Papers

Mixed-signal SoCs rely on nominally input-only analog pins to acquire off-chip signals, but the directionality of these interfaces is generally treated as a functional property rather than explicitly verified as a security property. This work identifies and experimentally demonstrates a directionality-based class of analog and mixed-signal (AMS) exfiltration attacks in which data-dependent circuit-offset modulation converts a nominally input-only pin into an outbound information channel. We analytically model the attack mechanism and identify three enabling host conditions: a closed-loop amplifier, an exposed amplifier input, and sufficiently high impedance at that pin. This attack class is validated through a representative silicon case study using a photoplethysmography (PPG) analog front-end (AFE) fabricated in a commercial 55-nm CMOS process. The payload incurs $<$0.001% area overhead relative to typical biosensing AFEs. Under the evaluated conditions, payload activation reduces the filtered PPG-output SNR by only 0.03~dB, while the maximum HT-induced perturbation of 5.9% of the PPG amplitude remains within the 34.3% benign variation at the exposed sensor-input pin across process and temperature. The raw exfiltration SINR remains below -20~dB, while targeted filtering increases it above 14~dB and enables signal recovery. Silicon measurements demonstrate data exfiltration through the input pin at bit rates up to 10~kbps and error-free recovery of a PRBS message. These results expose a conventional test-observability gap and establish analog pin directionality as an AMS security property requiring explicit verification, test coverage, and defense rather than being inferred from nominal signal flow.

We establish an upper bound for the symmetry rank of closed, simply connected, almost non-negatively curved manifolds of dimension 4 through 9 and in the case of maximal symmetry rank provide an equivariant diffeomorphism classification of this class of manifolds in dimensions 4, 5, and 6.

Randomized trials with limited concurrent control information—including but not limited to unequal-randomization settings—can offer ethical and practical advantages, especially in pediatric and rare diseases, but they often lose power because fewer control patients are available for direct comparison. Borrowing information from external controls may improve efficiency, but can also inflate the Type I error rate when the external and trial populations are not sufficiently comparable. We propose RECaST-Surv, a Bayesian transfer-learning framework for time-to-event outcomes that extends the RECaST method to survival settings. The method learns a structural survival model from external control data and calibrates it to the concurrent control arm of the current trial through a Cauchy random effect. To improve frequentist operating characteristics, we further develop a bootstrap-based procedure to calibrate the testing rule for Type I error control. RECaST-Surv can accommodate multiple external datasets and requires only summary-level information from external sources. Simulation studies show that the method maintains near-nominal Type I error across challenging settings while improving power by roughly 10%–12% over standard analyses. In an Amyotrophic Lateral Sclerosis trial emulation, RECaST-Surv increased power from 82.8% to 95.7% relative to the no-borrowing RCT analysis, while maintaining acceptable error control.

Large scale magnetic fields play a crucial role in shaping the dynamics and structure of the inner parts of accretion disks and the resulting jets from the vicinity of black holes and neutron stars. Currently, the primary mechanism considered for generating and amplifying large scale magnetic fields in accretion disks is the magneto-rotational instability (MRI). Here we show that non-conservative radiation fields provide a rapid and independent mechanism for generating and amplifying magnetic fields in accretion flows. A luminous, compact corona generates a radiation-driven poloidal field that is subsequently amplified by differential rotation, yielding quadratic magnetic-field growth and, over a broad range of coronal luminosities and sizes and MRI amplification locations, magnetization on timescales comparable to or shorter than those of the MRI. The mechanism therefore provides not merely an alternative to MRI, but an additional and, over a substantial region of parameter space, dominant channel for magnetic-field generation from initial conditions with zero magnetic field. Since the radiation-driven source arises directly from the non-conservative nature of the radiation field, such magnetic-field generation is an inevitable consequence of sufficiently strong and anisotropic radiation sources in black-hole accretion flows. More generally, the mechanism requires only a non-conservative radiation field and differential plasma motion, and is therefore expected to operate in a broad range of luminous astrophysical systems, including active galactic nuclei, gamma-ray bursts, and tidal disruption events.

