Papers

We present a quasi-static particle-in-cell scheme for beam-driven plasma wakefields in cylindrical geometry that works on an arbitrary non-uniform radial grid. The field equations are discretized with hat-function finite elements and conservative finite volumes on any monotone set of radial nodes, and the transverse magnetic field is obtained explicitly, without iterations, following Baxevanis and Stupakov. An optional azimuthal mode $m=1$ describes beam offsets, tilts and hosing. The discretization keeps the discrete Gauss law exact, deposits a uniform plasma exactly on every node including the axis, and remains second-order accurate on smoothly stretched grids. Resolution can therefore be placed where the physics needs it. For a tightly focused witness beam that pulls the plasma ions onto the axis, a grid that is fine only near the axis gives the same near-axis fields as a uniform grid with the same axis resolution, with thirty times fewer cells and in thirty times less computing time. Such a grid also resolves the singular closure of a cold-plasma bubble, which a uniform grid hides by smoothing it over one cell; smoothing the plasma sources over a fixed length, chosen independently of the grid, regularizes the closure and makes the wake behind it converge. The scheme is implemented in the open-source C++/Kokkos code QUARZ (Quasistatic Arbitrary-resolution RZ), which runs on CPUs and GPUs and uses MPI with a pipelined decomposition along the co-moving coordinate. Simulations of the self-modulation of the AWAKE proton bunch agree with the three-dimensional code HiPACE++. QUARZ is, to our knowledge, the first production-grade simulation code in plasma physics that is zero-touch: all of its source code, tests and documentation were written by an AI agent directed by a physicist who did not write a single line of the code.

We consider several families of sequences of Baire-one self-maps of $[0,1]$ investigated by A. Alikhani-Koopaei. They form a chain of inclusions where each space is closed and nowhere dense in the next one. We prove that each space is lower $2/3$-porous in the next one. If one modifies these families where sequences of Baire-one functions are real-valued uniformly bounded, then they are Banach spaces and each space of the respective chain is c-porous in the next one.

End-to-end driving requires rich spatiotemporal representations to support scene understanding and trajectory planning under strict latency constraints. However, most systems initialize their visual encoders from generic image pretraining and densely process all patch tokens for each camera view and input frame, limiting both representation quality and inference efficiency. To address these challenges, we present ConDenseDrive, a knowledge-dense and token-sparse visual encoder for end-to-end autonomous driving. Our three-stage framework first makes the encoder knowledge-dense by distilling complementary visual, semantic, and geometric knowledge from three vision foundation models. It then adapts the distilled encoder to multi-frame end-to-end driving and integrates spatiotemporal context into register tokens for planning. Finally, it makes the encoder token-sparse by applying register-guided token compression, reducing redundant patch computation and yielding a 2.0$\times$ speedup while improving planning performance. ConDenseDrive achieves 94.5 PDMS on NAVSIM v1 and 90.8 EPDMS on NAVSIM v2, and reaches 37.4 HD-Score in zero-shot evaluation on HUGSIM. Extensive experiments and qualitative analyses demonstrate that visual encoder design provides an effective route to reliable and efficient end-to-end driving.

The friends of a randomly chosen social media user are, on average, better connected than the user, a network property known as the friendship paradox. We use it to monitor misinformation on Twitter/X around the 2024 US election, comparing roughly 27 million tweets from random users with 31 million from the accounts they retweet, which we call sensors. Sensors share news of about the same quality as random users, because news quality follows the political orientation of linked outlets and not the user's position in the network. News links rated by NewsGuard reach sensors a median of 70 minutes earlier, across the quality spectrum. Over the election window, right-leaning content rises about 2.5-fold in visibility, measured as impressions per tweet, among sensors but not among random users. Friendship-paradox sampling therefore cannot separate low-quality from high-quality news, but it detects news early and tracks what a platform makes visible.

