Papers

High-fidelity audio coding requires faithful reconstruction of perceptually important high-frequency components, which are often lost due to the aggressive temporal decimation and quantization of neural codecs. State-of-the-art neural audio coding methods rely on adversarial learning to hallucinate these missing components, yielding perceptually plausible but imprecise reconstructions; a limitation for high-fidelity music applications. As a remedy, we propose high-efficiency neural audio coding (HE-NAC), which provides a multi-band extension of the popular residual vector quantization (RVQ) scheme. HE-NAC introduces an effective training mechanism that harmonizes a bitrate-free blind upsampling process, residual learning to compensate it with minimal bitrate, and a multi-head decoder architecture for band-specific reconstruction. As a result, HE-NAC achieves a balanced trade-off, reliably reconstructing the core-band ($\leq$ 3 kHz) component while preserving overall sound fidelity. Subjective listening tests and objective evaluations demonstrate that HE-NAC outperforms both the DAC baseline and MPEG HE-AAC at equal or lower bitrates.

We study the numerical radius \(\omega(T)\) of a bounded linear operator \(T\) on a complex Hilbert space. Write \(T=A+iB\), where \(A\) and \(B\) are the real and imaginary parts of \(T\). A central result is the exact formula \[ \omega(T)=\frac{\pi}{2}\sup_{\|x\|=1}\int_0^1 \left|\left\langle (A\cos \pi t+B\sin \pi t)x,x\right\rangle\right|\,dt . \] For every \(n\in\mathbb N\), we also prove the power form \[ \omega^{2n}(T)=\frac{4^n}{\binom{2n}{n}} \sup_{\|x\|=1}\int_0^1 \left\langle (A\cos \pi t+B\sin \pi t)x,x\right\rangle^{2n}\,dt . \] This yields sharp upper bounds; for \(n=1\), together with the matching integral lower bound, it recovers Kittaneh's classical two-sided inequality \[ \frac14\|T^*T+TT^*\|\le \omega^2(T)\le \frac12\|T^*T+TT^*\|. \] Furthermore, we obtain exact numerical radius formulas for some block operator matrices, including a \(3\times3\) nilpotent matrix and longer alternating paths. The factor \(\pi/2\) is best possible.

Hoffman constants quantify the distance to the solution set of a polyhedral system in terms of its residual; they control error bounds, geometric conditioning, the convergence rate of first-order iterative algorithms, and the stability of regression estimators to target perturbations. Despite their importance, explicit values of Hoffman constants are rarely available due to their computational complexity. In this paper, we derive explicit bounds on the Hoffman constant for a class of structured polyhedral systems arising in sparse regularization. We show that the constants admit a decomposition into spectral, geometric, and interaction components, which together determine their scaling behavior. This framework explains the gap between worst-case dimension-dependent bounds and the favorable conditioning observed empirically in structured problems. As a primary application, we analyze $\ell_1$-regularized least squares, demonstrating that the effective constants depend on low-dimensional active subspaces rather than the ambient dimension. We then extend to the elastic net and adaptive $\ell_1$-regularized formulations, demonstrating how the underlying optimization geometry is altered by the $\ell_2$ penalty and reweighting scheme. Furthermore, we relate our results to classical statistical assumptions and show that the restricted eigenvalue condition bounds only the primal curvature of the active set, leaving the dual interaction geometry unconstrained and is thus insufficient alone for fast theoretical convergence rates. We further show standard $\ell_\infty$ coherence conditions do not yield dimension-independent Euclidean bounds to close this gap. Our theoretical results show that Hoffman constants admit explicit, interpretable forms in structured regression settings and, in practice, provide actionable tools for post-hoc feature pruning and a priori optimal hyperparameter selection.

