Papers

Dynamic networks describe evolving relational systems in which abrupt structural changes may signal anomalous events or important transitions. Detecting such changes requires distinguishing genuine structural signals from fluctuations in network observations and learned representations. We propose a DeepWalk-based framework for detecting and localizing structural changes in dynamic networks. For each snapshot, we learn low-dimensional node embeddings, align them to a fixed reference using orthogonal Procrustes transformations, and aggregate them by mean pooling into comparable graph-level vectors. We then construct a multivariate cumulative sum (CUSUM) scan statistic to identify changes in the embedding mean. Under stated regularity conditions, we derive bounds on stochastic fluctuations under the null hypothesis and sufficient conditions for reliable detection and consistent localization under the alternative. The analysis connects detection performance with network sparsity, spectral separation, embedding dimension, and change magnitude, clarifying the balance between structural signals and representation variability. Simulation studies demonstrate the effectiveness of the proposed method in detecting and localizing structural changes across a range of dynamic network settings. An application to an international trade network further illustrates its practical usefulness in identifying shifts in trade allocation.

The manifold hypothesis suggests a natural criterion for clustering: partition data according to the manifold component from which each point is drawn. Whether two components are separable depends on a geometric tradeoff: the ambient separation between components versus the largest gap in sampling. In practice, this tradeoff is rarely assessed explicitly, leading standard methods to over-commit to a single clustering assignment even when the data do not support a unique answer. We formalize this tradeoff by combining intrinsic manifold geometry (volume growth and reach) with sample-level quantities (fill distance and density), yielding a threshold phenomenon for mutual-$k$-nearest-neighbor graphs: when the offset-to-fill ratio exceeds a conservative upper threshold, component separation is preserved; below a lower threshold, components fuse. The gap between these thresholds defines a geometric uncertainty zone in which the number of clusters is not identifiable from the data. Nevertheless, conventional approaches still seek one: sweeping parameters (an engineering approach) or fitting a generative mixture model (a model-based approach). Rather than forcing a single estimate of the number of clusters, we propose Manifold-Based Clustering (MBC), which returns an explicit bracket interval to quantify the underlying data uncertainty. This bracket acts as an empirically calibrated diagnostic: it narrows when a single resolution is supported, widens when multiple resolutions coexist, and collapses to one when no separated structure is detectable. Empirically, we find that many real datasets lie within the uncertainty zone rather than admitting one clear answer. Our results suggest that ambiguity in cluster number is often intrinsic, and should be quantified rather than resolved.

Eternal Vertex Cover (EVC) is a turn-based attacker-defender game on an undirected graph $G$. To begin with, the defender places $k$ guards on vertices of $G$. The attacker, on their turn, can choose an edge $e$ not already occupied at both endpoints to "attack". The edge $e$ is defended if a guard moves along the edge $e$. The defender, on their turn, can move any subset of guards. A guard can only move to a neighboring vertex. The minimum number of guards needed to indefinitely defend against any sequence of attacks is called the eternal vertex cover number, generalizing the classic vertex cover number. Determining this number is NP-hard in general, motivating the study of parameterized and approximation algorithms. The problem is known to be FPT when parameterized by the cover number, but structural parameters remain relatively unexplored in the literature. In this work, we explore structural parameterizations for EVC. We show that EVC is FPT parameterized by the cluster vertex deletion number, which generalizes the previously studied parameterization by vertex cover number. We next study the problem parameterized by vertex integrity, which is the smallest number of vertices we need to delete from $G$ so that the resulting graph is a disjoint union of constant-sized components. We first show that Eternal Vertex Cover is XP parameterized by vertex integrity. Then, we develop a polynomial-time approximation algorithm, which computes an additive $6k+1$ ($g(k)$) approximation, where $k$ is equal to the cluster vertex deletion number (vertex integrity). Finally, we show a FPT algorithm for when the deletion set produces "nice" connected components, which are components that are bounded in size and satisfy a technical condition.