Multi-modal fusion for 3D object detection assumes that cameras and LiDAR are broadly complementary. In practice, how much each modality is trusted at a given location is decided by learned weights that are neither characterized nor auditable. We label every ground-truth object by which modalities detected it, then mine the resulting 0.4M-object database across nuScenes, KITTI, and Waymo. Because the patterns shift with distance from the ego vehicle, we read the mined model through Spatially Stratified Feature Attribution (SSFA), which conditions Shapley attribution on distance zones and exposes structure that global attribution averages away. Three assumptions built into the current fusion design do not hold. The modality-preference boundary tracks the object itself: a traffic cone is nearly six times as likely as a truck to be seen by the camera alone (16.8% vs. 2.9%), regardless of range. Camera-only detections peak at 10-30 m, inside the band usually ceded to LiDAR, and fall away on either side. The drivers of failure are not additive either: the distance - density interaction alone outweighs the entire main effect of viewing direction. We further find that modality dominance is directionally non-stationary, with objects behind the vehicle being markedly more LiDAR-dominant than those in front. We compile the mined structure into a Modality Reliability Map and inject it into four pretrained fusion detectors through a lightweight attention layer. This improves performance by up to 1.3 mean Average Precision (mAP) while fine-tuning under 4% of their parameters in 2-3 GPU-hours. Our work lifts reliability out of the weights and treats it as a quantity that can be examined before deployment. That is what a safety measure for multi-modal perception must rest on.

Cascading failures develop through coupled power flow redistribution, protection actions, and topology changes, making remedial control dependent on how alternative interventions modify the subsequent trajectory. This paper develops an action-conditioned graph predictor (ACGP) for multi-step cascade prediction and closed-loop mitigation. A same-state counterfactual branching procedure replays identical post-contingency grid states under multiple legal actions while preserving the exogenous trajectory, providing direct supervision for action-dependent electrical states, line connectivity, automatic protection trips, and terminal risk. ACGP is embedded in a receding-horizon controller that evaluates five-step candidate futures, executes the selected intervention, and replans from the observed next state. The final dataset contains 2,860 counter factual roots and 22,880 action-conditioned branches. On the held-out test set, ACGP achieves a five-step line-loading MAE of 0.0369 and a redispatch pairwise ranking accuracy of 0.806; action ablations reduce the ranking accuracy to approximately chance level. In closed-loop Grid2Op experiments, terminal-failure and cascade rates decrease from 53.3% and 51.1% under do-nothing operation to 12.2% and 7.8%, respectively, close to the simulator-reference values of 11.1% and 6.7%. The results show that same-state counterfactual prediction can support effective action comparison and feedback-based cascading-failure mitigation.

An Orlicz ball is the set of points where the sum of a fixed even convex function of the coordinates does not exceed a given radius, here proportional to the dimension. For a broad class of such functions, including non-homogeneous ones, we find the exponential rate of the intrinsic volumes whose order is proportional to the dimension and express it by a two-parameter variational formula involving only one-dimensional integrals. As a function of the order-to-dimension ratio, this rate is concave and continuous on the closed unit interval, and the convergence is uniform in the order. This proves the exponential-profile conjecture of Kabluchko, Marynych, and Prochno for these bodies and recovers their result for $\ell_p$ balls with $p>1$. The proof relies on the theory of large deviations. An exact formula for the Laplace transform of the intrinsic volumes in the radius, extending theirs for $\ell_p$ balls, plays the role of a moment generating function, and a Laplace method gives its exponential rate. An exponential change of measure, analogous to that used in Cramér's theorem, then recovers the intrinsic volumes. The key step is a lower bound on the tilted density at its mean, obtained from log-concavity rather than a law of large numbers.

