Papers

Löfberg and Qi introduced the second order Zarankiewicz number \(z_2\), the recursive-line Zarankiewicz number \(z_{RL}\), and the signed Zarankiewicz number \(z_{SL}\) for doubly simple biquadratic forms. It was shown that \[ z_2(m,n)\ge z_{SL}(m,n)\ge z_{RL}(m,n) \] for all \(m\) and \(n\). However, there was no evidence that there exist particular \(m\) and \(n\) such that \(z_{SL}(m,n)>z_{RL}(m,n)\). The motivation for introducing \(z_{SL}\) was as follows: during the study of the exceptional case \(m=15\), \(n=6\), Löfberg and Qi showed that \[ z_2(15,6)=z_{SL}(15,6)=60, \] but the exact value of \(z_{RL}(15,6)\) was unknown then. In this paper we show that \[ z_{RL}(15,6)=60. \] This eliminates the motivation for introducing \(z_{SL}\). Whether \(z_{SL}(m,n)=z_{RL}(m,n)\) in general remains an open problem. Recently, Lebedev presented an explicit construction separating the augmented Zarankiewicz number \(z_A\) from the limited augmented Zarankiewicz number \(z_L\) at \(m=n=1893\). We hope that the separation problem for \(z_{SL}\) and \(z_{RL}\) can also be solved. We also present the exact values of \(z_{RL}(m,6)\) for \(6\le m\le 16\).

Keyword spotting (KWS), the task of identifying predefined words in speech, is a core capability of voice-enabled devices. Achieving high KWS accuracy under tight parameter budgets across different vocabulary sizes remains challenging. We present CircleMatch, a matching framework enabling KWS with very few parameters. Its encoder independently compresses frequency bands and fuses them into frame features. These features are then matched against learned class-specific prototypes to produce temporal response curves. Parameter-free circular aggregation encodes time as angles and summarizes response distributions and relative timing for classification. We develop four tiny variants, Circle-D4, Circle-D8, Circle-D16, and Circle-D32, ranging from approximately 1k to 7k parameters in the 12-class setting. Experiments with multiple random seeds on Speech Commands v1/v2 and the English and Spanish Micro subsets of the Multilingual Spoken Words Corpus demonstrate competitive accuracy with tiny models. Our qualitative analysis further suggests approximate shift equivariance of prototype responses and adaptation to temporal compression. Code and model weights are available at https://github.com/ora942878/CircleMatch.

Byzantine Fault-Tolerant (BFT) protocols guarantee safety and liveness despite the malicious failure of nodes. However, they do not prevent adversarial manipulation of transaction order, where the order a proposer assigns diverges from the order in which clients submitted their transactions. Exploiting this discretion for profit is known as maximal extractable value (MEV), and it is intensified in DAG-based BFT protocols, where every replica proposes blocks concurrently rather than routing transactions through a single designated proposer each round. The proliferation of MEV attacks on DAG-based BFT protocols has made the resulting landscape difficult to navigate: attacks are reported individually, on different protocols, and under different metrics, making it unclear whether two attacks differ fundamentally or merely in how they are described. This paper closes that gap by presenting an attack space for MEV on DAG-based BFT protocols, organized around four families: the adversary, the protocol, the target, and the deployment. For each family, we identify the dimensions that shape an attack's impact. Each point in the attack space fixes one value per dimension, thereby representing a distinct, potential MEV attack, which can then be instantiated on a specific DAG-based BFT protocol. We perform a set of experiments, each isolating a single dimension where the protocol permits it, to empirically measure its effect on the success rate of MEV attacks against six production DAG-based BFT protocols. Our experimental evaluation reveals that every protocol we evaluate is vulnerable to at least a subset of the MEV attacks in this space, and that which attacks succeed is mostly dictated by the protocol's own design rather than by attacker effort.