Large reasoning models (LRMs) generate long chain-of-thought traces before answering, creating significant inference overhead. Pruning can reduce this cost, but its effectiveness depends on the calibration data used to estimate parameter importance. Recent work calibrates on the model's own rollouts instead of generic dataset, but treats all reasoning tokens uniformly, regardless of whether they contribute to successful reasoning. As a result, pruning protects weights by statistical salience rather than by their contribution to correct reasoning, so weights behind erroneous computation survive as readily as those behind correct computation. These erroneous patterns then get carried into the pruned model, degrading reasoning quality, producing both lower accuracy and longer reasoning traces. We propose Outcome-Based Calibration for Large Reasoning Model Pruning (OBC-Prune) to close this gap. OBC first constructs difficulty-matched pairs of correct and incorrect rollouts from problems the model answers inconsistently. It then estimates the causal importance of each reasoning sentence through intervention-based analysis, quantifying how removing its influence affects subsequent predictions. These causal importance scores are converted into per-token weights that rescale the calibration activations used by one-shot pruning methods (SparseGPT, Wanda, ALPS), without modifying the underlying pruning algorithms. Experiments on DeepSeek-R1-Distill-Qwen 1.5B, 7B, and 14B models at 40% and 50% sparsity demonstrate consistent improvements over state-of-the-art calibration baselines across most model sizes and sparsity levels on MATH500, LiveCodeBench, and AIME 2025. These results indicate that preserving causally important reasoning circuits is a substantially more effective pruning objective than uniformly preserving observed activations.

We give an exact algorithm for minimizing an arbitrary rational quadratic polynomial $x^T Q x + c^T x + \gamma$ over the integer points of a bounded rational polyhedron $\{x : Ax \le b\}$. For $n$ variables and $m$ inequalities, the running time is $$2^{O(n \log(n+1))} (m+1)^{O(n)} \beta^{O(n)} (1+L)^{O(1)},$$ where $\beta$ is one plus the maximum binary encoding length of an entry of $A$ or $Q$, and $L$ is the full input encoding length. The polynomial degree in $L$ is absolute; in particular, the encoding of $b$, $c$, and $\gamma$ enters only this fixed-degree factor. Our algorithm refines the integral parallelepiped cover of Goemans and Rothvoss into cells with controlled displacement sets. On each cell, either an integer displacement of negative quadratic value rules out every point as a global minimizer, or the quadratic identity supplies a separation oracle for the convex hull of each integer objective sublevel set. The integer-query feasibility theorem of Hildebrand and Goess then finds the cell minimum. A refinement through scaled lattices solves the displacement search, and a localization argument separates the encoding dependence of the constraint matrix and quadratic part from that of the remaining data. Combining the bounded algorithm with the unboundedness test of Ari and Hildebrand extends the method to arbitrary rational polyhedra.

We study the problem of demonstration selection, which involves selecting a subset of examples for prepending to a query to a language model. This problem is closely related to in-context learning and language model inference. Since the inference cost of a transformer model scales quadratically with sequence length, the selection problem becomes especially challenging in a long-context scenario. In this paper, we tackle this problem by building on state space models (SSMs), which require only linear inference time given the input. Our approach involves two algorithms. The first learns a small set of SSMs through distillation of a (trained) transformer model. We partition all the layers into consecutive groups. Then for each group, we estimate a separate state space model to replicate the input-output behavior within the adjacent layers. Second, we map the distilled model outputs to a small set of tokens, and apply these embeddings for demonstration selection in downstream applications. We perform extensive experiments in both synthetic and real-world datasets to validate our approach. We demonstrate that the distilled SSMs only incur an approximation error of less than $0.7\%$ relative to the true output. In downstream evaluation, we show that on several text classification and reasoning tasks, our approach reduces FLOPs by $14.2\times$ and improves accuracy by $6.48\%$ relative to baseline demonstration selection methods.

We prove sharp upper and lower bounds for the Morse index and nullity of linearly full branched minimal 2-spheres in the round 2n-sphere. In particular, we show that the Morse index of a linearly full minimal 2-sphere in the round 2n-sphere is at least n(n-1)(2n+1), with equality if and only if the 2-sphere is twistor-equivalent to the Boruvka sphere. Our techniques also apply more generally to give bounds for the Morse index and nullity for totally isotropic surfaces in the 2n-sphere.

EEG decoding tasks can rely on different temporal dynamics and cross-channel relationships. We test whether specialized modules improve a fully fine-tuned EEG foundation model by augmenting CBraMod with cross-depth Attention Residuals (AttnRes) and two soft-routed expert banks. Across matched three-seed experiments on FACED, ISRUC, SEED-V, and PhysioNet-MI, the complete model changes mean balanced accuracy relative to full fine-tuning by -0.12, +1.27, +0.77, and -1.27 points, respectively. AttnRes alone improves mean balanced accuracy on three datasets, whereas adding experts on top of AttnRes helps only FACED and SEED-V. These gains come with substantial overhead: AttnRes requires 2.11 to 2.88x runtime and 1.78 to 2.67x memory, while the complete model requires 2.41 to 3.04x runtime and 1.86 to 2.85x memory. Overall, the added modules produce dataset-dependent, sometimes opposing effects rather than consistent gains over full fine-tuning.