Wide-field narrowband imaging provides an efficient approach for mapping low-surface-brightness line emission over large angular scales. We present initial performance tests of Multi-Application Survey Telescope Array (MASTA) for narrowband imaging. Using commissioning data obtained with the QHY461 and COSMOS-8K cameras, we characterize the basic reduction procedure, photometric calibration, image quality, and point-source detection limits. The measured surface-brightness and point-source detection limits become deeper with increasing exposure time, roughly following the expected background-limited scaling. Under the current observing and reduction conditions, the COSMOS-8K camera generally reaches deeper surface-brightness limits, particularly in the red filters, while QHY461 has smaller pixel size and provides better sampling of the telescope point spread function (PSF). As demonstrations, we perform continuum subtraction for the nearby galaxy M106 and the supernova remnant Cygnus Loop using adjacent narrowband filters and reveal the H{\alpha} and [O III] structures in M106 and filamentary structures in the Cygnus Loop. We further compare the MASTA surface brightness H{\alpha} map of M106 with an independent SITELLE measurement. After accounting for [N II] contamination and the wavelength-dependent response of the 6544 Å filter in the f /1.7 converging beam, the corrected median ratio is 0.973. These tests indicate that MASTA is a promising facility for wide-field narrowband imaging. Further improvements in calibration frames, including flux calibration, field-dependent bandpass characterization, and spatially varying PSF modeling and matching will be required for quantitative studies of diffuse ionized gas.

Bayesian Networks (BNs) are established tools for letting agents reason under uncertainty in sequential decision-making. They split a joint distribution into local conditional mechanisms arranged on a directed acyclic graph, which makes them modular, interpretable, and ready to perform probabilistic inference. Their classical formulation, however, has limitations in both expressiveness and scale: each conditional is usually stored as a table or a linear-Gaussian form, and inference evaluates the graph one node and one query at a time. In this paper we introduce Neural Bayesian Networks (NBNs), in which each conditional is a differentiable, tensor-valued mechanism, while the graph and its factorization are unchanged. NBNs retain the modularity and local mechanisms of BNs, can represent any learnable conditional distribution, and run natively on GPUs. We also release NBN, a PyTorch-based library for learning and inference in NBNs, together with a public benchmark. Our evaluation shows gains in both expressiveness and scale: NBNs fit distributions that classical BN libraries struggle to represent, and on large networks and large batches of queries they run two orders of magnitude faster thanks to GPU parallelization. NBN is available at https://github.com/Giovannibriglia/NeuralBayesianNetworks.

We study the possible dimensions of solution sets in linearly perturbed convex optimization problems and their behavior under convex duality. The dimensions of solution sets and inverse solution sets capture two complementary forms of nonuniqueness: that of optimal solutions for a given perturbation, and that of perturbations for which a given point is optimal. Although these two families are linked by Fenchel conjugacy, we show that their collections of dimensions can be prescribed independently for finite supercoercive convex functions. As a geometric consequence, we prove that the facial dimension signatures of a convex body and its polar can be prescribed independently. The connection between these two realization results is obtained by homogenizing the epigraphs of a function and its conjugate. In contrast, under simultaneous facial exposedness, we establish a dimensional obstruction relating the smallest positive proper face dimensions of the body and its polar. These results resolve two open questions posed by Roshchina and Tunçel.

We study vector-valued local minimizers of the borderline double phase functional whose integrand is $|D\mathbf{w}|^p+a(x)|D\mathbf{w}|^p\log^\gamma(e+|D\mathbf{w}|)$, where $p>1$, $\gamma>0$ and the coefficient $a(\cdot)$ is nonnegative and bounded. If the modulus of continuity $\omega(\cdot)$ of $a(\cdot)$ satisfies $\omega(r)\log^\gamma(1/r)\to0$ as $r\to0$, then minimizers are locally Hölder continuous for every exponent less than one. If $a(\cdot)$ is Hölder continuous, then the gradients of minimizers are locally Hölder continuous. In the vector-valued setting these results were previously available only for $\gamma=1$. The proof combines a comparison with frozen functionals, whose regularity theory applies uniformly in the frozen coefficient, with the higher integrability of minimizers.

Type Ia supernovae are useful as cosmological distance indicators and are significant sources of chemical enrichment in galaxies, but much about their origins remains uncertain. The double detonation explosion mechanism is one promising model for these transients. We present a suite of thermonuclear hydrodynamic double detonation models of sub-Chandrasekhar mass white dwarfs spanning thin to thick helium shells. Thin shell models produce light curves and spectra consistent with normal Type Ia supernovae, and thicker shell models have early time luminosity bumps from radioactive ashes in the shell and early reddening in color sometimes observed in peculiar Type I supernovae. The reddening is due to line blanketing from heavy elements produced in the shell detonation encompassing the central emission. We perform the computations using $\texttt{Cattails}$, a moving mesh nuclear hydrodynamics code introduced in this work. After carrying out subsequent radiative transfer calculations using the $\texttt{Sedona}$ code, we relate the time of early reddening to the mass of the initial helium shell. We also consider how the relation changes as a function of total mass as well as how the peak brightness depends on the total mass. Finally, we provide a series of fitting functions that can be used to estimate the mass of the shell consistent with an observation of reddening in the early color evolution of a type Ia supernova.

