Papers

Localized lesion evidence may improve automated acne severity grading, but detector errors and differences in clinical grading criteria can limit generalization. We evaluated LENS-GRF, a lesion evidence network with permutation-invariant aggregation and gated residual fusion that combines a global Vision Transformer with lesion-region embeddings derived from YOLO11s proposals. Fully automated four-class grading was evaluated on 292 held-out ACNE04 images and, without external adaptation, on 200 PLSBRACNE01 participants represented by 600 facial views. Annotation-assisted inference used registered lesion boxes from three dermatologists in a matched subset of 148 participants. Performance measures included accuracy, macro-averaged precision, sensitivity, and one-versus-rest specificity. Paired comparisons used exact McNemar tests with Holm adjustment. On ACNE04, automated LENS-GRF achieved 80.82% accuracy, 78.80% macro precision, 78.92% sensitivity, and 92.78% specificity. With supplied lesion boxes, internal accuracy averaged 95.89% across three seeds. On the full external cohort, automated LENS-GRF achieved 35.00% accuracy, compared with 42.50% for an independently trained global baseline. External macro precision, sensitivity, and specificity for LENS-GRF were 50.52%, 34.31%, and 78.19%, respectively. In the matched subset, accuracy using Doctor A's lesion annotations was 47.97%, compared with 35.14% for automated inference (unadjusted $p = 0.0094$; Holm-adjusted $p = 0.0846$). Strong internal performance with supplied lesion annotations did not translate into reliable automated grading on the external cohort. More reliable lesion detection, modelling that accounts for differences in grading criteria, and independent validation are needed before clinical use.

We study braid representations obtained from character-twisted Burau inputs by the Katz-Long-Moody (KLM) construction, which corresponds to multiplicative middle convolution for KZ-type equations. For $n\ge2$, let $q=e^{2\pi ia}$, $\tau=e^{2\pi ic}$, where $a,c>0$ and $nc+(n+1)a<1$. Known form and signature results give a positive-definite invariant form for $\lambda=e^{2\pi il}$, $0<l<1-nc-(n+1)a$. For fixed input, unitary realizations are unique up to simultaneous unitary conjugation. We address two questions. First, we determine spectra and invariant summands of the $M=n(n+1)$-dimensional output. The generator spectrum recovers $(q,\tau)$. The output decomposes into two trivial and two reduced Burau summands, and an $n(n-1)$-dimensional summand isomorphic to Long's reduced construction, generically irreducible for $n=3,4$. If $a$ or $c$ is irrational, every generator is non-Clifford in every finite-dimensional Weyl-Heisenberg frame; if $1,a,c$ are linearly independent over $\mathbb{Q}$, every generator is entangling for every nontrivial bipartition. The full braid image is not projectively dense. For general positive-definite unitary inputs, irreducibility of the full braid output at a nonexceptional parameter forces the free-group input operators to commute. Second, we construct one orthonormal basis giving each generator one block of size $2(n+1)$, $n-2$ blocks of size two, and identity elsewhere. Each generator is a product of $2n$ rank-one phase reflections and, in a fixed binary encoding, an $O(M)$-length word in one-qubit unitaries and CNOTs, without auxiliary qubits and including direction preparation and its inverse. We give finite-alphabet approximation, conditioning and error bounds, and a matched-resource comparison with a Quantum Shannon reference compiler. The gate bound is exponential in the encoded qubit count and excludes classical preprocessing.

We develop an intermediate-derivative theory for Banach-valued evolution classes with Morrey control in time. Let $E_0\hookrightarrow E$ be Banach spaces, $m\ge2$, $1<p<\infty$, and $0\le\lambda<1$. If $u\in\mathcal M^{p,\lambda}(E_0)$ and $u^{(m)}\in\mathcal M^{p,\lambda}(E)$, then every intermediate derivative satisfies \[ u^{(j)}\in\mathcal M^{p,\lambda}\bigl((E_0,E)_{j/m,\infty}\bigr),\qquad 0<j<m, \] with no UMD, Fourier type, or operator-valued multiplier assumption. The proof is based on an exact rational-frequency splitting of $D^j$, the Peetre $K$-functional, and the Hardy–Littlewood maximal operator on Morrey spaces. On the line the estimate has the scale-sharp multiplicative form. On finite intervals we construct a graph-Morrey extension and obtain the same embedding. The weak fine index is optimal for arbitrary Banach couples. Combining the derivative theorem with the exact Morrey trace theorem yields an exact onto trace formula for every $u^{(j)}$, together with mixed Hölder/interpolation embeddings and a trace-powered $p$-to-$q$ Morrey gain. If $E_0\hookc E$, these embeddings become compact both in the same Morrey norm after an arbitrarily small loss of interpolation smoothness and in time-Hölder spaces above the derivative-trace threshold. For positive selfadjoint Hilbert scales we further improve the weak interpolation target to the fractional domain $D(B^{1-j/m})$ and show that this exponent is sharp.

