Papers

Material and energy flows underpin sociotechnical metabolism. However, despite growing sustainability concerns over expanding material stocks and declining stock productivity, the link between material use and energy consumption remains poorly understood. This gap reflects a limited distinction between structures and the activity they enable, and the lack of quantification of the installed power of energy consuming structures. Here we reconstruct the long-term growth dynamics of U.S. road vehicles, distinguishing professional and consumer assets. We show that installed power, mass, and fuel energy use follow divergent patterns within and across vehicle categories. By introducing the usage factor as a metric linking structure to activity, we quantify decoupling mechanisms such as engine oversizing and fleet redundancy, which drive up material immobilization. As electrification requires large-scale fleet replacement, our findings highlight that avoiding power oversized vehicles could reduce material demand, emphasizing the need to account for structure-activity decoupling in energy transition policies.

We report a proof found by an artificial intelligence system for the following statement: The hyperbolicity cone of every strictly hyperbolic polynomial is spectrahedral. This establishes the generalized Lax conjecture for the generic case, while the full conjecture remains open.

We prove that Chapoton's $q$-Zeta numerator has nonnegative coefficients for the positive-root poset of every finite reduced irreducible crystallographic root system, graded by root height minus one and normalized by Chapoton's prescribed denominator. The same holds for every interval of the root poset with zero adjoined. The key observation is that adjoining a minimum changes the numerator only by the substitution $t\mapsto qt$. The numerator thereby becomes a nonnegative combination of flag $h$-numbers of a lower-semimodular lattice, and a classical labelling of the dual lattice gives a positive descent expansion. To make the coefficients explicit, we construct signed edge-lexicographic (EL) labellings of Ferrers-cell posets with nonincreasing boundaries. They give ballot-word formulas in types $A$, $B$, and $C$, which prove an observation of Chapoton in type $B$, and a coloured path formula in type $D$. For trapezoidal boundaries, one-boundary major-index enumerators evaluate the path sums in Gaussian-binomial form.

Characterizing exoplanets and finding biosignatures are among the hottest topics in astronomy. This quest is challenged by the brightness contrast between the faint planet and the overwhelming glare of the host star, their small angular separation, and observing conditions degraded by optical aberrations. Nulling interferometry is a promising technique to achieve this goal by fulfilling requirements for both high contrast and high angular resolution. Photonic Integrated Circuits (PICs) provide compactness, design versatility, and scalability needed for nulling. With the PHOTONICS project, we aim to create novel coherent combination architectures, based on a multimode interferometer (MMI) coupler and on-chip active phase control with no moving parts. We present the first lab tests of a four-beam kernel-nuller made out of a single MMI coupler with active phase control: ABCD fringe-tracking and the characterization of the contrast detection limits of a four-beam kernel-nuller.

Multi-modal object Re-Identification (ReID) benefits from complementary information across heterogeneous imaging modalities. To further enrich semantic representation, text descriptions have recently been incorporated as an additional modality. However, recent vision-language approaches often treat text descriptions as clean, deterministic signals and overlook their inherent noise, including modality-mismatched phrases and semantically ambiguous expressions. Moreover, prevailing methods lack explicit mechanisms to reconcile fine-grained structural discrepancies between modalities, even after high-level semantic alignment. To address these challenges, we propose a novel framework centered on Positive-Incentive Noise ({\pi}-noise) and structured prompt modulation. First, the Semantic Cross-Modal Modulator harnesses task-aware {\pi}-noise, sampled from a distribution conditioned on both visual and text inputs, to perturb global tokens and enable semantics-guided cross-modal compensation. Second, the Structure-Aware Prompt Adapter injects learnable geometric priors via prompts to enhance spatial consistency. Third, the Context-Aware Sparse Fusion module distills structural context to guide adaptive fusion while shielding identity features from noisy local details. Experiments on three multi-modal ReID benchmarks demonstrate the effectiveness and robustness of our approach. The code is available at https://github.com/zw-absin/INSPI.