We study the number of improving steps that local search may require for $(2,2,r)$-MCA (Maximum Constraint Assignment), a bounded-occurrence version of MAX-CSP with valued constraints in which every constraint involves at most two variables, every variable occurs in at most two constraints, and every variable takes one of $r$ values. We consider the flip neighborhood, where two assignments are neighbors if they differ in the value of exactly one variable; moving to such a neighbor is called a flip. Local search repeatedly performs improving flips, that is, flips that strictly increase the objective value, until a local optimum is reached. Our main result is that $(2,2,5)$-MCA has the all-exp property: there is an infinite family of instances with initial assignments for which every sequence of improving flips ending in a local optimum has length exponential in the number of variables. Thus, on these instances, local search requires exponentially many steps regardless of which improving flip is chosen at each step. This is the first all-exp result for $(2,2,r)$-MCA for any value of $r$, and our result extends to every $r\ge 5$. In contrast, for $(2,2,2)$-MCA every sequence of improving flips has length at most quadratic in the number of variables~\cite{Kaz2020,KCJ2020}. We give a short, direct proof of this result.

Deep learning programs are fundamental to modern AI applications, and automatically generating them from natural language requirements can substantially reduce DL development effort. Large language models have demonstrated promising capabilities for this direction. However, generated DL programs often remain unreliable because they must satisfy domain specific API usage constraints and tensor shape dependencies, violations of which can cause API level syntactic issues and runtime failures. Existing retrieval augmented generation and feedback guided code repair methods do not adequately address these DL specific constraints. In this paper, we propose DeepGroundRepair, a three stage framework that establishes a generation localization repair workflow to improve the reliability of LLM-generated DL programs. Its key idea is to progressively narrow the generation and repair spaces using DL specific knowledge and runtime tensor information. Specifically, it grounds generation in task-relevant API knowledge, localizes the upstream causes of tensor shape mismatch failures, and uses runtime tensor shapes to guide parameter repair. We evaluate DeepGroundRepair on the 100 model-level DL programming tasks in DeepEval using six open-weight LLMs across TensorFlow, PyTorch, and PaddlePaddle. We compare it with four baselines: two generation-only methods and their counterparts incorporating traceback guided self debugging. The results show that, relative to these baselines, DeepGroundRepair reduces the combined number of API-level syntactic issues by an average of 5.4 per 10 program files and achieves an average relative improvement of 85.3% in code executability. Compared with the two self debugging baselines, it improves semantic consistency by an average of 18.1% and reduces token cost by an average of 28.4%.

We establish quantitative weak convergence for the joint terminal law of the solution to a stochastic wave equation and the normalized error of its exponential Euler approximation. For multiplicative trace-class noise and spatial regularity $\alpha\in(1,2]$, the normalized error converges to its limiting distribution at rate $O(m^{-(\alpha-1)})$, where $m$ is the number of time steps. This estimate identifies the leading weak bias and yields a first-order weak-error expansion with remainder $O(m^{-\alpha})$. Moreover, by canceling the leading weak-error term, we construct a Richardson extrapolation scheme with weak convergence order $\alpha$ for $\alpha\in(1,2]$ and show that this rate is sharp. To overcome the lack of parabolic smoothing and control the remainders amplified by normalization, we combine dimension-uniform regularity estimates for the joint Kolmogorov equation with a conditional weak expansion and backward transport of coefficient directions.

