the-wild recordings where the speaker moves and lip cues are degraded or missing. As an alternative, we propose a physics-aware detector for dynamic speaking videos that leverages an acoustic constraint: in real recordings, speech energy varies predictably with speaker-to-camera distance, whereas deepfake generation can break this coupling. Our method combines distance estimates from video with distance-dependent acoustic measures from speech to detect deepfakes. Experiments on in-the-wild benchmarks show that the proposed physical cue is effective in dynamic scenarios, and that it complements lip-sync-based detectors, with a simple ensemble achieving consistent gains across datasets. Codes are available at https://byulharang.github.io/PADD/.

Terminal agents have shown strong abilities in complex coding tasks. However, they often struggle to recover from errors during long-running execution (e.g., command errors, faulty implementations), eventually leading to task failures. To this end, we present ReTerm, a self-improving terminal agent trained by learning how to recover from its own failed terminal tasks. To support its training, we construct a customized data pipeline and produce ReTerm-10K, a high-quality dataset that provides effective recovery demonstrations for SFT cold start. Furthermore, we propose ReTerm-GRPO, an online RL algorithm that forks from the agent's own failure states to generate multiple independent self-recovery attempts. By learning from whether these attempts successfully complete the task, the agent self-improves through its own recovery experience. Built on Qwen3.5-9B, our ReTerm-9B achieves 34.8% Pass@1 on Terminal-Bench 2.0, improving over the base model by 14.6 points. Further analysis shows that our method achieves consistently higher recovery rates across diverse error categories compared with standard GRPO training. All code, data and model are released at https://github.com/twothsnd/ReTerm.

We consider the linear operator for metamaterial modeling $$L_{c,d }=(\chi_{\RE^{3}\backslash\overline \Omega}+c)\nabla\!\cdot (\chi_{\RE^{3}\backslash\overline \Omega}+d)\nabla\,,$$ where the material parameters $c>0$ and $d$ are constant on each connected component of the bounded domain $\Omega$, $d$ is negative on at least one component of $\Omega$ and transmission boundary conditions hold at the interfaces. It turns out that $L_{c,d }$ has, as in the sign-definite case, an absolutely continuous spectrum equal to $[0,+\infty)$; however, contrary to the latter, it has a non-empty point spectrum; in particular, we find conditions on the parameters so that zero is a threshold eigenvalue. In the case $\Omega$ is connected, we study how such a threshold eigenvalue behaves under $\varepsilon$-small analytic perturbations of the parameters. We show that, depending on the position of the number $\frac12\,\frac{1+d(\ve)}{1-d(\ve)}$ relative to the nearest eigenvalue of the Neumann-Poincaré operator of the interface, the zero eigenvalue splits into two branches (analytic in $\varepsilon^{1/2}$), consisting either of two branches of resonances, or of one branch of negative eigenvalues and one of resonances.

Quantum computing promises new capabilities beyond classical computation. Mid-circuit measurements (MCMs) enable error correction and outcome-dependent control, but their reliability is limited by noise on superconducting hardware. These operations depend on accurate quantum state discrimination (QSD), which assigns measured signals to state labels. Neural network-based (NN-based) QSD improves this assignment, yet its error remains bounded below by the Bayes risk of the available readout distributions. A complementary challenge is state deterioration as successive measurements accumulate and circuit execution advances, making static calibration less representative of the workload. We present Lifting, a QSD framework that addresses both challenges through repetition encoding, neural decoding, and in situ calibration. Encoding supplies joint in-phase and quadrature (I-Q) readout signals from the target and auxiliary qubits, while contextual calibration trains the decoder for the conditions encountered during execution. Our theoretical analysis shows that retaining additional channels from a fixed joint distribution cannot increase Bayes risk and establishes sufficient conditions for contraction of an overlap-based upper bound. Experiments across three IBM processors evaluate the framework on repeated stabilizer measurement, parity-check, and teleportation workloads.

Protein sequence, structure, and functional annotations each capture complementary aspects of protein biology, yet existing tokenizers encode each modality independently, limiting the expressiveness of discrete protein representations. We present ProTok, a unified protein tokenizer that maps all three modalities into a modular discrete vocabulary via product quantization with per-modality codebook groups and modality dropout. A single ProTok checkpoint supports flexible inference from any modality subset without retraining. On seven StructTokenBench benchmarks spanning 14 tasks and 28 test splits, ProTok achieves an average rank of 1.4 across all structure-only tokenizers, placing first on 21 splits and among the top two on 27 of the 28. These gains come without sacrificing reconstruction: ProTok's tokens reach 0.939 lDDT on CATH 4.2, showing that multi-codebook quantization and multi-modal training yield tokens that are both reconstructable and informative. ProTok's structure tokens further lead all baseline structure tokenizers on zero-shot functional retrieval across CATH, Enzyme Commission, and Gene Ontology label hierarchies. The vocabulary also supports generation: a compact language model trained from scratch over ProTok tokens jointly generates backbone and sequence, with 52% of sampled backbones designable versus 21% for a parameter-matched GeoBPE baseline. ProTok shows that structure, sequence, and function can share one discrete vocabulary, motivating protein language models that reason over a unified token stream.

