Papers

In the canonical Difference-in-Differences design, the control group's post-treatment change serves as an imputation of the treated group's counterfactual change in the same period, an imputation justified by parallel trends. However, differences in group composition can produce between-group differences in how outcomes would evolve over time, rendering this imputation vulnerable to confounding. An alternative imputation – such as one based on the treated group's pre-treatment change – avoids such between-group confounding but introduces the risk of confounding from within-group temporal shifts. Ideally, both imputations, each vulnerable to different sources of confounding, would have concordant values, thereby yielding the same causal conclusions. When the imputations are discordant, conclusions under parallel trends hinge more critically on that assumption since alternative imputations would point to different results. Yet in these scenarios, existing pretrends-based sensitivity analyses can show low sensitivity because they ignore post-treatment deviations from pretrends in the control group. This paper therefore proposes a discordance-based sensitivity model in which parallel pretrends are necessary but not sufficient for low sensitivity. I formally justify this model in terms of the expected distance between the ATT under parallel trends and under alternative assumptions, weighted by the joint plausibility of those assumptions. I then provide a decision-theoretic rationale for benchmarking violations of parallel trends using the worst-case discordance between the parallel trends imputation and alternative imputations. Finally, I apply both pretrends- and discordance-based sensitivity models to assess how a labor supply shock influenced electoral support for apartheid-era policies in South Africa, showing how the two approaches yield different results.

As robot capabilities increase, quadratic programming (QP)-based controllers must account for a similarly increasing number of constraints to ensure safe, reliable operation. Yet, with each added constraint, this introduces more chances of momentary conflict: in which case, a QP solver that returns an "infeasible" status leaves the controller with nothing to execute. To address this, we introduce ElastiQP, a modified dual active-set QP solver that relaxes every inequality constraint with an exact, per-constraint l1 penalty while keeping equality constraints (dynamics) hard. Notably, ElastiQP does so by folding the slack variables into the solver analytically, maintaining a constant size of the condensed linear system. On a suite of robot control benchmarks, ElastiQP achieves microsecond-level performance, matching or outperforming leading modern solvers on feasible problems. On infeasible problems, ElastiQP handles these gracefully, confining violations to strictly the conflicting inequality terms, returning a usable solution up to 40x faster than the best alternative solvers. ElastiQP is available as an open-source C++ header-only library, with Python and JAX interfaces, at https://github.com/StanfordASL/elastiqp.

This note establishes a geometric foundation for trajectory-manifold representations of deterministic nonlinear systems in a behavioral setting motivated by data-enabled predictive control. For a discrete-time system $x_{k+1}=f(x_k,u_k)$ with measured state and a $C^r$ transition map, $r\geq 1$, we consider the terminal-state-augmented finite-horizon behavior consisting of all admissible state-input trajectories over a prediction horizon $N$. We prove that this behavior is a $C^r$ embedded submanifold of the ambient trajectory space with intrinsic dimension $n+Nm$, where $n$ and $m$ are the state and input dimensions. Moreover, the rollout map from the admissible initial-state and input coordinates $(x_0,\mathbf u)$ is a $C^r$ diffeomorphism onto the behavior manifold, providing explicit global smooth coordinates. This yields a canonical exact encoder–decoder representation and implies that any exact differentiable latent representation of the full behavior must have latent dimension at least $n+Nm$. The geometric result does not require controllability, stabilizability, or invertibility of the dynamics. Corresponding results are given for zero-order-hold sampled continuous-time systems and fixed-step numerical transition maps. These results provide the deterministic geometric foundation for subsequent data-driven approximation and predictive-control development.

We propose a notion of simplicity for Cayley permutations that is compatible with inflation and agrees, under a natural relational encoding, with indecomposability in the sense of Schmerl and Trotter. We establish a substitution decomposition analogous to that of permutations, in which the components are modules of the associated relational structure. We use it to enumerate simple Cayley permutations as well as simple restricted growth functions.