Functional annotation of newly sequenced proteins remains a bottleneck in molecular biology: the number of sequences in public repositories grows far faster than the capacity for manual curation. Most computational approaches consider annotation as multi-label classification over a fixed ontology, which constrains predictions to a predefined label set. In this work we study the the protein annotation as a sequence-to-text generation problem. We fine-tune the 3B-parameter Ministral 3 base model with QLoRA (4-bit NF4 quantization with low-rank adapters) on sequence annotation pairs. We assess predictions with an LLM-as-expert protocol: a GPT model prompted as a senior molecular-biology curator scores organism identification as binary and function annotation quality. We conclude that QLoRA-fine-tuned compact LLMs can generate curator-style annotations with genuine biological value for a substantial subset of proteins. We also discuss future directions in data quality, model scaling, and evidence grounding that are needed to make the approach sufficiently reliable for practical use.

Video recording on smart glasses exposes more than faces. Continuous capture reveals full-body biometric signatures, including gait, posture, and silhouette, that enable person re-identification (ReID) even after conventional face sanitization. We present MIRAGE, a three-tier architecture for privacy-preserving smart glasses that enforces full-body privacy, supports synthetic full-body replacement, and retains encrypted recovery material for consent-based restoration. We implement MIRAGE on a Raspberry Pi~5 (a CPU-only proxy for smart-glasses compute), companion phones, and a cloud generative backend. Compared to prior systems, MIRAGE achieves 0.948 AP and 0.976 AR while accurately detecting the complete visible body. Its bounding box masking reduces learned silhouette-based ReID to essentially random guessing, with 10.86% Rank-1 accuracy compared with an 11.12% measured chance level. Even against an adaptive adversary retrained on MIRAGE's sanitized pose signals, Rank-1 gait identification drops from 90.25% to 26.20%, removing 72.5% of the adversary's identification advantage.

We study the spectroscopy and decays of the $B_c$ meson in a nonrelativistic quark model in which all observables follow from a single set of wave functions, with spin-dependent effects included directly in the bound-state equation. With parameters calibrated to the measured $B_c(1S)$ and $B_c(2S)$ masses, we predict the $S$-, $P$-, and $D$-wave spectrum up to $n=5$, the pseudoscalar and vector decay constants with one-loop QCD corrections, the E1 and M1 radiative widths, and the radial Regge trajectories of ten spin-parity families. The $1P$ multiplet is predicted at 6692–6746~MeV with the normal fine-structure ordering, compatible with lattice QCD and located in the region of the two structures observed by LHCb in the $B_c^+\gamma$ spectrum. The $1D$ states lie near 7008~MeV, below the $BD$ threshold, and all four $D$-wave families are provided. The decay constant $f_{B_c}=507.1$~MeV is consistent with recent QCD sum-rule results and corresponds to $\mathcal{B}(B_c\to\tau\nu_\tau)\approx3\%$. The E1 widths follow the expected angular weights, while their magnitudes are governed mainly by the radial overlap. The $1P\to1S$ (81–112~keV) and $1D\to1P$ (71–93~keV) widths suggest the $1D\to1P\to1S$ cascade as a promising route toward the first $D$-wave $B_c$ state. The Regge trajectories are nearly linear, with slopes decreasing from about 5.8~GeV$^2$ for the $S$-wave to 4.7–4.8~GeV$^2$ for the $D$-wave states. These results may guide forthcoming measurements at the LHC and future $e^+e^-$ facilities.