This paper builds a theoretical bridge between the economic notion of marginal utility and two machine-learning constructs, matrix factorization and the Key–Value cache of transformer language models. The singular value spectrum of a rating matrix is shown to be a diminishing marginal utility schedule for latent factors, the eigenvalue spectrum of the projected covariance operator to be the marginal utility schedule of a model's learned representation, and cache eviction and low-rank cache compression to be instances of constrained utility maximization under a memory budget. The three collapse into a single allocation rule: retain the top dimensions whose eigenvalue exceeds the shadow price of the binding constraint. The framework is applied to the automated extraction of structured information from geo-mining documents, where it motivates a multi-pass inference protocol, a layer-wise TIES model merging procedure, and a selection policy combining extraction quality, localization drift and energy, scalarized with a Conditional Value-at-Risk term on drift. Two empirical contributions are reported. An 11.2-million-parameter hierarchical classifier, trained in about five minutes on a single GPU, reaches 90.0 per cent level-1 accuracy on a held-out test set from a 973-document uranium-exploration corpus, against 92.0 per cent for a proprietary model on a fifty-document human audit of the same corpus, at a latency of 2.62 ms per card against approximately 2,000 ms for the API and at negligible cost. A diagnostic of uniform-density TIES merging exposes a reproducible degenerate mode in which the merged model returns token-identical outputs across five geographically distinct districts while declaring high confidence; re-executing the merge under layer-wise calibrated densities removes that signature on the diagnostic sample. The full-scale extraction benchmark, including LoRA fine-tuning, is reported as projected rather than measured and remains an empirical extension of this work.

Deep learning models for multi-modal breast cancer diagnosis achieve high predictive accuracy but remain clinically unacceptable without actionable, counterfactual explanations. Attribution-based methods (LIME, SHAP) are categorically inapplicable to this purpose, as they generate no alternative instances and thus cannot be evaluated on counterfactual quality metrics. This investigation provides empirical evidence that FCA-Guided Counterfactual (FCA-CF) framework that uses a Formal Concept Analysis (FCA) concept lattice as a hard structural constraint on counterfactual search, operating over a multi-modal TCGA-BRCA dataset. We benchmark against four genuine counterfactual methods: Wachter-style CF, DiCE, FACE, and NICE, evaluated on 60 benign-predicted TCGA-BRCA instances. The FCA-CF framework achieves Validity = 1.0000 (100% of counterfactuals successfully flip the prediction), Sparsity = 2.37 features changed (best among all valid methods), and Proximity = 0.900 (normalised L2-based, matching NICE as joint best). The classifier achieves Accuracy = 0.980, F1 = 0.976, ROC-AUC = 0.9947. Ablation analysis confirms that the FCA lattice constraint is the primary sparsity driver (removing it increases sparsity by +40%, p < 0.001, Cohen's d = 0.78), while Phase C greedy refinement accounts for the largest individual contribution (+113% sparsity increase when disabled, p < 0.001, d = 5.01). FCA-guided counterfactual generation achieves a clinically important Pareto-dominant outcome; it is simultaneously the sparsest and among the most proximate of all valid methods, with perfect validity. The emergent sparsity property arising from lattice topology rather than numerical penalty terms constitutes a structurally novel contribution to the counterfactual explanation literature.

Event cameras offer high temporal resolution and motion sensitivity for tiny UAV detection, yet distant targets generate sparse and fragmented events that are easily overwhelmed by clutter and ego-motion. Existing methods mainly rely on dense event representations or local sparse spatiotemporal modeling, resulting in redundant computation or fragmented modeling of motion continuity across distant asynchronous events. To address this limitation, we introduce serialized motion evidence accumulation, which treats motion continuity as an ordered evidence propagation process. Specifically, the same event stream is organized into locality-preserving spatiotemporal paths and chronology-preserving temporal paths through the latent complementary serializations. Based on this principle, we propose PointEvent, a lightweight event-wise state-space framework that alternates serialized scans across the complementary orders, progressively consolidating fragmented motion evidence beyond fixed local neighborhoods. A high-resolution event branch preserves fine-grained target responses, while compact context modulation suppresses interference. Experiments demonstrate that PointEvent achieves SOTA with the fewest parameters and fastest measured inference among the compared methods. Code: https://github.com/wzz-z/PointEvent

