Papers

Equivalence groups associated with the field equations of arbitrary motions of inhomogeneous hyperelastic solids are investigated. The explicit forms of the infinitesimal generators, namely the components of the isovector field associated with the equivalence groups are derived. Additional constraints on the isovector components are established to ensure that the transformed equations are supported by a strain energy function. Possible mappings between the equations of materials with different properties are examined. Not only the transformations between homogeneous and inhomogeneous hyperelasticity equations, but also the transformations between the equations and strain energy functions of isotropic and anisotropic materials are investigated. The results are illustrated with several examples.

In the dual-superconductor picture, the QCD vacuum behaves like a superconductor for chromoelectric fields, with characteristic penetration and coherence lengths. These scales have so far been studied primarily through lattice calculations of static flux tubes. We show that they are also imprinted on exclusive diffraction, where the transverse profile of a gluonic hotspot reflects the response of the vacuum to a localized color source. Using the Clem vortex profile, we fit all 104 H1 and ZEUS measurements of exclusive $J/\psi$ photoproduction and find $\chi^2/{\rm ndf}=0.72$, the penetration depth $\lambda=0.19(2)~{\rm fm}$, the hotspot core size $\xi_v=0.087(13)~{\rm fm}$, and the Ginzburg–Landau parameter $\kappa=2.7(7)$, placing the effective vacuum description in the type-II regime. The corresponding vector mass $1/\lambda=1.03(11)~{\rm GeV}$ agrees with the lattice gluelump mass, and the extracted parameters reproduce the QCD string tension with no free normalization.

Dynamic Spectrum Access (DSA) through the Spectrum Access Systems (SAS) elevates spectral efficiency, yet existing centralized models face allocation logic opaqueness and a lack of independent verifiability. While blockchain-based SAS architectures offer transparency and verifiability by default, they introduce critical privacy risks and prohibitive on-chain computational overhead. We introduce zkSAS, a practical zero-knowledge proof (ZKP) system designed to address the verifiability and privacy gaps in SAS deployments, with direct applicability to both the existing CBRS SAS model and blockchain-based SAS models. The system features a suite of ZKP circuits, encompassing proofs of allocation constraint validity and proofs of move list validity to verify that channel assignments and move list-based incumbent protection measures, respectively, adhere to regulatory constraints without exposing sensitive user data. Comprehensive evaluation of our prototype in both centralized and blockchain-based settings indicates that while proof generation scales with spectrum user population, verification remains lightweight and constant-time. We envision that zkSAS offers a scalable and practical path to secure, verifiable dynamic spectrum sharing.

We present a safe receding-horizon mixed-integer differentiable predictive control methodology for residential battery energy storage dispatch that combines neural-network speed with recursive feasibility guarantees. Unlike open-loop learning-to-optimize methods, it incorporates real-time state-of-charge feedback and sinusoidal time-of-day conditioning, enabling closed-loop re-planning at every timestep without re-solving a mixed-integer program. A differentiable rainflow cycle-counting layer enables self-supervised training of the mixed-integer policy on exact degradation physics. The controller is a hybrid closed-loop system pairing a neural mode-selection and continuous-action policy with a quadratic-programming safety filter that guarantees recursive feasibility independent of network weights or mode optimality. We establish mode-conditioned Lipschitz continuity and a conditional regret decomposition into training-quality, mode-mismatch, and forecast-error terms. On a 7-day net-metering evaluation, the method attains a 6.9% cost gap versus the closed-loop mixed-integer MPC benchmark with a 25x speedup (0.11 s vs 2.7 s per step), while average regret rises by under 4% across 0-30% forecast noise. The learned and benchmark modes agree at every step, so the bound reduces to its training-quality and forecast-error terms, both empirically validated.

Scientific tasks specify a desired capability, but realizing it often requires building a computational system tailored to the task—acquiring data, designing representations, training models, implementing tools, and deciding how they are used at inference. We present, a framework in which an AI builder turns a scientific brief into an executable AI lab: a task-specific solver that integrates models, knowledge resources, tools, and a controller behind a fixed interface. The builder develops and packages the lab in a metered workspace; a separate host then executes the delivered artifact on held-out inputs, with reference labels kept outside the solver's input interface, and scores its outputs under the task's protocol. This makes the delivered system, rather than the builder's account of its progress, the object of evaluation. We document 10 selected constructions across six scientific task categories—from molecular and genomic prediction to medical imaging, clinical decision support, and biomedical text—whose delivered labs exceeded their configured reference values on all 12 subtests under host-side execution. Four contain predictive models fitted during construction; the others assemble executable analysis environments, knowledge resources, and tool-driven workflows around a fixed platform LLM. Together they show that an AI agent can carry a scientific brief all the way to a working lab that can still be invoked, inspected, and checked after construction ends.