Computer-use agents that operate through screenshots and simulated actions are advancing rapidly, yet their evaluation remains anchored to general desktop and web tasks. Enterprise Resource Planning systems run the finance, procurement, inventory, and customer operations of organizations worldwide, and pose distinct challenges for computer-use agents: dense interfaces, coordinated multi-step interactions, and errors that alter persistent business records rather than surfacing on screen. Existing enterprise computer-use benchmarks rely on proprietary platforms or on simulated approximations of such software. We introduce ERPBench, a benchmark that evaluates screenshot-only agents on a live and reproducible system and scores each task against ground-truth values in its database. Beyond the benchmark, we present a production-grade harness that gates agent actions behind human approval for safe deployment. Evaluating six closed and open-source agents, we demonstrate that strong general performance does not transfer to enterprise reliability. Even when an agent reaches the right form and saves it, the stored record is often wrong: some agents save in up to 85% of runs but write the correct value in as few as 3%. We further characterize failure modes specific to enterprise workflows.

As unmanned aerial vehicles (UAVs) become increasingly prevalent in consumer and defense settings, classifying them reliably from limited, modality-specific data is an urgent challenge. The dominant approach, large pretrained networks fully fine-tuned on task data, carries a substantial computational and memory weight that is hard to bear in resource-constrained UAV deployments, where edge inference and rapid retraining for emerging platforms are both required. This paper systematically scales across both model architectures and fine-tuning methods for UAV audio classification, asking when that weight is justified and when lighter alternatives prevail. Using a custom dataset of 3,100 audio clips spanning 31 drone classes, we evaluate transformer (ViT, AST) and convolutional (custom CNN, ResNet-18/152, MobileNet-V3-S/L, EfficientNet-B0/B7) backbones under full fine-tuning, classifier-only fine-tuning, and four parameter-efficient fine-tuning (PEFT) methods: SSF, IA3, OFT, and selective batch-norm tuning. All configurations are evaluated with 5-fold cross-validation across accuracy, training time, trainable-parameter share, and inference-time memory footprint. Selective batch-norm fine-tuning of EfficientNet-B7 with three-fold augmentations achieves the highest validation accuracy (97.65% +- 0.30) while updating under 0.5% of model parameters. Across the sweep, lightweight CNNs consistently outperform transformers on both accuracy and efficiency. For UAV audio classification under data scarcity, scaling the method outperforms scaling the model.

The rapid adoption of generative AI has made final artifacts unreliable evidence of student learning, and AI detectors that examine only the finished product are inaccurate and ethically contentious. Process data offers an alternative, but prior work covers only English essay writing. We ask whether AI assistance carries a temporal signature, whether it generalizes from writing to programming, and whether it distinguishes ordinary collaboration from wholesale delegation. We analyze three public corpora: CoAuthor (1,447 keystroke-level co-writing sessions), RealHumanEval (editor telemetry from 243 programmer records), and a pre-LLM CS1 corpus (5.1 million keystrokes) as a human-only baseline, comparing minimal-AI work, collaborative AI use, and simulated wholesale delegation. Three findings emerge. First, the signature generalizes: AI contributions arrive in bursts far outside the author's own baseline in both mediums (paired d_z = 1.13 and 3.54). Second, engagement diverges by medium: 93% of AI-inserted characters survived to writers' final documents, while only 14% of accepted code suggestions survived intact. Third, classifiers using only observable temporal features separate simulated delegation from authentic work nearly perfectly (F1 $\geq$ 0.997; at most 0.5% of real work misclassified), while ordinary collaboration remains hard to distinguish from unassisted work. Temporal evidence flags wholesale delegation rather than assistance, positioning process visibility as a candidate evidentiary basis for academic integrity, pending validation in authentic coursework.