Formal explainability provides mathematically grounded justifications for individual predictions. However, abductive explanations often exceed human cognitive limits by involving too many features, while probabilistic relaxations have remained largely limited to categorical classification. We present a unified framework for probabilistic explainability based on sparse, anchored linear models, applicable to both binary classification and continuous regression. By mapping instances to the Boolean hypercube, our linear explanations strictly generalize subset-based approaches: they capture both the magnitude and direction of feature contributions while enforcing a prescribed sparsity budget $k$. We show that minimizing the relevance error for such explanations is \ClassNPPP-hard when the underlying model is a neural network, and we relate this intractable objective to a tractable surrogate—the fidelity error. For a parameterized family of local distributions, the relevance error of any $k$-sparse explanation is bounded by its fidelity error up to a multiplicative factor that remains small locally. We address the resulting empirical problem using two complementary approaches: a Mixed Integer Programming (MIP) formulation that yields provably optimal empirical solutions while maintaining polynomial sample complexity, and a polynomial-time Iterative Hard Thresholding (IHT) algorithm with provable approximation guarantees. Empirical evaluations show that, unlike state-of-the-art baselines such as LIME and MAPLE, our explanations satisfy both the anchoring and sparsity constraints by construction, while consistently achieving lower relevance error.

The test error of a model plotted against its number of parameters $d$ falls, peaks when the model can just fit the training data, and falls again, exhibiting the double descent phenomenon. We explain the phenomenon with statistical mechanics. The training trajectory of a stochastic gradient-based method is a particle wandering over the energy landscape of the training loss at an induced temperature $T$, and a run that has equilibrated visits every parameter vector of a given training loss equally often, the fundamental postulate of statistical mechanics, with probability given by the Boltzmann distribution. Because training starts at an initial point and has only finite time to diffuse, it carries an effective weight decay, which makes every parameter a quadratic degree of freedom. The equipartition theorem then distributes the energy among the $d$ degrees of freedom in shares of $T/2$, so at a fixed training loss adding parameters lowers the temperature and drives the Boltzmann distribution toward the stationary path. Finally, adding parameters can only lower the $L^2$ norm of the stationary path, so a solution sampled at fixed loss is less likely to be large with increasing $d$, effectively increasing weight regularization.

We study how $SL(2,\mathbb Z)$ transformations act on pole-truncated linear-response effective theories in $(2+1)$ dimensions. For correlators meromorphic within a finite low-frequency domain, the EFT data include both derivative-expanded transport coefficients and the retained non-hydrodynamic poles. Since the $S$-transformation inverts the optical conductivity and exchanges its poles and zeros, it does not necessarily commute with the infrared truncation. We derive explicit maps for static susceptibilities, the Einstein relation and AC transport coefficients. In the purely hydrodynamic sector the map closes on the original transport data, while in quasihydrodynamic regimes the transformed pole positions and, in general, residues constitute additional infrared data. We test the construction in the alternatively quantised D3/D5 probe-brane system, where an EFT retaining one original gapped pole can correspond to transformed EFTs retaining zero, one or two. The holographic results verify the analytic maps and exhibit an inverse-Drude conductivity at large values of the control parameter.

Reinforcement learning (RL) is an exciting concept as well as a remarkable success story worth sharing. However, RL builds on rather complex interactions between different objects that play out over several cycles. Such dynamics are often best explained with an easily accessible implementation. We present RLLBC-Lib, a carefully crafted code library with the goal of lowering the entry barrier for students and other learners of RL in the context of learning-based control. At its heart, RLLBC-Lib comprises a comprehensive library of tabular RL approaches to enforce a clear understanding of the theoretical foundations. A deep RL library follows the same design principles, underscoring the parallels between simple tabular and state-of-the-art deep RL approaches. Additionally, RLLBC-Lib provides a collection of implementations illustrating core RL principles and contrasting RL to other learning-based control approaches. Finally, RLLBC-Lib provides an ideal basis for creating programming assignments with automated grading.