How much entropy must a physical classifier produce to achieve a prescribed accuracy? Rate–distortion theory specifies the minimum information required, but does that information threshold suffice to determine the physical cost? We show that it does not, even for a binary task and a two-state memory. For a uniform binary target observed through a finite symmetric experiment, replacing the classification-error constraint with its necessary mutual-information threshold strictly lowers the infimum of entropy production under a common operation time, integrated mobility budget, and sufficiently large finite transition-rate cap. The separation holds whenever the target error lies strictly between the Bayes error of the observations and chance. Two results establish this physical gap. First, ordering observations by posterior confidence gives exact transport–risk and transport–information frontiers. Observations with the same Bayes error can have different cost frontiers. Second, we construct bounded-rate protocols that realize prescribed encoders with write probabilities below one, starting from exact reset, with an explicit excess cost above the transport bound. An achievable information-constrained cost then falls below a lower bound valid for every task-feasible protocol. Examples with repeated noisy observations illustrate the separation. The results identify a limitation of information-only benchmarks for physical classification: task accuracy and kinetic constraints must be retained explicitly. The cost analyzed is total entropy production during memory writing, excluding data acquisition, controller operation, and subsequent reset.

Oral assessment with generative AI requires more than a conversational interface: educators must connect a spoken response to its source material, scoring criteria, model outputs and subsequent human judgement. This technical report presents CALLIOPE, a source-grounded oral assessment system integrating versioned instructional material, learner-turn recording and transcription, adaptive questioning, two-provider rubric scoring, educator review and exportable evidence. We examine implementation and retained synthetic verification records from 25 September 2026. Three spoken fixtures and a silence control were exercised across two release runs. In the final release rehearsal, the spoken fixtures received aggregate AI scores of 100, 62 and 8 out of 100; two elicited provider-disagreement flags. All eight retrieved audio files across the two runs were byte-identical to their inputs. These observations establish operation of specific exercised paths, not scoring validity or learning gains. A later zero-traffic candidate added version-bound consent checks, insert-only first-pass rating receipts and separately authorised coded exports, supported by local regression tests but not a new full live research workflow evaluation. We distinguish deployed functionality, candidate safeguards and remaining recovery, concurrency and study-operation requirements. The contribution is an inspectable response-to-review workflow and a release-specific account of what its engineering evidence does, and does not, establish. No human-participant outcomes are reported. OpenAI Codex assisted with technical verification, evidence synthesis and manuscript preparation.

We compare motivic nearby cycles at infinity with classes computed directly on rational compactifications. Let $f$ be a regular function on a smooth variety over a field of characteristic zero, and let $X$ be a smooth proper compactification. Suppose that a reduced divisor containing the boundary and the support of $\operatorname{div}_X(f)$ has simple normal crossings near the polar locus. We prove that the open-pair class defined by $1/f$ agrees with Raibaut's compactification-independent motivic nearby cycle at infinity. The key step is a local cancellation under blow-ups of transverse zero-pole intersections. For Laurent polynomials nondegenerate at infinity, this comparison yields a direct toric proof of Raibaut's essential-face formula. Equivariant Hodge realization and weighted Ehrhart theory give Newton formulas retaining cohomological degree and the limit-weight filtration, and determine irregular Hodge numbers through the limiting-irregular comparison. The weight-forgetting specialization computes the zero-potential stringy invariant of toric stacky fans with the same radial support, yielding a motivic-Hodge derivation of the corresponding Fano-Landau-Ginzburg mirror identity. In the full-dimensional weak Fano case, the refined formulas identify monodromy eigenvalues and Jordan-block sizes with inertia ages and anticanonical Lefschetz strings, giving a noncanonical comparison over $\mathbb C$.

