Papers

Machine-learning libraries such as Weka and scikit-learn were designed for human programmers. Language-model agents now use these same libraries by recalling APIs from memory and writing code, an approach that hides what a library offers, delays errors until runtime, and loses experimental state between turns. We present TuiML, a self-contained machine-learning library built for AI agents, with native algorithms across supervised, unsupervised, time-series, data handling, tuning, and evaluation tasks. Every component describes itself through machine-readable metadata and parameter schemas, so an agent can search the library, inspect components, compose validated workflows, and register new ones that become discoverable in turn. Every call is validated, seeded, and traced, and sessions export as runnable notebooks, making experiments reproducible by construction. One specification layer drives the Model Context Protocol (MCP), agent-framework adapters, a Python API, a CLI, and local model serving, while data and models never leave the machine. Benchmarks show TuiML remains predictively competitive with scikit-learn and Weka. While looking like a conventional library to a human user, TuiML is designed for agents first, allowing them to read, extend, and operate machine learning autonomously. TuiML is open source, with documentation at https://tuiml.ai.

KV-cache reuse can reduce inference cost in retrieval-augmented generation and agentic systems, but cached contexts may become stale when retrieved knowledge, working memory, or user state is edited. Under causal self-attention, even a local edit can affect downstream KV states. A full re-prefill reliably restores consistency but is costly, whereas refreshing only the edited span can leave downstream dependencies stale. We formulate in-place repair as budgeted recomputation and compare training-free position-selection policies on a factual RAG benchmark with matched direct and derived edits. Across three model families, all policies repair direct cases, but derived cases clearly separate them. At the primary budget, a contiguous edit-local window recovers at least 0.94 of the post-edit answer margin and substantially outperforms attention-based, KV-deviation, and structural selectors. Mechanistic analysis shows that position sets effective under clean-state transplantation can fail under actual recomputation because scattered positions inherit surrounding staleness. The edit-local advantage also depends on adjacency and largely disappears when the answer-bearing text moves downstream. Because answer-relevant edits almost always corrupt model behavior, failure severity is difficult to predict, and repair is 13-21 times faster than full re-prefill, our results support unconditional edit-local repair when the dependent text remains adjacent to the edit.

Can the terminal macroscopic outcome of a many-body system be inferred from its microscopic initial data without simulating the full trajectory? Rather than construct such a shortcut, we address a more fundamental question for Gaussian microscopic inputs: can any fixed Wiener-Hermite degree retain a nonvanishing fraction of the variance of the terminal outcome as the system grows? We consider homogeneous systems with independent Gaussian disorder in which all microscopic coordinates are symmetry-equivalent, the terminal event is monotone in each disorder variable, and a uniform disorder shift is exactly equivalent to a control-field shift with a size-independent conversion factor. Using forward and inverse Gaussian influence bounds together with a Gaussian Russo formula, we derive a directly measurable criterion that is both necessary and sufficient for noise sensitivity. Specifically, the correlation between the original and coordinate-perturbed terminal outcomes vanishes asymptotically for every fixed nonzero level of coordinatewise noise if and only if the slope of the outcome probability with respect to the control field at the balanced threshold grows more slowly than the square root of the system volume. Event-driven simulations of the three-dimensional driven random-field Ising model up to linear size 192 find that both the normalized response and the correlations between perturbed samples decrease overall, consistent with the noise-sensitive regime at finite size. For spatial Stag-Hunt dynamics with prescribed seeds, the criterion generalizes through an effective number of influential coordinates. Separately, simulations of a path-dependent best-response game show, over the sizes studied, that the terminal equilibrium can depend on the update schedule while still carrying substantial finite-order predictive information.

Speech Large Language Models (Speech-LLMs), typically built from a pre-trained speech encoder, a modality projector, and an LLM fine-tuned with Low-Rank Adapters (LoRA), have shown strong Automatic Speech Recognition (ASR) performance on general-domain speech. However, adapting them to domain-shifted speech, such as child or dialectal speech, remains challenging under limited target-domain data. Given the dominant role of the LLM in Speech-LLMs, with cross-entropy loss applied only at the LLM output, the speech encoder may receive insufficient adaptation to new acoustic conditions. In this paper, we propose Encoder Awakening via Adapters (EAVA), a simple yet effective domain-adaptive fine-tuning method for Speech-LLM-based ASR. First, lightweight adapters are inserted into each encoder layer and trained exclusively, enabling target-domain acoustic knowledge to be incorporated into the encoder while preserving its pre-trained knowledge. Second, the full model is jointly fine-tuned on the target domain with LoRA applied to the LLM. Experiments on three domain-shifted ASR datasets, covering child and dialectal speech, show that EAVA consistently outperforms vanilla fine-tuning and other baselines, achieving new state-of-the-art performance.