We show that an isotropic, lossless dipolar particle, locally embedded in a homogeneous, lossless host, cannot experience axial optical torque under any illumination, in any photonic environment, whatever its own chirality–a general identity extending the sphere-in-free-space result to arbitrary chiral and substrate-coupled environments. Shape anisotropy is the essential escape route, and the resulting torque is not generic: closed-form, radiative-reaction-dressed polarizabilities for a chiral dielectric ellipsoid show its loss-free "optical spanner" torque changing by an order of magnitude between enantiomers (\kappa \to -\kappa), a mechanical response impossible for any sphere. Above a high-index or lossy substrate like gold or silicon, standing-wave enhancement, or simply a larger particle at a near-contact gap, brings it beyond optical-torque-wrench thresholds.

This work presents a federated framework for training Averaged $n$-Dependence Estimators (AnDE) in distributed environments. The proposed method focuses on the discriminative setting, where model weights are learned locally and aggregated globally, supporting any dependency order $n$. This design allows federated training without transmitting semantically meaningful parameters, improving privacy. Additionally, generative AnDE models are federated to provide a comparative baseline, with optional differential privacy applied to the aggregation of probability tables. Experiments on 12 discrete datasets show that discriminative models with $n \geq 1$ consistently outperform federated Naive Bayes (NB, $n=0$), and that privacy-preserving aggregation is effective with limited accuracy loss. These results establish federated AnDE as a viable and privacy-preserving framework, showing that probabilistic models remain applicable in modern federated learning settings.

We propose a scheme for mediating many simultaneous, fast entangling gates between pairs of polar molecules using Rydberg atoms. By using microwave drives, the dipolar interactions between Rydberg atoms are nullified. Using the freedom left in the microwave dressing parameters, the Rydberg van der Waals interactions are minimized and the Rydberg-molecule interaction is tuned into resonance, allowing for the mediation of a modified iSWAP gate between molecules. In the example of mediating gates between $\rm{{}^{23}Na {}^{133}Cs}$ molecules with $\rm {}^{133}Cs$ atoms, the gate is more than two orders of magnitude faster than an equivalent direct molecule-molecule gate. We model the decay of the dressed Rydberg states and the motion of the atom and molecules and obtain a leading-order estimate of the resulting gate infidelities. Finally, we show that by detecting the state of the Rydberg atom after a gate, a subset of gate errors can be converted into erasure errors and mitigated by post-selection or quantum error-correction.

Large Language Model (LLM) agents struggle to scale safely when exposed to vast enterprise toolsets. Providing an agent with access to every internal tool leads to oversized context windows, degraded tool selection, and severe governance vulnerabilities - as system policies defined purely in prompts remain probabilistic advice rather than hard constraints. Existing mitigations, such as multi-agent domain delegation, decentralize audit logs and fail to guarantee policy compliance across sessions. We introduce skilder, a framework that packages capabilities into roles: bundles of skills, tools, and instructions, together with the limits that bound them. An agent begins with a minimal role catalog, learns the roles a task requires, and receives each role's skills, instructions, and tools through a single MCP server. Because tools reach the agent only inside learned skills, the same server enforces the scope of what was learned deterministically. We evaluate skilder against flat-context tool selection and multi-agent orchestration across 13 tasks using six models (10 runs each). Our results show that, when models completed discovery and issued a governed call, the skilder simulated authorization layer enforced governance boundaries: no unauthorized tool call or parameter violation (e.g., a spending-limit breach) executed. Aggregate task pass rates also reflect whether each model followed the discovery protocol and satisfied response-quality checks; those misses are not authorization failures. Furthermore, by allowing agents to dynamically acquire cross-role capabilities mid-task, skilder preserves problem-solving flexibility while providing hard system-level enforcement.