Discussing working preferences may support reflection within a design team, but a personality label should not become a performance prediction or a condition of participation. This technical report presents TeamLens, an optional Critsly interface for voluntarily sharing a self-reported MBTI type with a particular board. It separates account activation from disclosure, displays descriptive composition counts, and provides distinct controls for disabling visibility, withdrawing one report and deleting all of one's reports. The evaluation combines released-source inspection, independently specified synthetic aggregation cases, access and lifecycle checks, browser component tests, a local database microbenchmark and deployment records. All 65,536 binary eligibility subsets of sixteen fixed, distinct type reports matched an independent oracle; 128 seeded multiplicity fixtures also matched, after 4,259 synthetic share calls. The isolated HTTP suite passed 183 assertions. In 180 sequential in-memory SQLite read trials, median service-call time increased from 0.064 ms with no profile rows to 200.932 ms with 1,024 rows; instrumented SQL operations followed 11+3n. These findings concern exercised software behaviour and a bounded workload. They do not establish human usability, psychometric validity, learning gains, team-performance effects or production capacity. The contribution is an implemented disclosure-to-aggregation workflow and an auditable technical account of its correctness boundaries, privacy limitations and scaling cost. OpenAI Codex assisted with implementation, evaluation and manuscript preparation; the paper discloses this use and its limits.

Identity assurance is the cost a digital system pays for dishonesty and uncertainty: it exists to make acts attributable when not everyone can be trusted at their word. A common way to pay that cost is flat maximum verification, asking each participant to meet a single high level of identification at entry, before any capability is exercised. Paid on everyone, it over-collects, excludes participants who cannot meet a bar they never needed to clear, taxes every interaction with the cost of the rarest high-risk case, and binds the strength of identification to the activity it unlocks. Existing frameworks compound this by fixing a small number of per-credential levels inside a single legal space and binding each verification to the institution that performed it, leaving cross-border reuse and the tension between data erasure and evidentiary retention unaddressed. This paper develops, as a design-science proposal, a tiered and reusable model of identity assurance for natural, juridical, and machine entities across jurisdictions. Reading the problem through systems theory, where a system changes only when an entity acts, the model holds the assurance state apart from the capability gate that consumes it, so that identity demand follows the act and the weight of its consequences rather than mere presence: a participant may take part with minimal disclosure and supply more only as an act requires. It comprises a typed entity taxonomy, a two-axis coordinate of disclosed assertion scope and source of information, jurisdiction as a time-indexed attribute of the entity, and reliance recorded as bitemporal, liability-allocated, point-in-time snapshots. Requirements are derived from anti-money-laundering, electronic-identity, and data-protection law, and the proposal is evaluated against flat maximum verification, per-credential level-of-assurance designs, and institutional reusable-KYC reliance.

Collective spin systems in solid-state materials are promising platforms for quantum-enhanced sensing. In systems such as nitrogen-vacancy centers in diamond, donor spins in silicon, and magnetic materials, interactions among many spins can generate collective quantum correlations that improve measurement precision beyond the standard quantum limit. This tutorial develops an intuitive, materials-oriented framework for understanding these effects through nonlinear collective-spin dynamics. We show how nonlinear interactions reshape collective spin states in phase space, redistribute quantum fluctuations, and generate metrologically useful states such as spin-squeezed and entangled states. We then connect these ideal collective dynamics to microscopic interactions and realistic solid-state systems, discussing how interaction strength, disorder, decoherence, and experimental control affect sensing performance. Different platforms and experiments are compared to highlight key material properties, advantages, and limitations. The tutorial focuses on a materials-oriented understanding of nonlinear collective-spin sensing, rather than a comprehensive comparison of experimental platforms or a practical guide to sensing experiments.

Runtime assurance pairs a verified fallback with an untrusted controller and a switching monitor, and is the leading route to admitting learned policies into safety-relevant network control. Its guarantee rests on a condition it assumes rather than requires: that the monitor's estimation error is zero, or at worst stochastic with a characterisable rate. In mobile networks many measurements originate at untrusted endpoints, where the error is neither. We state this assurance precondition and prove it: at zero measurement noise the guarantee survives an adversary controlling $q$ channels if and only if the plant is $2q$-sparse observable with respect to the safety-relevant output. This is functional observability over attack supports, strictly weaker than full-state observability: on our topology a per-cell outage condition doubles the budget and one stated over total offered load triples it. The converse is a constructive attack making a safe and an unsafe trajectory observationally identical; it defeats every monitor on those channels, not one detector, at any noise level. As the trust split is static and known before deployment, confining the adversary to one family yields a confinement threshold, above which trusted channels alone resolve the state and all untrusted channels may be corrupt at once. Three uninfluenceable counters cross it here, lifting the budget from two to six and making placement the dominant lever. Below the precondition the monitor faces a frontier, not a dichotomy; a set-valued monitor is optimal and carries sufficiency into non-zero noise at the residual test's false-rejection rate. An adversary reaching the trigger radius owns the switch regardless. The same argument bounds any monitor reading agent messages rather than measurements. A rank test decides the budget and identification does not preserve it, so a published budget must name its margin floor.