LLM agents now write their own schematic and layout generators, run EDA tools, read the results, and fix the design. This "vibe tapeout" is becoming practical for analog circuits as well. This paper measures how far it has come in two settings. (A) On an open PDK (SKY130), a cloud LLM agent designed an 11-bit, 5.12-MS/s SAR ADC from its specification. The agents produced DRC- and LVS-clean macros and met the specification after parasitic extraction (PEX). In particular, under the condition in which the agent received a sanitized reference design derived from our 65-nm design (vibe porting), it produced the best layout in the shortest time. Its area was 1/1.6 to 1/2.8 of that of the conditions without a reference. This condition reached signoff without human intervention. The agents also identified the causes of post-PEX degradation (CDAC wiring coupling and common-mode-dependent comparator offset) by their own experiments. On the other hand, agents sometimes reported false passes, and verification independent of the design agent was essential. (B) A commercial PDK is under NDA and cannot be given to a cloud LLM. We therefore evaluated local LLMs running on university servers with a six-task benchmark on a commercial 65-nm CMOS PDK. Kimi K3 passed five of the six tasks, while MiniMax M3 passed two. Neither solved the debugging task, which requires finding the cause from symptoms. Finally, we discuss the prospects for extending vibe tapeout from ADCs to entire SoCs, and ask whether vibe tapeout is a dark age or a golden age for analog design. Our answer is that it is a golden age for designers who know what to verify.

Most benchmarks for large language models in medicine are built from licensing examinations and theoretical questions. The few that draw on real clinical data do so only in part, and rarely require a model to read a patient's own imaging. ClinEdge addresses this gap with 32 real, de-identified patient cases from active clinical practice, each evaluated across seven frontier systems for a total of 224 expert-graded evaluations. Each case pairs primary imaging with a short vignette, contains a feature known to defeat pattern-matched reasoning, and is scored against the patient's documented clinical course. The suite is built for depth rather than volume. Grading followed a two-stage expert process. First, a senior orthopaedic surgeon graded all 224 responses on a weighted rubric and a pass-or-fail verdict. Second, a panel of nineteen physicians, largely senior specialists at teaching medical colleges, independently reviewed every case and every one of the 224 grades. All seven production systems were evaluated through their public interfaces, and all 224 conversations are preserved as replayable links. Performance was poor across all systems, and the failures were shared: different vendors missed the same findings and converged on the same wrong plans. From the experts' notes we catalogue 18 recurring failure modes in five families. The models stop reading an image at the first finding. They give generic plans and lean toward over-treatment. They trust a misleading history over correct imaging. Their answers vary across systems and runs, and change with question format. Failing answers were delivered fluently and without any expressed uncertainty. Four cases are released in full; the remaining 28 are held out, and we invite frontier AI labs and healthcare AI companies to evaluate their models against them (research@futrbridge.com)

Use of carbon electrodes integrated with CMOS technology has great promise for lab-on-chip, biomedical, environmental, and industrial applications. One method of developing carbon electrodes is to 3D print polymer nanostructures on a CMOS chip, and use a thermal annealing process to pyrolyze them into carbon at high temperature, approximately 950 {\deg}C. Such high temperature is detrimental to the CMOS sensor circuits, causing severe degradation. We present a novel solution of localized Joule heating of these polymer nanostructures to achieve complete carbonization of the electrodes. Both analytical and COMSOL simulations guided the experiments to characterize the carbonization process conditions. Partial carbonization was achieved at 500-600 {\deg}C of global temperature, and complete carbonization was achieved by localized Joule heating. Pyrolized nanostructures monolithic samples on a silica wafer were fabricated using standard material processing, such as 2-Photon Polymerization. Pyrolysis was achieved by Rapid Thermal Processing (RTP). Observations using optical microscopy, scanning electron microscopy, and Raman spectroscopy demonstrated the feasibility of polymer carbonization within a CMOS compatible temperature window.

Autonomous Surface Vehicles (ASVs) have been increasingly deployed to perform different kinds of maritime tasks in recent years, which motivates the need for a reliable task allocation policy that can adapt to heterogeneous tasks and maritime disturbances. In this work, we formulate a multi-robot task allocation problem in which a team of ASVs with heterogeneous capabilities needs to complete tasks of different types and appearance times under unknown stochastic spatio-temporal uncertainties from maritime disturbances. We propose a decentralized Reinforcement Learning (RL) based policy network that is trained to be robust towards uncertainty-induced observation deviations, and is able to perform individual decision making that leads to efficient execution behaviors toward heterogeneous task requirements. We evaluate the proposed policy and four baseline methods in simulated experiments with varied proportions of different tasks types, numbers of tasks, robot species and robots per species. Experiment results show that our proposed policy achieves the lowest makespan and can be deployed to address scenarios with 100 robots and 400 tasks.