Scaling laws predict how loss decreases with increases in computation. We show, contrary to conventional wisdom, that architectural interventions can modify scaling exponents in pre-training, leading to power-law improvements in performance as computation increases. As an anchoring point, we consider the architectural formulation of looped transformers. Although not typically used in this way, looping, also known as recursive depth, provides a mechanism for model growth, by increasing the number of loops during training. Model growth, with and without shared weights, provides the biggest changes to the scaling exponents. In particular, a 7.4B model growth architecture matches GPT-3 13B on CORE with roughly $20\times$ less compute, and has compute efficiency gains that increase with scale. Moreover, simply using a boundary operator in a vanilla transformer, which normalizes and injects an earlier block, also provides an exponent increase, although to a lesser extent. In the data-constrained, multi-epoch setting, standard looping has a useful regularizing effect, where we find it is compute-optimal to increase the number of loops with scale. These results can be understood through the lens of computational depth: for a given computational budget, we wish to increase the usable depth of the transformer, which can lead to efficiency gains that increase with scale.

This paper addresses leader-follower formation control using only relative bearing and velocity measurements. Bearing-based leader-follower control strategies commonly use fixed control gains, for which the guaranteed convergence rates explicitly depend on the persistence of excitation (PE) properties of the desired formations. We propose a time-varying matrix gain that evolves according to the bearing information available to each follower and decouples the convergence rate from the PE bound. We establish the well-posedness and uniform boundedness of the proposed gain for bearing-persistently exciting formations, and characterize the exponential convergence rate through a tunable design parameter. The proposed control design is further extended to leader-follower formations with double-integrator dynamics. Simulations illustrate the resulting convergence properties compared with fixed gain designs.

The Chinese Space-station Survey Telescope (CSST) is a flagship mission designed to carry out a large-area high-resolution multiband imaging and slitless spectroscopic survey over a decade. The survey's science drivers, ranging from precision cosmology to stellar astrophysics, impose stringent requirements on the performance of its focal plane detectors. This paper is the first in a series that present ground-based characterization of the 31 flight-model charge-coupled devices (CCDs) of the CSST Survey Camera. Measurements of basic electro-optical performance are reported here. Key results include: full-well capacity $\geq 80\ \mathrm{ke}^{-}$ (limited by the test electronics), non-linearity $<1.4\%$ in the range of $7-70\ \mathrm{ke}^{-}$, median readout noise $3.6\ \mathrm{e}^{-}$, dark current $\leq 0.02\ \mathrm{e}^{-}\mathrm{pix}^{-1}\mathrm{s}^{-1}$ at the operating temperature of $-85\,^{\circ}\mathrm{C}$, high quantum efficiency across the survey's spectral range (255-1000 nm), typical pixel response non-uniformity $<1\%$, and charge transfer efficiency $>99.9994\%$ at the flat-field level of $10\ \mathrm{ke}^{-}$. All 31 CCDs meet or exceed the Survey Camera's specifications. These measurements establish a performance baseline and provide inputs for CSST image simulation and data processing pipelines

Factory work is a promising early scenario for embodied AI: assigning repetitive manual jobs to robots has clear economic payoff, and a structured station keeps the jobs tractable for current policies. Vision-Language-Action (VLA) models now dominate as the policy paradigm for these robots. The inference latency of VLA models directly affects robot responsiveness and motion smoothness. However, existing VLA inference frameworks do not fully exploit the characteristics of embodied workloads or account for the distinct bottlenecks across different stages of VLA inference. In this paper, we first characterize embodied workloads and identify substantial task similarity across repeated robot executions. We further find that such similarity extends beyond observations and action trajectories to internal model states. Drawing on these observations, we present rMuscle, a real-time VLA inference framework inspired by human muscle memory. It exploits cross-execution similarity through a dual-phase muscle-memory cache. The Context Cache reuses visual-token outputs to reduce computation, while the Action Cache reuses neuron activation patterns to reduce weight accesses. We keep both the cache memory footprint and access overhead low through online cache recomputation, sliding-window cache retrieval, and mask sharing across consecutive denoising steps. rMuscle achieves 1.29-1.42X speedup on RTX 4090 and Jetson Thor across LIBERO, RoboTwin, and physical manipulation tasks, while maintaining the original success rates on real-world robots.