The theoretical foundation for model checking timed systems against Metric Interval Temporal Logic (MITL) was established in the early 1990s, yet the first practical tool supporting future MITL (MightyL) did not emerge until 2017. Recently, there has been growing interest in extending this toolchain to support more expressive logical operators, including past modalities, Pnueli modalities, and limited use of singular intervals. MightyPPL is one such toolchain. We introduce an upgraded version of MIghtyPPL that enables for the first time, the model checking of Metric Temporal Logic (MTL) properties of the form (whenever an event p occurs, it is eventually followed by some event q after exactly some k time units) in addition to Pnueli and Past modalities. We discuss the tool's underlying architecture and implementation, and present a performance evaluation against the Tempora tool across diverse satisfiability and model checking benchmarks, demonstrating that MightyPPL delivers significantly better performance.

Adults with intellectual and developmental disabilities (IDD) are increasingly transitioning from family homes towards semi-inde\-pendent living. As parents hand off the role of primary caregiver, they face numerous challenges in arranging consistent and quality support. Our research centers on understanding these caregiving routines. By focusing on the unique lived experience of parents, who possess extensive explicit and tacit knowledge of their adult child's requirements, we aim to map the management of care they provide. This foundational understanding is essential to identifying how assistive technologies can effectively serve a key role in supporting adults with IDD in this transition. In this work, we interviewed 16 parents of adults with IDD beginning this transition to understand: 1) how they currently provide support for daily living and what makes their support effective; 2) what their experiences and perceptions are regarding the use of technology; and 3) how they envision assistive technology successfully integrating with their adult child's new home or with other supports to promote independence. Our thematic analysis produced four themes: common modes of support, inside the routine to support growth, the fragility of continuity of care across transitions, and participants' perceptions and experiences of assistive technology. Building on these findings, we derive four design principles for growth-oriented assistive technology. These include pre-transition onboarding to capture caregiver tacit knowledge; structured scaffolding towards long-term growth; adaptive sensing that responds to day-to-day variability; and customization for the individual balanced with consistency for the care network.

Let $X$ be a normal variety in arbitrary characteristic, and let $\tilde X$ be the successive blowup along subvarieties $Z_1,\dotsc,Z_n\subseteq X$ of codimension at least two that have simple normal crossings and satisfy $Z_h\not\supseteq Z_i$ whenever $h<i$. We prove that the relative cone of curves $\overline{\operatorname{NE}}(\tilde X/X)$ is generated by the classes of finitely many elementary curves, and that every face admits a contraction over $X$. Moreover, we prove that every small face contraction admits a $D$-flip for every $\mathbb R$-Cartier divisor $D$ that is relatively anti-ample. We also compute the relative Cox sheaf and prove its finite generation.

A game character should not have to reread its entire life before every conversation. For locally deployed language-model characters, however, revising a few memories can invalidate a long reusable prefix. The resulting preparation cost competes with both foreground dialogue and the maintenance of other characters. This matters especially when dialogue feeds game-defined actions and value judgments: a fluent but incorrect account of who owns an item, or whether a transfer has already happened, can corrupt the input to otherwise deterministic rules. We study incremental memory maintenance for long-lived game NPCs in a quantized Qwen hybrid recurrent-attention model. Our runtime removes superseded attention KV entries, computes replacement records at the true sequence tail, and preserves the continuing recurrent state and unchanged KV. Existing local experiments combine multi-update dialogue replays, fixed-input placement ablations, and attention diagnostics. Independent block composition weakens query-conditioned memory selection without a uniform chunk-initial attention collapse. True-tail updates preserve important current-state and historical bindings across eight scripted maintenance rounds; a placement case recovers the full-refill quantity in three reconstructions, while slot-preserving alternatives repeat a double-subtraction error. Attention-distribution proximity alone does not explain these semantic differences. The results motivate treating a character's inference state as a maintained, history-dependent resource, rather than only a disposable encoding of its latest memory text.