Artificial Intelligence agents based on large language models provide convenient natural language interfaces to scientific software, but reliability is not automatic. Here we introduce the Epydemix Agent Framework, an additive layer over Epydemix, an open-source Python library for stochastic compartmental epidemic modeling. The framework extends the library with four capabilities to facilitate interaction with an AI agent: discovery of available models and parameters, preventive validation of a declarative scenario specification, execution through tested library code, and inspectability of results. These capabilities let an agent handle the entire modeling process, from the natural-language description of the scenario to quantitative results, figures, and interpretation of findings without writing custom code. Each step reads input files and saves results in a separate output bundle, making the process auditable and reproducible. First, we show the end-to-end workflow with a case study comparing vaccination strategies for a novel respiratory virus. Second, we assessed the framework across 50 agent sessions and five modeling tasks by comparing the agent use of the framework against the direct use of the Python interface. The framework reduced turns, output tokens, and cost on most tasks, unless it trades resources for per-point reproducibility.

A communication problem can have far more possible inputs than its communication cost would suggest. Must its difficulty already be present on a much smaller set of inputs? We prove that every finite total Boolean matrix of deterministic communication complexity $c\ge4$ has a submatrix on $2^k$ of its original rows and $2^k$ of its original columns, with $k=\Theta_\varepsilon(c)$ and complexity at least $(1-\varepsilon)(k+1)$, for every fixed $0<\varepsilon<1$. Since $k+1$ is the maximum possible cost on such a square, the retained problem can be arbitrarily close to maximally hard. This answers affirmatively the lossless condensation question of Hamed Hatami; Göös, Newman, Riazanov, and Sokolov (STOC 2024), who recorded it as Open Problem 2, conjectured a negative answer. Hrubeš previously guaranteed input length $\Omega(\sqrt c)$. The same argument gives an original $2^{c-2}$-by-$2^{c-2}$ square retaining at least $c/3-O(\log c)$ bits of communication complexity. The proof builds on Hrubeš's counting and covering argument. We count submatrices equipped with short communication protocols: a player names a covering submatrix, then the players run its protocol. This avoids the loss from converting rectangle partitions into protocols. A recursion on rectangles makes the argument constructive. For fixed rational $\varepsilon$ and any target depth $d\ge4$, a deterministic algorithm returns either a protocol of depth below $d$, or a square of original inputs at input length $\Theta_\varepsilon(d)$ with the same near-maximal guarantee. Its running time is $2^{O(2^d)}$ times a polynomial in the table size. If the original complexity is at least $d$, the algorithm necessarily returns the square. An extension gives constant-factor condensation for any fixed number of number-in-hand players, with bounds independent of the finite output alphabet.

Faithful user simulation is fundamental to building, evaluating, and improving interactive AI at scale. Yet current simulators often produce plausible individual responses without reproducing the intent evolution and outcomes observed in real interactions. We propose TRACER, a multi-turn user simulator that models evolving user intent and aligns simulated trajectories with real ones. TRACER is trained in two stages: supervised fine-tuning on real user dialogues, followed by multi-turn reinforcement learning. The RL stage combines hierarchical outcome- and trajectory-level rewards with deviation-aware advantage modulation, jointly addressing reward sparsity and credit assignment challenges in long dialogues. On real customer-service sessions organized into reference cohorts, TRACER-7B surpasses the strongest baseline by 11.4 conversion F1 points, while outperforming all baselines on group-level conversion-rate error and semantic trajectory distance and generalizing to out-of-distribution scenarios. In human Turing tests, annotators identified TRACER conversations at near-chance accuracy. Building on this simulator, we further introduce the Dynamic Marketing Benchmark, which jointly evaluates persuasion and response quality via simulated interactions, revealing that higher response quality does not necessarily correspond to higher conversion rates.

In this paper, one provides a comprehensive mathematical and practical overview of Functional Data Analysis (FDA) specifically applied to parametrized curves in Rp. One observes that curves depending on continuously parameter are naturally present across many fields, such as, for example, monitoring child development in pediatrics, assessing meteorological phenomena, analyzing financial portfolios, tracking neurological functions, and mapping geographic pollution levels. One considers a formal theoretical framework given by a Cartesian product of real separable Hilbert spaces, to model these curves mathematically. To bridge the gap between discrete experimental measurements subject to errors, and smooth continuous functions, the paper details the essential phase of data smoothing and fitting and sets its mathematical formulation via of the Ordinary or Penalized Least Squares criteria which, for the later, using the Sobolev spaces framework, incorporates a smoothing parameter ${\lambda}$ and differential operators to prevent erratic geometric behaviors by penalizing excessive curve roughness. Furthermore, one extends the usual Principal Component Analysis to its functional counterpart in $\mathbb{R}^3$, using the calculus of variations and the Euler-Lagrange multiplier theorem in order to find eigenfunctions and eigenvalues of the covariance operator to exhibit the optimal decomposition of the spatial variance and finally, one highlights the geometric advantages of FDA over traditional multivariate data analysis, emphasizing its unique capacity to capture critical differential features as velocity, acceleration, curvature, and torsion.