Condensed matter stands to gain profoundly from widespread adoption of artificial intelligence (AI). However, its current means of data organization impedes this endeavor. As a premier measure of electronic structure underlying material properties, Angle-Resolved Photoemission Spectroscopy (ARPES) has accumulated over four decades of spectra, yet the community's publication-centered workflow preserves only a highly selected fraction of its experimental record. A shared data ecosystem could transform these fragmented measurements and their contexts into a persistent, collective scientific memory, creating immediate value for reproducibility and reuse while laying the foundation for AI-enabled discovery. In this Perspective, we report outcomes of a recent community workshop and propose a practical path toward such an ecosystem. Its benefits unfold along three timescales. In the near term, standardized, searchable, and citable datasets strengthen analysis pipelines independently of AI. In the intermediate future, community-validated tools operating across laboratories could enable broader reuse and increasingly closed-loop automated experiments. In the long term, a diverse corpus of measured electronic spectra could support foundation models for quantum matter. Looking forward, a diverse corpus of measured electronic spectra could support foundation models for quantum matter and new discoveries. We discuss lessons from existing scientific databases, the current state of AI in ARPES, as well as areas of community convergence on data organization, access, credit, governance, and a staged pilot program.

Despite remarkable progress in language understanding and generation, decoder language models continue to exhibit striking failures on numerical data. Numerical examples are typically serialized as text by concatenating feature names with their values (e.g., fat:3.4), while conventional task adaptation applies loss only to the downstream prediction target. This leaves two structures weakly supervised: within-value sensitivity, where digit position determines numerical magnitude, because token cross-entropy contains no explicit numerical metric; and across-field structure, where measurements in the same record are statistically dependent, because target-only tuning provides no direct loss on the measurements or their dependencies. We introduce MoMaTune (Model, Match, then Tune), a two-stage post-training strategy organized around these supervision gaps. Stage 1 applies Model, ordinary next-token prediction densely over label-free serialized records, and optionally adds Match, a same-record consistency objective that aligns representations of different partial views of the same example. Stage 2 applies Tune, supervised fine-tuning for downstream target prediction. We evaluate MoMaTune on 169,285 records from eight public datasets, with 339 of 340 input fields numerical. At 1.5B parameters, Model raises the eight-dataset masked-value imputation aggregate from 0.106 to 0.401, while the three-dataset correct-context gain rises from 0.058 to 0.167. On diagnostics, Model also increases sensitivity to numerically consequential digit changes, while Match improves robustness to informative partial views. Adding Tune yields higher target-supervised embedding aggregates for each tested Stage-1 parent, and the two-stage recipes obtain higher aggregate scores than Tune alone. The same pattern is observed at 4B, 9.6B, and 27B parameters when model embeddings are used for downstream prediction.

Consider an $n$-dimensional sum of the form $S_k=\sum{q^{f({\bf z})}}$ over lattice points ${\bf z}$ which lie in $K{\mathcal P}$, the $K$ scaling of an $n$-dimensional rational polytope $\mathcal P$. We formulate a conjecture on the structure of $S_K$ considered for $K$ prime, as a power series in $h=q-1$ modulo the $K^{th}$ cyclotomic polynomial, and in particular the existence of a decomposition in powers of the Gauss sum $\mathbb G$, up to the $n^{th}$, whose coefficients are almost independent of $K$, where the leading coefficient is related to the volume of $\mathcal P$ and the coefficient of ${\mathbb G}^r$ has contributions from the codimension $r$ skeleton of $\mathcal P$. The conjecture is proved for $n=1,2$.

We give a single counterexample to Conjectures 1–3 as stated in Luo's paper: a minimal two-tetrahedron triangulation of the lens space L(3,1) with a null-homotopic loop edge. The proof uses quadrilateral matching equations, an explicit calculation of shape parameters, and known results on volume maximization.