Unlike conventional rigid-link robots defined by discrete joints, continuum robots pose a fundamental challenge for expressing their complex continuous bending configurations for closed-loop control. Several modelling approaches have been proposed for conventional continuum robots, but tensegrity-based continuum robots remain largely open. Moreover, many of these approaches assume a continuous elastic backbone and are therefore not directly applicable to tensegrity manipulators, whose bodies are networks of rigid struts and tensioned cables. This work presents a reduced-order model for shape and posture control of a tensegrity-based continuum manipulator. The manipulator is modelled as a serially connected parallel-link mechanism. The proposed method is formulated as an optimization problem that uses geometric constraints of the tensegrity structure together with information from the Inertial Measurement Unit (IMU) sensors embedded in the strut elements. To the best of our knowledge, this work presents the first experimental demonstration of a real-time IMU-based shape estimation method on a full-scale tensegrity manipulator and demonstrates posture control using a simple Proportional-Integral (PI) controller. The results show that the proposed method can estimate the shape of both single-module tensegrity structures and multi-module tensegrity manipulators from arbitrary static configurations and achieve desired postures.

FACSAT-2 Chiribiquete, the second satellite of the Colombian Aerospace Force and the first South American nanosatellite mission dedicated to greenhouse gases, re-entered on 27 October 2025, 926 days after its deployment into a Sun-synchronous orbit, against a declared service life of at least five years and an estimated orbital lifetime of fifteen. The orbital evolution was built from the epochs of the TLEs (two-line elements) of NORAD ID 56205. We reconstruct its decay using its 3696 orbital elements, the solar and geomagnetic indices from the OMNI2 database, and NRLMSISE-00 densities sampled along the orbit. Inverting the drag yields a ballistic coefficient of 72.3 kg/m2 (6% statistical, 20% systematic), equivalent to an effective area of 0.047 m2, consistent with the declared geometry. With it, the model reproduces the trajectory with a root-mean-square error of 7.4 km and, calibrated on 2023-2024 alone, the re-entry with a 28-day out-of-sample error. F10.7 averaged 170.8 sfu over the mission, against the 139 sfu of the environmental scenario derived from the official 2019 forecast, which lengthens the orbital lifetime by x1.52; two co-launched CubeSats give x1.50 and x1.57, a consistency check across objects rather than independent evidence. Imposing quiet geomagnetic conditions returns 102 days, 22% of the shortening, with strong sensitivity to the adopted threshold; a superposed-epoch analysis over 149 storms gives a median drag enhancement of x1.92 for the intense events. We discuss the consequences for the design of FACSAT-3 and for the public communication of a mission's expected lifetime.

Josephson junctions can be employed to reveal a sinusoidal signal in presence of Gaussian noise. To mimic realistic setups, the detection is performed linearly ramping the bias current until a switch to the finite voltage occurs; the analysis of the resulting switching currents can be exploited to decide about the presence of the harmonic drive. The signal is applied in two conditions: with an unknown initial phase (incoherent strategy) and with a known initial phase (coherent strategy). In both conditions, the analysis of the efficiency of the detection, performed through the signal-to-noise ratio, as estimated by the Kumar-Carrol index, shows that the dependence upon the Josephson junction ramp rate is beneficial, especially for relatively fast speed. One can conclude that the collection of the switching currents is a robust technique, and thus it is possible to exploit the advantages of a predetermined finite time to collect the data.

Simulating student personas with large language models (LLMs) enables scalable evaluation of educational systems. However, behavioral drift, a progressive decline in persona consistency, can emerge over extended conversations, limiting the validity of such simulations. We evaluate five prompt-level mechanisms using separate monitoring and intervention pipelines. Across 1,200 28-turn conversations spanning four LLMs and two ADHD persona intensities, we varied when to intervene (static vs. adaptive) and what to inject (reinjection vs. reflective reminder), plus a novel adaptive condition in which a monitor generates behavior-specific instructions. Relative to no intervention, reinjection reduced the modeled rate of LLM-rated drift by 35–38%, reflective reminders by 22–27%, and behavior-specific instruction by 87%. None eliminated drift. We found no evidence that adaptive timing outperformed static scheduling. Monitoring therefore appears more useful for deciding what to correct than when to intervene, although behavior-specific instruction requires component-level testing.