The partial area under the receiver operating characteristic curve (pAUC) is an important performance metric for binary classification that summarizes true positive rates within a specific range of false positive rates (FPRs). Classifiers that achieve high pAUC need to be obtained in many real-world applications such as cybersecurity, medical care, and advertising. Although many methods for maximizing the pAUC have been proposed, they typically require both labeled positive and negative data for training. However, in practice, labeled negative data are often difficult to collect due to privacy concerns or the need for high expertise to annotate them. In this paper, we propose a method for maximizing the pAUC from positive and unlabeled (PU) data without negative data. Within an empirical risk minimization framework, we show that the pAUC, including its FPR-dependent thresholds, can be represented using only the positive and marginal densities, and derive an empirical estimator from PU data. A classifier is then trained by maximizing the derived smoothed empirical pAUC estimator. We experimentally demonstrate the effectiveness of the proposed method with ten real-world datasets.

The extensive diversity of viral genomes challenges alignment-free representations to capture both nucleotide composition and the higher-order organization of recurring sequence patterns. Conventional $k$-mer representations quantify pattern abundance but do not explicitly encode how these patterns are organized across scales. Here, we introduce CANN, an alignment-free framework that combines persistent commutative-algebraic descriptors with neural representation learning for viral family classification. CANN uses persistent facet descriptors to encode the multiscale organization of $k$-mer patterns and complementary $k$-mer counts to capture sequence composition. Convolutional and Transformer encoders independently learn latent representations of these features, and cosine distances within their respective embedding spaces are averaged before $k$-nearest-neighbor classification. Across multiple NCBI viral genome collections, CANN achieves robust family-level performance, with the fusion of encoder-specific distances consistently improving classification relative to either encoder alone. Evaluation on genomes present in the 2026 NCBI collection but absent from the 2024 reference set further supports generalization to unseen members of families already represented in the reference data. Together, these findings show that persistent commutative-algebraic descriptors can complement neural representations of viral genomes, linking algebraic descriptions of genomic organization with data-driven classification.

How should an embodied agent respond when a person's correction may be wrong? We formulate grounded correction arbitration as a choice among accepting, rejecting, inspecting the world, and asking the speaker. GAVA implements this interface with observation-bounded evidence, legal probes, and a one-step expected-loss rule. In text-only ALFWorld, 162 checkpoints produce 972 paired true and false interventions. Complete local inspections give GAVA and always verify 100 percent correction accuracy, establishing the evidence contract rather than a comparative advantage. In same-episode execution, GAVA reduces interaction cost against always verify but ties a cost threshold under a perfect speaker. An exploratory training-only object-location prior lowers interaction and declared joint cost on 340 unseen scenarios by 0.490 and 0.420 relative to uniform GAVA. After freezing the policy, costs, baselines, and multiplicity plan, the gains replicate on 77 non-overlapping seen checkpoints, covering 308 scenarios: 0.595 and 0.517, with both 95 percent checkpoint-bootstrap confidence intervals excluding zero. Joint cost also improves over an identical-prior fixed policy, while the matched calibrated no-VOI comparison remains inconclusive. Semantic GAVA makes four factual errors in each cohort, corresponding to 98.8 percent and 98.7 percent accuracy, and all methods complete every task. Results support selective information gathering with semantic priors under declared costs, but do not establish a general advantage of environmental value of information over clarification. The study uses normalized claims, complete symbolic observations, and controlled speakers; it evaluates neither human participants, visual input, nor physical robots.