How much can we trust an agent to find the paper we need? As researchers, we search the literature from what we have read toward what we have not. We thus describe what we want in our own terms, which a paper may show only implicitly; our requirements grow as we read; and what we seek may lie in an empty region no paper yet covers. We introduce CompLit, a literature search benchmark spanning all eight arXiv domains, with one diagnostic setting for each of these needs. The strongest agents, Codex (GPT-5.6-Sol) and Claude Code (Opus 4.8), answer 86-87% of Standard queries, yet fall to 66-68% when requirements are implicit (implicit), lose another 6 and 15pp, respectively, as they accumulate (cumulative), and abstain on at most 53% of the queries no paper satisfies (unmet). No agent leads in every domain, and all are less accurate on papers from before 2019 or after 2023. Tracing their search, we find that agents often reach the right paper, or the closest one, yet misjudge it. Doing well on CompLit is a step toward agents that we can trust to find the paper we need, or to tell us that none exists.

Currently, voice-related privacy risks are studied under the assumption that the attacker has access only to spoken audio. In contrast, real-world collections often pair the speech signal with side information; yet to our knowledge, no publicly available dataset provides sufficiently detailed and directly linkable speech and side-information pairs to evaluate the combined risk. We propose a distribution-constrained method to build a semi-synthetic dataset and study singling out risk when geographic side information is assumed to accompany anonymized speech. We instantiate it using the English portion of Mozilla Common Voice and the 2021 UK Census, under ignorant and semi-informed attackers, and introduce a conditional reference that isolates the contribution of the audio beyond the candidate-set reduction induced by the side information. In our controlled geographic case study, for single-utterance speakers, the semi-informed attacker reaches an observed isolation probability of 0.718 in the finest OA-plus-household setting, compared with 0.380 in the signal-only setting; its excess over the conditional reference increases from 0.012 to 0.340. The ignorant attacker shows the same trend at a lower level. The effect is largest at fine granularity and short recordings, precisely the setting in which signal-only evaluation looks safest. Our results show that geographic side information can increase the singling out risk of anonymized speech, and we recommend including attacker settings with side information in future studies of voice privacy.

Equation-based neural modeling offers flexibility, but executing models across processors and nodes requires explicit control of order, ownership, and numerical behavior. We present brian2-atlas, a rebuilt execution architecture retaining Brian2's modeling interface and bringing heterogeneous and distributed targets under a common model-to-execution contract. Its unified intermediate representation, AtlasIR, describes typed state, clocks, schedules, effects, events, and random-stream identities, and is checked by an independent Rust validator. Target-specific implementations support Rust CPU execution, CUDA and Apple Metal GPUs, browser WebAssembly, and MPI within declared contracts. In a repeated full-connectome CPU cohort, the best measured Rust configuration reduced simulation-and-recording time by 5.43-fold relative to the best measured Brian2 C++ configuration on the same Linux host. A 298.9-million-synapse model completed on a 16 GB laptop while the compared C++ preparation path exceeded its controlled memory budget. Distributed execution completed 100.5 seconds of model time for 4,129,924 neurons and 24.1 billion recurrent synapses on four nodes and 32 ranks. A five-point synthetic weak-scaling study reached 860 million neurons and 860 billion recurrent connections for 100 ms on 30 hosts and 240 physical worker cores. These establish tested capacity configurations rather than statistical equivalence or a matched speed advantage over NEST. Published-model workflows extend validation to explicit NMDA dynamics and contextual dendritic plasticity, with up to 2.10-fold acceleration in a matched eight-core NMDA cohort. The results characterize semantic, numerical, and resource boundaries rather than universal compatibility or performance superiority.

Phylogenetic inference is a fundamental problem in computational biology, with applications ranging from epidemiology and oncology to developmental biology and comparative genomics. Many major phylogenetic problems are NP-hard; consequently, existing methods often explore tree space using local search or MCMC based on a limited repertoire of combinatorial rearrangements. However, the size and ruggedness of tree space make it difficult for such heuristics to reliably reach optimal or near-optimal solutions. Recently, there has been growing interest in alternative approaches that embed trees into numerical spaces and apply numerical optimization techniques. However, such methods are still limited in practical applicability. We propose a new approach to phylogenetic inference based on embeddings of trees into the non-Archimedean space of $2$-adic numbers. The hierarchical organization of $2$-adic space naturally encodes tree topologies, while its rich topological, algebraic, and measure-theoretic structure provides a natural foundation for a coherent theory of tree calculus and optimization. Here, we introduce 2-adic tree embedding, establish their basic topological, probabilistic, and algebraic properties, and show that they support natural representations of tree distributions, algebraic operations, and broad classes of tree rearrangements extending standard operations such as NNI, SPR, and TBR. Building on these results, we introduce a general local search framework in which tree neighborhoods are generated by parametric families of $2$-adic polynomials. We show that even infinitely many transformations induce only quadratically many distinct neighboring trees, which can be generated in polynomial time. These results suggest a new mathematically rigorous and flexible approach to representing and exploring tree space.