Thermography plays a vital role in military and broader thermal analysis applications. Recent progress in 3D thermal reconstruction has extended temperature analysis from 2D to 3D space, yet most existing works assume static temperature distributions, neglecting the temporal dynamics of heat transfer in real-world environments. To address this limitation, we propose the first dynamic RGB-Thermal reconstruction framework for complex scenes. Our method jointly models RGB appearance, thermal observations, and scene geometry as they change over time. Specifically, we introduce a multimodal dynamic scene representation that anchors both the color and thermal modalities to a shared geometric substrate, ensuring their consistency under spatiotemporal deformations. We further design multimodal embeddings to enhance the motion expressiveness for each modality, and propose a multimodal routing mechanism that retains a unified set of shared multimodal Gaussians as the geometric backbone while adaptively spawning modality-specific Gaussians to strengthen the representational capacity in detail-rich regions of each individual modality. In addition, we contribute a novel benchmark dataset featuring high-frequency temperature variations to facilitate the evaluation of 4D reconstruction. Extensive experiments demonstrate that our method achieves high-fidelity spatiotemporal reconstruction of both appearance and temperature. Our code and dataset are available at: https://github.com/LinLif1869/DTG.

Ear-ECG enables unobtrusive cardiac monitoring, but existing approaches often struggle with low signal amplitudes and limited morphology preservation. We evaluate a finger-to-ear ECG paradigm that combines an in-ear electrode with a rear housing finger-contact electrode in a speaker-equipped earbud. A study with 30 participants investigated four finger-to-ear electrode geometries against chest-reference ECG and additionally assessed robustness under music playback, talking, and walking disturbances. Left-finger configurations achieved R peak detection F1-scores >99% with high agreement of key ECG morphology features. In contrast, right finger configurations as well as walking led to severe signal degradation. The results reveal a trade-off: while cross-body setups provided the highest signal fidelity, users preferred same-side contacts for comfort reasons. This establishes finger-to-ear ECG as a robust, morphology-aware paradigm for opportunistic sensing in earables.

Droplets in complex environments often encounter compositional gradients that drive their propulsion. For example, surfactant gradients induce surface-tension-driven propulsion via the Marangoni effect. Here, we show that such propulsion emerges generically, even in the absence of surfactants. Employing a thin-interface approximation, we derive a compact expression for the droplet velocity in terms of droplet size, viscosity, the sensitivity of surface tension to a regulating component, and the chemical potential gradient of that component. Our theory reveals that droplets move toward regions of lower stability, as encoded in the morphology of the phase diagram, particularly near critical points. Numerical simulations confirm these results, which establish a general route to predicting and designing droplet motility from the phase behavior of complex fluids.

Random forests (RFs) predict well but are opaque, whereas single decision trees are interpretable but unstable. Artificial representative trees (ARTs) were developed as interpretable surrogate models for RFs, but their use as standalone prediction models with uncertainty quantification has not been systematically investigated. We combine ARTs with leaf-wise Mondrian conformal predictive systems (CPS), enabling a single tree to provide continuous predictions, prediction intervals, and probabilities of exceeding arbitrary thresholds. We compared ARTs with CPS against decision trees with CPS and separate regression and probability trees across five simulation scenarios, 21 benchmark datasets, and a cross-sectional NHANES example data set. Repeated cross-validation assessed predictive performance, interpretability, and stability. ARTs with CPS yield compact, structurally stable trees with substantially more reproducible split-variable selection than decision trees across benchmark datasets and NHANES. Decision trees showed slightly better predictive performance and narrower prediction intervals, while coverage was broadly comparable. CPS-based trees generally achieved lower and less variable Brier scores than multi-model approaches. Combining ARTs with CPS therefore provides a single, interpretable, and stable model for continuous predictions and calibrated probabilities, balancing predictive performance with reproducibility and transparency in settings where stability and interpretability are essential.