This paper develops a design-based asymptotic theory for two-stage sampling over a continuous spatial domain. The target parameters are integral totals, or smooth functions of such totals, defined over a fixed bounded territory partitioned into an increasingly fine collection of primary sampling units. Within this fixed-area framework, we derive the order of the variance components of the Horvitz-Thompson estimator when secondary sampling units are points selected from continuous sub-regions. We establish design consistency of the estimator, as well as consistency of variance estimators under explicit regularity conditions on inclusion probabilities, sampling densities, and the study variable. The results are extended to plug-in estimators of smooth scaleinvariant functions of totals. For high-entropy first-stage designs, we further show that a Hájek-type variance estimator based only on first-order inclusion probabilities is consistent, and we prove asymptotic normality of both total and plug-in estimators. A simulation study inspired by forest inventory applications illustrates the finite-sample performance of the proposed estimators and variance estimators.

Despite impressive reported scores, large vision-language models have seen limited practical uptake in historical automatic text recognition because of their computational cost, dependence on large-scale pretraining, and hallucination. Historical ATR therefore continues to rely largely on compact CRNN line recognizers, which are visually grounded and trainable on modest data. Lightweight recurrence-free recognizers promise the accuracy of larger models with the practical advantages of CRNNs, yet have not been comprehensively evaluated on historical writing. We adapt PP-OCRv6, a recent compact text recognizer without strong language modeling, for historical line recognition and compare it with a conventional CRNN across generalized pretraining, domain-specific training, corpus-level fine-tuning, and manuscript-specific few-shot adaptation on multilingual Latin- and Arabic-script material. While PP-OCRv6 does not consistently outperform the baseline when trained from scratch, heterogeneous pretraining produces markedly better generalization. Comparisons with the Qwen3.5-based Medusa recognizer further show that fine-tuned PP-OCRv6 can outperform a large VLM tailored towards historical Latin-script HTR.

The rapid advancement of speech synthesis and voice conversion technologies has made audio deepfakes increasingly realistic, posing serious security risks in practical applications. While existing detection methods achieve strong performance under controlled conditions, they often fail to generalize under real-world perturbations and corruptions. In this paper, we propose ROGUE, a framework that dynamically constructs robust detection workflows by orchestrating multiple detection tools. ROGUE formulates workflow generation as a sequential decision-making problem and introduces a dual-agent paradigm, where a perturbation agent generates audio perturbations and a policy agent learns to select and execute detection tools under perturbed conditions. Through adversarial learning, ROGUE enables perturbation-aware tool selection, adaptive execution strategies, and improved robustness to distribution shifts. Extensive experiments across multiple datasets and real-world corruptions demonstrate that ROGUE consistently outperforms strong baselines in both robustness and generalization. Our results highlight the effectiveness of adversarially optimized workflow generation for building reliable audio deepfake detection systems in real-world deployment settings.

Selecting soft ferrites for alternating-field applications requires balancing magnetic response, dissipation, nonlinearity, and heating. We use a field-driven steepest-entropy-ascent quantum thermodynamic (SEAQT) model to compare the electron, phonon, and magnon responses of Fe$_3$O$_4$, MnFe$2$O$4$, and (Mn${0.5}$Zn${0.5}$)Fe$_2$O$_4$ within a common first-principles framework. The model treats spatially uniform longitudinal relaxation and neglects domain-wall motion, transverse rotation, resonance, eddy-current effects, and heat removal. We use $\tau_e=0.05$ ps and $\tau_p=3$ ps for all three materials, with effective longitudinal magnon relaxation times of 500, 200, and 85 ps, respectively; these literature-motivated values are model inputs, not fits to measured losses. Within this framework, the Mn–Zn ferrite gives the largest peak longitudinal magnetization change, retains its response best at high frequency, and shows the largest work per cycle and peak-to-peak magnon temperature change, whereas MnFe$_2$O$_4$ gives the largest normalized $\chi''$ peak. Thus, no single ferrite ranks highest across all metrics: the preferred material depends on the property, frequency, field amplitude, and cation configuration of interest. The model therefore provides a spectrum- and kinetics-resolved screening tool for engineering comparison of ferrites rather than a prediction of total core loss.