Correlation geometry and topology in a random, scalar beam carrying Orbital Angular Momentum (OAM) in $L$ modes are shown to be linked to the real and imaginary parts, respectively, of its orbitalization matrix (OM). The OM is obtained by filtering the cross-spectral density in the polar Fourier basis at a given cross-section and radius for each pair of OAM indices. The symmetric real part of the OM has the diagonal canonical form, specifying the ellipsoid-like correlation geometry of the beam. The skew-symmetric imaginary part of the OM has the Darboux canonical form, enabling decomposition into $N\leq L/2$ mutually orthogonal circulation states and $L-2N$ trivial circulation-free states, mutually orthogonal and $L-2N$ trivial circulation states thereby defining the $N$-dimensional orbitalization torus associated with the correlation topology of the beam. The canonical forms are then used to define the degrees of linear and circular orbital anisotropy and stability, and the degrees of linear and circular orbitalization, in analogy with corresponding quantities in 2D and 3D polarization theory. These results demonstrate the emergence of fundamentally new correlation structures in random multimode OAM-carrying light, not accessible in lower-dimensional systems and absent in the deterministic limit.

Variance swaps are a convenient instrument for trading vega and convexity, and a listed contract now trades on Cboe. We ask when a trader should put such a position on and when she should take it off, and for a perpetual, continuously settled contract we answer both in closed form: each threshold is the unique root of a smooth-pasting equation in confluent hypergeometric functions. Under the pricing measure the question has no content, the mark-to-market being a martingale. Under the physical measure with a variance risk premium it becomes meaningful, and then reduces: the accrued variance separates exactly, the maturity, strike and costs are absorbed into a single forcing term whose sign fixes the geometry of the exercise region, and what is left on the perpetual is an affine reward on a CIR process, which the optimal-stopping literature already solves. Entering the position and exiting it are not mirror images. An exit rule follows from the premium and the trading spread, both observable. For the short — the only side worth opening under the empirical sign of the premium — an entry rule exists only for an interval of carrying charges, and even there triggers only deep in the upper tail of the physical law: a trader who is out of the market pays nothing to stay out, so an operational entry rule needs a cost of idle capital that the exit rule does not.

As models scale, reward hacking becomes more frequent, more sophisticated, and more consequential. Does it leave a telltale signature in model representations? This work analyzes how reward hacking is represented internally in frontier open source LLMs, and how those representations can be used to understand and discover the range of hacking behaviors a model displays. In particular, we find that simple difference of means vectors coherently represent reward hacking in Kimi K3, GLM 5.2, and Qwen 3.8 Max across a variety of behaviors in common evaluations. Despite their simplicity, these vectors are both generalizable and interpretable, and we can use them to reliably detect reward hacking. We first evaluate reward hacking in commonly reported benchmarks like DeepSWE and SWE-bench, finding that models reward hack excessively in these environments; GLM 5.2 hacks in 57.2% of rollouts on DeepSWE and in 73% of rollouts on SWE-bench. Catching these requires monitors; LLM monitors are effective, but expensive detectors. We show that DoM vectors are similarly effective but virtually free, catching 3.1% more hacks in Kimi K3 and 7.9% fewer hacks in GLM 5.2 on DeepSWE at a monitor matched false positive rate. DoM vectors run on the chain-of-thought also predict reward hacks in the model's subsequent actions, meaning we can run them online and catch potential hacks before they occur. Finally, we analyze probe-hits that LLM monitors do not catch and discover other undesirable behaviors, as well as show transfer to finding hacks in non-SWE evaluations. Together, these results provide evidence that simple, white-box methods can be used to scalably study and monitor reward hacking behaviors in frontier open source models

The Model Context Protocol (MCP) has emerged as the dominant interface for connecting autonomous agents to external data sources and execution environments. The ecosystem's transition from local process execution to remote Streamable HTTP deployments introduces unmeasured architectural and security constraints at scale. This paper presents a three-tier observability framework comprising catalog metadata (O_0), passive compliance signals (O_1), and live vulnerability analysis (O_2), applied to empirically characterize the public MCP server ecosystem. Evaluation of a stratified sample of 179 remote endpoints across two primary public registries reveals significant infrastructural consolidation. The Herfindahl-Hirschman Index (HHI) computed over the Autonomous System Number (ASN) distribution yields a value of 0.736, well above the 0.25 threshold for a highly concentrated market. Analysis further indicates that server authentication is strongly correlated with hosting platform choice rather than individual operator configuration, with 95% of commercial PaaS-hosted servers enforcing gateway-level OAuth 2.1 with PKCE. The empirical results identify a Security-Observability Tradeoff observed in the current ecosystem: the platform-level authentication mechanisms that secure the majority of servers simultaneously limit automated vulnerability scanning capabilities, constraining the ability of AI gateway operators to assess tool-poisoning vectors without prior credential provisioning.