The ATLAS Collaboration has searched for Higgs-boson decays into a photon and missing transverse momentum using $135~\mathrm{fb}^{-1}$ of Run~3 proton–proton collision data at $\sqrt{s}=13.6~\mathrm{TeV}$. For the benchmark decay $H\to\gamma\gD$ with a massless invisible dark photon, ATLAS reports observed (expected) 95% confidence-level limits of $1.4\%$ ($1.2\%$) on the branching fraction. We reinterpret this search for a massive detector-invisible dark photon with $0\leq m_{\gD}\leq70~\gev$, focusing on Higgs production through gluon–gluon fusion. \audit{The relative signal acceptance, normalized to the massless benchmark, remains nearly unchanged up to $m_{\gD}\simeq40~\gev$, but decreases to $0.888$, $0.736$, and $0.524$ at $50$, $60$, and $70~\gev$, respectively, as the photon-$p_T$ and transverse-mass spectra move toward the analysis thresholds.} Using the published massless gluon–gluon-fusion yield for normalization, we obtain simplified expected (observed) 95% confidence-level limits on $\BR(H\to\gamma\gD)$ from $1.64\%$ ($1.76\%$) at $m_{\gD}=30~\gev$ to $3.50\%$ ($3.75\%$) at $70~\gev$. These results extend the ATLAS interpretation to massive invisible dark photons and quantify the resulting loss of sensitivity at large dark-photon mass.

Physical AI requires models to ground visual and linguistic understanding in real-world environments while accounting for environmental constraints and execution feedback. We introduce MachEmbodied-VLM (ME-VLM), a unified vision-language model with two variants, 4B and 35B-A3B, that brings together embodied cognition and multimodal agent capabilities. Our work emphasizes physical perception and spatiotemporal reasoning, together with planning, interaction, and outcome assessment in both digital and physical environments. We construct training data spanning embodied and multimodal agent tasks, including execution observations and feedback to support outcome assessment and decision refinement. The training pipeline comprises embodied capability injection, separate reinforcement learning of embodied and multimodal-agent experts, and multi-teacher on-policy distillation that consolidates their complementary capabilities into a single model. Experiments show competitive performance on both embodied and agent benchmarks, as well as on autonomous-driving and embodied-navigation tasks. For edge deployment, visual token compression, W4A8 quantization, and hardware-software co-optimization enable on-device inference of the 4B variant on the M100, reducing prefill latency from 400 ms to 188 ms. Project Page: https://machembodied.com/ME-Brain/ME-VLM.html Code Repository: https://github.com/MachEmbodied/ME-VLM

Vision-Language-Action (VLA) models have demonstrated remarkable generalization in robotic manipulation via large-scale multimodal pretraining. However, VLA models are mainly trained on 2D-centric observations, which inherently constrains their capacity for precise spatial manipulation. Previous methods enhance 3D awareness by introducing implicit spatial priors, but still lack explicit geometry guidance. In this paper, we propose Bridge3D that integrates both implicit and explicit 3D geometry guidance into pre-trained 2D VLA models, enabling them to ”see” and ”act” in 3D. Bridge3D introduces two strategies: 1) Implicit Fusion, which enriches visual tokens with features from 3D foundation models to improve ”seeing” in 3D; 2) Explicit Conditioning, which integrates action denoising with an explicit 3D semantic field to achieve ”acting” in 3D. Furthermore, we utilize the proposed layer-wise linear probing to improve learning efficiency. Experiments show that Bridge3D achieves superior performance against state-of-the-art methods. On the RoboTwin 2.0 benchmark, Bridge3D exceeds $\pi_0$ by 14.0 percentage points, while in real-world experiments, it outperforms Spatial Forcing by 11.7 percentage points. These results demonstrate Bridge3D's strong capabilities in high-precision and spatial-sensitive manipulation tasks.