The rapid expansion of data centers presents both economic opportunities and systemic risks for Caribbean Small Island Developing States~(SIDS). This paper develops a PyPSA-based capacity expansion framework for optimal co-location of data centers with renewable energy infrastructure, incorporating behind-the-meter battery storage, workload flexibility (70%/30% inflexible/flexible split), and multi-bus transmission topology. Two case studies are examined: Trinidad~&~Tobago (single-bus, 92\,MW Brechin Castle solar, 5\,MW data center) and Jamaica (4-bus 138\,kV JPS network, 15\,MW data center at Kingston). Jamaica's optimum deploys 405\,MW solar, 278\,MW wind, 800\,MWh grid-scale BESS, and 84\,MWh behind-the-meter BESS, achieving 42.5% renewable penetration; Trinidad's gas-anchored optimum builds no new RE, and a sensitivity analysis shows solar entering at gas costs above \$65--70/MWh, a carbon price of \$25–50/tCO$_2$, or solar CAPEX of \$800/kW. A post-hoc distributionally robust stress test evaluates hurricane resilience, and a novel 10-factor siting framework addresses the regulatory gap in SIDS that lack data-center-specific zoning. Results show that energy-optimal locations may score poorly on societal criteria—noise, freshwater stress, zoning readiness. This demonstrates the need for integrated planning tools in small island contexts.

Estimating quantum state properties is essential across a wide range of applications, from studying quantum many-body physics to benchmarking quantum hardware. We present Qurrium, a Python package built on Qiskit that implements randomized measurement protocols for estimating purity, second-order Rényi entropy, expectation values of Pauli observables, and state overlap. In this paper, we focus on the classical shadow protocol and demonstrate two workflows in Qurrium. One is the end-to-end workflow that integrates quantum circuit preparation, simulation, measurement, and analysis. The other is the standalone estimation workflow that accepts pre-collected measurement data from any hardware platform in Qurrium's data format. We demonstrate both workflows through examples of a cluster state and an Ising time-evolved state. Furthermore, we report results obtained from a superconducting quantum processor developed by Academia Sinica and analyzed using the standalone estimation workflow. Qurrium is built on Qiskit, the dominant framework in quantum computing software, making it directly accessible to the large community of researchers already working with Qiskit. The source code is openly available at https://github.com/qurrium/qurrium and the example code is provided at https://github.com/qurrium/classical-shadow-examples.

We study a quadrature-surface free boundary problem driven by the Riemannian $p$-Laplacian on a smooth compact finite-dimensional Riemannian manifold. We formulate the problem as a shape optimization problem and develop an intrinsic admissible class based on a uniform Riemannian $RC$-$GNP$ condition~\cite{DS3}. We establish compactness of admissible domains and stability of the associated Dirichlet problems under strong $RC$-$GNP$ convergence. In particular, the states converge strongly in $W^{1,p}$ and the associated $p$-torsional energy is continuous. Under additional boundary regularity, we derive the first variation of the shape functional and obtain the free-boundary Euler–Lagrange condition \[ |\nabla_g u_\Omega|_g^p=\sigma H_{\partial\Omega}+k^p. \] We also formulate the contact optimality inequality, prove the Riemannian comparison of second fundamental forms at tangential contact, and obtain a sufficient condition on a reference domain which rules out contact and yields a solution of the free-boundary problem. Explicit radial examples on geodesic balls of the round sphere are included.