The random hopping Hamiltonian is a toy model for a disorder-driven topological phase transitions in one-dimensional chiral Hamiltonians. It has a vanishing Lyapunov exponent and a Dyson peak in the density of states at zero energy. This work shows how the quantum dynamics leads to a logarithmic growth of the moments of the position operator, similar as in classical Sinai diffusion. The mechanism at the origin of this phenomenon is that the eigenfunction of the smallest eigenvalue is well-approximated by the exponential of a classical random walk, leading to two essentially independent subexponential localization centers.

Quantum geometry governs a wide array of physical observables in topological quantum materials. In its ideal limit, quantum geometry yields exact bounds and analytical results for a growing class of observables. However, a comparable framework for the shift current remains elusive because it depends on geometric relations between multiple bands. In this work, we show that the shift current is proportional to the cyclotron shift, the displacement of the cyclotron center induced by Landau-level mixing. This mechanism yields a universal scaling law: the integrated weight and the peak magnitude scale as $l^{i+1-n}$ and $l^{2i+1-n}$ in the magnetic length or moiré period $l$, where $n$ is the momentum order of the symmetry-breaking perturbation and $\Delta E \propto l^{-i}$ is the level spacing. We verify the scaling law in exactly solvable chiral-$N$ Landau levels under a uniform magnetic field and in Schrödinger and Dirac moiré skyrmion crystals, which capture the flat Chern bands of twisted MoTe$_2$ and twisted bilayer graphene. For a Schrödinger flat band with a distorted skyrmion texture, the integrated weight grows linearly with the moiré period and the resonant peak grows cubically.

A quantum field-theoretical description of neutrino oscillations in matter in adiabatic approximation is developed. Estimates of the oscillation coherence lengths have been made for several solar neutrino production and detection processes. It has been shown that, within the framework of the developed approach, the results of solar neutrino detection experiments can be correctly described in terms of neutrino mass eigenstates without taking oscillations into account.

Social media platforms are embedded in teenagers' daily lives, supporting friendship and identity while exposing teenagers to unwanted contact and privacy harms. Previous scholarship has documented how attention capture strategies and dark patterns shape social media use, and we extend this work to better understand platform settings that ostensibly provide privacy and safety protection. We report on think-aloud sessions with 11 teenagers aged 14 to 17 who completed six privacy and safety tasks on Instagram, TikTok, Snapchat, and YouTube. We show how participants worked out what a setting meant through their routines, boundaries, and prior experiences, how they accommodated protections softer and less predictable than expected, and how they treated the platform as the authority on what protection should look like. We argue that feature-by-feature evaluation cannot establish whether teenagers are protected, and that platforms should carry the obligation to show that a protective action took effect and is durable.

Encoding input coordinates with sinusoidal functions into multi-layer perceptrons (MLPs) has proven effective for implicit neural representations (INRs) of surfaces defined as zero-level sets. However, existing methods often struggle to balance training efficiency, rendering speed, and noise robustness: single-MLP approaches are expensive at inference, grid-based representations are fast but can limit surface smoothness and overfit input noise, and previous multiscale approaches frequently capture noise and produce artifacts due to hard spectral truncation. To address these limitations, we propose M-plicits, a multiscale framework that models surfaces as a residual sum of MLPs trained via a sequence of nested neighborhoods. Unlike existing residual approaches that rely on standard domain-wide sampling and require costly mesh extraction for visualization, our method strictly localizes supervision to narrow bands around the previous zero-level sets. This nested design naturally provides robustness against noisy input data: the coarse network acts as a low-pass filter that establishes a clean geometric prior, while subsequent residuals progressively refine the geometry without fitting to high-frequency artifacts. We further introduce a multiscale sphere-tracing algorithm and a GEMM-based analytical normal computation that bypasses auto-differentiation entirely, yielding high-fidelity real-time rendering. On Stanford and Thingi32, M-plicits achieves the best mean Chamfer distance in the coarse configuration and the best median Chamfer distance and IoU in the fine configuration, with substantially better noise robustness than iNGP, BACON, and IDF, while using an order of magnitude fewer parameters than grid-based baselines. Code, models, and data are available at https://github.com/dsilvavinicius/m-plicits.