An important component of urban accessibility, particularly for wheelchair users and people with reduced mobility, is sidewalk compliance with measurable requirements. We test whether effective width, longitudinal slope, cross slope, and pavement condition can be assessed reliably from pedestrian-level imagery using vision-language models (VLMs). We present the first application of sampling-based conformal prediction (CP) for VLM-based accessibility assessment. We evaluate four VLMs on 514 sidewalk images from Seoul, South Korea, with field-measured ground truth. Conformal calibration attains the nominal 90% coverage for all models and attributes, but the calibrated regions differ in informativeness. Effective width yields the most informative estimates, with a mean interval half-width of about 1.0 m for the best model. Since every model overestimates width, asymmetric calibration shortens the intervals by up to 33% at unchanged coverage. Longitudinal slope is marginally informative, cross-slope intervals are too wide to resolve regulatory thresholds, and pavement-condition sets degenerate to all five grades (A-E) for three of the four models. Uncalibrated intervals from raw sampling dispersion cover only 17-47% of field-measured values at a nominal 90% level. Among the images with the most self-consistent responses, these intervals miss the field-measured value in up to 96% of cases. Response self-consistency is therefore not evidence of accuracy, and sampling dispersion cannot be interpreted as uncertainty until it has been calibrated against field-measured ground truth. No quantitative attribute reaches the precision required for general compliance assessment, but CP identifies from calibration data alone which attributes can support screening of segments far from the thresholds. We release the annotated pedestrian-level images and their corresponding field-measured attribute values.

We propose pointwise representations of the Stein solution to a weighted first-order Stein equation associated with a univariate absolutely continuous distribution. The representation extends to all the derivatives of the solution and with respect to any derivative of the test function. The mechanism behind these representations is an array of kernels that satisfy two key identities, yielding a specific calculus for the Stein framework considered here. The representations record every correction term appearing by differentiation, explaining how choosing the Stein kernel as weight has a special role in Taylor and pairing arguments. The calculus of the kernel extends these representations to any order and exhibits natural and explicit conditions to obtain a one term representation of the $n$-th derivative of the solution with respect to exactly one of the three neighbouring test-function orders of derivatives, \(n-1,n,n+1\). These conditions are simple to ensure by choosing the weight accordingly. The representations yield pointwise envelopes, uniform and weighted Stein factors, and ensure sharpness of the constants. We recover the known sharp results for the Gaussian and the Gamma distribution, improve known factors for the rest of the integrated Pearson family, which is the family under which every correction term cancels. We also study the Subbotin and symmetrized Maxwell families, for which the formulas retain additional pointwise terms. Applications sharpen constants in known distributional approximations and use the higher-order calculus to obtain Edgeworth corrections for the Beta approximation of the Pólya–Eggenberger urn and the quartic Subbotin approximation in the critical Curie–Weiss model.

We derive explicit Gamma–Stein bounds for the Satterthwaite approximation of weighted sums of independent chi-square random variables and, more generally, of independent Gamma random variables. The approximating Gamma distribution is chosen by matching the first two moments. Our approach relies on new kernel representations of the solution to the Gamma–Stein equation and of its first derivatives on the positive real line. These representations yield weighted Stein-factor bounds adapted to the moment-matching structure and show that the quality of the approximation is controlled directly by the discrepancies between the individual scale parameters and the matched scale parameter. Kolmogorov bounds are obtained by smoothing. The results provide quantitative guarantees for the widely used Satterthwaite approximation and are applied to pooled variances, sample variances of stationary Gaussian time series, Wishart traces and sums of Wishart traces, and high-dimensional repeated-measures statistics.

Let $\Gamma$ be the mapping class group of the plane minus a Cantor set, acting on the ray graph $\mathcal{R}$, and for $\gamma \in \Gamma$ let $\tau(\gamma)$ denote the translation length of $\gamma$ on $\mathcal{R}$. We prove that $\tau(\gamma) \le h(f)/\log(2)$ for every $C^\infty$ diffeomorphism $f$ of $S^2$ representing $\gamma$, where $h$ denotes topological entropy. The proof falls into two parts: a combinatorial argument bounding distance between two rays in $\mathcal{R}$ by the logarithm of the geometric intersection number; and a geometric argument that promotes geometric control (coarse length of iterates of a fixed ray) to combinatorial control (geometric intersection number). We conjecture that the $C^\infty$ hypothesis on $f$ can be removed.