Emotion recognition in conversation (ERC) is a production capability behind agent-assist prompts, escalation routing, and post-call analytics in contact-center-as-a-service (CCaaS) platforms, where cost and latency constraints matter as much as accuracy. We report a systems-level comparison of three deployment options for dialogue-contextual ERC: a low-cost stacked ensemble (sentence embeddings, windowed context, RandomForest/XGBoost/logistic-regression stacking), off-the-shelf LLM prompting (GPT-4o-mini; zero-shot, few-shot, chain-of-thought), and a confidence-gated hybrid that escalates only the ensemble's least-confident predictions to the LLM - modeled on IVA-to-human-agent escalation policies used in production contact centers. On IEMOCAP, the ensemble significantly outperforms every LLM configuration (0.595 vs. 0.460-0.536 weighted F1, p < 0.0001) at a fraction of the cost and sub-10ms latency; on MELD and CMU-MOSI the ranking reverses, showing neither pure system is a safe default. The confidence-gated hybrid resolves this by Pareto-dominating both pure systems on all three datasets (0.620, 0.643, 0.824 weighted F1) while routing the majority of traffic through the near-zero-cost ensemble, translating to roughly $10-85 per million utterances versus $99-170 for an LLM-only pipeline. The escalation policy is not an opaque cost/accuracy dial: escalated turns disproportionately follow an emotion or sentiment shift, giving operators an interpretable, auditable routing signal, and the ensemble's confidence is well-calibrated and safely under- rather than over-confident. The pattern holds across three datasets and two LLM providers. Confidence-gated cascading is established in general ML systems; our contribution is showing it transfers cleanly to dialogue-contextual ERC, yielding a concrete deployment recipe for CCaaS and conversational-AI platforms deciding how to allocate LLM spend.

We report the environmental qualification and performance of CombSat, a dual optical frequency comb payload designed for deployment on a 12U CubeSat in low Earth orbit. The payload integrates two self-referenced, 200 MHz hybrid fiber-waveguide frequency combs, a narrow-linewidth optical reference, a heterodyne beat detection unit, and FPGA-based control electronics in a total mass of 8.3 kg and volume of 5.7 L, and nominal power consumption of 21W. We describe the mechanical, thermal, and radiation-tolerant design features of the system and present the results of random vibration, storage temperature cycling, and thermal-vacuum testing conducted in accordance with NASA's General Environmental Verification Standard. We show that key comb performance metrics including oscillator and amplifier output power, frep, fCEO, and fopt signal-to-noise ratios, and integrated phase noise, remain within specification after environmental exposure, and we discuss observed failure modes and design modifications that improved robustness. These results demonstrate that compact, low power, fully stabilized, autonomous dual-comb systems can be engineered and qualified for spaceflight on CubeSat platforms, providing a path forward for future low-cost comb-based space applications.

For an algebraically closed field $k$ of characteristic $p>0$, we study unramified $\mathbf{Z}_p$-towers $\{X_n\}_{n\ge 0}$ of smooth, projective and connected curves over $k$. Our main result provides an Iwasawa-theoretic description of the Newton polygons of their Jacobians, establishing that the slopes of the new part at level $n$ are eventually affine functions of $p^{-n}$ with rational coefficients.

High-energy hadron reactions could be appropriate to find exotic evidences in exotic hadron candidates instead of global observables such as masses, spins, parities, and decay widths, because quarks and gluons are explicit degrees of freedom. One of possible methods is to use fragmentation functions (FFs) by taking advantage of properties on favored and disfavored functions, which corresponds to valence-quark and sea-quark distributions in parton distribution functions. Looking at these FFs, we should be able to find the exotic nature as the valence-quark distributions reflect the nature of valence constituents as shown in the pion and the proton. Recent accurate measurements of the $f_0$(980) FFs by the Belle collaboration made it possible to find its internal configuration by looking at their second moments and functional forms. Global analysis results of the $f_0$(980) FFs indicate that its internal configuration looks like $s\bar s$, which is different from a tetraquark or $K\bar K$-molecule like configuration suggested from low-energy studies. This fact indicates that the internal configuration looks different depending on the energy. At low energies, it looks like a tetraquark ($K\bar K$ molecule) hadron, but it looks like a $q\bar q$ hadron at high energies. In the similar way, some exotic hadron candidates could become ordinary $q\bar q$ or $qqq$ hadrons at high energies, although they are interpreted as exotic at low energies. This kind of new idea should be tested by future experiments especially by looking at energy or momentum dependencies in high energy hadron reactions.