Neural methods for audio restoration are typically framed as rigid mappings from degraded inputs to single clean outputs, enforcing decisions about what audio content is removed, and potentially adding unwanted content to the restored signal. Because what constitutes a restored audio signal is subjective, we introduce RESTORE, a framework that formulates audio restoration as a six-source semantic decomposition to allow for real-time interactive user control over the process. By expanding a pretrained HTDemucs backbone, a single forward pass disentangles a degraded mixture into vocals, music, broadband hiss, impulsive transients, and an unmodeled residual, while jointly synthesizing a high-frequency extension. Users may steer the restoration by adjusting stem gains, ensuring generative content remains isolated and auditable. RESTORE improves audio quality on diverse historical recordings compared to baselines,lowering Frechet Audio Distance (FAD) (12.13 VGGish; 0.92 CLAP) and delivering aesthetic steerability (Spearman rho greather than 0.91) at 50x real-time on a single GPU. Code and audio samples are available at https://melissachen15.github.io/restore-audio-demo.

Post-training hybrid reasoning models in NoThink mode has attracted growing interest as a way to improve performance while keeping inference fast. However, these gains may draw on thinking behavior already accessible through the base model's Think mode. We formulate this thinking leakage in a causal mediation framework and audit its contribution using bidirectional interventions along a simple base-derived activation direction. Across three models and three post-training methods on competition math benchmarks, we find that leakage is real, causal, and substantial: behavioral and representational analyses reveal shifts toward Think, steering the base model along this direction reproduces most of the post-training accuracy gain, and counter-steering a checkpoint removes a substantial share of what it gains. Across nine aligned checkpoints with positive NoThink gains, the resulting leakage ratio ranges from 42% to 79%. These interventions support a substantial causal contribution of thinking leakage. Our findings show that a post-training method's apparent advantage can therefore reflect greater drift toward Think, obscuring whether it improves capability within NoThink or more effectively re-invokes existing Think behavior.

Generative AI makes a paradox newly visible: learning from a common source can improve what each firm does today while narrowing the variety available for tomorrow's discoveries. The tension extends beyond AI. Fields turn recurring features of successful organizations into portable practices, such as just-in-time production, freemium business models, or mixture-of-experts architectures. These collective abstractions are partial templates others can adapt, not designs or universal prescriptions. We study how they shape discovery in a model of firms searching interdependent landscapes. A collective repertoire extracts practices from patterns shared by leading configurations; firms vary in how they evaluate those practices locally. The model reveals a generativity chain: population diversity supplies heterogeneous experience, collective abstraction turns it into reusable options, and situated judgment matches options to local needs. Collective learning is not inherently homogenizing. Copying leaders consumes diversity quickly, whereas repertoires paired with local judgment preserve generative capacity. Environmental disruption exposes the consequences: it devalues accumulated knowledge but reopens local search, helping homogeneous, exhausted industries while harming diverse industries whose repertoire remains useful, even though diverse industries still perform better overall. Recurring practices may also outlive their usefulness, making popularity a poor test of validity after change. These findings matter for organizations using generative AI, best-practice communities, and research fields converging on dominant strands. Generativity requires governing the diversity feeding knowledge and the judgment applied to it. Learning systems should be judged not only by the answers they spread today, but by whether they preserve the differences from which tomorrow's answers can be made.

A common belief in Kondo physics is that a magnetic impurity can act as an efficient probe of key properties of its host bath. In altermagnets, however, this intuition fails in a symmetry-enforced way: the momentum-dependent spin splitting cancels in the local impurity spectrum, making a conventional single-impurity Kondo resonance essentially blind to the altermagnetic form factor. Here, we overcome this constraint by introducing Floquet symmetry conversion. We show that an in-plane AC field converts the hidden altermagnetic spin splitting into a locally detectable spin-dependent hybridization channel, which is further amplified by Kondo correlations into a novel altermagnetic Kondo effect. Remarkably, the Kondo splitting exhibits a nontrivial dependence on the field orientation and inherits the same crystalline form factor as the altermagnetic host, thereby serving as Kondo tomography of altermagnetic spin splitting. This field-controlled response further provides a natural route to symmetry-controlled Kondo logic gates. Our results establish a field-controllable altermagnetic Kondo effect, linking symmetry-resolved impurity spectroscopy to Kondo logic functionality.