We prove the André–Oort conjecture for hypersurfaces $V \subset Y(1)^n \cong \mathbb{A}^n_\mathbb{C}$ defined by an equation $a_1 x_1^m + \ldots + a_n x_n^m = b$, where $a_1, \ldots, a_n, b \in \overline{\mathbb{Q}}$ and $m \in \mathbb{Z}_{>0}$. Unlike previous proofs, our result is both effective and uniform in the height of the coefficients $a_1, \ldots, a_n, b$. This is the first effective proof of a uniform André–Oort statement for a class of subvarieties with arbitrary dimension and non-empty special locus. We also prove an analogous result for hypersurfaces $V \subset Y(1)^n \times \mathbb{G}_m^l$.

The traditional $\alpha$ effect is extended by the first temporal derivative, so that in turbulent flows the magnetic field entering the induction process is effectively sampled in the past. As a consequence, dynamo excitation becomes easier and cycle times are prolonged relative to solutions obtained from the local standard formulation. The temporal shape of the magnetic cycles is also modified, with rise times becoming shorter than decline times, so that the profiles acquire a characteristic “sawtooth” appearance. In the nonlocal formulation, the induced magnetic-field amplitudes acquire an additional dependence on the correlation time. For fixed dynamo number, the field amplitude reaches a maximum at a certain correlation time. For correlation times larger than this peak value, the model can reproduce Waldmeier-type trends known from solar sunspot observations. If the actual correlation time fluctuates around this value, the long-term magnetic cycle can occasionally enter weak-cycle episodes reminiscent of grand minima such as the Maunder minimum. For smaller dynamo numbers close to the critical one, however, rather long correlation times are required for this behaviour to occur.

Function-as-a-Service (FaaS) has emerged as the prominent programming model for the edge-cloud continuum. FaaS inherently decouples stateless functions from their persistent state. We study how to jointly schedule functions and place data to minimize client latency, considering data replication under heterogeneous consistency requirements. We introduce a Binary Linear Programming (BLP) model to compute optimal placements, establishing a rigorous theoretical baseline. Since the BLP scales cubically with the infrastructure nodes, we propose a topology-aware greedy heuristic that efficiently approximates the optimal solution. Our evaluation shows that the heuristic achieves near-optimal placement quality at a fraction of the computational cost, making it suitable for periodic system reconfigurations.

In this work, we present a computational model to investigate transdermal insulin delivery using coated microneedles. A detailed skin geometry incorporating a coated microneedles was developed to analyze insulin release through the different skin layers and to evaluate the influence of key transport parameters. The model represents the major skin layers: the stratum corneum, viable epidermis, and dermis. Unstructured grids were used to achieve a reliable resolution of the model. The simulations provide insights into the permeation of insulin from the coated microneedles and the transport and distribution across the different skin layers. Finally, the simulation results were compared with experimental data to evaluate the predictive capability of the model.

Bipedal loco-manipulation enables robots to interact with objects beyond the nominal workspace of their arms by coordinating locomotion and manipulation. Realizing this capability requires a low-level whole-body controller that translates task-level manipulation goals into coordinated arm and leg motions while maintaining balance. We present a unified whole-body controller trained with reinforcement learning that directly maps 6-DoF end-effector targets to coordinated actions for the bipedal base and robotic arm. Given only an end-effector target, the learned controller autonomously coordinates reaching, postural adaptation, and stepping without explicit base-velocity or footstep commands. A reward-gating strategy regulates the trade-offs among end-effector tracking, locomotion, and balance during training, while a temporal context estimator combines windowed Transformer encoding, recurrent GRU memory, and auxiliary dynamics prediction to extract dynamics-relevant information from observation history. Real-robot experiments demonstrate that the same controller supports reaching, postural adaptation, and stepping under commands from VR teleoperation, a learned diffusion policy, and scripted trajectories, providing a common end-effector interface for diverse manipulation tasks.