We propose a controlled Large Language Model (LLM) workflow for explaining risk score differences using similar historical transactions. The workflow combines reference retrieval and contrastive SHapley Additive exPlanations (SHAP) evidence with reference-based LLM reasoning and deterministic validation. Experiments on a test dataset show that the workflow produces more consistent, evidence-grounded and traceable diagnoses than the same LLM without structured workflow guidance.

We give a self-contained derivation of the closed form of the power sums $S_m(n)=\sum_{i=1}^{n}(a_0+(i-1)d)^m$ in which the Bernoulli numbers enter as constants of integration rather than as prescribed coefficients. The derivation rests on an elementary fact: a sum whose terms are polynomial in the index is the restriction to the integers of a unique polynomial, which satisfies the defining difference equation identically and may therefore be differentiated and integrated exactly. Differentiating lowers the power by one; integrating back introduces a single constant, equal to the slope $S_m'(0)$ of the polynomial at the origin and fixed by the value $S_m(1)=a_0^m$. This yields a closed form for $S_m(n)$ in terms of the constants and a recurrence that determines them, obtained without induction on the exponent and without generating functions. With the Bernoulli numbers defined by their classical recurrence, we identify the constants as $d^mB_m(a_0/d)$; the progression starting at $0$ reproduces that recurrence exactly. In the normalized case they are $B_m(1)$, so $C_1=B_1(1)=+\tfrac12$, a value that reflects the summation range; a reflection identity shows, without generating functions, that the odd constants beyond the first vanish. The coefficients of the recurrence are scaled binomial coefficients from a single row of Pascal's triangle, and the same approach gives closed forms for sequences with polynomial differences. The integral recursion behind the method is known in the normalized case; each result is related to its classical counterpart, and a verified implementation is provided.

For every $n\ge22$, we construct a language over a fixed three-letter alphabet whose two-way deterministic state complexity is $n$ and whose complement has state complexity $2n$. Acceptance is at the left endmarker, and infinite computations reject. The lower bound holds for arbitrary deterministic recognizers. The proof uses the group of transformations induced by the witness to constrain the behavior of a smaller recognizer, then derives a contradiction from a permutation query problem. A matching halting complement follows from a $2n$-state construction for sources whose destination states determine the direction of each transition. Splitting states by incoming direction gives a $2n+2b$ upper bound for general sources, where $b$ counts states entered in both directions. In the acceptance-anywhere model of Geffert, Mereghetti, and Pighizzini, the same family has exact complexities $N$ and $2N-1$ for every $N\ge23$.

In this paper, we study hypersurfaces $M^4$ in the Minkowski space $\mathbb{E}^5_1$ whose shape operator $S$ is non-diagonalizable, having a triple real eigenvalue $\lambda$ with a one-dimensional eigenspace together with a simple eigenvalue $\mu$ (Case~(iii) in the classification of Magid). Assuming that $\lambda$ and $\mu$ satisfy a functional relation $\lambda=f(\mu)$ and that the eigenvector field of $\mu$ is geodesic, we show that $\lambda$ and $\mu$, as well as the pseudo-orthonormal frame, are intrinsic invariants of $M$, determined by the induced metric up to sign. As a consequence, we prove that such hypersurfaces are unique up to isometries of $\mathbb{E}^5_1$. We also obtain a classification of the warped product hypersurfaces of this type.

In 2012, D. Karp studied a family of polynomials constructed from Polya frequency sequences and conjectured that all their zeros are real and negative. We prove this conjecture for positive sequences and establish further results concerning the location of these zeros.

The Diophantine equation $F_n^x+F_m^y=2^a,$ where $F_k$ denotes the $k$-th Fibonacci number and $n,m,a\in \mathbb{Z}_{\geq0}$, has attracted attention in recent years. The cases $(x,y)=(1,1)$ and $(x,y)=(2,2)$ were completely resolved by Bravo and Luca, and by Jeong and Park, respectively. In this note, we investigate the mixed exponent case $(x,y)=(2,1)$ and we completely determine all nonnegative integer solutions.