This work presents a consistent formulation of body-force and heat-source terms within a double-distribution-function lattice Boltzmann framework for simulating compressible flows of generic fluids. The proposed approach extends a recently developed kinetic framework for non-ideal compressible fluid dynamics by incorporating external forcing and volumetric heating through shifted quasi-equilibrium states. The standard lattice Boltzmann discretization is applied with a second-order accurate integration along characteristics and product-form equilibria on nearest-neighbor lattices are employed, supplemented by necessary correction terms. This formulation ensures the consistent recovery of the Navier-Stokes-Fourier equations, including the Korteweg stress tensor, across arbitrary equations of state, while maintaining independently controllable thermodynamic and transport coefficients. The methodology is rigorously validated and applied for two different flow regimes, with ideal-gas compressible flows and non-ideal/multiphase compressible flows, respectively, where a broad hierarchy of benchmarks is employed, including non-classical shock tubes, thermal Couette flows, and force-driven Poiseuille and Womersley flows. The framework's ability to capture complex thermodynamic processes using forcing and heating is further demonstrated through Rayleigh and Fanno flows, Joule-Thomson effects, and throttling processes. Furthermore, the model is validated for multiphase phenomena, including interface consistency and liquid-vapor co-existence. The results demonstrate excellent agreement with analytical solutions and reference data, while spatio-temporal grid-refinement studies confirm the expected second-order accuracy of the scheme. This establishes the model as a robust and efficient foundation for simulating highly compressible flows of generic fluids in the presence of numerical and physical s...

This article develops an identification framework for heterogeneous policy effects when individual-level data are available only in the treated jurisdiction. The framework combines outcome changes from repeated cross-sections within that jurisdiction with a population-average effect identified from aggregate panel data. Under conditional relative parallel trends and overlap, this information identifies subgroup effects standardized to the treated jurisdiction's overall post-treatment covariate distribution, but generally not effects averaged over each subgroup's own distribution. I establish how these subgroup-average effects can nevertheless be recovered using covariate-specific aggregate effects or additional pretreatment observations under assumptions about the evolution of untreated trends. Simulations and an application to the Massachusetts health reform illustrate the framework.

In this paper, we obtain an exact sequence connecting $H_2(\rm{SL}_2(\mathcal{O}_{K,S}), \mathbb{Z})$ to $H_2(\rm{SL}_2(\mathcal{O}_{K,T}), \mathbb{Z})$, where $\mathcal{O}_{K,S}$ is a ring of $S$-integers and $T$ is a set of primes containing $S$. We apply this sequence to establish a relation between $H_2(\rm{SL}_2(\mathcal{O}_{K,S}), \mathbb{Z})$ with the second $K$-group $K_2(\mathcal{O}_{K,S})$, for $S$ large enough. This leads to a description of the rank and size of the torsion of $H_2(\rm{SL}_2(\mathcal{O}_{K,S}), \mathbb{Z})$. As an application, we propose a homological version of the Birch-Tate formula (conjecture) under these assumptions.

Longitudinal spacing models describe the speed–spacing states that vehicles maintain, while longitudinal controllers regulate vehicle motion through spacing and speed errors. Less explicit is how one spacing state should be connected to another through a finite, physically meaningful vehicle transition. This paper develops such a connection through r-Safety and Adaptive Kinematic Smoothing (AKS). The r-Safety relation represents speed-dependent spacing through a braking-normalized reserve, whose change, together with leader motion, determines the follower displacement required during a transition. AKS then converts this displacement into a low-dimensional analytical trajectory with consistent position, speed, spacing, and acceleration. Experiments using controlled platoons and NGSIM trajectories identify r-Safety values of 0.307 and 0.249–0.281, respectively, and show that AKS can both represent observed transitions and generate prospective references under prescribed endpoint states, transition horizons, and leader motion. In same-controller ablations, adding AKS reduces integrated acceleration effort by 21–47% and integrated squared jerk by 73–81% across the controlled and naturalistic datasets. FHWA ACC/CACC trajectories further provide an empirical illustration of finite-horizon execution under automated following, showing how spacing adjustment can continue beyond the prescribed speed transition. The framework therefore provides a direct path from a speed–spacing relation to an analytical finite transition and its use as a longitudinal control reference.