Self-emulsifying drug delivery systems (SEDDS) can improve the oral bioavailability of poorly soluble drugs, but identifying high-performing formulations remains experimentally intensive. We present Andromeda 2, an agentic system that reasons over structured in-house experimental evidence and invokes computational and experimental tools to design and execute successive formulation batches. Using a miniaturized automated laboratory at a matched budget, we benchmark it against Andromeda 1, a probabilistic optimization model deployed across dozens of live development projects, and a wet-lab design-of-experiments (DoE) campaign. For paclitaxel, Andromeda 2 achieved a 50% high-performance hit rate versus 17% for Andromeda 1 and 2% for DoE, and identified 12 formulations meeting all four target product profile (TPP) objectives versus 6 and 0, respectively. Median $AUC_{10-240}$ was 70.1, 12.0, and 3.5 mg$\cdot$min/mL, while maximum AUC was comparable between Andromeda 2 and Andromeda 1. A selected full-TPP formulation achieved an apparent effective paclitaxel loading of $19 \pm 5\%$ w/w at the first FaSSIF measurement, approximately 3.3-fold higher than the 5.7% w/w loading reported for a published paclitaxel S-SEDDS. A controlled ablation showed that access to structured in-house experimental evidence increased mean AUC by 34%.

The generalized packing–covering conjecture asks whether, at every order, the packing radius of a linear code is at most its covering radius. We prove the conjecture for every linear code of redundancy at most fourteen over every finite field, extending the previously established range of redundancies at most seven. We also prove the bound on generalized Hamming weights $d_t(C)\le2R_t(C)+1$ whenever the alphabet size $q$ satisfies $q\ge R_t(C)$. Both results use an auxiliary-code criterion that converts a covering property in the syndrome space into a weight bound. For binary primitive BCH codes, the packing radius is strictly smaller than the covering radius for every fixed error parameter and order, both at least two, once the extension degree is sufficiently large; this follows from existing covering bounds.

We consider solving (convex) conic linear optimization problems, at the scale where matrix-factorization-free methods are attractive or necessary. The restarted primal-dual hybrid gradient method (rPDHG) – with heuristic enhancements and GPU implementation – has been very successful in solving huge-scale linear optimization problems (LPs). However, its application to more general conic convex optimization problems is not so well-studied. We analyze the theoretical performance of rPDHG for general (convex) conic linear optimization, and LP as a special case thereof. We show a relationship between the geometry of the primal-dual $\delta$-(sub-)level sets ${W}_\delta$ and the convergence rate of rPDHG. Specifically, we prove a bound on the convergence rate of rPDHG that improves when there is a primal-dual (sub-)level set ${W}_\delta$ for which (i) ${W}_\delta$ is close to the optimal solution set in Hausdorff distance, and (ii) the ratio of the diameter to the “conic radius” of ${W}_\delta$ is small. And in the special case of LP, the performance of rPDHG is bounded only by this ratio applied to the (sub-)level set corresponding to the best non-optimal extreme point. Depending on the problem instance, this ratio can take on extreme values and can result in excellent or poor performance of rPDHG both in theory and in practice.