We study corank-two distributions $D$ of odd rank $2N+1$ whose associated pencil of skew-symmetric forms $\{d\alpha|_{D}(q)\mid \alpha\in\Omega^1(M),\ \alpha|_{D}=0\}$ lies, at every point, in the generic orbit of the natural $\mathrm{GL}\bigl(D(q)\bigr)$-action; equivalently, $D$ has maximal first Kronecker index. In corank two, this class is the analogue of contact and even-contact distributions. We prove that the corresponding differential relation is ample and hence satisfies the multi-parametric $C^0$-close $h$-principle, and we deduce a complete topological characterization for a $(2N+3)$-dimensional manifold to admit such a distribution. The criterion is satisfied by non-parallelizable manifolds as well. To the best of our knowledge, ampleness has been verified so far for two classes of distributions defined by an open $\mathrm{Diff}$-invariant relation: even-contact distributions (McDuff, 1987) and distributions of rank greater than two with maximal small growth vector, in arbitrary ambient dimension (Martínez-Aguinaga, 2026); for $N\ge2$, our class is a proper open subclass of the latter, singled out by a further condition on the pencil. The verification of ampleness reduces, via Kronecker–Weierstrass normal forms of the restrictions of the pencil to hyperplanes, to computing the convex hulls of the connected components of the complement of the resultant hypersurface in the space of pairs of real binary forms of fixed degrees, components separated by a winding number, i.e., by the classical Cauchy index. This is in contrast with the even-contact case of McDuff, where the set to be removed is thin (i.e., of codimension at least two), so that its complement is automatically connected and ampleness is immediate.

We introduce a dataset of approximately 10,000 Reynolds-Averaged Navier-Stokes (RANS) simulations of steady, incompressible, two-dimensional subsonic flow around downforce-generating NACA 4-digit airfoils, targeting aerodynamic regimes relevant to automotive and motorsport applications (openly available on https://huggingface.co/datasets/ratiolabs/downforce-airfoils). Using this resource, we study geometry-conditioned neural surrogates for fast flow prediction, comparing neural fields with neural ODEs, MLPs with graph-based models, and several spectral geometry-conditioning methods. We further propose Airfoil2Vec, an airfoil-specific spectral geometry encoder that combines the joint contour spectrum with separate spectral representations of camber and thickness, for predicting continuous pressure and velocity fields. We evaluate generalization through angle-of-attack interpolation, interpolation and extrapolation to unseen NACA 4-digit geometries, and generalization to unseen non-NACA airfoils. The resulting surrogate accurately captures aerodynamic quantities and qualitative flow features while providing orders-of-magnitude speedups over conventional computational fluid dynamics.

Let D_N be the determinant of the generic symmetric N x N matrix, and let differential operators act by ordinary differentiation over a field of odd characteristic p. We determine the apolar ideal of D_N in every size. In addition to the classical quadratic relations, it is generated by one (p-1) x (p-1) determinant of differential variables for each set of 2p-2 indices. These additional generators are minimal modulo the quadratic ideal. An exterior-algebra realization identifies the remaining apolar relations with radicals of invariant pairings for SL_2. Semisimplification gives a Hilbert series in terms of Dyck paths of height at most p-2, and the Steinberg symmetrizer gives the explicit generators of the entire radical. We also compute the ranks of powers of a general linear form. The weak Lefschetz property holds exactly when N <= 2p-2, and the strong Lefschetz property holds exactly when N < p.

Retrieval-augmented language models are expected to answer from the retrieved evidence, but in practice they often keep answering when that evidence is missing. We trace this behavior to the training signal: answer-focused fine-tuning assigns no target to unsupported contexts, so it cannot distinguish a reader that abstains from one that guesses, and unsupported answering stays near 100% even as supported accuracy improves. We introduce Regime Boundary Alignment (RBA), which trains a single reader on matched variants of the same question and gold answer. The reader is trained to produce the gold answer when the context supports it, including when conflicting evidence is also present, and to abstain when the correct support is removed; inference is ordinary decoding, with no verifier, threshold, or regime label. On three multi-hop QA datasets across three seeds, RBA reduces the unsupported-answer rate by more than sixty percentage points relative to conflict-focused training while matching its supported accuracy. On a held-out TriviaQA retrieval-miss slice, the same reader reduces unsupported answering from 100% to below 1% while also improving supported accuracy. These results indicate that evidence-gated answering must be learned on both sides of the support boundary.