We introduce a new single-loop algorithmic framework for smooth nonconvex–concave minimax optimization. The resulting projected damped extragradient method combines projected extragradient updates, dual momentum, and a moving proximal center. Under both the optimization-stationarity and game-stationarity criteria, our method achieves the best-known complexity among single-loop first-order methods. For optimization stationarity, our method achieves a gradient complexity of $O(L^2D_Y\bar\Delta_0\varepsilon^{-3})$, where $L$ is the gradient Lipschitz constant, $D_Y$ bounds the diameter of the dual feasible set, and $\bar\Delta_0$ is an initialization quantity involving the value-function gap and the initial gradients. Moreover, by incorporating a fixed-center warm-up phase, the complexity can be improved to $O(L^2D_Y\Delta_\phi\varepsilon^{-3})$, up to an additive lower-order cost, where $\Delta_\phi:=\phi(x_0)-\inf_x\phi(x)$. We further establish a lower bound of $\Omega(L^2D_Y\Delta_\phi\varepsilon^{-3})$ for optimization stationarity over projected zero-respecting first-order methods. This lower bound proves that the warm-started version of our algorithm is optimal up to a constant factor for optimization stationarity within this oracle class. For game stationarity, our method achieves $\mathcal{O}\!(L^{3/2}D_Y^{1/2}\Delta_\phi\varepsilon^{-5/2})$ gradient complexity. This matches the best-known complexity of multi-loop first-order methods, thereby establishing the same complexity with a single-loop algorithmic structure. Under dual strong concavity, the proposed framework achieves $O\!(\sqrt{\kappa}\,L\Delta_\phi\varepsilon^{-2})$ leading complexity for both stationarity criteria, where $\kappa=L/\mu$ is the dual condition number, up to an additive initialization cost. The $\varepsilon^{-2}$ accuracy dependence is optimal under fixed regularity and initialization bounds.

We investigate structural properties of the ideal-null sequence spaces c_{0,I} and c_{0,I}(X), and of the quotient l_infty/c_{0,I}, emphasizing the interaction between Banach space theory and combinatorial, topological, and measure-theoretic properties of the underlying ideal. We study classical problems related to c_0, including the dual space, compactness criteria, bounded and compact c_{0,I}-valued operators, Sobczyk-type extension phenomena, and complemented copies of c_0. We identify c_{0,I}^* isometrically with a space of bounded finitely additive measures on I and obtain a canonical atomic-singular decomposition, with l_1 as an isometrically complemented summand. A Dini principle for ideal convergence yields characterizations of relatively compact subsets of c_{0,I} and of compact operators with range in c_{0,I}. We prove a Sobczyk theorem for c_{0,I} and show that its separable-injectivity constant is exactly 2 for every proper ideal. We also construct, in ZFC, a class of statistical ideals for which c_{0,I} is not complemented in l_infty, and characterize complemented copies of c_0 in c_{0,I}(X) via the corresponding properties of c_{0,I} and X. Finally, we describe quotients associated with direct and Frolik sums of ideals, characterize Banach-lattice copies of c_0(kappa) in l_infty/c_{0,I} through I-almost disjoint families, identify ad(I) with the cellularity of the associated Stone space, and determine its behavior under Fubini products.

We consider a soft version of the spherical Sherrington-Kirkpatrick model, where the spherical constraint is replaced by a radial confinement term. We prove that, for a real symmetric disorder matrix under suitable spectral assumptions, the free energy exhibits two distinct fluctuation regimes. In the high-temperature regime, the fluctuations are asymptotically Gaussian. In the low-temperature regime, the fluctuations are governed by the largest eigenvalue and converge to the GOE Tracy-Widom distribution. These results show that the soft radial constraint preserves the fluctuation transition of the classical spherical Sherrington-Kirkpatrick model.

In this paper, we investigate the Fourier uncertainty principle through infinite banded matrices by way of a variational approach to minimizing the uncertainty product. Traditional methods for analyzing the Fourier uncertainty principle rely heavily on the Heisenberg–Weyl structure that underlie the Fourier transform and therefore do not generalize well beyond this setting. We provide three distinct approaches to developing the uncertainty principle based on the spectrum of a shifted quantum harmonic oscillator Hamiltonian, $H_{a,b}$. In the Hermite–Gauss basis, $H_{a,b}$ has an infinite, tridiagonal form which is central to the analysis. One approach exactly solves for the spectrum through analytic methods, another decomposes $H_{a,b}$ into an infinite sum of $2\times 2$ matrices, and the third approach is an algebraic approach to establishing the spectrum via a unitary equivalence with the quantum harmonic oscillator. The approaches taken herein provide alternate avenues that are more broadly applicable to other canonically conjugate operators for other integral transforms which maintain a tridiagonal form.