In multi-agent environments, coordinating agents to prevent interference and ensure robust individual performance is a critical challenge. Previous research on social laws for multi-agent systems has primarily focused on deterministic, goal-based settings. This paper extends the concept of social laws to stochastic, reward-based environments, proposing a formalism for defining and verifying their robustness under various conditions. We introduce the notion of $\alpha$-robustness, a measure of the guaranteed utility each agent retains while pursuing its optimal single agent policy, assuming all agents obey the social law. We then present an approach for robustness verification of social laws in stochastic settings, based on a reduction to solving a series of Markov decision processes. Empirical evaluations on toy environments illustrate the potential of our framework.

In particle collider experiments, event reconstruction is the task of inferring the kinematics of short-lived particles produced in the hard scatter from the stable final states recorded by detectors. We decompose event reconstruction into two primary tasks: assigning measured jets and charged leptons to parent particles, and predicting unmeasured neutrino kinematics. We present VyPER, a novel geometric learning framework that represents collider events as hypergraphs with a physics-inspired topology. VyPER combines the supervised classification of hyperedges for particle assignment with a diffusion model for predicting neutrino kinematics, leveraging a joint loss function to optimize both reconstruction tasks within a unified framework. We showcase VyPER across several proton-proton collision processes, comparing its performance to existing analytical and machine-learning-based reconstruction techniques. In doing so, we demonstrate that accurate event reconstruction is achievable across a diverse range of Standard Model physics processes, opening new avenues for precision measurements in the Higgs boson, electroweak, and top-quark sectors.

Soft materials store, dissipate and release mechanical stresses through relaxation processes that often span many orders of magnitude in time. Such relaxation spectra are widely used to infer internal material dynamics and are usually regarded as fingerprints of microscopic complexity, disorder, or heterogeneity. Here we show that a broad relaxation spectrum can instead be generated by the geometry of mechanical excitation itself. Using rotationally driven colloidal dimers in a wormlike micellar fluid with a dominant bulk relaxation time of order one second, we demonstrate that torsional driving converts distance from the driven object into relaxation time. This produces a geometry-controlled hierarchy of relaxation modes: orientational recoils persist for hundreds of seconds and encode past torque protocols over comparably long times. Particle velocimetry reveals rapid angular-momentum transport away from the probe, in contrast to the slow relaxation of stored torsional stress. A continuum shell model captures the observed recoil dynamics and the selective suppression of long-lived contributions under spatial confinement. Our results show that geometry can transform a material with simple intrinsic relaxation into a system with long-lived, space-dependent memory, suggesting a route to tune material dynamics through mechanical excitation rather than composition, with potential implications for microscopic mechanical memory elements.

This paper establishes the necessary and sufficient conditions for asymptotic stability of the time-varying Kalman filter applied to a linear time invariant system with semidefinite initial state covariance and positive definite process and measurement noise. Rather than analyze the discrete Riccati equation as in the classic literature, the equivalent state smoothing optimization problem is stated and all results are established using properties of this optimization problem. A Lyapunov-like function, termed a modified $Q$-function is derived and used for this analysis. This optimization approach removes the need for the classic but cumbersome Riccati iteration algebra and provides better generalization and application for nonlinear systems.

Function-as-a-Service (FaaS) is a widely adopted paradigm to simplify application deployment across the edge-to-cloud continuum. However, its stateless nature forces functions to retrieve their state from external, typically cloud-centric, data stores, reintroducing the very latency that edge computing aims to eliminate. This issue is further exacerbated by location-agnostic schedulers and rigid, one-size-fits-all consistency models that fail to capture the diverse requirements of edge applications. In this paper, we propose Ermes, a distributed platform that natively integrates state management into the FaaS paradigm, enabling the joint distribution of computational workloads and application state across the edge-to-cloud continuum. Ermes organizes application state into logical units, termed collections, and employs a distributed coordination algorithm that jointly maps collections and functions onto the available nodes seeking to minimize the latency perceived by the clients. In addition, it supports fine-grained replication and per-collection consistency levels, ranging from sequential to eventual consistency, leaving developers the choice of how to resolve the trade-off between consistency and performance. The experimental evaluation shows that Ermes quickly turns remote state accesses into local ones and sustains low latency as the workload grows, and as clients move across the edge.