Large-scale pervasive sensing increasingly relies on high-resolution satellite imagery, yet task-specific onboard vision is constrained by costly annotation and limited computation, memory, energy, and communication resources. Existing approaches largely rely on either data-hungry supervised learning or large vision-language foundation models, limiting efficient adaptation and deployment under these constraints. We present SatLabel, a resource-aware learning framework that transforms limited satellite labels into progressively refined onboard models through adaptive sample acquisition and semi-supervised model adaptation. Rather than repeatedly training on uniformly sampled labels, SatLabel closes the loop between model uncertainty, class imbalance, and pseudo-label quality to selectively acquire informative samples while exploiting abundant unlabeled imagery. This enables a compact student to adapt to target sensing domains with reduced annotation and inference costs. We further introduce an optional Mixture-of-Experts (MoE) student with graph-based feature refinement to enhance representation capacity while retaining a lightweight footprint. We evaluate SatLabel on 11 remote-sensing datasets spanning core, extended, and unseen domains against RemoteCLIP zero-shot inference. SatLabel improves Macro-F1 on most core and extended datasets while maintaining strong cross-dataset transfer to unseen domains. More importantly, the Balanced student contains only 11.2 M parameters and occupies approximately 42.8 MB, compared with 151.3M parameters and 577 MB for RemoteCLIP, while requiring 3.65 versus 5.89 GFLOPs. Across four efficiency benchmarks, it achieves approximately 2x higher GPU-forward throughput and reduces energy per image on datasets.

Behavioral tests measure how a language model reads evidence. We ask whether those measurements help choose a recommendation interface. We evaluate six small instruction-tuned checkpoints across four recommendation domains with chronological evaluation and 3,426 evaluation users. Each request ranks eight candidates. A baseline selector chooses among history-only prompting, prompting with collaborative evidence, and score fusion. It uses observable features and six stability prompts that vary wording and candidate order. An augmented selector adds features from six evidence-reading prompts that ask the model to compare support counts. An interface chosen once on development (validation) data for each domain and checkpoint scores 0.5524 NDCG@5, compared with 0.5447 for the baseline selector and 0.5428 for the augmented selector. Adding the diagnostic features changes NDCG@5 by -0.0019 (95% interval [-0.0046, 0.0004]). The interval includes zero, and its upper bound is below the analysis plan's 0.005 improvement target. Matching the selectors' hyperparameters also leaves the interval upper bound below that target. Evidence from retrieved similar users improves prompting by 0.0999 NDCG@5 over a control using randomly selected users matched for activity. The evidence-reading tests also reveal answer-position and tie-response biases. These results concern the tested selectors and candidate sets. They illustrate why diagnostic measurements should be evaluated by whether they improve recommendation choices beyond existing features and a fixed interface.

Industrial standards often encode the same engineering concept through incompatible hierarchies, identifiers, roles, and structural constraints, so the nearest lexical or embedding match can still be technically inadmissible. This article presents CRASM, a deterministic constraint- and role-aware semantic mapping method, and CRASM-Gate, its selectively model-assisted extension. The framework separates standard-specific canonicalization, bounded retrieval, deterministic rules, destination-versus-origin role interpretation, semantic and structural ranking, ambiguity refusal, and target validation. CRASM-Gate adds a confidence/disagreement gate that may invoke a candidate-constrained large language model, while final authority remains with deterministic validation. A controlled artifact covers six directed industrial-standard pairs, three difficulty levels, and ten configurations, yielding 14,400 sample-level decisions. With a fixed local model endpoint, CRASM-Gate reaches mean F1 0.9938 and an implemented structural-validity rate of 1.0000; deterministic CRASM reaches 0.9931 without generative-model calls; and the model-only baseline reaches 0.5347. Relative to the model-only baseline, CRASM reduces top-1 errors from 670 to 10 while exhibiting 0.0688 s/sample rather than 24.5263 s/sample observed latency. CRASM-Gate improves CRASM by one additional correct decision out of 1,440, with observed latency increasing to 15.7666 s/sample. The results support a deterministic-first interoperability architecture in which model assistance is optional, measurable, candidate-bounded, and unable to bypass structural validation.

In 1918, Gross proved that a regular local inverse of a meromorphic function in the plane can be continued analytically along every ray from its centre except for directions in a set of Lebesgue measure zero. Eremenko asked whether the same conclusion holds for an implicit function defined by an entire relation in two variables. We prove that there exist an entire function $F$ of two variables and a regular implicit germ $\varphi$, defined by $F(z,\varphi(z))=0$, whose analytic continuation fails on every ray from its centre. In fact, along each ray, the modulus of the continuation tends to infinity as the singular point is approached.