Long-term memory is becoming a core substrate for personalized AI, yet most systems still represent personalization as discrete records in a largely static latent space, accessed under one global similarity notion. For data mining, this creates a mismatch: the evidence is a temporal event stream, while the dominant abstraction is a searchable record set. We argue that long-horizon personalization should instead model memory as a user-specific dynamical state space with locally heterogeneous geometry. Geometry here is a computational language, not a literal claim about cognition: it captures stable versus volatile regions, variable-rate drift, heterogeneous neighborhoods, and uncertainty about current user state. Profiles and isolated events remain useful as points, but interaction, feedback, and elapsed time induce trajectories. Memory access then becomes trajectory-conditioned reconstruction of the relevant user state, not only nearest-neighbor lookup.

We test whether the maximum penetration depth of a circular intruder into a two-dimensional granular bed can be predicted from its early trajectory using machine learning, without giving the intruder density. From 100 DEM simulations with varying density, we extract kinematic features from the first 50 ms. Ridge and Random Forest predict the maximum penetration. A single feature (the intruder height at 50 ms) concentrates almost all predictive power, showing that density information is already encoded in the early impact response.

In this paper, we study the upper box dimensions, the packing dimensions and the quasisymmetric minimalities of some homogeneous Moran sets. We obtain the upper box dimension formula and the packing dimension formula for three classes of homogeneous Moran sets under some conditions. And two classes of them with packing dimension 1 are shown to be quasisymmetrically packing-minimal.

We reformulate average-cost (ergodic) control of a Markov jump process as a finite-horizon stochastic optimal transport (SOT) problem that jointly optimizes over the controlled evolution and the marginal law from which it starts and returns to (i.e., a self-transport). The constraint relating the marginal flow to the controlled generator is the basic adjoint relationship (BAR), so we call the resulting problem BAR-SOT. For any time horizon T>0, its optimal value is a constant scaling of the long-run average-cost rate. We give three equivalent formulations (through controlled processes, a Fokker–Planck constraint, and relaxed marginal measures) and show that the optimal dual is a stationary potential plus a term linear in time, with slope equal to the rate. A relative-entropy penalty on the control yields a cost-tilted Schrodinger bridge problem, computable by a Sinkhorn-type iteration when every transition rate is controlled, whose value converges to the unregularized optimum as the penalty vanishes. We develop the theory for finite Markov decision processes and then for general controlled Markov jump processes. A neural parametrization of the dual, trained as a physics-informed neural network (PINN), that encodes Harrison's equivalent-workload formulation (see Harrison 2000) matches the strong reinforcement-learning baseline of Dai and Gluzman (2022); numerically conditioning the fit of a sub-dominant transverse correction then improves on both that baseline and the best priority heuristic. On the input-queued switch, a graph-attention parametrization of the dual improves on the strongest matching heuristic we are aware of, with a parameter count that does not grow with the switch size.

AI is changing what leaders must judge, explain, learn, and coordinate, yet existing measures do not capture these behaviors at the level needed to study leadership in AI-enabled work. We develop the AI Leadership Battery, which organizes 36 behaviorally specific subdimensions into 11 theory-specified content families. Following established scale-development procedures, the research used deductive item generation; content validation of definitional correspondence and definitional distinctiveness; exploratory factor analysis and item reduction; confirmatory factor analysis in independent samples; and tests of internal consistency reliability, convergent validity, discriminant validity, and criterion-related and incremental validity. Across the development and validation studies, the analyses provided evidence for the Battery's content, multidimensional structure, reliability, and distinction from selected orbiting constructs. The Battery also contributed additional information beyond orbiting constructs across organizational growth, decision speed, customer/stakeholder response capability, AI-enabled team performance, AI-enabled work experience, AI security and risk management, and AI adoption and integration. The resulting measure provides researchers with a behavioral framework for examining how leaders in AI-enabled work regulate judgment, learning, adaptation, transparency, and accountability.

This paper extends Mixed-Integer Differentiable Predictive Control (MI-DPC) to multi-modal discrete decisions and nonconvex polynomial dynamics arising in Underground Pumped Hydro Energy Storage Systems (UPHES). A neural policy mapping problem parameters to continuous setpoints and integer mode selections via a Gumbel-Softmax layer is trained in a self-supervised manner by differentiating the expectation of the finite horizon control objective through the nonlinear dynamics model. Three methodological contributions enable this extension: a parallel differentiable simulator that preserves gradient magnitude, a Transformer encoder that captures long-range temporal dependencies, and a Gumbel-Softmax temperature annealing schedule that regularizes the combinatorial search. We demonstrate the framework on day-ahead scheduling of a UPHES, a large-scale mixed-integer optimal control problem with nonlinear unit performance curves and volume-head coupling. MI-DPC achieves only 1.6% suboptimality relative to a piecewise mixed-integer quadratic programming baseline, while providing five orders of magnitude speedup in online scheduling time.