Artificial intelligence (AI) is increasingly integrated into healthcare systems worldwide, yet its successful clinical adoption depends critically on workforce readiness, particularly in low- and middle-income countries (LMICs) where infrastructural and training gaps persist. This cross-sectional study evaluated awareness, attitudes, preparedness, and barriers to AI adoption among 761 healthcare professionals across multiple disciplines and practice settings in Nigeria. Data were collected between December 2025 and March 2026 using a structured, validated questionnaire. Overall awareness of AI in healthcare was high (92.6%); however, objective knowledge and self-reported preparedness remained limited, with 40.9% reporting low or very low knowledge and only 63.0% feeling adequately prepared. Willingness to adopt AI was high: 92.5% expressed interest in training, and 78.7% supported inclusion of AI education in undergraduate curricula. Key barriers included lack of training (84.7%), poor infrastructure (71.1%), high cost of AI tools (61.0%), fear of job displacement (60.6%), ethical concerns (52.9%), and data privacy concerns (52.7%). Significant differences in preparedness were observed across geopolitical zones (chi-square (5) = 24.28, p < 0.001), and awareness differed across professional groups (chi-square (6) = 68.38, p < 0.001). Attitudes toward AI differed significantly across professional groups (F = 3.32, p = 0.003), with professionals who felt prepared demonstrating more positive attitudes (mean = 3.74) compared to those who did not (mean = 3.46). These findings reveal a critical disconnect between high awareness and actual readiness, underscoring the need for targeted training, infrastructure investment, and clear implementation frameworks to bridge the gap between AI technological potential and clinical reality in resource-constrained settings.

Let $q$ be a prime power and $\mathbb{F}_{q^2}$ be the finite fields of $q^2$ elements. The Hermitian function field $H=\mathbb{F}_{q^2}(x,y)$ defined by $y^q+y=x^{q+1}$ is a well-known maximal function field with the largest possible genus. Let $A(P_\infty)$ be the decomposition group of the infinity place $P_\infty$ of $H$ which is the common pole of $x$ and $y$. For every subgroup $G\le A(P_\infty)$, we construct explicit generators of Galois subfield $H^G$ of $H$ with respect to $G$ and determine an absolutely irreducible equation defining the smooth affine plane model for such a Galois subfield. For $p$-subgroups, the generators can be chosen so that the defining equation has an additive polynomial on the left-hand side and an $\mathbb{F}_p$-quadratic polynomial on the right-hand side. For $q=27$, we can construct a genus-two subfield $D\subset H$ that is not isomorphic to $H^J$ for any subgroup $J\le \text{Aut}(H)$ from the explicit equations of Galois subfields of the Hermitian function field. To the best of our knowledge, this is the first example of a maximal function field covered but not Galois-covered by the same Hermitian function field.

We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the $G$-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic $G$-BSDE for the logarithmic price. Under suitable assumptions, we establish existence, uniqueness, comparison, and stability for bounded finite-horizon solutions. An additional strict monotonicity condition yields a unique bounded infinite-horizon solution and exponential convergence of finite-horizon approximations on compact time intervals. We apply these results to inverse short-rate design, constructing discount-rate coefficients that reproduce admissible smooth bond-price targets at a fixed maturity. For long maturities, we construct feedback rules under which the compensated logarithmic price converges exponentially to a prescribed bounded state-dependent profile, while the asymptotic yield equals a specified target.

Radiologists follow heterogeneous reporting practices. Two radiologists examining the same image and identifying the same clinical findings might nevertheless compose superficially distinct reports, varying in terminology, shorthand, formatting, and level of detail. These variations in reporting norms represent an under-appreciated obstacle in efforts to evaluate AI-based radiology report generation (RRG) models, where machine-generated reports are typically assessed based on their concordance with human-generated references. In this paper, we quantify the sensitivity of established evaluation metrics to variations in reporting practices, revealing impacts large enough to alter the rankings of models. We introduce a radiologist-informed taxonomy of variations in radiology reporting practice and a method (ReRef) that rewrites reference reports along the axes of our taxonomy while preserving clinical interpretation. For instance, when comparing the performance of nine RRG models on MIMIC-CXR using RadCliQ-v1, condensing the discussion of normal findings in the reference reports causes Libra to drop from first to second place while CheXOne rises from third to first. Our results suggest that many current metrics fail to decouple clinical interpretation from conformity to reporting practices and that choosing the “right” references that accurately reflect the desired reporting practices can be important in practice. To support future research, we release MIMIC-CXR-Ext-ReRef, a radiologist-validated dataset of 120 (original, alternative) reference report pairs derived from MIMIC-CXR.