Let $G$ be a group and let $A$ be a set with at least two elements. A lazy cellular automaton over $A^G$ acts as the identity except at the cells where a fixed pattern occurs, where it replaces the central symbol by a fixed different symbol. Let $M(G;A)$ be the submonoid of $\mathrm{CA}(G;A)$ generated by the lazy and the invertible cellular automata. We study when $M(G;A) = \mathrm{CA}(G;A)$. Since no lazy cellular automaton is surjective, every surjective element of $M(G;A)$ is invertible; hence $M(G;A) \neq \mathrm{CA}(G;A)$ whenever $A$ is infinite or $G$ has an element of infinite order. Moreover, if $|A| = 2$ and $G$ has a quotient isomorphic to the Klein four-group $C_2 \times C_2$, then $M(G;A) \neq \mathrm{CA}(G;A)$. For locally finite $G$, and in particular for finite $G$, these are the only obstructions: we prove that $M(G;A) = \mathrm{CA}(G;A)$ if and only if $3 \leq |A| < \infty$, or $|A| = 2$ and $G$ has no quotient isomorphic to $C_2 \times C_2$.

Sonar was one of the first sensors with which mobile robots built maps, and in-air sonar keeps working where cameras and lidar fail, in darkness, smoke, dust and next to glass. Classical sonar SLAM, however, relied on geometric features or occupancy grids built from sparse range readings, and both struggle with the specular reflections that dominate indoor sonar. In this letter, we introduce RTISSLAM, a novel sonar-only SLAM system for an embedded 3D imaging sonar, which combines the robust pose graph of BatSLAM 2.0 as back-end with an occupancy grid as map. Energyscapes from delay-multiply-and-sum beamforming with a range-wise CFAR serve as place descriptors for sequence-verified loop closures, acoustic odometry calibrates the wheel odometry online, recognized revisits are registered metrically, and the grid is stored per keyframe and anchored to the pose-graph nodes, so that it follows every loop closure. In simulated worlds with specular walls, RTISSLAM reduces the trajectory error of the wheel odometry from \SI{8.2}{\meter} to \SI{0.31}{\meter} in an office, while lidar-style grid SLAM on the same sonar data fails.

Large vision-language models (LVLMs) have shown strong potential for embodied vision-language navigation (VLN), yet their performance degrades on long-horizon trajectories due to context-length limits, redundant historical observations, and unstable spatial alignment across time. These issues make it difficult to both compress long navigation histories and reliably reuse past spatial experience. To address these limitations, we propose MemoryVLN, a unified memory-driven navigation system built around memory construction and management. During memory construction, Long Sequence Compression employs forgetting-curve-inspired temporal sampling to preserve dense recent evidence and sparse yet representative distant observations under a limited token budget. Ego-Aware Memory Representation further integrates 2D semantic tokens, 3D geometric tokens, and 6D agent poses, allowing each memory to encode both what was observed and where it was observed. During memory management, Hierarchical Memory Bank maintains in-episode and context-level memories through cross-context warm-start and confidence-controlled write-back. Memory Enhancement then retrieves the Top-$K$ relevant memories according to the current navigation state and fuses them with the current visual tokens. Together, these mechanisms transform raw navigation history into compact, spatially grounded, selectively retrievable, and reusable navigation experience. Extensive experiments on R2R-CE and RxR-CE demonstrate consistent improvements over the state-of-the-art baselines by a substantial margin (i.e., 2% and 6.5% in successful rate).

Fast entangling gates and low-interaction idling require distinct operating conditions in superconducting quantum processors. We experimentally realize a transmon-C-shunt-transmon (TCT) device in which a flux-tunable, three-junction capacitively shunted flux-qubit coupler connects two transmon data qubits. The C-shunt coupler provides a flux-tunable, positively anharmonic spectrum for tailoring the interactions between the data qubits. Conditional Ramsey and swap measurements identify an idle region with near-zero residual ZZ interaction strength and suppressed transverse exchange. At this bias, simultaneous single-qubit interleaved randomized benchmarking yields X-gate fldelities above 99.7%, consistent with individual operation. A 45 ns nonadiabatic controlled-Z (CZ) gate achieves an interleaved randomized benchmarking fldelity estimate of 99.23(15)%. Numerical simulations identify coupler energy relaxation as an important limitation on CZ-gate fldelity and indicate that extending the coupler lifetime can improve gate performance. These results demonstrate the experimental feasibility of C-shunt flux-qubit couplers for combining low-interaction idling with fast entangling operations between transmon qubits.