In 1854 Riemann presented his Habilitationsvortrag Über die Hypothesen welche der Geometrie zu Grunde liegen to the Faculty of Philosophy of the University of Göttingen. The lecture does not contain analytical developments and Riemann never explained the reason for this choice. According to Dedekind this choice was done in order to make the lecture understandable to the non-mathematician professors of the Faculty. This is the suppression thesis. Nevertheless, in 1851, three years before, Riemann has presented his Inauguraldissertation Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse to the same professors of the Faculty of Philosophy. The Inauguraldissertation contains many analytical developments but, on that occasion, they were not suppressed. Therefore, the presence of non-mathematician professors is unrelated with the presence or absence of analytical developments in the lectures. The ideas contained in Riemann's Habilitationsvortrag –manifold, line element, curvature– were so new at the time that there was not even a proper language to express them. Therefore, Riemann was forced to adopt a non-technical expository style. This explanation for the absence of analytical developments in Riemann's Habilitationsvortrag is more credible than the suppression thesis.

We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$-gates are studied, not the $S$-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths ($p$). We provide a series expansion form to the logical error rates, through order $(p/(1-p))^{10}$. The analytical results recover the numerical values from Clifft and SOFT at both $d=3$ and $d=5$ to within their sampling uncertainty. Then, we show that the $d=3$ and $d=5$ circuits actually have fault distances of $d_{\text{fault}}=2$ and $d_{\text{fault}}=3$ respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].

Let $k=\overline{\mathbb{F}_2}$. We construct a nine-dimensional $F$-rational affine variety $X$ admitting a locally closed embedding $X\hookrightarrow \mathbb{P}_k^{19}$ together with a dense open set $U\subseteq (\mathbb{P}^{19})^\vee$ such that $X\cap H$ is not $F$-rational (or even $F$-injective) for all $H\in U$. We also construct a nine-dimensional projective $F$-rational variety $\mathfrak{X}$ and a closed embedding $\mathfrak{X}\hookrightarrow\mathbb{P}^{29}_k$ under which the same conclusion holds.

Physical properties, such as friction, hardness, stiffness, and density, govern how robots should grasp, manipulate and interact with objects, yet estimating these properties from RGB images remains challenging. Existing methods typically employ per-object reconstruction augmented with physical properties or directly query vision-language models at test time, which results in substantial computational overhead that limits their applicability. In this work, we present PhysVGGT, a feed-forward model that predicts dense maps of friction coefficient, Shore hardness, Young's modulus, and density, together with object-level mass, from a single RGB image in one forward pass. The key idea of PhysVGGT is to formulate physical property estimation as a dense per-pixel prediction problem and employ a visual geometry transformer to extract geometry-aware tokens from the input image followed by a dense prediction branch for estimating local physical properties and a global prediction branch for estimating object-level mass. In addition, we introduce a scalable pseudo-label generation pipeline that enables large-scale weakly supervised training for dense physical property prediction, substantially reducing the need for expensive direct physical measurements. Extensive experiments show that PhysVGGT achieves state-of-the-art performance on the ABO-500 dataset and generalizes effectively to the out-of-distribution NeRF2Physics dataset. Moreover, PhysVGGT eliminates the need for per-object reconstruction and test-time optimization, achieving an inference latency of only 0.13s per image, making it $27\times$ faster than the previous state of the art.

Let $G$ be a compact connected semisimple Lie group, and let $\pi:G\to U(V_\lambda)$ be a finite-dimensional irreducible unitary representation associated with the highest weight $\lambda$. We prove that coherent projectors are the unique minimizers of the Wehrl entropy over all density matrices on $V_\lambda$. Similar extremal properties hold for power functions in place of the entropy function. The proof uses a second variation at the extremizer by perturbation in directions associated with Killing fields, similar to the strategy of Frank and Lieb used in \cite{FrankLieb}. Then the problem reduces to the uncertainty principle characterizing coherent states. This solves the Wehrl-type entropy problem for arbitrary compact connected semisimple Lie groups.