Starting with the vertices of a simplex in $\R^n$, we build a cubic vector field. If the semiaxes of the simplex's John ellipsoid are distinct, the Jacobian of this field has repeated eigenvalues exactly on the ellipsoid's focal sets. This works in every dimension $n\geq2$. We give examples in $\R^4$, $\R^3$, and $\R^2$: three focal quadrics, an ellipse and a hyperbola, and finally two points. In the plane, these two points are also the zeros of the derivative in the Siebeck–Marden theorem. Complex numbers explain why the planar case has a shorter formula.

SEC 10-K filings contain substantial financial information that is not consistently captured in structured datasets, creating a missing-data problem affecting over 70% of firms and half of total market capitalization. This can disproportionately bias quantitative analysis against smaller firms, which may be excluded due to limited available data. Traditional financial extraction methods such as Regular Expressions (Regex) and BERT, have been widely used. However, they are highly brittle when parsing complex SEC 10-K filings, which leads to data that is existent in the files being lost since these methods do not consider that a data attribute could be located in a different section or a footnote. This study evaluates several Large Language Models (LLMs), including Llama-3 8B, Qwen-2.5 14B, and Llama-3.3 70B, to figure out individual model strengths and weaknesses when extracting specific attributes from SEC 10-K text. The extraction quality was evaluated across four financial variables of varying structural complexity: Cash and Cash Equivalents (tabular), Short-Term Debt (hybrid), Credit Facilities (narrative), and Research and Development (hybrid). Results show that while smaller models like Llama-3 8B experience performance degradation under complex negative prompting, aligning parameter scale with document complexity yields high zero-shot accuracy. Qwen-2.5 14B excels as a tabular specialist with an 83.33% F1 score on Cash, whereas Llama-3.3 70B effectively navigates dense narrative footnotes, achieving a 76.92% F1 score on R&D. This scalable framework addresses critical information gaps in quantitative finance datasets and eliminates missing-data bias through a more thorough analysis of the SEC 10-K files.

Modern bioacoustic foundation models like Perch and BirdNET can identify species with high discriminative accuracy, yet their confidence scores are often uncalibrated and difficult to interpret as probabilities of real-world occurrence. This limits their use for ecological inference beyond threshold-based detection. We leverage a global annotated acoustic dataset (WABAD) to produce calibration priors for an acoustic model, optionally incorporating species-level information. We introduce new methods of fusing the acoustic predictions with geopriors, which empirically improves calibration while preserving discrimination. Together, these results suggest a path to simpler and more reliable acoustic monitoring for broad biodiversity.

One examines a codimension-one thick braneworld in the scalar representation of $f(Q,B)$ gravity, where $Q$ is the nonmetricity scalar, and $B$ is the boundary term satisfying $R=Q-B$. We write the gravitational sector in terms of two auxiliary scalar fields, $\varphi=f_Q$ and $\psi=f_B$, and an interaction potential $U(\varphi,\psi)$ obtained by a Legendre transformation from the $f(Q,B)$ function. Working in the coincident gauge and assuming a five-dimensional warped geometry with four-dimensional Poincaré symmetry, we derive the complete set of brane equations sourced by a canonical bulk scalar field. To accomplish our purpose, we address two models of smooth asymptotically AdS thick brane with localized scalar profiles. Furthermore, we also analyze tensor perturbations and demonstrate the localization and stability of the massless graviton.

We report on the design, simulation, and initial testing of Low Gain Avalanche Diode (LGAD) sensors fabricated in 65 nm CMOS technology on 12 inch wafers. These sensors were developed as part of a project to demonstrate full wafer to wafer hybrid bonding of sensors and 28 nm Readout Integrated Circuits (ROICs). The sensor submission and test included standard (reach-through) LGADs, AC coupled LGADs, and Deep Junction LGADs as well as various test structures.

Sampling based consistency is widely used for hallucination detection, yet aggregate performance can conceal systematic differences in which errors are detectable. This work studies that heterogeneity across four language models and three factual question answering datasets. Partitioning hallucinations by answer agreement reveals high agreement (Ghost) and low agreement (Flickering) regimes with an apparent detectability gap of $0.35$ to $0.46$ AUC. Because the statistics used to define the regimes and measure this gap are strongly coupled ($|\rho|\approx0.94$ to $1.00$), the raw result is treated as a property of agreement based detection rather than independent evidence. After freezing regime assignments, lexical and semantic response dispersion preserve the asymmetry, with bootstrap $95\%$ intervals excluding zero in all $12$ model and dataset settings. A stricter test using individual diffusion trajectories and no cross seed information preserves the asymmetry across all three LLaDA datasets ($p<0.005$) and directionally across all three Dream datasets, with one reaching significance. The hard regime varies substantially in prevalence across models ($16\%$ to $77\%$), and matched prompts frequently change regimes between models. These findings show that aggregate detection metrics conceal persistent, model dependent heterogeneity in language model failures and motivate regime conditioned evaluation.