LLMs are used as high-level controllers for embodied agents, but it remains unclear whether they support collaborative reasoning, such as anticipating a collaborator's actions in real-time teamwork without dialogue. We ask if observing the partner's state, exchanging object knowledge, and predicting the partner's next action, shape task outcomes and coordination when agents can share percepts but never intentions, plans, or task-level messages, and whether the two agents occupy symmetric roles. Using the Habitat-based PARTNR benchmark, we introduce a Decoupled Partial Observability regime that enforces strictly individual perception, and we augment decentralized zero-shot ReAct planners with Other Agent's State (OAS) observation, object Knowledge Exchange (KE) between co-located agents, and Other Agent's Next Action (OANA) prediction, evaluated on the full 2 x 2 x 2 grid with four planners on 1,000 validation tasks. OAS observation improves task quality, reducing extraneous effort for every planner, whereas KE primarily improves execution efficiency, cutting simulation steps by up to 25% with little change in success. The two are largely redundant for strong planners but complementary for the weakest, for which KE without the OAS is the worst configuration. OANA prediction lowers the success rate in 15 of 16 model x context pairs while raising explicit partner mentions to 55-100%, and its accuracy gains lie mainly in the coarse action type, partly because agents recognize the action the partner is already performing. The robot retrieves objects sooner and completes its tasks earlier than the simulated human. Shared context reduces total task time by shortening the remaining duration that the human works alone. Also, coordination benefits arise from responding to shared context, especially the OAS, rather than explicit anticipation, yielding shallow, planner-dependent partner modeling.

We unify known mutual-linearity relations for Markov jump processes and chemical reaction networks within a common framework based on classical finite-response theory. In a Markov jump process, an exact finite-response identity shows that all stationary probability changes share a common factor when the rates of one edge change. Eliminating this factor gives the relations between probabilities, observables, and currents, even far from equilibrium. We also explain how the same argument applies when one coefficient of a linear system changes and recovers the known relations in Laplace space and between stationary complex activities in chemical reaction networks.

We give improved approximation algorithms for two graphic TSP variants. First, we consider Multi-Depot TSP on graphic instances. In this variant, we are given an undirected graph with a set of depot vertices, and we are tasked with finding an Eulerian multi-edge set that connects each non-depot vertex to at least one depot. For this problem, Deppert, Kaul and Mnich (ESA 2023) presented a 3/2-approximation algorithm with running time exponential in the number of depots. We improve this result to a fully polynomial 3/2-approximation. Our algorithm is a variant of the classic Christofides-Serdyukov algorithm with an improved and simple analysis. On subcubic instances, we improve the approximation guarantee to 4/3 using the technique of removable pairings introduced by Mömke and Svensson (J. ACM 2016). We use a removable pairing to construct a set of disjoint cycles that can be completed to a cheap feasible solution. Second, we consider the Graphic Multi-Path TSP, which was previously considered by Alimi, Dahlmeier, Mömke, Pabst and Vargas Koch (SOSA 2026) who give a 2-approximation for this problem. Additionally, the authors present a reduction that shows that any better-than-two approximation for Graphic Multi-Depot TSP immediately leads to an improvement for Graphic Multi-Path TSP. We give an improved algorithm and analysis that yield an approximation guarantee of 1.9304.

Emotions are expressed on a continuum and are naturally described in the valence-arousal (VA) space. Existing VA-based image editors are typically training-based and domain-specific, limiting them to VA regions seen during training and making them brittle across datasets and domains. Meanwhile, despite producing high-quality edits, state-of-the-art foundation image editors are not continuous affective controllers: non-linear emotion representations in text encoders makes prompt interpolation poorly calibrated, so accurate and continuous VA control remains unreliable. To fill this gap, we introduce Barycentric Guidance, a training-free framework that turns pretrained foundation image editors into continuous affective controllers over VA, requiring no finetuning, extra data, or model changes. Our method maps any target VA point to simplex-based guidance weights, enabling VA controllability in three aspects: (i) accurate targeting of VA states, (ii) broad coverage across the VA plane, and (iii) continuous control. Across three face datasets, we improve VA target accuracy by 25-29%, expand VA-plane coverage by 28-50%, and increase expression diversity by 29-49%, over the strongest baseline. Unlike prior domain-specific methods, our training-free approach exploits the foundation model's inherent versatility, enabling generalization beyond human faces to animals, artworks, and complex scenes within a single framework. Code is available at https://github.com/harveymannering/BarycentricGuidance.