The Minimum Vertex Cover problem is a fundamental combinatorial optimization problem, aiming to identify a minimum subset of vertices in a graph such that every edge is incident to at least one vertex in this subset. Among its variants, the Min-Power-Cover problem stands out due to its practical applications, such as camera placement at intersections: in an edge-weighted graph, an edge is covered if one of its endpoints is assigned a power value at least as large as the edge's weight. In this paper, we introduce the Emergency Vertex Cover (Em-VC) problem where an edge may be covered not only by its endpoints, but also by a distant vertex, provided the vertex is given sufficient power to "cover" the cumulative weight of the edges along a shortest path to one of the edge's endpoints plus the weight of the edge. Em-VC is motivated by different practical scenarios, e.g. the need for urban disaster response, where ensuring accessibility to all road segments (edges of the graph) is crucial for effective aid delivery. We prove that Em-VC is NP-hard, derive lower bounds, and design a polynomial-time algorithm for its continuous version. Moreover, we present a 4/3-approximation algorithm for the discrete case and identify several special graph classes for which the problem can be solved in polynomial time.

We analyze a nonlocal operator in space and time, called the multidimensional fractional material derivative. We derive its pointwise representation, which allows us to study its other properties. We define an inverse operator, called fractional material integral, and derive its pointwise representation. Furthermore, we analyze a class of linear partial differential equations, which corresponds to deterministic descriptions of the scaling limits of multidimensional Lévy walks, in which transport is driven by a multidimensional fractional material derivative with a speed vector integrated with respect to a suitable probability measure and a distributional source term. Using Fourier-Laplace transform techniques and a direct convolution-kernel construction, we prove the existence and uniqueness of exponentially integrable measure solutions for measure data. Moreover, we identify a necessary and sufficient condition on the source term for conservation of unit mass and provide separate sufficient conditions for non-negativity and weak convergence to $\delta_0$. We also prove weak continuity and self-similarity of the kernel and continuous dependence on the directional distribution.

AI systems can strengthen democracy by supporting deliberation at scale by addressing cognitive, social, platform-design, and market-driven frictions, while preserving human agency. Unlike proposals such as liquid democracy that restructure representation through vote delegation, in this position paper, we argue that AI-assisted deliberation offers a more promising path by lowering barriers to meaningful engagement without substituting machine judgment for human choice. Drawing on evidence from online deliberation platforms and experimental research, we identify four guiding principles: preserving agency and autonomy, encouraging mutual respect, promoting equality and inclusiveness, and augmenting rather than substituting active citizenship. We also address critical challenges, including alignment, sycophancy, training bias, and over-reliance on AI systems. We call on the machine learning community to develop deliberation-focused AI systems evaluated not on engagement metrics but on their capacity to facilitate informed, representative, and friction-robust discourse.

Explanations of machine learning models are usually judged by criteria that are hard to compare. We propose a simpler test: if an explanation really describes how a model uses its features, it should be possible to rebuild the model's predictions from it. We turn each explanation into a predictor by reading each feature's effect and adding them up, and measure how well that predictor reproduces the model on unseen data. Nothing is fitted, so the score reflects the explanation itself. The test applies to any explanation that can be written as a function of the features; we demonstrate it on partial dependence plots (PDP), accumulated local effects (ALE), SHAP and LIME. We prove that summing partial dependence curves gives the best possible additive summary of a model when its features are independent, and that this fails when they are dependent. Across 13 real datasets and 9 synthetic designs and four model families, which method scores best depends entirely on feature dependence: where features are independent SHAP is slightly worse than PDP, exactly as the theory predicts; on dependent real data SHAP leads. Some widely used quality metrics even prefer a damaged explanation to an intact one.