Thermonuclear and core-collapse supernovae are statistically expected to happen within extragalactic jets, as these jets cross the inner regions of their host galaxies, and supernova ejecta-jet interactions can potentially lead to strong non-thermal activity. We model the non-thermal emission from a supernova interacting with a jet on kiloparsec scales, using detailed numerical simulations of the interaction. Using a post-processing method, we applied a non-thermal model of the acceleration and transport of electron and their synchrotron and inverse Compton emissions, simplified and tuned for flexibility and computational speed, to the results of a three-dimensional relativistic hydrodynamics simulation of the ejecta of a supernova interacting with an extragalactic jet. For intermediate jet powers, radio, optical and X-ray fluxes from supernova ejecta-jet interactions may be detectable for distances < 100Mpc. The non-thermal luminosity budget and local conditions associated with these interactions could be enough to explain knots seen in kiloparsec scale jets at different energies. These conditions might also be suitable for the production of heavy ultra high-energy cosmic rays, but photon and neutrino generation from hadronic processes would be minor on kiloparsec scales. The leptonic gamma-ray fluxes are modest but might non-negligibly contribute in TeV for the nearest or more powerful jet sources.

How a relativistic star responds to a time-dependent tide has lacked a first-principles counterpart of the Newtonian normal-mode expansion. In general relativity, the tidal field is gauge sensitive, radiative modes are non-Hermitian and incomplete, and the direct and late-time responses are intrinsically nonmodal. In this work we present, to our knowledge, the first causal relativistic theory that treats all of these components on equal footing. We first develop the spectral decomposition of the retarded Green function of the matched stellar interior–Schwarzschild exterior, which classifies four separate regimes in time domain: acausal region, prompt wave, surface-reflected wave, and mode+tail. The prompt signal is identical to that of a Schwarzschild black hole with the same mass, which is combined with the surface-reflected wave to be referred as the "direct part". With the Green function and a complex bilinear form on the full metric–fluid phase space, we decompose the linear response of a nonrotating perfect-fluid star into direct, quasinormal-mode, and late-time-tail sectors. Crucially, every sector admits an explicit first-order driven evolution equation: discrete bilinear projections determine the dynamically evolving quasinormal-mode amplitudes, while continuum projections of the same tidal source onto branch-cut states determine the direct and tail amplitudes. The result is a complete modal–nonmodal decomposition of the spacetime and fluid perturbations, which is physically described by the dynamics of a discrete and a continuous-frequency set of oscillators. We verify the decomposition numerically under generic time-dependent tidal driving and discuss applications to black hole perturbations.

The ergotropy, or unitarily extractable work, of a quantum system naturally splits into incoherent and coherent contributions, respectively set by population inversion and coherences in the energy eigenbasis. We show that this split makes the coherent ergotropy of a Mach–Zehnder qubit sensitive to path predictability that the output interference fringes do not reveal. We send the path qubit, prepared as a thermal quantum battery, through two quantum-controlled interferometers built from the same elements, a fixed beam splitter and a beam splitter coherently controlled to be present or absent, differing only in the order in which these two act. The two arrangements share identical visibility, stored energy, and incoherent ergotropy at every point in the parameter space. Yet, for work extracted from the output battery alone, placing the controlled beam splitter first never yields less coherent ergotropy, and at fixed visibility and interferometric phase the difference is governed by the path predictability that this ordering creates. The same expression reappears as a purity deficit on the beam-splitter controller, so the work advantage comes with a Landauer bound on the cost of locally resetting the controller that is never larger at the same temperature. We further examine the effects of decoherence on the battery and consider a relativistic realization in which a Wigner rotation correlates the particle's spin with its path. Tracing out the spin decoheres the battery and allows the two arrangements to exhibit different coherent ergotropies even in regimes where their non-relativistic counterparts coincide. These results show that interference visibility is not a complete measure of the coherence available as work.