Distributed quantum sensing is an emerging application of quantum networking, where entangled probe states are employed to sense combinations of delocalized parameters with enhanced precision relative to using separable states. Squeezed states of light are a prime resource for experimental demonstrations of entanglement-enhanced sensing, because they can be generated and entangled deterministically. Existing distributed quantum sensing experiments have been fundamentally limited in scalability due to their bulk-optic architectures. Meanwhile, integrated photonics provides a scalable and compact platform for quantum sensors. Here we demonstrate entanglement-enhanced sensing of linear functions of four phase shifts in an integrated photonic circuit. We find an entanglement-enhanced precision of 0.199(16) dB below the shot noise limit compared to 0.041(18) dB for separable states. A four-mode entangled state is generated on-chip with entanglement verification and phase sensing also performed on-chip with an array of four integrated homodyne detectors.

The Model Context Protocol (MCP) standardizes communication between autonomous Artificial Intelligence (AI) agents and remote tools over Streamable HTTP. This shift introduces a class of machine-generated, authenticated, and high-frequency JSON-RPC traffic directly into enterprise networks. Enterprise network defenders have historically relied on machine-like cadence as an Indicator of Compromise (IoC). In this study, we show that without explicit network-layer indication, MCP traffic structurally and temporally resembles Command and Control (C2) beaconing behavior, specifically the polling architectures used by advanced persistent threats like Cobalt Strike. Counter to theoretical assumptions about machine-generated polling, our measurements reveal a visibility gap: standard enterprise Intrusion Detection Systems (IDS) and behavioral beacon-scoring frameworks do not classify MCP remote tool usage as anomalous within our testbed scope. Through a controlled Docker-based testbed simulating eleven mathematically defined traffic profiles across three TLS conditions (Opaque, TLS-Inspected, and Cleartext), we evaluate Suricata signature matching and RITA behavioral scoring against MCP JSON-RPC patterns. Our results show that MCP traffic, regardless of temporal smearing (jitter) or TLS inspection visibility, evades detection within this configuration, yielding a consistent 0.0 behavioral beacon score and near-zero IDS content alerts under the Emerging Threats (ET) Open ruleset. While opaque TLS obscures HTTP content, it exposes agent traffic to flow-level temporal analysis; however, NIDS heuristics tuned to identify traditional malware do not flag the lognormal inter-arrival distributions characteristic of generative AI reasoning loops. To address this gap, we propose an agent-native network indication standard including Agent-Native ALPN and standardized out-of-band headers.

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent $X$ rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

We study the space complexity of diameter estimation for a set of points in Euclidean space in the dynamic (turnstile) streaming model. The seminal work of Indyk (SODA 2003) gives a $c$-approximation to the Euclidean diameter of $n$ vectors using $n^{O(1/c^2)}$ space. Our main contribution is giving an essentially matching lower bound. Any dynamic streaming algorithm which can $c$-approximate the diameter of $n$ Euclidean vectors must use $n^{\tilde{\Omega}(1/c^2)}$ space.

Large vision-language models have achieved remarkable progress in multi-modal understanding, yet their capabilities in educational settings remain insufficiently evaluated. In AI-assisted language learning, models must interpret artistic imagery, understand its semantic, affective, and cultural content, and reason about visual context to support meaningful interaction. However, existing benchmarks primarily focus on real-world images or domain-specific educational reasoning, providing limited coverage of artistic educational content. To address this gap, we introduce MUSE, a benchmark for evaluating large vision-language models on artistic image understanding in situated educational applications. MUSE decouples image annotation from question generation, enabling diverse tasks with controllable difficulty while reducing annotation effort. It comprises twelve tasks spanning visual perception, semantic and affective interpretation, culture understanding, and compositional reasoning, together with diverse artistic images deliberately curated to center Singaporean and Southeast Asian multicultural contexts alongside Western art traditions, covering multiple themes and difficulty levels. Evaluation of open-source and proprietary models reveals substantial disparities across capability dimensions, particularly in affective interpretation and compositional reasoning. Our analysis further identifies common failure modes and key challenges for developing trustworthy multi-modal models for education. We hope MUSE will serve as a standardized benchmark for advancing multi-modal understanding in situated educational applications.