Because of its collaborative nature, Wikidata suffers from errors, in- consistencies, and excessive complexity, such as redundant classes, ambiguity between instances and classes, wrong taxonomic paths, and type constraint violations. The manual curation of these issues is infeasible at scale. To address these challenges, we introduce WiCleanData, a refined version of Wikidata with a consistent tax- onomy and free from type constraint violations. Specifically, we have designed an automated pipeline that first cleans the taxonomy with language model assistance, then simplifies type constraints by hierarchical aggregation, and finally filters facts accordingly. The resulting knowledge graph, free from any type violation, is made publicly available via a Web interface, enabling easy exploration and downstream applications.

Hierarchical robotic systems executing long-horizon manipulation tasks must make high-level semantic decisions that orchestrate stochastic low-level skills. In this setting, failed rollouts are ambiguous: a poor downstream state may reflect an invalid high-level decision, partial observation, or a valid decision whose physical execution failed. Traditional supervised learning lacks data for such recovery states, while reinforcement learning struggles with sparse rewards and non-local credit assignment. We propose MAGMA-GEN, an on-policy data-generation pipeline that converts ambiguous failed rollouts into validated recovery supervision. MAGMA-GEN first uses a privileged coach to hypothesize an early decision-level error and propose localized correction or recovery actions. Because this diagnosis is fallible, candidates are retained only if re-execution from the same state under matched conditions improves downstream progress. This produces supervised examples from the agent's own failure distribution without per-step human demonstrations. Evaluated on interactive long-horizon manipulation tasks, MAGMA-GEN improves task success and recovery capabilities, against distillation and trajectory-repair baselines under evolving task constraints in both simulation and real-robot execution.

LLM-based social simulations are primarily evaluated for behavioral fit, testing whether agents reproduce the actions or response distributions of the people they are simulating. However, the promise of simulation extends beyond behavioral fit. Simulations can explain human behavior, diagnose barriers, and compare large-scale interventions. These use cases depend on understanding why people acted a certain way, not just what they did. As a result, behavioral fit is insufficient for these types of claims because behavior underdetermines the reasoning process behind it. For instance, the behavior of staying silent may be due to disinterest or suppressed speech, and not answering a call may be due to distrust of the caller or limited phone access. In this paper, we propose representational adequacy as a new evaluation target for LLM-based social simulations. By leveraging LLM reasoning traces, representational adequacy measures whether a simulation's scenario–reasoning–action triples preserve the reasoning process behind the behavior in a way that is faithful to the population and scenarios being simulated. We distinguish representational adequacy from interpretability and alignment metrics, propose ways to integrate it into simulation research, and pose its measurement as an open problem.

Using the exact renormalization group (functional RG) formalism, we construct the energy-momentum tensor of a four-Fermi theory in the Euclidean space of dimensions 2 < D < 4 in the large N limit, where N is the number of Dirac fields. The energy-momentum tensor is a functional of the Dirac fields, and its cutoff dependence is controlled by the exact RG equation. In the zero cutoff limit the functional reduces to the one-particle-irreducible effective action with a single insertion of the energy-momentum tensor. At a finite cutoff the energy-momentum tensor satisfies the Ward-Takahashi identity for translation invariance, and its antisymmetric part is determined by rotation invariance. We also show that the critical theory is conformally invariant by deriving the corresponding Ward-Takahashi identity.