Background: Microvascular invasion (MVI) predicts recurrence and survival in hepatocellular carcinoma (HCC) but requires postoperative histopathology for diagnosis. We developed and validated a model integrating multimodal ultrasound and clinical data for preoperative MVI prediction. Methods: This multicenter study included 489 patients with HCC from eight centers. All patients had B-mode ultrasound (BUS), color Doppler flow imaging (CDFI), dynamic contrast-enhanced ultrasound (DCE-US), and clinical information. Data from seven centers (n = 421) were used for model development with five-fold cross-validation; data from the remaining center (n = 68) formed an independent external validation cohort. The proposed multimodal information fusion network used modality-specific encoders, a hemodynamic temporal change module for bidirectional DCE-US perfusion changes, and a representation consistency learning module to align heterogeneous ultrasound representations before Transformer-based fusion. Results: In external validation, DCE-US achieved the highest single-modality area under the receiver operating characteristic curve (AUC; 0.8545+/-0.0198), versus clinical information (0.6715+/-0.0156), CDFI (0.6435+/-0.0344), and BUS (0.6087+/-0.0417). Pixel-difference sampling and the proposed temporal module outperformed alternative sampling and video representation methods. The full model achieved the best performance, with an AUC of 0.8953+/-0.0180, accuracy of 81.18%+/-2.83%, sensitivity of 86.40%+/-6.69%, and specificity of 78.14%+/-6.28. Conclusions: Integrating multimodal ultrasound and clinical information enabled promising preoperative MVI prediction in HCC. DCE-US was the main source of predictive information, while BUS, CDFI, and clinical information provided complementary value. The proposed framework may support preoperative risk stratification and individualized clinical decision-making.

This paper studies commutators in finite-dimensional unimodular Hopf algebras and invariants derived from them. For a unimodular Hopf algebra $H$ with the distinguished group-like element $g$, the commutator of $a,b\in H$ is defined by $\{a,b\}=a_{1}S^{2}(b_{1})S(a_{2})S^{-1}(b_{2})g^{-1}$. We show that the span of all commutators is a left coideal and generates a normal left coideal subalgebra $N$ of $H$ for which $H/HN^{+}$ is commutative. The main result asserts that for any central element $a$ and any integral $\Lambda$ of $H$, the commutator $\{a,\Lambda\}$ and the value $\lambda(\{a,\Lambda\})$ for a right integral $\lambda$ of $H^*$ are invariant under twisting. This yields several gauge invariants, including ratios of characters of iterated commutators with $\Lambda$. In the semisimple characteristic-zero case, explicit descriptions of these invariants are given. As applications, we compute some invariants for the group algebra of a finite group, its Drinfeld double, and the restricted quantum group $\overline{U}_{q}(sl_{2})$.

In this work, we develop a unified theoretical framework for analyzing the convergence of rotation-based matrix optimizers, which apply orthogonal transformations to map the momentum into a rotated space, perform coordinate-wise or normalized updates there, and then rotate the updates back. Our framework encompasses prominent matrix optimizers, including SOAP, Conda, and truncated SPlus, as well as matrix-parameterized Adam as a special case. As our main result, we establish, for the first time, the convergence rate of SOAP with sharp dimensional dependence, as well as the convergence rate of Adam measured by the nuclear norm. Our framework also covers a more general variant of rotation-based optimizers that allows arbitrary orthogonal rotation matrices, allowing these matrices to depend on the current stochastic gradient at each iteration. Technically, our framework leverages a row-column trace-control argument that converts elementwise bounds into bounds on two diagonal control matrices, thereby improving the dimension dependence of the resulting bound.

We investigate the classical double copy of the rotating black-hole geometry induced on the brane in the Randall-Sundrum II scenario. The influence of the five-dimensional bulk is encoded in the effective four-dimensional geometry through a tidal charge, while the metric admits a Kerr-Schild representation over a flat background. We construct the corresponding single and zeroth copies and find that their regular sources are entirely proportional to the tidal charge, whereas the mass-dependent contribution is source-free in the regular region. Comparison with Kerr-Newman reveals a formal correspondence between the tidal charge and the squared electromagnetic charge at the level of the induced geometry and its double copies, despite their different physical origins and the fact that the tidal charge may take either sign. When an electromagnetic field is included on the brane, both contributions enter the low-energy Kerr-Schild geometry and its double copies only through the combination $Q^2+\beta$. These results illustrate how physically distinct brane and bulk contributions can become indistinguishable in the classical double copy of an effective geometry.