Gas–grain astrochemical models predict that a substantial fraction of elemental nitrogen in dense cores and protoplanetary disks is locked in molecular nitrogen (N$_2$), in the gas or ice phase, although interstellar N$_2$ ice has not been directly identified. Rosetta measurements at comet 67P/Churyumov–Gerasimenko showed strong N$_2$ depletion relative to CO, while NH$_3$ was the dominant detected nitrogen-bearing ice. We experimentally quantify the conversion of NH$_3$ ice into N$_2$ and N$_2$H$_4$ under astronomically relevant conditions by studying its temperature- and fluence-dependent VUV photochemistry. Experiments were performed under ultra-high vacuum using 40-monolayer NH$_3$ ice at 15, 25, and 70 K irradiated at 115–170 nm to a total fluence of $3.8\times10^{18}$ photons cm$^{-2}$. Laser desorption with post-ionization reflection time-of-flight mass spectrometry (ReTOF-MS) was used to monitor N$_2$ and N$_2$H$_4$ simultaneously. VUV photolysis efficiently forms both products, with formation kinetics and product ratios depending on temperature and photon fluence. Initial-growth fits gave the highest apparent ice-retained N$_2$ formation yield at 15 K, approximately an order of magnitude above those at 25 and 70 K. The N$_2$/NH$_3$ column-density ratio was determined as a function of fluence and compared with astronomical constraints. These results suggest that NH$_3$ ice photochemistry may provide an additional pathway to N$_2$ ice in cold outer planetary environments.

We present an exposition of a proof, discovered by GPT-6 Astra, of the Erdős–Sós Conjecture, which states that every graph with average degree greater than $t-2$ contains every tree on $t\geq 2$ vertices.

The surface chemistry of additively manufactured aluminum alloys plays a critical role in corrosion resistance and joining with external materials. In this work, the near-surface elemental composition of a laser powder bed fusion (PBF-LB/M) processed Al-Mg-Si-Zr alloy was characterized by glow discharge optical emission spectroscopy GDOES depth profiling. The measurements reveal pronounced Mg enrichment within the near-surface region extending to approximately 10 {\mu}m, consistent with the characteristic scale of surface roughness, together with an increase in oxygen concentration, whereas Al, Si, and Zr approach stable bulk-like levels at greater depths. To understand this observation on the atomic scale, first-principles calculations based on density functional theory (DFT) were performed on low-index Al surfaces. The calculated results show a strong thermodynamic driving force for Mg surface segregation, with diffusion energy differences ranging from approximately -0.30 eV to -0.41 eV, while Zr exhibits a pronounced preference for remaining in the bulk matrix. Vacancy migration calculations further demonstrate that full structural relaxation substantially reduces the migration barrier for Mg to below that of Si, which makes Mg diffusion kinetically highly favorable. Moreover, the presence of adsorbed surface oxygen dramatically promotes the tendency of Mg to diffuse toward the surface, which lowers the diffusion energy difference of Mg to as much as -3.0 eV. This promotes the formation of a locally reconstructed Mg-O-Al coordinated precursor structure accompanied by localized electron transfer shown by an electron localization function analysis.

We prove that broad families of finite Dirichlet sums exhibit deterministic concentration of normalized vertical zero density on a single line. The main result gives a general criterion under which the normalized Jessen potentials converge locally uniformly to a piecewise-linear convex function with a single corner. The associated normalized measures describing the distribution of real parts of zeros in vertical mean density then converge weakly to a Dirac mass. Thus, for each fixed truncation, zeros may occupy a nontrivial range of real parts, while asymptotically their normalized vertical density concentrates on one line. The proof combines the finite Bohr lift with a translation-uniform anti-concentration estimate for isolated prime coordinates. We apply the criterion to partial sums of the Riemann zeta function, fixed Dirichlet $L$-functions, and primitive holomorphic Hecke eigenforms of fixed level, trivial Dirichlet character, and without complex multiplication. The concentration line is $\operatorname{Re} s=1/2$ in the normalized setting and becomes $\operatorname{Re} s=k/2$ for the classical Fourier coefficients of a form of weight $k$.

We study linearizations of dynamical systems and some of its topological properties. Special attention is paid to the case of Lipschitz-free operators, and they are shown to model the dynamics of very general linearizations. We provide a new criterion, called the targeting property, for the (weakly) mixing property in a linear dynamical system through a (possibly) non-linear restriction of it. We then apply this criterion to the linearization $T_f$ of a Lipschitz map $f\colon M\to M$, where $M$ is a metric space and the operator $T_f$ is defined on the corresponding Lipschitz-free space $\mathcal F (M)$—the so-called Lipschitz-free operators. We show that, under some natural assumptions on the distance considered in $M$, the operator $T_f$ is hypercyclic if and only if the map $f$ has the targeting property.