Inferring tumor-growth laws from sparse, noisy observations requires more than accurate curve fitting. We study an AI-assisted workflow involving symbolic regression, mathematical admissibility checks, coefficient refitting, and large language model (LLM) ranking. Synthetic Gompertz data allow trajectory fit, forecasting, and recovery of the governing growth law to be assessed separately. A dense noiseless control recovers the generating family, but sparse noisy sampling frequently leads to alternative forms. Among retained candidates in the tested configurations, physics-informed neural network refitting often increases growth-law error, whereas classical nonlinear least squares usually reduces it. A separate exploratory analysis of archived LLM rankings shows no consistent improvement over selection by training error and identifies errors in mathematical reasoning. Plausible saturation, accurate trajectory fits, and convincing explanations can therefore coexist with incorrect growth laws. Mathematical validity and law recovery require evaluation alongside predictive performance.

We introduce FORGE (Fast On-chip Rotor Generation for Experts), a procedural weight generation system for Sparse Mixture-of-Experts (MoE) inference. Rather than storing and loading every expert weight tensor from HBM, we show how a compact accelerator inside each Streaming Multiprocessor can regenerate them on-the-fly from $O(\log^2 d)$ rotor parameters per projection. Per replaced layer, gigabytes of stored expert weights are approximated with under a megabyte of seeds. This addresses the dual memory bottleneck of autoregressive Sparse MoE decode, where per-expert FFN operations are HBM-bandwidth-bound at small routed-token counts and the aggregate expert footprint forces multi-node Expert Parallelism (EP) with all-to-all traffic. We realize the approach as the Rotor Generation Unit (RGU), a fixed-function datapath that generates FFN weight tiles without competing with Tensor Core execution. With 30% of the MoE FFN layers replaced across five Sparse MoE models, we estimate 1.3-2.8x higher system throughput at matched GPU count and 1.10-1.15x lower per-user decode latency at short context. In exchange, downstream accuracy on three model families falls below that of the same model fine-tuned without rotor replacement, and the replacement ratio controls this tradeoff. FORGE also expands KV cache capacity by 1.2-2.6x. It is agnostic to the bit width at which weights are stored, so it can compose with quantization. The RGU is fully implemented/verified in SystemVerilog at ~0.9% SM area overhead (0.032 mm^2/SM, 7nm).

Can collective quantum-noise measurements distinguish different mode temperatures from one common temperature when the coupling spectrum is unknown? For stationary Gaussian oscillator environments, we derive a sharp bandwidth threshold for an exact thermal alias on the integer-time sampling lattice. The threshold depends on temperature order through the quantum response. For frequencies within the first alias period, fixing sufficient integer-time correlations makes one additional fractional-time fluctuation observation enough to exclude every common-temperature fit. A calibrated second pulse width provides another route through the same collective port: both widths must probe one spectrum and retain their measured variance scales. For a specified two-mode example, continuous-frequency certificates cover all common temperatures and uncertainty in a shared pulse ramp. A binary-readout protocol combines randomly interleaved matched references with collective-variance and coherence checks to handle Gaussian oscillator loss and predictable readout drift. The selected fractional-clock and two-width designs require approximately $3.8\times10^7$ and $1.6\times10^8$ outcomes for at most 5% type-I error and at least 95% power on the stated alternative class. These theoretical and numerical acquisition guarantees assume independently validated preparation, spectral support and control specifications; validation costs are additional. The result identifies which new observation makes thermal-model testing informative when mode-resolved access is unavailable.