In galaxies, stellar populations represent a superposition of both in situ and accreted components, tracing internal chemical evolution as well as the histories of merged satellites. We investigate how assembly history shapes the chemical properties of present-day stellar populations in low-mass dwarf galaxies. We analyze a suite of EDGE-INFERNO star-by-star cosmological zoom-in simulations of galaxies with present-day halo mass $\sim1.4\times10^9\,{\rm M}_{\odot}$. We systematically vary galaxy growth while preserving the present-day halo mass, engineering our simulations to span a continuum of assembly histories. Early-forming systems form most of their stars in a single progenitor, with centrally concentrated star formation and a continuous enrichment history. In contrast, our late-forming systems assemble by accretion of multiple progenitors with their own stellar populations, resulting in fragmented star formation across several halos with independent chemical evolution tracks. These regimes produce qualitatively different chemical signatures: single-progenitor systems exhibit connected, well-defined trends in abundance space, while multi-progenitor systems show multiple, distinct stellar populations with limited overlap. We find that metallicity distribution functions provide initial constraints on assembly history for samples of at least $50$-$100$ member stars. Multi-element abundance analysis significantly improves the recovery of distinct components, although robust reconstruction still requires larger samples. Fully separating in situ and accreted populations likely requires kinematic information. Accreted stars can contribute substantially even at high metallicities in multi-progenitor systems, while external enrichment can cause accreted material to follow similar chemical trends as in situ stars, particularly in the single-progenitor regime.

Few-step distillation reduces the sampling cost of diffusion and flow models, but existing approaches often require auxiliary score models or specialized architectures. We show that simple on-policy velocity regression already provides a strong foundation for 4-NFE generation. To represent teacher velocity variation within each coarse transition, we introduce Pivot, a training-only residual proxy that separates local corrections from the student's interval-mean prediction. We further repel the student from weaker teacher predictions, providing a lightweight mechanism for avoiding undesirable modes. The resulting framework, Simplified Matching Distillation (SMD), remains entirely regression-based, requires neither online score estimation nor adversarial training, and leaves the deployed generator unchanged. We evaluate SMD on image generation and editing, 3D generation, video synthesis, and joint audio–video generation, scaling to 33 billion parameters. At 4-NFE, SMD outperforms strong few-step baselines and surpasses multi-step teachers on several benchmarks. It also supports cross-model, multi-teacher, and causal-video distillation.

Weight-space learning treats the weights of neural networks as data, processed by other models called metanetworks. A key challenge is that different weights can realize the same function, related by a group of symmetries the metanetwork should respect. While symmetry-aware metanetworks for simple architectures such as MLPs are well developed, a comprehensive treatment of transformers, and in particular transformer-based language models, is still missing. Importantly, their weight space has a richer symmetry group: beyond neuron permutations, attention introduces continuous general-linear symmetries of the attention matrices and permutations of entire heads. Existing methods for transformer weights either capture only part of these symmetries or are restricted to a single, fixed architecture, and none accounts for language-model-specific components such as the token embeddings. Building on graph metanetworks, we propose a graph-based approach that is both symmetry-aware and applicable across depths and widths. We formalize a weight-space symmetry group of complete decoder-only language models and provide a graph construction that is invariant to it. We further introduce two new transformer-population datasets with novel tasks, such as training-corpus prediction and fine-tuning detection, on which our approach notably outperforms existing baselines.

Continuous-wave light near 148.4 nm enables direct absorption spectroscopy of the thorium-229 nuclear transition. We demonstrate single-pass frequency doubling in strontium tetraborate, delivering an estimated 8.1 nW at 920 mW pump power. At this power, oxygen admission leaves a background of 1.22 kHz, corresponding to an estimated signal-to-background ratio of 3.8 x 10^4 after current-integration calibration. Several crystals grown by top-seeded solution growth produce polarization-dependent VUV signals. Temperature scans reveal distinct maxima among specimens cut from one boule and among positions within a specimen. The source sustains operation over 33.3 h. In a separate 3-h record acquired with 1-ms gates, local referencing achieves near-Poisson averaging, reaching a fractional Allan deviation of 3.5 x 10^-5 at 1000 s. These results establish a practical VUV source for stable, long-duration spectroscopy of weak nuclear absorption.

We investigate how speech token representations can support both understanding and generation within a unified speech language model. We present PhonoVoxtLM, built on the existing VoxtLM framework using phonological tokens designed to retain linguistic content and prosodic information. The existing tokenizer is jointly trained for speech recognition and resynthesis. Its single-codebook units serve as both speech inputs and generation targets, without additional speech-token prediction modules. Experiments show improvements over HuBERT-based baselines across understanding and generation under different training-data scales. Further comparisons with WavLM-based tokens reveal trade-offs between recognition and synthesis, highlighting the importance of evaluating shared representations across both capabilities. We further extend the framework to spoken question answering through fine-tuning with replay. The adapted model improves answering performance over similarly adapted HuBERT baselines while retaining advantages on the original speech tasks. Our findings support single-codebook representations designed for both content and prosody as a practical choice for unified multitask speech modeling.