High-throughput data movement is a defining requirement of the WLCG computing model, yet end-to-end performance is often constrained less by the network backbone than by host-level configuration. We present the results of a WLCG mini-capability challenge focused on host optimization at ATLAS and CMS sites (FNAL, UCSD, UNL, BNL, AGLT2, MWT2, and Vanderbilt), using EL8/9 hosts with 25\,Gbps or higher NICs. NET2 participated in a subsequent trans-Atlantic test. The methodology combines ESnet Fasterdata guidance with the OSG-hosted fasterdata-tuning.sh framework, applying TCP, queue, offload, and ring-buffer tuning with save and restore support for safe baseline comparisons. Results show that tuning benefit depends critically on the local bottleneck. Where DTNs and storage were both capable (UNL), FTS throughput rose from 60 to 90\,Gbps. Where storage was the binding constraint (UCSD), iperf3 throughput improved from 20 to 90\,Gbps while FTS was unchanged. Where the NIC was the binding constraint (Vanderbilt, 25\,G NIC), the tuning profile actively reduced throughput, motivating a review of per-site applicability. The challenge also surfaced and resolved a dCache proxying misconfiguration at AGLT2, demonstrating that mini-challenges serve a diagnostic function beyond raw performance measurement.

Let $M_f$ be the closed hyperbolic $3$–manifold which is the mapping torus of a pseudo-Anosov homeomorphism $f$ of a closed surface $S$ of genus at least two. The inclusion of the fiber subgroup \(\pi_1(S)\hookrightarrow \pi_1(M_f)\) has a Cannon–Thurston boundary map \(\partial\pi_1(S)\cong S^1\to S^2\cong\partial\pi_1(M_f)\), which is a Peano curve. We relate this map to two variational representatives of the fiber homotopy class: the harmonic map of Eells–Sampson and Hartman, and a least-area embedded minimal surface. Equivariant lifts of homotopic maps are a bounded distance apart; hence, for every marked conformal structure on $S$, the lift of the harmonic representative extends continuously to the closed disk with boundary value the Cannon–Thurston map, and a least-area fiber lifts to a properly embedded minimal plane in $\Hh^3$ with the same boundary map. We give area and curvature bounds for a least-area fiber, show that its largest principal curvature is at least one, and study the energy of the harmonic representatives as a function on Teichmüller space, its critical points, which are the zeros of the Hopf differential, and its invariance under the monodromy.

Substituting a velocity constraint into the kinetic energy before forming Lagrange's equations yields, in general, incorrect equations of motion. Recent literature calls this failure "Hamel's paradox," a term introduced in 2010. We show that there is no paradox. The inadmissibility of the substitution was recognized in the 1890s; C. Neumann (1899) named the operation the illegitimate form of the kinetic energy, and Hadamard (1895), Chaplygin (1897), Appell (1899) and Hamel (1904) established its limits of validity. Hamel's textbook of 1949, the nominal source of the paradox, states the prohibition and uses Neumann's term; the result remained in print in the specialist literature and in geometric mechanics. The modern debate cites none of this record; we collect it from the primary sources and measure the debate's claims against it. A geometric analysis identifies the substituted function as the restriction of the mass metric to the constraint distribution. If the distribution is integrable, the restriction is the induced metric of an integral manifold, and the substitution is legitimate. If not, the correctly embedded Boltzmann–Hamel equations differ from those of the restricted energy by a single residue, $\mathrm{Res}_\alpha=c^{s}_{\alpha\beta} \omega^\beta P_s$, relative to the complement of the constraint distribution that the shortcut selects. The residue vanishes exactly when the symmetric part of its coefficient vanishes. The two classical admissibility mechanisms, decoupling of the mass metric and vanishing bracket components, are sufficient for this and, for a single constraint, also necessary; for several constraints they are not, which corrects a necessity claim in Hamel's paper of 1904.