In 2014, we introduced a new experimental approach to study the UV photo-processing of cryogenic ices of astrophysical interest using laser ablation in combination with ionization and time-of-flight mass spectrometry (ToF-MS). The setup, MATRI$^2$CES (Mass Analytical Tool to Research Interstellar ICES), allowed us to detect newly formed species at low abundances. However, we found that with increasing molecular complexity, the detection of larger photoproducts was hindered by the dynamic range of the detector. Here, we introduce a method to overcome this issue that we expect to be useful for similar applications in other research fields. The concept is based on a precisely controlled high-energy pulser that regulates the voltage across the deflection plates of the ToF-MS to deflect the most abundant species and prevent them from reaching the detector. In this way, the detector sensitivity can be increased from an operating voltage of 2500~V up to 3000~V. The applicability is first illustrated using an argon matrix, in which $^{40}$Ar$^+$ ions are deflected to increase the detection sensitivity for $^{40}$Ar$^{2+}$ at $m/z=20$ and $^{40}$Ar$_2^+$ at $m/z=80$ by a factor of 30. Similarly, we show that substantially larger complex organic molecules can be measured in UV-irradiated methanol ice.

We examine the different methods of extracting the anomalous Hall conductivity using SrRuO$_3$ and GdAlSi. For SrRuO$_3$, where the ordinary Hall background is well defined and the magnetoconductance is small, subtracting the ordinary Hall contribution either before or after conversion from resistivity to conductivity yields nearly identical anomalous Hall conductivities. In GdAlSi, in contrast, the transverse response does not exhibit clear saturation, and both low- and high-field regions can appear approximately linear. We show that different interpretations of these linear regions as the ordinary Hall background, together with the treatment of the measured longitudinal resistance in the resistivity-to-conductivity conversion, can produce completely different estimates of the anomalous Hall conductivity. We also examine whether the nonlinear Hall response can instead be described within an ordinary Hall framework without invoking an anomalous contribution. Our analysis provides practical cautions for extracting excess Hall contributions in quantum materials.

We study negative spheres obtained from exceptional sections of Gurtas Lefschetz fibrations. Starting with the known system of $4n$ disjoint $(-1)$-sections, we show that a marked double sum contains $4n$ symplectic $(-2)$-spheres and $2n$ smooth $(-4)$-spheres obtained by pairwise tubing. By carrying the same sections through a fourfold sum, we instead obtain $4n$ disjoint symplectic $(-4)$-spheres and hence symplectic rational blowdowns. We then consider the Lefschetz fibrations on knot-surgered elliptic surfaces. Their branched-cover description gives $2n$ branch sections together with simultaneous geometric duals arising from node resolution. In the knot-surgery double these sections glue to symplectic $(-4)$-spheres, while the duals make the complement of every subcollection simply connected. The resulting rational blowdowns provide simply connected exotic symplectic four-manifolds under the parity condition stated in the main theorem. We also record the boundary-multitwist relation determined by the Gurtas sections.

Spatial and temporal correlations in quantum noise challenge the local Markovian models commonly used in quantum information processing. We develop a unified operational framework for quantifying temporal, spatial, and total spatiotemporal correlations in general quantum processes. Using process tensors, we define these quantities through optimal distinguishability from Markovian, spatially local, and fully uncorrelated processes. Optimization over admissible probing combs ensures monotonicity under every superprocess that preserves the corresponding free set, while Choi-state functionals and restricted probes provide accessible lower bounds. We establish hierarchy and interpolation relations among the correlation measures and derive dimension-dependent upper bounds on temporal correlations transmitted by quantum memories, with tighter bounds for classical memory, together with universal ceilings imposed by the system dimension. These bounds turn certified lower estimates into witnesses of minimum memory dimension, nonclassicality under a memory-dimension constraint, and inconsistencies in the assumed process model. We illustrate the results with effective superconducting-qubit models featuring \(ZZ\) and \(XY\) interactions, exhibiting saturation of classical-memory, quantum-memory, and system-dimension ceilings. These results pave the way toward practical approaches to characterizing and addressing spatiotemporally correlated errors in quantum devices.