In this work, we study a theoretical scheme to investigate the monogamy of quantum steering in a hybrid exciton–cavity optomechanical (EOM) system. Within the Gaussian-state formalism, we quantify the steerability among the exciton, photon, and mechanical modes in both the steady-state and dynamical regimes. We establish and verify CKW-type monogamy inequalities for Gaussian steering and demonstrate that the distribution of bipartite steering among the three modes can be controlled through the system parameters. We further examine the influence of thermal noise and temporal evolution on the steering properties and the corresponding monogamy relations. Our results show that increasing the temperature generally suppresses the strength of Gaussian steering and modifies the degree of steering sharing imposed by the CKW-type monogamy relations. In contrast, in the dynamical regime, the steerability can increase with evolution time over suitable temporal windows, indicating that the transient dynamics can be exploited to enhance quantum correlations. These results highlight the potential of hybrid exciton–optomechanical platforms for controllable quantum correlations and provide a promising route toward the generation and manipulation of multipartite quantum resources.

We study the uniqueness of bound states for the following scalar field equation $$ -\Delta u+u=-\varepsilon |u|^{q-1}u+|u|^{p-1}u \,\ \ \mbox{in}\,\ \mathbb R^N, \,\ \varepsilon>0,\tag*{$(*)$} $$ where $ N\ge3,\ 1<p<(N+2)/(N-2)$ and $q>1$ satisfies $q \neq p$. For each integer $k \geq 1$, we prove that the equation $(*)$ has, up to translation and reflection, a unique bound state with precisely $k$ nodes in a natural coupling regime, where $\varepsilon>0$ is sufficiently small. Our results address a conjecture of [H. Berestycki and P. L. Lions, ARMA, 1983][M. X. Tang, Invent. Math., 2026] on the uniqueness of fixed-node bound states for the equation $(*)$.

Generative artificial intelligence (GenAI) models, particularly large language models (LLMs), are increasingly used in educational settings for tasks such as item generation, automated scoring, and feedback delivery. The quality of these outputs depends not only on the AI model but also on how users construct the prompts that guide model behaviors. Current prompt engineering practices are largely ad hoc, relying on trial and error rather than principled design. This lack of structure introduces validity threats including construct misrepresentation, construct-irrelevant variance, and limited reproducibility. We propose that Evidence-Centered Design (ECD), a framework in educational measurement for structuring valid inferences from observed performance, can serve as a principled foundation for prompt engineering in educational applications. We map the three core ECD models, the student model, the evidence model, and the task model, onto the components of educational prompt design, and describe a workflow for ECD-based prompt engineering. We derive five design principles from this mapping and present an empirical study contrasting ECD-designed prompts with state-of-the-art (SOTA) prompting baselines on an automated scoring task. Our empirical study demonstrates the usefulness of this framework on automated scoring. Results suggest that treating prompting as assessment design rather than informal instructions strengthens the validity, reliability, and fairness of AI-generated educational outputs.

Optical and resonant inelastic X-ray scattering (RIXS) experiments in the van der Waals antiferromagnet NiPS$_3$ have revealed narrow excitonic resonances near 1.5 eV whose microscopic origin remains under debate. In this work we study the momentum dependence of these excitations using the singlet-polaron theory (SPT) previously developed for NiPS$_3$. Within its framework, we calculate the spectral function of the corresponding effective model and extract the dispersion of the resulting quasiparticles. The theory naturally predicts two singlet excitations whose dynamics arise from their propagation in the zig-zag antiferromagnetic background ($S=1$) coupled to two-magnon processes. We show that the dispersion of the lowest-energy quasiparticle agrees very well with the excitonic dispersion measured by RIXS, reproducing both its overall shape and bandwidth along high-symmetry directions of the Brillouin zone. Our results provide a consistent interpretation of the optical excitations in terms of dispersive singlet polarons, and suggest that similar mechanisms may govern excitonic dynamics in other layered van der Waals antiferromagnets.