Topology optimization (TopOpt) is a standard tool for structural conceptual design, providing optimal structures with great design freedom. However, it has a high computational costs due to the repeated evaluation of high-fidelity finite element models and frequently produces complex geometries that require extensive interpretation for manufacturability. As an alternative, this work presents a parameterized optimization framework based on Reduced Order Modeling (ROM) and preconditioning techniques. We employ the Empirical Interscale Finite Element Method (EIFEM) coupled with the Discrete Empirical Interpolation Method (DEIM) to construct localized, parameter-dependent reduced operators. From an optimization perspective, this approach can be interpreted as a preconditioning strategy in which inexact gradients are used to accelerate convergence. Furthermore, parameterizing the design space in terms of explicit geometric features, such as inclusion radii or lattice widths, significantly improves the manu facturability of the resulting optimized designs. We assess the performance of the method in terms of computational time, design topology and structural performance with TopOpt as baseline for three differ ent unit cell geometries and three different benchmarks. While the parametric ROM framework requires an initial offline training phase, our comparative analysis demonstrates that it drastically accelerates the online optimization loop and that it can produce even stiffer design in some of our experiments.

We study the off-diagonal matrix elements of real-space observables in time-reversal-invariant single-particle chaotic systems. By analyzing the semiclassical expression for the off-diagonal variance derived from Berry's conjecture, we show that the banded structure of the observable matrix emerges naturally. For local observables, we identify a characteristic bandwidth associated with a late-time timescale inversely proportional to the particle velocity. We further show that, for systems with steep-wall confinement, the predicted magnitude follows the entropy scaling of the eigenstate thermalization hypothesis (ETH), multiplied by an additional kinetic-energy-dependent factor that is independent of spatial dimension and is not captured by conventional many-body ETH. We illustrate these results through a case study of quantum billiards and verify the semiclassical scaling numerically in a generalized quarter-Sinai billiard. Our results elucidate the dynamical implications of Berry's conjecture and provide a comparison between single-particle eigenstate thermalization and many-body ETH.

Few-step distillation reduces the inference cost of image-to-video generation, but directly reusing LoRA adapters trained for long denoising trajectories can weaken their intended effects and degrade video quality. We observe that adapters with similar measured static parameter geometry can behave differently under the shortened target schedule, motivating response-aware transfer. We propose DART, a training-free reparameterization method that transports source LoRAs into aligned coordinates through a low-rank distillation bridge. Paired forward evaluations measure channel-level incremental responses under the target schedule to fit coefficients that calibrate response direction, source-relative magnitude, and timestep allocation. Coordinate transport establishes update directions, while calibration adapts their contributions, requiring neither source training videos nor backpropagation. Experiments across multiple distilled I2V models demonstrate improved generation quality and aggregate functional retention over direct reuse. Further analyses show that coordinate transport complements response calibration, with adapter-level benefits encompassing both functional preservation and reduced negative transfer.

Retrieval assembles repository context by ranking passages for relevance to the current query. A coding agent halfway through an issue has already read much of what such a ranker returns. Relevance is scored per passage, but sufficiency belongs to the set: independently scored passages can fill the budget with support for one requirement while another goes unmet. We formulate state-conditioned minimal sufficient evidence recovery: given a captured agent state, recover a compact evidence combination supplying what its next decision still lacks. SERBench measures this on 500 held-out states from 45 repositories, recording what the agent has seen, crediting only sets that satisfy every annotated evidence requirement of the current decision, and separating set recovery from candidate discovery. MSS-Complement treats acquisition as set construction, not ranking. Three semantic calls propose a jointly sufficient set, search for what it lacks, and return 4-8 intact source units within 6,144 tokens. One configuration, fixed on calibration data, recovers a complete set for 73.0% of those states at five items and 80.6% at eight, against 61.4% and 72.4% for Qwen3 embedding with reranking. A matched control ranking by similarity alone recovers fewer complete sets, placing the margin over it in the set-level policy, not the computation. The lead persists from frozen repository source with no gold-derived pool. On AMA-Bench it answers from a 76.2% smaller answer prompt, with accuracy 2.08 points above that benchmark's own memory agent. Removing one required group from a complete set costs repair-localization precision under two executors. Retrieval for agents is better posed as recovering what a decision lacks than re-ranking what an issue resembles.