Functional principal component analysis (FPCA) provides low-rank representations of functional data but generally produces dense components, making it difficult to identify the localised regions contributing to dominant modes of variation. This limitation is particularly relevant in Raman spectroscopy, where spectra are observed over an ordered domain and interpretation often focuses on chemically meaningful spectral regions. This study proposes variable-projection sparse FPCA (VP-SFPCA) for interpretable functional dimensionality reduction through sparse weight functions that promote localisation. The method formulates sparse FPCA as a regularised matrix-factorisation problem that incorporates the functional inner-product geometry and distinguishes sparse weight functions used to generate component scores from orthonormal loading functions used for reconstruction. Variable projection conditionally minimises over the loading functions, reducing the optimisation problem to the sparse weights. Performance was evaluated through simulation studies and empirical analyses of surface-enhanced Raman scattering (SERS) spectra, with conventional FPCA and SCAD-SFPCA serving as dense and sparse functional benchmarks, respectively. In the simulations, VP-SFPCA recovered localised functional structure while requiring substantially less computation than SCAD-SFPCA. In the empirical analysis, VP-SFPCA retained this computational advantage while yielding held-out reconstruction error close to that of conventional FPCA. Several prominent features of the estimated weight functions also coincided with established adenine SERS bands. Overall, VP-SFPCA provides a computationally practical approach to improving the interpretability of dominant functional modes through localisation.

We provide a unified description of a stable variational family of traveling vortex dipoles for the two-dimensional incompressible Euler equations, connecting the classical Lamb dipole to asymptotically radial dipoles in the large-impulse regime. We show that this family undergoes a sharp transition from the Lamb dipole, where the mass constraint is inactive, to non-explicit traveling waves for which the mass constraint becomes active, and determine the critical value exactly. We further prove that the variational solutions are unique up to translation both near the Lamb dipole and in the large-impulse regime. As a consequence, the corresponding individual traveling waves are orbitally stable. Our results provide a unified picture of these two distinct asymptotic regimes within a single variational family of traveling vortex dipoles.

It is crucial to monitor the levels of Non-Ionizing Radiation (NIR) to which the general population may be exposed and compare them to the limits defined in the current standards, in view of the rapid rise of communication services and the prospects of a connected society. A high number of people visits shopping malls and since these locations usually have several indoor antennas close to the public, it is therefore a kind of place that must be evaluated. Thus, this work presents measurements of the electric field in a shopping mall located in Natal, Brazil. We proposed a set of six measurement points, following two criteria: places with great the flow of people and the presence of one or more Distributed Antenna System (DAS), co-sited or not with WiFi access points. Results are presented and discussed in terms of the distance to DAS (conditions: near and far) and flow density of people in the mall (scenarios: low and high number of people). The highest peaks of electric field measured were 1.96 and 3.26 V/m, respectively corresponding to 5% and 8% of the limits defined by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) and the Brazilian National Telecommunication Agency (ANATEL).

We show that an autoregressive time series on Banach space can be canonically identified with a finite direct product of self-contained and self-determined natural components defined on separate subspaces by the spectral projections for each spectral point of the characteristic linear pencil. We assume the resolvent of the pencil is analytic everywhere except for the spectral points which may be poles or isolated essential singularities. Each natural component is represented as a forward, backward or outward flow fixed by an upstream boundary condition in the far distant past, the far distant future, or at a nominated initial time—depending on whether the corresponding spectral point is outside, inside, or on the unit circle.

For blind and low-vision (BLV) screen-reader users, a website that appears accessible in a static snapshot can become difficult or impossible to navigate once interaction begins. Yet, most automated accessibility checkers miss failures involving focus, interface state, and accessible feedback across interactions. We present A11yLTLNav, a property-based approach for automatically detecting accessibility navigation failures. Through a structured review of prior research, we organize accessibility navigation failures into a failure taxonomy and formalize a browser-observable subset as executable Linear Temporal Logic properties over action-state traces. A11yLTLNav combines random keyboard exploration with runtime property monitoring to detect these failures during interactions. We evaluate A11yLTLNav on 31 generated websites based on real-world websites and tasks. It reported 309 accessibility failures, of which 274 were confirmed, achieving 88.7% precision and identifying more confirmed failures than the comparison checkers. Our results show that A11yLTLNav transforms accessibility knowledge into reusable checks of interface behavior over time.