Hydrodynamics as an effective field theory (EFT) has been immensely successful for predicting the behaviour of time-ordered correlation functions in the long-time, large-distance regime. In this paper, we analyse the predictions of hydrodynamics for scrambling as probed by out-of-time order correlators (OTOCs). To do so, we consider an all-derivative order generalisation of the Schwinger-Keldysh EFT of hydrodynamics extended to a four-fold time contour required to capture OTOCs. A crucial ingredient of the construction is a local SL(2,R) symmetry, which has previously been suggested as a mechanism for scrambling. We also derive this exact EFT from the microscopic formulation of the maximally chaotic low-temperature limit of the SYK lattice, thereby determining all transport coefficients for this model. As a novel application, we compute the OTOC of energy currents, find that its exponential growth saturates the chaos bound, and match it to expectations based on a shockwave (or scramblon) effective description. Our work shows that the universality of hydrodynamics degrees of freedom extends beyond traditional time-ordered correlators to more complex observables such as OTOCs.

Transparency in AI-supported decision systems is widely required but poorly defined. Existing approaches treat transparency as a property of systems or components, producing characteristic failures: assessments that do not transfer across organizational boundaries, stakeholder questions that cannot be formulated within the available frame of analysis, and component-level findings that say nothing about system-level behavior. We propose treating transparency as a relation: a system is transparent to a stakeholder to the degree that their legitimate questions are answerable from its structure. We formalize this using information flow networks, in which transparency questions are expressed in terms of network structure and answerability is the condition that the system settles them. The framework supports three dimensions of analysis: structural answerability from the network alone, compositional answerability across organizational boundaries for deployed systems, and role-dependent answerability given a stakeholder's accessible sub-network. We demonstrate the framework on a real pre-integration assessment of an AI recruitment tool in a public sector municipality. The assessment uses participatory design and interviews to model the decision system structure. We show how structural and role-dependent transparency questions can be formally stated and analyzed across the Provider and Deployer boundary where the AI system is composed together with the deployer's decision process.

Variational inequalities (VIs) capture a broad class of optimization problems central to modern machine learning, including min-max optimization and equilibrium computation in multiplayer games. Traditionally, algorithms for solving VIs, such as Extragradient (EG) and Past Extragradient (PEG), have been analyzed under the standard $L$-Lipschitz assumption. However, this condition is often overly restrictive, and recent works have instead turned to the more relaxed $(L_0,L_1)$-Lipschitz setting. Existing guarantees for $(L_0,L_1)$-Lipschitz VIs require a quasi-sharpness condition [Vankov et al., 2024], while monotone guarantees for EG cover only unconstrained root finding [Choudhury and Loizou, 2025]. In this work, we provide the first convergence guarantees for EG and PEG for monotone $(L_0,L_1)$-Lipschitz VIs. We also improve upon prior convergence guarantees for strongly monotone VIs by supporting larger stepsizes in the constrained setting and eliminating exponential dependence on the initial distance from the solution for convergence rates in the unconstrained setting. Lastly, we propose line-search variants for when Lipschitz parameters are unknown. Numerical experiments complement our theoretical results and demonstrate the practical efficacy of our methods.

Borzellino and Brunsden introduced a general notion of suborbifold and proved that a suborbifold is the image of a complete orbifold embedding if and only if it is both saturated and split. Their definitions and proofs are formulated in the classical language of orbifold charts. In this paper we translate these notions into the language of proper étale Lie groupoids.We introduce the groupoid analogues of saturation and splitting, which we call orbit saturation and stabilizer splitting, and prove that they coincide with the chart-based conditions. Our main theorem states that a subgroupoid is the image of a complete orbifold embedding if and only if it is both orbit saturated and stabilizer split. We then prove that these notions are Morita invariant: if two orbifold groupoids are Morita equivalent, then their orbit saturated and stabilizer split subgroupoids correspond naturally to each other. This solves an open problem raised by Mestre and Weilandt and explains why the embedding definition of Cho–Hong–Shin fails to be Morita invariant. Along the way we provide detailed examples, including the diagonal embedding, the non-split example of Borzellino and Brunsden, and explicit Morita equivalences.