Taming the exponential increase of the Hilbert space dimension with system size in the simulation of gapped quantum lattice models is of the highest relevance for understanding and designing exotic quantum materials, where nonlocal interactions are of particular interest. High-order linked-cluster expansions provide access the solution of the eigenvalue problem for the infinite system, yet rely on the computation of high-dimensional oscillatory lattice sums with a graph structure, only approachable with Monte Carlo methods so far. This work resolves this issue, rendering all required graph lattice sums, referred to as graph zeta functions for kernels involving power-laws, computable. The resulting method reduces the evaluation time for state-of-the art series expansions from tenthousands of core-hours to minutes. After factorizing the lattice sum over blocks, each block is evaluated by the cheapest available strategy depending on its treewidth $\mathrm{tw}$. Basic blocks admit analytic forms in terms of generalized zeta functions. Series-parallel blocks with $\mathrm{tw}\le 2$ can be computed at linear cost in the number of graph nodes and in the size of the momentum grid using a semi-analytical algebra based on Epstein zeta functions and rapidly decaying Fourier series. Finally, for $\mathrm{tw}>2$, the method is combined with tensor-network bucket elimination yielding polynomial scaling of numerical work and memory in momentum grid size with exponents only growing with $\mathrm{tw}$ rather than with the number of vertices. Through use of FFT, the full momentum grid is recovered at the cost of a single momentum evaluation. We provide a detailed analysis of the precision and runtime of our method against analytic and numerical benchmarks. We further reproduce published Monte Carlo data for the transverse-field Ising model on different 1D, 2D, and 3D lattices, obtaining full agreement.

Three-dimensional CFD-DEM simulations were used to investigate the influence of fluidizing medium on the hydrodynamics and mixing of a binary fluidized bed containing equal-density 3 and 4 mm particles. Water and air were compared using identical geometry, particle properties, and initial conditions over matched normalized superficial velocities of 0.5-3.0 times the minimum fluidization velocity. The numerical framework was validated against published liquid-solid bed-expansion data and benchmarked against an established gas-solid CFD-DEM case. At matched normalized superficial velocities, water fluidization produced a comparatively dense and homogeneous bed with stable bed height and pressure drop and weak velocity fluctuations. Air fluidization resulted in greater expansion, persistent oscillations, void- and bubble-like structures, stronger circulation, and greater spatial heterogeneity. Mixing, quantified using the Lacey mixing index, increased with superficial velocity in both media but developed more rapidly and reached higher levels in air. Particle trajectories and mean-square displacement further showed greater particle mobility and transport in air. The results demonstrate that normalization by the minimum fluidization velocity does not collapse the hydrodynamic or mixing behavior across fluidizing media because fluid properties strongly influence the underlying particle-transport mechanisms.

Mixture-of-Experts (MoE) language models suffer from large parameter counts, which create a significant memory bottleneck. Expert pruning is the most direct approach for reducing this parameter count, yet existing methods make pruning decisions for each expert independently, and assume experts' contributions are purely additive. In reality, expert usage in MoEs is inherently cooperative. We derive HOPE (Higher-Order Pruning of Experts), a second-order pruning objective which provably minimizes an upper bound on the error resulting from pruning. We show that REAP (a state-of-the-art first-order pruning method) is a special case of HOPE where interaction terms are ignored. Across three frontier MoE models (up to 122B parameters), two distinct calibration sets, and multiple benchmarks (including math, instruction following, coding, and an agentic suite), we demonstrate that HOPE produces better pruning decisions than existing methods, and its advantage is most pronounced at high pruning rates and on challenging agentic workloads. At 50% pruning, HOPE outperforms all baselines and achieves an average rank of 1.58 out of 5 methods (versus 2.42 for the next-best method, REAP), with gains of up to +6.1% on agentic coding. Over all conditions, HOPE again achieves the best average rank and surpasses every other method in the majority of head-to-head comparisons. By preserving cooperative expert structure that first-order methods ignore, HOPE enables aggressive compression with minimal degradation, particularly on complex tasks where diverse expert combinations are invoked over long sequences.