In this paper we provide a purely metric and derivative-free characterization of continuous mappings in the local supercritical Sobolev space. More specifically, we show that a continuous mapping $f\colon\mathbb{R}^n\to\mathbb{R}^m$ lies in the local Sobolev space $W^{1,p}_\text{loc}(\mathbb{R}^n\colon\mathbb{R}^m)$ if and only if $f$ is a $(p,1-n/p)$-compactly Hölder mapping, where $p>n$. In fact, we prove the following more general result: whenever $X$ is a complete $Q$-Ahlfors regular metric space supporting a $p$-Poincaré inequality with $p>Q$, and $V$ is any Banach space, the compactly Hölder class $CH^{p,1-Q/p}(X\colon V)$ consists precisely of the continuous representatives of the local Hajłasz and Newtonian Sobolev spaces $M^{1,p}_\text{loc} (X \colon V)$ and $N^{1,p}_\text{loc}(X\colon V)$. We also establish quantitative comparisons between the corresponding seminorms.

Emulation of high-accuracy floating-point matrix multiplication, as in the Ozaki scheme, splits the inputs into low-precision components and multiplies them pairwise. These products must be error-free, and each is an integer matrix product times a scale factor. FP4 Tensor Cores are the fastest on the NVIDIA B200 and B300 but cannot hold INT8 operands. The FP4 values scaled by 2 form the set $S = \{0, \pm1, \pm2, \pm3, \pm4, \pm6, \pm8, \pm12\}$, which contains every residue modulo 13, so with carries any integer splits into base-13 digits that FP4 can store. Prior work splits each INT8 operand into 3 such digits (limbs) with weights $(1, 13, 169)$ and multiplies them pairwise, 9 FP4 matrix multiplications (GEMMs) for INT8$\times$INT8. The classical ways to reduce products, such as the Karatsuba and Toom–Cook methods, do not apply as they stand: sums of limbs reach $\pm 24$ and leave $S$. This paper asks how many FP4 GEMMs are needed for one integer matrix product. We propose Adaptive Weight Encoding (AWE): the limbs take freely chosen integer weights, the stored planes are linear combinations of limbs, and the exact product is the sum of the FP4 GEMMs scaled by reconstruction coefficients. For each input range, we searched these choices for encodings with fewer products and found INT8$\times$INT8 in 6 products and INT4$\times$INT8 in 4. The formulation also holds modulo $m$, which covers the residue number systems of Ozaki scheme II: for the FP64 significand, the 75 products of prior work are reduced to 59. The boundary in product count between encodings with and without residues lies near input width 15. We release the encodings found.

We show that for $n \geq 6$ each element of the commutator subgroup in the symmetric group $\mathfrak{S}_n$ resp. in the signed symmetric group $(\mathbb{Z}/2\mathbb{Z})^n\rtimes\mathfrak{S}_n$ is the commutator of two $n$-cycles resp. the commutator of two $n$-cycles with a negative sign product; with one exception. If $n \equiv 2$ $\mathrm{mod}~4$, the element $-\mathrm{id}$ of $(\mathbb{Z}/2\mathbb{Z})^n\rtimes\mathfrak{S}_n$ is not such a commutator. In the language of Coxeter groups, this yields a description of commutators of Coxeter elements in types $A$ and $B$.