We prove a multiplication formula for the Wang-Wei-Zhang cluster character on a Hom-finite $2$-Calabi–Yau Frobenius extriangulated category $\mathcal C$ with a cluster-tilting object under the assumption that its stable category has constructible cones with respect to the induced cluster-tilting object. This formula generalizes those obtained by Wang-Wei-Zhang for $\mathcal C$ in the one-dimensional case and by Keller-Plamondon-Qin for (stably) $2$-Calabi-Yau Frobenius or triangulated categories. As a consequence, we express the frozen term in an Auslander-Reiten mesh with the character of a minimal cosyzygy middle term. For acyclic quivers with principal coefficients, we compute these frozen multiplicities in Higgs categories and obtain explicit principal coefficient mesh relations.

Herbicide-based weed control is increasingly unsustainable due to rising weed resistance and the adverse environmental impacts of chemical use. While mechanical weed control avoids these drawbacks, it is typically implemented using large machines that cause soil compaction. We propose a novel alternative based on small mobile robots for mechanical weeding. Compared with existing automated mechanical weeding approaches, the proposed method offers reduced soil compaction, simpler automation, and improved scalability. Our solution involves a Boston Dynamics Spot quadruped robot equipped with a custom weed removal tool featuring a milling bit at its end. The tool is rigidly attached to the robot and uses the degrees of freedom of the robot base by actuating the legs, while keeping the feet stationary. We develop a software architecture that enables autonomous weed removal and integrate this system with all other required components. We analyze the accuracy and efficiency of the current proof of concept both in an indoor and outdoor environment and provide recommendations for future work to make the system more accurate and efficient.

The paper studies the weighted dual Minkowski problem for the weighted $q$th dual curvature measure of convex bodies in $\mathbb R^n$ first posed by Huang, Lutwak, Yang, and Zhang. Most of the results are in the G-invariant setting, i.e. when the convex bodies are invariant under a closed subgroup $G$ of $O(n)$. They generalize previous results on the existence of solutions to the dual Minkowski problem for origin-symmetric convex bodies. It is proved: (i) a full characterization of the G-invariant weighted dual curvature measure for q\in(0,1], (ii) a necessary and sufficient condition for the existence of solutions to the G-invariant weighted dual Minkowski problem for q\in(1,n), (iii) a sufficient condition for the G-invariant weighted dual curvature measure for q>1, and (iv) an extension of Henk-Pollehn's dual curvature measure concentration property.

We present observations of the recent 2025.6 X-ray minimum and recovery of $\eta$~Carinae, obtained with NICER/XTI, Swift/XRT, XRISM/Xtend, and Chandra/HRC-I. We construct light curves in the soft (0.5–2 keV) and hard (2–10 keV) bands and derive hardness ratios. The X-ray emission reached its minimum about 10 days earlier than in the previous five cycles. As in previous events, the spectrum softened during the decline, while the X-ray luminosity varied on short timescales. These findings strengthen the conclusion that enhanced line-of-sight absorption, such as that expected during an eclipse, does not have a significant role in producing the spectroscopic event. Instead, they indicate that the X-ray decline is caused by stochastic variations and instabilities in the two stellar winds and their interaction, destruction of the colliding winds region, and accretion of primary wind onto the secondary. The main process behind the deep X-ray minimum near periastron is the accretion of mass lost by the primary star onto the secondary star. Accretion at periastron passages in $\eta$ Carinae implies that accretion occurred at much higher rates during the nineteenth-century Great and Lesser Eruptions, when the primary star lost mass at much higher rates. Such accretion likely launches jets. The broader implication is that accretion events in binary systems, possibly with jet launching, power other luminous blue variable giant eruptions and intermediate-luminosity optical transients.