Veins are commonly subjected to altered mechanical loading in clinical settings such as vein grafting, arteriovenous fistula creation, and tissue-engineered vascular graft implantation, making accurate constitutive models of venous tissue clinically important. Venous mechanical behavior differs characteristically from that of arteries, and existing constitutive models struggle to simultaneously fit the circumferential and axial stress-stretch responses across vein types. Here, we present a constitutive artificial neural network (CANN) framework that discovers a compact, interpretable hyperelastic constitutive model from biaxial mechanical data across three types of veins (saphenous, jugular, and inferior vena cava). The framework incorporates an expanded candidate function library with structurally motivated terms representing progressive fiber recruitment and fiber-family interactions. Sobol sensitivity analysis, correlation-based pruning, and response-level family collapse were then used to reduce the discovered basis to a compact strain-energy density function (SEF). The resulting eight-term SEF achieved significantly higher fitting accuracy than established venous constitutive models across all three types of veins $(R^2>0.9, p<0.01)$. These findings establish a framework for constitutive model discovery in veins and propose a candidate constitutive form for further validation across larger, independent cohorts.

Words are increasingly becoming an interface for action: large language models (LLMs) can now invoke tools, operate devices, and make decisions that affect the physical world. However, current benchmarks largely evaluate LLMs through static text responses, offline tool calls, or simulated tasks, leaving open the question of how well they can act in real physical environments. We present a benchmark for measuring LLMs in closed-loop physical interaction, where models control a harness system connected to real-world components including robotic arms, cameras, and sensors. In each task, the model must issue instructions, receive physical feedback from the environment, interpret the resulting state, and adapt its next action accordingly. This setting evaluates capabilities beyond language understanding, including grounded perception, action planning, tool selection, spatial reasoning, feedback-driven correction, and robustness to execution uncertainty. Through experiments with representative LLMs, we characterize their ability to translate linguistic reasoning into physical actions and identify common failure modes such as hallucinated state changes, poor recovery from unexpected outcomes, and unstable long-horizon plans. Our benchmark aims to provide a systematic foundation for evaluating LLMs as interactive agents that connect words, tools, and the physical world.

Unified vision-language models (VLMs) perform both text-to-image (T2I) and image-to-text (I2T) generation with one shared Transformer backbone, yet how the backbone processes the condition in either direction remains poorly understood. We study this question from the perspective of conditional guidance: we probe every attention head to show the activation difference between two branches of classifier-free guidance (CFG) with different conditional guidance. On two unified VLMs of autoregressive and masked-diffusion paradigms, the probing reveals a subset of heads that are more sensitive to the change of condition while others are agnostic to it. This characteristic pattern holds in both T2I and I2T generation and is largely stable across data samples, demonstrating the internal mechanism of unified VLMs. Motivated by this, we propose a new inference-time intervention approach for unified multimodal generation, named HeadTuned-CFG, which uses the probed condition-change awareness to select and tune the conditional guidance at the attention-head level. Experiments show consistent benefits in both multimodal generation directions of unified VLMs without additional training, and in particular substantial improvements over strong baselines in T2I generation. These results further support the key finding of our probing analysis: the observed pattern of functional specialization is an intrinsic property of unified VLMs.

The 1-Meixner random vectors consist of $d$ real-valued random variables, having finite moments of all orders, for which the commutators between their joint semi-quantum operators and the multiplication operators that they generate are linear combinations of these multiplication operators and the identity operator. This property of random variables imposes a system of first-order partial differential equations on their joint Laplace transform on a neighborhood of $0$ in a Euclidean $d$-space. We provide explicit descriptions of all solutions of the system just mentioned in every dimension $d$.

Zeroth-order (ZO) optimization enables memory-efficient fine-tuning of large language models (LLMs). However, ZO optimization suffers from high variance in high-dimensional parameter spaces. While recent methods restrict perturbations to random low-rank subspaces, these subspaces often misalign with task-specific descent directions. We propose AdaSub-ZO, a novel forward-only fine-tuning framework in learnable low-rank subspaces. Instead of relying on fixed random matrices, AdaSub-ZO iteratively learns layer-wise projection matrices directly from finite-difference feedback to track task-aware descent directions. Furthermore, AdaSub-ZO incorporates a subspace momentum acceleration mechanism to smooth noisy gradient estimates across evolving subspace bases. Extensive experiments on natural language understanding tasks demonstrate that AdaSub-ZO outperforms existing ZO baselines, substantially reducing gradient estimation variance and accelerating convergence.