Model merging aims to combine multiple fine-tuned models derived from a common pretrained model into a single multi-task model without additional joint training. Recent spectral merging methods improve over simple weight averaging by exploiting low-rank structures of task-specific updates, but they commonly assign the same rank capacity to every task. This uniform allocation ignores that task vectors can have heterogeneous spectral complexity, causing the shared merging space to be used suboptimally. In this paper, we propose Spectral Energy-proportional Rank Allocation (SERA), a simple task-adaptive strategy that allocates ranks according to the singular-value energy structure of each task vector. By assigning richer spectral capacity to complex or isolated tasks and fewer directions to compact tasks, SERA extends SVD-based model merging from uniform-capacity merging to task-dependent capacity allocation. Experiments under standard vision model merging protocols show that SERA improves multi-task merging performance while preserving the same total rank budget as existing spectral merging methods. Further analysis demonstrates that task-level spectral concentration is closely related to the per-task effect of adaptive rank allocation, providing insight into when and why SERA is effective.

In recent years, large language models (LLMs) have emerged as a popular alternative for evaluation. Often referred to as LLMs as judges (LLJs), these systems have been widely adopted by researchers and practitioners across a broad range of measurement tasks, driven by their strong performance, scalability, and cost-effectiveness relative to human judgment. However, a growing body of work has shown that the use of LLJs raise concerns about their validity and reliability as evaluators. Existing efforts to address these challenges have largely focused on developing bias-mitigation techniques and refining prompting strategies. While these approaches represent an important step forward, they primarily offer technical fixes and leave a more fundamental challenge unaddressed: the lack of standardized, transparent, and reproducible evaluation practices. In this paper, we introduce LLJ Cards, a framework that synthesizes best practices from measurement theory, natural language generation, and machine learning literature into practical guidelines for LLJ-based evaluations. While LLJs offer a promising path toward scalable evaluation, their effective use requires grounding in rigorous evaluation principles to ensure validity, reliability, and reproducibility. LLJ Cards addresses this need by providing a structured framework for applying these principles in the design and reporting of automated evaluations.

AI agents are being deployed rapidly, accompanied by a growing number of AI-specific attacks and corresponding incidents. As incident reporting becomes increasingly important for legal compliance, governance, accountability, and security; current frameworks must be adapted to the unique characteristics of AI agents. In this paper, two editorial authors compare AI systems and AI agents and, drawing on input from 23 experts in academia and industry, identify the information required for reporting incidents where the security of AI agents is harmed. %involving AI agents. Potential reporting elements include, for example, agent memory and memory accesses, actual and potential levels of autonomy, and tool usage. Based on these findings, we identify several open research questions, including how to efficiently record incidents and how to determine whether vulnerabilities and incidents generalize. Expert feedback also highlighted potential reporting weaknesses, such as risks of data leakage and attacks targeting the reporting infrastructure itself, creating additional research needs. Lastly, we summarize privacy requirements and outline research directions for the secure and trustworthy deployment of AI agents.

For an additively idempotent semiring (ai-semiring) $S$, let $S^0$ denote the ai-semiring obtained from $S$ by adjoining a new element $0$. In this paper, we develop an approach to investigate the interval $[\mathsf{V}(S), \mathsf{V}(S^0)]$ of ai-semiring varieties between the variety generated by $S$ and that generated by $S^0$. We establish a general sufficient condition under which this interval has the cardinality of the continuum. This is applied in particular to $[\mathsf{V}(S_7), \mathsf{V}(S_7^0)]$, where $S_7$ is a $3$-element ai-semiring and is a nonfinitely based algebra of the smallest possible order, thereby resolving an open problem proposed by Jackson, Ren, and Zhao (J. Algebra 611 (2022), 211–245). The same conclusion holds for $[\mathsf{V}(B_2^1), \mathsf{V}((B_2^1)^0)]$, where $B_2^1$ is the ai-semiring whose multiplicative reduct is the $6$-element Brandt semigroup. We also present a sufficient condition for the nonfinite basis property in ai-semiring varieties. As a corollary, we obtain a new proof of Dolinka's theorem (Internat. J. Algebra Comput. 17 (2007), no.~8, 1537–1551) that the $7$-element ai-semiring $(B_2^1)^0$ has no finite basis for its identities.