Alòs, Gatheral and Radoičić derived the Bergomi-Guyon expansion of the implied variance smile from the forest expansion of the cumulant generating function. Its coefficients are sums of products of diamond trees, with prefactors that are polynomials in the log-strike $k$. Matching moments order by order produces, at order $\epsilon^\ell$, terms of degree greater than $\ell$ in $k$ that mysteriously cancel. We show that, in suitable variables, the matching condition can be formulated as a nonlinear heat equation. The resulting recursion computes the prefactor of each product of trees from those of products of fewer trees, without generating the higher-degree terms; its only model-independent input is a cumulant series, which we compute in closed form. Consequently, at order $\epsilon^\ell$ every prefactor has degree exactly $\ell$ in $k$. The prefactors are universal and need only be computed once. Code and coefficients are provided.

Pathology vision-language models are commonly built by pretraining or fine-tuning large encoders on paired image-caption data. We asked whether a pathology vision-language model can instead be assembled by parameter-efficient alignment of frozen unimodal foundation models, leaving their pretrained representations untouched. Here we present Lumen, which aligns frozen Virchow2 and BioMedBERT backbones using rank-4 adapters and projection heads, training only 0.40% of the total parameters on the public QUILT-1M corpus. Across nine public zero-shot patch benchmarks, Lumen achieved the highest mean chance-corrected balanced accuracy, 0.546 versus 0.461 for the strongest baseline (paired difference 0.086, 95% CI 0.042-0.136). On lymph-node metastasis detection, Lumen reached an AUROC of 0.964 (95% CI 0.956-0.971) on 4,214 held-out internal slides and 0.955 (95% CI 0.942-0.966) on 2,368 slides across nine external cohorts and six organs. At the internally calibrated threshold, it outperformed all vision-language baselines, with a balanced accuracy of 0.909 (95% CI 0.896-0.923) internally and 0.915 (95% CI 0.902-0.929) externally. Lumen performed competitively across the evaluations, with the exception of cross-modal retrieval, where it ranked third behind CONCH and PathGen-L/14. Fully fine-tuning both encoders gave Lumen no consistent benefit over low-rank adaptation, although it improved retrieval. Aligning frozen unimodal foundation models therefore yields strong and transferable performance at patch and slide level while training only a small fraction of the parameters.

Acetylene (C$_2$H$_2$) is commonly observed in star-forming regions, young stellar objects, and the Solar System. Laboratory and theoretical studies have linked this simplest alkyne to volatile hydrocarbons and polycyclic aromatic hydrocarbons (PAHs) through UV- or cosmic-ray-driven chemistry, but it remains unclear whether refractory material can efficiently form through solid-state reactions of C$_2$H$_2$ on dust grains. We experimentally investigate the chemical complexity induced by UV irradiation of pure C$_2$H$_2$ ice and characterize both volatile and nonvolatile photoproducts. Experiments were performed with MATRI$^2$CES under ultra-high-vacuum conditions at 15 K using 7.2–10.2 eV photons. UV-processed ices were monitored in situ by laser desorption post-ionization reflection time-of-flight mass spectrometry (LDPI ReTOF-MS) combined with pulsed ion deflection (PID). Volatile and refractory products were measured in situ at 15 and 300 K, respectively. After a fluence of $3 \times 10^{17}$ photons cm$^{-2}$, corresponding to about $10^6$ years in dense clouds, large saturated and unsaturated hydrocarbons containing up to 13 carbon atoms are formed. After sublimation of the volatile products, the 300 K residue shows a rich and distinct mass spectrum consistent with refractory material containing conjugated triple (-C$\equiv$C-) and double (-C=C-) bonds. These results demonstrate that UV processing of pure C$_2$H$_2$ ice can produce substantial molecular complexity and refractory hydrocarbons under astronomically relevant conditions, with possible implications for unidentified infrared emission bands.