In the past two decades, the Bayesian approach to inverse problems in infinite dimensional spaces has seen significant developments in theory, Markov chain Monte Carlo (MCMC) methods, and in applications. The Bayesian approach in finite dimension produces posterior distributions of finite dimensional random variables. In infinite dimensions, the desired objects are random fields and their laws as measures on Hilbert or Banach spaces. There are many textbooks and tutorials available that explain Bayesian methods and MCMC in finite dimensions. To enter the field of Bayesian inverse problems in infinite dimensions, a newcomer has to engage with a quite diverse and extensive literature. The purpose of this article is to provide a basic path to the subject that is easily accessible to a reader with general knowledge in probability and mathematical analysis. We start with a swift introduction to the finite dimensional case. The infinite dimensional case is introduced for Gaussian priors on Hilbert spaces and Gaussian-type likelihood functions. In this situation, mere continuity of the forward map suffices to prove that the posterior measure is well-defined. We also give some new and simple stability results. Two application examples are elaborated, one finite dimensional, one infinite dimensional.

A far-infrared (far-IR) interferometer from a space-based platform would bring about a transformational improvement in the spatial detail of astronomical observations that are inaccessible from ground-based observatories. This orders-of-magnitude improvement would significantly advance studies of newly formed and mature exoplanetary systems and their potential for supporting life, the earliest stages of star formation, and the evolution of galaxies up to the peak of the Universe's star formation activity and beyond. In this work, we discuss the potential for such an instrument and the science it enables in complement to current long-term plans of the global astronomical community and in preparation for the next generation of observatories. We also outline notable far-IR mission concepts, pathfinder instruments, and technology development platforms that have been studied and developed throughout the past few decades and briefly discuss key enabling technologies.

We rigorously derive a dynamic membrane theory for nonlinear viscoelastic solids with Kelvin-Voigt rheology from the corresponding three-dimensional bulk theory, in the limit of vanishing thickness. The bulk model accounts for inertia, a nonsimple elastic energy depending on the second deformation gradient, and a frame-indifferent dissipation. Orientation preservation is ensured by the energy, while self-interpenetration of the limiting membrane is prevented by a uniform averaged invertibility condition. Our analysis relies on a hyperbolic minimizing movements scheme with two time-scales, which recasts the evolution into a hierarchy of incremental, sequential, and time-delayed problems. For fixed thickness, we prove the existence of solutions to the scheme and their convergence to a weak solution of the continuous-time problem as the time-scales vanish. We then identify the membrane limit at each level of the hierarchy, proving the $\Gamma$-convergence of the incremental functionals and the convergence of solutions to the sequential and time-delayed problems. Since the constant in the Korn inequality is not uniform in the thickness, these limits rely on estimates for the time derivative of the Cauchy-Green tensor rather than for the velocity gradient. Finally, as the outer time-scale vanishes, the membrane time-delayed solutions converge to a measure-valued solution of the membrane continuous-time problem.

People increasingly bring their health questions to ChatGPT, yet safety evaluations of LLM health advice rest almost entirely on clinician-authored vignettes, synthetic prompts, or simulated user profiles. The gap is widest for the Global South, where concerns about demographic bias and unsafe recommendations are well documented but have never been tested on real usage. We present, to our knowledge, the first demographically grounded safety evaluation of real-world health conversations with ChatGPT. From a consent-based data-donation corpus of 202,590 conversations from 1,252 users in India, Nigeria, Brazil, and Pakistan (December 2022 to February 2026), each linked to self-reported age and gender, we identify 15,555 health conversations, classify their health intent using an LLM classifier adapted from an established taxonomy, and score response safety under both a context-blind and a user-context-aware rubric. Roughly one in five health conversations receives a high-risk rating. Risk concentrates in symptom and condition queries and recurs through identifiable failure modes: unsafe medication or dosage guidance, harmful self-diagnosis, missing safety warnings, encouraging over-reliance on the model, and failure to refer users to professionals. Supplying the user's own accumulated context raises the high-risk share by 13-17 percentage points, and about one in four conversations rated safe in isolation turns out to be unsafe for the specific person asking. Safety evaluations built on synthetic cases are likely to miss these harms.

We prove that every Lie group can be realized by permutations of a countable set, answering a classical question of Ulam. The key deformation construction originated in an argument produced by OpenAI's GPT 6 Astra during extended mathematical discussions.