A long-standing goal across heterogeneous catalysis, materials science, and condensed matter physics is to design alloys with prescribed local atomic arrangements. Recent experiments show that dilute trimetallic alloys unlock chemistries inaccessible to bimetallics, but realizing this potential requires knowing which dopant structures form across an enormous compositional space. Using density functional theory screening, we construct an atlas spanning transition metal single- and dual-atom alloys in Cu and Ag surfaces, which we validate by scanning tunneling microscopy. The stability follows an electron count: dopants pair most strongly when their combined d-electron count approaches ten. Host metal and surface facet can be used to tune the resulting active site motifs, while size mismatch and spin explain variations around this trend. We further introduce a reactor-anchor concept, in which one dopant anchors a second, otherwise bulk-segregating dopant at the surface. Together, these results establish design principles for engineering alloys with targeted active site structures.

Given a finite dimensional Lie algebra $L$ on a finite field $\mathbb{F}_{p^n}$ of prime power order $p^n$ (with $n$ positive integer and $p$ prime), we consider the number of modular pairs $(A,B)$ in the lattice of all subalgebras $\mathcal{L}(L)$ and introduce the notion of “subalgebra commutativity degree” of $L$. This represents the probability to find that two randomly chosen subalgebras $A$ and $B$ of $L$ are permutable. We investigate the subalgebra commutativity degree of $L$ in connection with recent techniques of algebraic combinatorics and number theory, providing upper and lower bounds which may influence the structure of $L$. A specific study for the subalgebra commutativity degree of Heisenberg algebras is executed.

We study the $\theta$-congruent number problem for $\cos\theta=\pm3/5$ and $\pm4/5$ using the generalized theta series construction of Sirolli–Tornaría. We describe its specialization to newforms of weight $2$ over $\mathbb Q$ with nontrivial square-free odd part of the level, and explain the reduction of quadratic twists to odd fundamental discriminants. The same construction gives an effective procedure for every $\theta$-congruent number problem with nonzero rational cosine. For the four angles, we construct explicit forms of weight $3/2$ whose Fourier coefficients determine the central $L$-values of the associated elliptic curves. This gives Tunnell-type criteria for every positive square-free integer: a nonzero coefficient implies non-$\theta$-congruence unconditionally, and the converse holds assuming the Birch–Swinnerton-Dyer conjecture. We also prove unconditional non-$\theta$-congruence for primes in explicit arithmetic progressions.

We study an uncountable system of McKean-Vlasov SDEs with coefficients of Nemytskii-type which are driven by a family of essentially pairwise independent Wiener processes. These SDEs interact through a Graphon kernel by means of their one-dimensional time marginal law densities evaluated in the spatial coordinate. We prove the existence and uniqueness of probabilistically weak solutions to such SDEs under mild conditions on the drift coefficient and the Graphon kernel. Furthermore, we prove that these solutions are, in fact, probabilistically strong by essentially proving a (restricted) Yamada–Watanabe theorem on Fubini extension spaces. For the associated system of nonlinear Fokker-Planck equations, we prove a new uniqueness result where we can allow for density dependent diffusion coefficients of Nemytskii-type.

Kernel methods, and Gaussian Processes (GPs) in particular, require a Hilbertian distance measure—one whose square is conditionally negative definite (CND)—to guarantee positive semi-definiteness (PSD) of the kernel matrix; a condition that fails for many natural input spaces, including smooth manifolds and spaces of probability distributions. We propose the Sparse Landmark Embedding (SLE) kernel, which eliminates this requirement entirely. Each input is embedded into a sparse feature vector via compactly supported bump functions centered at all |D| training points; applying any standard PSD kernel in this embedding space yields a kernel that is provably PSD for arbitrary distance measures. The compact support automatically controls embedding sparsity, keeping kernel matrices well-conditioned and computationally tractable despite the high ambient dimension. We provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show that the SLE kernel matches or substantially exceeds domain-specific baselines in both predictive accuracy and uncertainty quantification using geodesic and Wasserstein distances.

For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the Discrete Series found by Harish-Chandra. In this paper, we study the structure of symmetry breaking operators for Discrete Series when restricted to a subgroup $H$ of the same type by combining classical results with recent work of T. Kobayashi, Nakahama and Pevzner. This we do by using reproducing kernels for the representations and our previous duality principle in order to find some explicit details on the nature of the differential operators representing symmetry breaking operators, in particular to what extent they are given by differentiations in normal directions to the $H$-orbit in $G/K$.