We study the structure of random $d$-regular triangle-free graphs and show that a sharp phase transition occurs at $d=\frac{\sqrt 3}{2}\sqrt{n \log n}$. For smaller $d$, asymptotically almost surely the graph is non-bipartite, whereas for greater $d$, asymptotically almost surely the graph is bipartite.

We study decompositions of holomorphic isometries of complex hyperbolic space into holomorphic involutions. We prove that, for every n>=3, the involution length of PU(n,1) is 4. This improves the higher-dimensional upper bound 8 of Paupert–Will, as well as the projective upper bound 5 implied by Bünger's linear decomposition theorem, to the optimal value 4. Combined with the two-dimensional result of Paupert–Will, this shows that the involution length of PU(n,1) is 4 for every n>=2. The core of the proof is a three-involution decomposition theorem for square roots: every g in PU(n,1) has a square root of involution length at most 3, and this uniform bound is optimal. The key construction is carried out first on a two- or three-dimensional indefinite block and then completed in higher dimensions by a necessary and sufficient spectral pairing criterion on the positive-definite orthogonal complement. The four-factor lower bound is provided by complex reflections in a point. As a consequence, every element of PU(n,1) is a single commutator, and the two elements in the commutator representation can be simultaneously reversed by the same nontrivial holomorphic involution. This extends the two-dimensional single-commutator result of Paupert–Will to every n>=2 and thereby verifies Djoković's Conjecture A for the family PU(n,1), n>=2.

Large-scale machine-translation (MT) systems are typically evaluated on random samples from a corpus whose distributional composition is an artifact of how it was assembled. Such a sample inherits the phenomena the collection happens to contain rather than the full space a system must handle, spanning rule-governed conventions (terminology, punctuation, currency formatting) and context-dependent phenomena (tone, honorifics, document-level coherence), and thus provides no coverage guarantee for assessing robustness. We propose TACTICS (Taxonomy-Aware Coverage-opTimized Intelligent Corpus Sampling), which recasts coverage as an explicit objective. TACTICS induces a hierarchical taxonomy from a locale style guide, classifies segments against it, and selects a fixed-budget subset jointly optimizing coverage of rare categories, document-level coherence, and distributional fidelity to the full corpus. Applied to MT evaluation across four translation directions, TACTICS improves coverage of rare categories over lexical and embedding-based selection. By targeting the phenomena that separate systems, TACTICS makes a fixed evaluation budget go further, recovering the true system ranking from far fewer segments than random sampling wherever a real quality gap exists and never signaling a difference where none exists.

In lepton scattering from nuclei, it has been taken for granted that nuclear modifications do not exist for the longitudinal-transverse structure-function ratio $R$, although nuclear effects in $F_2$ have been investigated for a long time. In fact, experimental data of lepton-nucleus scattering have been analyzed with this assumption. It is obviously not appropriate because nuclear modifications exist in the function $R$ theoretically as shown in this work. In this work, we explain nucleon's Fermi motion's effects by using a convolution description for nuclear structure functions, especially on the deuteron. The longitudinal and transverse structure functions are defined by taking the virtual photon momentum direction along the $z$ axis. However, nucleons in a nucleus could move in any direction, so that nucleon's longitudinal and transverse structure functions could mix with each other in the nuclear medium. Such mixing effects could be of the order of $\vec p_\perp^{\,2}/Q^2$, where $\vec p_\perp$ is the nucleon's transverse momentum and $Q^2$ is given by $Q^2=-q^2$ with the virtual-photon momentum $q$, because the transverse Fermi-motion is the source of such a mixture. In addition, nuclear effects are different between the longitudinal and transverse structure functions in the convolution model because their $x$-dependent functional forms are different. Convolution integrals have different results between the longitudinal and transverse structure functions for nuclei. Because the experiment is in progress at the Thomas Jefferson National Accelerator Facility to measure the function $R$ for the deuteron, the numerical results are shown on the nuclear effects of $R$ in the deuteron. Hopefully, such nuclear effects are found experimentally by future experiments including heavy nuclear targets.