Generative artificial intelligence illustrates a broader organizational puzzle: young, resource-constrained firms can build on knowledge produced across a wider field to address problems that exceed their internal experience. We theorize one mechanism as social imitation: a distributed and recursive process through which communities observe practices and outcomes across organizations, distill recurrent elements into portable strategies, circulate them, and revise the collective repertoire as adoption produces new evidence. This perspective endogenizes the object of imitation. Organizations do not merely copy practices; communities collectively produce what becomes available to copy. We distinguish the source of a candidate (directly observed organizations or a collective) from its mode of adoption (blind or informed), and examine four forms of imitation in an agent-based model of organizational search. Collective sourcing alone does not improve performance. Its value depends on situated evaluation: assessing whether a candidate fits the adopter's configuration. As interdependence increases, informed social imitation improves population performance and the best solution discovered. As problems grow, it becomes more likely to outperform informed imitation from one or several directly observed peers because collective distillation sustains a broader candidate repertoire. Most gains arise from evaluating a small candidate set, and population performance can improve when only a minority of organizations possesses evaluative capability. Social imitation thus reveals a division of cognitive labor: communities expand the strategies organizations can consider, while organizations create value by determining which strategies fit. It explains how firms can mobilize knowledge beyond their boundaries, and why widespread access to collective knowledge does not produce equal benefits.

Let $\pi=\pi_1\cdots \pi_n$ be a permutation. We say that $\pi$ is $run$-$sorted$ if $\pi_1=1$ and the entries immediately following the descent positions of $\pi$ form an increasing sequence. Let $\mathcal{R}_n$ denote the set of run-sorted permutations of length $n$, which has cardinality given by the Bell number $B_{n-1}$ for all $n \geq 1$. In this paper, we consider the joint distribution $A_n(q,u)$ on $\mathcal{R}_n$ for the parameters tracking the numbers of inversions and runs leading to a new polynomial generalization of the Bell numbers. Among our results, we find a general recurrence for $A_n(q,u)$, from which one may derive explicit formulas for the total numbers of inversions or runs in all the members of $\mathcal{R}_n$ as well as for the sign-balance on $\mathcal{R}_n$ of either parameter. A simple expression for the Eulerian generating function for $A_n(q,1)$ may be found upon making use of Gessel's $q$-exponential formula which can be extended to general $u$. Finally, a formula is found by a direct argument for the maximum number of inversions within a member of $\mathcal{R}_n$.

Large Language Models (LLMs) are increasingly deployed as argumentative agents in persuasive dialogues, necessitating rigorous evaluation of their debating competence relative to human interlocutors. In this study, we focus on character attacks (ad hominem arguments), traditionally dismissed as fallacies, which play a pivotal role in political persuasive dialogues where ethos often rivals propositional content. Specifically, we investigate whether modern LLMs can replicate human competence to strategically use and respond to such attacks. We analyse a corpus of natural language political dialogues to identify defensive strategies human interlocutors naturally employ in ethos-centred debates and structure them into a dialogue game. Empirically, we benchmark LLM-generated dialogues against the ElecDeb60to16-fallacy corpus of U.S. presidential debates, contrasting human debaters' repertoire of defensive strategies with those of artificial agents. Results reveal a substantial difference: most LLMs rigidly prioritise logical defences, failing to exploit ethotic counterattacks as valid moves in political discourse. We argue that current safety fine-tuning constraints the strategic action space of these LLMs, making them unable to fully engage in naturalistic interactions within domains where character contestation is a normative expectation rather than a mere fallacy.

Social media platforms are central to teenagers' lives, and their designs can expose users to privacy, safety, and wellbeing harms. Platforms increasingly offer protective settings, though the presence of a control reveals little about whether teenagers can find, use, and benefit from it over time. We paired an expert evaluation of six privacy and safety tasks across TikTok, Instagram, Snapchat, and YouTube with moderated think aloud sessions in which 11 teenagers aged 14 to 17 attempted the tasks. Interaction cost and dark patterns analysis allowed us to compare the complexity designed into each task with the effort participants incurred as they located, configured, and interpreted controls. Recurring dark patterns appeared across tasks, and most participant attempts exceeded the expert baseline. Protective settings therefore risk being insufficiently usable or durable in practice, and we propose a wayfinding audit that integrates expert evaluation, usability testing, interaction cost, and dark pattern analysis.