A memory can answer a current query correctly while discarding distinctions required by a later update. We investigate this failure with a paired-history audit: two histories have the same current answer, receive a shared future update, and require different subsequent answers. A pilot evaluates 24 history pairs across six synthetic mechanisms, 12 memory conditions, two repeats, and two model backends. A deterministic frontier selector obtains strict reveal accuracy of 96/96 on DeepSeek and 82/96 on GLM; a structured writer obtains 62 successes with one unresolved outcome and 56/96. The configured four-outcome joint contrast has finite-sample identification intervals of [0.521, 0.542] and [0.292, 0.313], not confidence intervals. A record-level audit distinguishes retained-state adequacy, response delivery, and answer-schema compliance without changing those original scores. It finds 26 and 25 well-formed but semantically wrong structured reveal memories, while all 14 GLM frontier reveal failures contain correct values in the wrong wrapper. Tombstone removal produces 16/16 exact replay failures in the targeted mechanism. Identifier renaming then exposes a separate flaw: original frontier late-reference adequacy falls from 8/8 to 94/320 transformed instances. We provide and test a label-equivariant repair, but it preserves only 2/8 original late-reference answers: eliminating a naming shortcut does not solve unknown future relevance. These results support a scoped evaluation methodology and reproducible failure analysis, not general superiority of the repaired algorithm. Paid pilot evidence, retrospective diagnostics, and new offline tests are reported separately; no independent held-out or natural-task validation is claimed.

Economic networks are often estimated separately over two periods, and changes in their edge sets are interpreted as structural rewiring. Since both networks are estimated, observed turnover also reflects graph-selection error. We study the two-snapshot Hamming-turnover functional under a homogeneous edge-misclassification model. With known sensitivity and specificity and conditional independence of the estimated edge indicators across periods, latent turnover admits a closed-form unbiased adjustment based only on observed turnover and the two estimated graph sizes. We then examine the effects of sparsity, calibration error and dependence across periods. When the number of true links is proportional to $p$, a false-positive probability of order $p^{-1}$ generates expected spurious turnover of order $p$. An error of the same order in calibrating the false-positive probability can likewise leave order-$p$ bias after adjustment. We also derive the bias induced by cross-period dependence and give sufficient conditions for consistency relative to network size. Numerical results illustrate the finite-sample implications.

We report progress toward the development of a quantum silicon-on-insulator (QSOI(R)) technology compatible with 300mm CMOS fabrication and adapted from the 28nm Fully-Depleted SOI (28nm FD-SOI) platform for scalable quantum computing. We compare quantum devices fabricated with standard 28nm FD-SOI and QSOI(R) technologies, and show striking improvements of room temperature electrostatic properties of the individual device. Moreover, the QSOI(R) technology has significantly reduced the device variability and the dispersion of device properties at the wafer level. Transistor metrics are reproduced by TCAD simulations showing that the electrostatics of the devices behave as expected for QSOI(R) technology. Wafer-scale measurements at sub-2K show reproducible quantum dots down to the few-electron regime with 69% yield for successful charge detection of the first electron and a dispersion of the first electron position of $\mathrm{\pm 35 mV}$ over 377 quantum dots. These results establish QSOI(R) as a promising platform for CMOS-compatible quantum device co-integration.

The existence and structure of non-simple blow-up are fundamental questions for the self-dual Chern–Simons–Higgs equation. Physically, this phenomenon describes magnetic-flux concentration in several cores whose mutual distances are much larger than their widths, although all cores approach the same vortex point. Despite substantial progress for singular Liouville equations, the existence of non-simple blow-up solutions to the full Chern–Simons–Higgs equation on closed surfaces has remained open in both the Chern–Simons (CS) and mean-field regimes. We prove that the cores of every non-simple cluster have equal limiting masses, share a common profile type, and form an asymptotically regular polygon. These identities yield an explicit finite list of admissible cluster masses and a four-unit mass-gap criterion. We also construct non-simple blow-up solutions on closed Riemannian surfaces in both regimes. Together, these results establish a sharp arithmetic criterion for single-point non-simple CS blow-up on each fixed flat torus when a suitable exterior divisor may be chosen, and show that vortex blow-up need not be simple, answering Li–Liu's question in the negative.