Continuous symmetry discovery is typically formulated as a separate estimation problem for each function or dataset. We instead investigate whether the map from a function to its symmetry structure can be learned across a family of functions from finite observations. Using the infinitesimal differential characterization of continuous symmetries, we formulate this map as an inverse symmetry operator, analogous to an inverse PDE problem. For global Lie-group symmetries, we establish a representation-theoretic population characterization: the symmetry Lie algebra is the nullspace of a positive-semidefinite operator constructed from representation coefficients and the infinitesimal group action. We also show that the inverse symmetry operator is equivariant under coordinate changes through the adjoint action. This characterization separates the geometric symmetry map from finite-sample estimation, motivating a hybrid approach that amortizes statistically difficult components while retaining analytic structure. On SO(5) benchmarks, amortized equivariant estimation of harmonic coefficients improves symmetry recovery from sparse observations, whereas ordinary least squares suffices for SL(2,R). We extend this viewpoint to local symmetries, where symmetry directions form smoothly varying tangent distributions rather than a fixed Lie algebra. Under the Lie-bracket consistency condition, Frobenius' theorem guarantees local integral submanifolds along which observables remain unchanged. We recover this geometry using a hybrid estimator that learns observation weights while preserving analytic differential and geometric recovery. Across global, non-compact, local, and physically motivated synthetic benchmarks, our results support learning the statistically difficult finite-sample components while preserving the known geometric structure of symmetry recovery.

We study a stochastic optimization problem in which the random vector follows a semiparametric elliptical distribution with unknown location and shape parameters and an unspecified radial distribution. Assuming that the decision maker only has access to samples of the random vector, we develop a framework to jointly address parameter uncertainty and distributional ambiguity arising from this composite structure. To update the posterior distribution of the parameters, a key challenge is that the density of an elliptical distribution depends on the unknown radial distribution, and hence conventional likelihood-based Bayesian inference is infeasible. To overcome this challenge, we propose a novel estimating-equation-based Gibbs inference framework that updates posterior distributions of model parameters solely through estimating equations. For elliptical distributions, we construct a pair of estimating equations for the location and shape parameters that are invariant to the radial component, which enables posterior learning without specifying the density. For the distributional uncertainty, we construct an ambiguity set for the radial distribution by transforming observed samples into pseudo-samples of the radial variable. Combining the above components, we formulate a composite Bayesian risk–distributionally robust optimization model, in which the inner problem captures worst-case radial distributions within the ambiguity set, and the outer problem evaluates the decision risk induced by the parameter uncertainty through a user-specified risk measure. We further develop a cutting-plane algorithm to solve the resulting optimization problem. Numerical experiments demonstrate that the proposed approach provides substantial performance improvements over benchmark methods, including sample average approximation and distributionally robust optimization.

Seeking a pictorial representation of four-party absolutely maximally entangled (AME) states of local size six, we independently construct a real AME$(4,6)$ state from a table of signed Pauli matrices. Its two-unitary matrix has $60$ nonzero entries, equal to $1$ or $\pm 1/\sqrt{2}$. A locally equivalent representative yields a genuine geomagic square, where every row, column and main diagonal tiles a hexagon and all $36$ pieces are pairwise non-congruent. Colors, shapes and hatching retain the full tensor, allowing its reconstruction from the picture.

There is a specific challenge designers face in developing autonomous robots capable of open-ended learning. This challenge is how one can develop such systems in an ethically sound way when there are many unknowns during design time about their manner of deployment, what they can and will learn, and how these systems will act on the basis of what they have learned. One response to this challenge is to align, as far as possible, the activities and goals of autonomous robots with human values, raising the question of how to make this alignment possible, a question known as the value alignment problem. We argue that the value alignment problem faces a number of challenges that show that full alignment is both theoretically and practically impossible, meaning that misalignment incidents will keep occurring. This undermines current alignment approaches, as the attempt to maximize alignment cannot properly deal with the possibility that the risk of misalignment that remains after alignment methods have been implemented might still be unacceptable to society. To overcome this difficulty, we argue that a shift in perspective is required from a focus on the maximization of alignment to the conditions under which misalignment incidents become acceptable. In this paper, we explore what this shift in perspective entails. We introduce the concept of acceptable misalignment, formulate normative requirements for alignment mechanisms aimed at bringing misalignment incidents to an acceptable level, and we conclude by presenting a new methodological framework that consists of alignment mechanisms that can meet these requirements.