Real-world intelligent systems increasingly operate under open-world conditions, where user intents are not fixed or exhaustively known a priori and may evolve as new interaction patterns emerge. This paper proposes a unified uncertainty-aware probabilistic framework for continual new intent discovery under an evolving label space. Each utterance is encoded through an adaptive $\beta$-VAE into a latent mean, used for classification and density modelling and a posterior uncertainty estimate acting as a global reliability signal. Classifier confidence, posterior uncertainty and DP-GMM likelihood are combined through a multi-signal decision mechanism to distinguish known intents from potentially novel samples. Candidate novel instances are clustered through a density-based discovery module and only reliable clusters are promoted to new labels, enabling controlled label-space expansion. Replay and Elastic Weight Consolidation mitigate catastrophic forgetting and preserve previously acquired knowledge. The paper formalises continual intent discovery as a structured multi-phase open-world problem, introduces adaptive label-space expansion under stability–plasticity constraints and uses posterior uncertainty to regulate trusted-sample selection, pseudo-labelling, novelty admission and replay. Experiments show high novelty precision, stable adaptation across sequential phases and limited forgetting. Near-zero NMI and ARI indicate limited reconstruction of the complete fine-grained intent taxonomy, consistent with the framework's conservative promotion strategy. Qualitative analyses nevertheless reveal dense and locally coherent semantic clusters, showing that reliable novel structures can be discovered without exhaustive recovery of the underlying taxonomy.

Frontier models are often evaluated on how they respond to safety information once it is already in context. We study an earlier decision point: whether models choose to acquire safety-relevant evidence before acting. We introduce SAFE, a controlled benchmark in which models make deployment decisions with optional evidence that varies in retrieval cost, probability, severity, and presentation. Across GPT-5.5, o3, Claude Opus 4.8, and Claude Sonnet 4.6, we find distinct evidence-acquisition policies: Opus inspects nearly by default, o3 is the most skip-heavy and threshold-sensitive, and GPT-5.5 and Sonnet occupy intermediate regimes. Inspection increases strongly with severity and decreases with retrieval cost, whereas probability has much weaker behavioral influence: increasing the stated likelihood of a problem from 10% to 70% changes inspection by at most 21 percentage points. Despite these differences, Stage 1 rationales are dominated by expected-value reasoning across models. A cost-obligation decomposition further shows that avoidance is driven primarily by retrieval friction and explicit threats to the deployment payoff rather than by the remediation duties created by knowing. Counterfactual interventions reveal a further mismatch between behavior and explanation: evidence framing can strongly change decisions near the inspection boundary while going largely unmentioned, whereas probability is frequently cited despite having little causal influence. These results suggest that deployment-time safety depends not only on how models respond to known risks, but also on whether they acquire the evidence needed to know that acting is safe.

In this paper, we investigate integral solutions satisfying the system of two forms in many variables of different degrees. Let $d_1$ and $d_2$ be natural numbers with $d_2>d_1\geq 2$. Let $F_{i}(\boldsymbol{x}) \ (i=1,2)$ be forms in $n$ variables of degrees $d_i\ (i=1,2)$, respectively. Define $$N(\boldsymbol{F};P):=\#\{\boldsymbol{x}\in [-P,P]^n\cap \mathbb{Z}^n:\ F_{i}(\boldsymbol{x})=0\ (i=1,2)\}.$$ When each dimension of singular loci of $F_1=0$ and $F_2=0$ is small, we obtain a number $n_0:=n_0(\boldsymbol{F})$ such that whenever $n> n_0$ one has the expected asymptotic formula \begin{equation*} N(\boldsymbol{F};P)=c_{\boldsymbol{F}}\cdot P^{n-d_1-d_2}+O(P^{n-d_1-d_2-\delta}),\ \text{for some }\delta>0, \end{equation*} where the constant $c_{\boldsymbol{F}}$ is the product of local densities. We note that this asymptotic formula agrees with the Manin-Peyre conjecture. Compared to the previous work, we lower the admissible threshold $n_0(\boldsymbol{F})$ in most cases, with the exception of case $d_2-d_1=1$. In particular, if $F_1$ and $F_2$ are non-singular forms, then we obtain $$n_0(\boldsymbol{F})=3(d_2-1)2^{d_2-1}+(d_1-1)2^{d_1},$$ provided that $d_2\geq 5d_1$ with $d_1\geq2$. This yields a substantial improvement over the previous bound $n_0(\boldsymbol{F})=(d_1+2)(d_2-1)2^{d_2-1}+d_12^{d_1-1}$. To achieve this, we develop a new differencing argument together with the van der Corput differencing argument, delivering an efficient upper-bound estimate for mean values of exponential sums associated with two forms in many variables of different degrees, when the difference between degrees is sufficiently large. Furthermore, the method described in this paper is flexible enough to apply to forms in many variables of differing degrees in general.