Papers

We propose a two-dimensional benchmark for fluid-structure-contact interaction consisting of a deformable elastic disk falling under gravity within a viscous incompressible fluid and rebounding in the vicinity of the bottom wall. Solid deformability is essential, as rigid solids do not rebound in this framework. Besides this, the setting is deliberately kept simple to facilitate reproduction. The configuration is particularly challenging due to the well-known no-contact paradox, which can lead to a contactless rebound and forces numerical methods to resolve a vanishingly thin fluid layer in the near-contact region, making the dynamics highly sensitive to the spatial and temporal discretizations. In addition to no-slip boundary and interface conditions, a reduced porous modeling of surface roughness, either on the disk boundary or on the bottom wall, is also considered; this circumvents the no-contact paradox and enables genuine contact. An energy balance law is derived theoretically for all three cases. Eight numerical methodologies, developed by five research groups and spanning different model formulations, numerical methods, and codes (including both fitted and unfitted discretizations), are applied to the benchmark at several levels of spatial and temporal refinement. Quantities of interest of varying complexity are collected and compared, showing close agreement during the falling phase and increased sensitivity in the near-contact and rebound regimes. The setting and the results provide a suitable reference for the systematic assessment of fluid-structure-contact interaction solvers. The time histories of all quantities of interest for every approach and refinement level are provided as supplementary material.

A central challenge across control and learning is the design of mechanisms regulating the interactions between humans and autonomous agents. Inspired by the free energy principle from computational neuroscience, we introduce a control-theoretical framework to integrate human preferences online into an agent policy. We turn the framework into an open control architecture and validate our approach using a human-in-the-loop experimental testbed involving a rover navigating via onboard sensing. The human, remotely located and equipped with virtual reality headsets, shares the same sensory information as the rover. Human preferences are provided to the rover via gestures which introduce both cooperative and competitive interactions between the agent goal and the preferences. The experiments show that interactions are regulated, validating the proposed approach.

Longitudinal electronic health records (EHRs) capture years of patient history across notes, codes, labs, and procedures, and contain evidence needed to reason about likely clinical outcomes. However, comprehensive clinician review of these records is impractical, and LLM-based processing is costly and often unreliable, missing some relevant observations while hallucinating others. We therefore propose EviGen, a three-layer framework for verifiable clinical rationale generation that addresses these challenges. The first layer is a patient-conditioned retriever that uses learnable queries to find evidence predictive of, not just textually relevant to, a clinical outcome and ranks it by prediction attribution scores. The second layer is an LLM generator that consumes this ranked evidence as a scaffold to produce a clinical rationale grounded in the retrieved spans. The third layer is a process-supervised verifier that checks the generated rationale at the reasoning-step level, flagging unreliable claims. Across three medical prediction datasets, EviGen improves prediction performance and rationale faithfulness over full-context LLM and RAG baselines, and is preferred by clinical reviewers in a usability evaluation.

For a diffusive system on a ring, with a battery at the origin, we use the macroscopic fluctuation theory (MFT) to obtain the large deviation function of the current. In the case of non-interacting particles, the predictions of the MFT agree with the result of a direct exact microscopic calculation. To our surprise, the large deviation function of non-interacting particles with a battery has the same form as for the Symmetric Simple Exclusion Process (SSEP) with open boundary conditions. For the SSEP on a ring with a battery, the predictions of the MFT seem to agree with the results of long Monte Carlo simulations, although much longer simulations would be needed to better test the validity of these predictions.

We prove the exponential convergence in relative entropy of the Sinkhorn algorithm for the entropy martingale optimal transport. We assume that the marginals have compact supports and are in strict convex order, the terminal marginal support is convex, and the initial marginal support lies in the relative interior of the terminal marginal support; the reference cost is assumed to be Lipschitz in each variable. Under these assumptions we establish uniform bounds on the dual variables modulo affine gauges. This result allows us to obtain the existence and uniqueness of the optimizer, and its exponential representation in terms of dual variables. We then establish a relative-entropy stability estimate for martingale couplings with different terminal marginals. Proving that the constant in the stability estimate stays uniform throughout the Sinkhorn iteration allows us to establish the exponential convergence of the Sinkhorn algorithm.

An agentic request spends substantial wall-clock time waiting for tools, and its KV cache holds GPU memory the whole time. Serving systems decide whether that cache stays, leaves, or comes back by guessing how long the tool will run, from the tool's name, its history, a duration declared before the call, or the engine's own occupancy. We show that no estimate fixed before a call starts can know its duration, and such estimates may not even rank the calls. Meanwhile, the running tool already holds the answer, but the agent stack together with the tool silences it. We propose that tool calls report their progress explicitly while they run, and we measure what that takes. A census of four public agent corpora finds a readable signal in most tool time once it is revealed, in two strengths: a fraction of the work remaining, or an accurate signal that the end is near. A harness recovers it without changing what the agent sees, at no measurable cost to the agent's benchmark score. At the points where a KV cache decision is made, the reported progress is between several times and an order of magnitude more accurate than the best published predictors, and it stays accurate when the environment changes. Plugged into a production engine through a few small hints, it cuts the p90 time to first token (TTFT) after a tool call by 20.7% (HBM only) and 20.8% (HBM + DRAM) against LRU, close to an oracle. A serving system should not guess what its tools can tell it.

We study continuous-time fictitious play in 2-bidder, symmetric first-price auctions with independently distributed discrete values and a discrete bid set. We first exhibit a minimal instance — two bidders, two values, three positive bids — on which fictitious play with the standard uniform-split tie-breaking rule does not converge to the symmetric Bayes–Nash equilibrium: the equilibrium is unstable and the dynamics converge to a stable limit cycle far from the Nash equilibrium. We then show that a small modification of the tie-breaking rule — awarding a payoff of zero to every bidder in case of a tie — restores convergence: fictitious play converges to a Nash equilibrium of the modified game. This limit is an $\epsilon$-equilibrium of the original auction in a broad range of settings.

The rapid proliferation of grid-edge distributed energy resources has significantly increased the operational complexity of modern power systems. Consequently, conventional computational techniques face growing scalability and computational-efficiency challenges in addressing large-scale optimization and control, uncertainty management, nonlinear dynamics, and combinatorial decision-making in smart grid operations. Quantum computing has therefore emerged as a promising computational paradigm that can complement classical methods in addressing selected computationally intensive problems. In this context, this paper presents a comprehensive structured review of quantum computing applications in smart grid operations. Following a transparent keyword-based literature search, the paper classifies and assesses existing studies across monitoring and estimation, system planning, operation and control, security, reliability and resilience, stability assessment, data-driven intelligence, and digital twin technologies. The paper also describes fundamental quantum-computing concepts and key algorithms, highlighting their relevance for power system applications. Furthermore, it reviews the current state of quantum hardware, software frameworks, simulators, cloud services, and emerging hardware-agnostic ecosystems that support cross-platform application development and deployment. The reviewed studies are examined by implementation environment, benchmarking practices, application scale, and evidence of computational advantage. Finally, the principal challenges associated with practical implementation are discussed, and future research directions are outlined. This paper provides a consolidated and evidence-calibrated perspective on the current state and future potential of quantum computing for next-generation smart grid operations.

Zero-Knowledge Proofs (ZKPs) are critical for privacy-preserving and verifiable computation, but their cryptographic primitives impose high computational overheads. One such primitive is point addition (PADD) on elliptic curves. Several prior works have implemented PADDs in hardware, but only for a few specific elliptic curves and design points, leaving a large design space unexplored, and lacking systematic guidance on hardware design trade-offs. To address this gap, we present Locus, a framework dedicated to optimizing and exploring point addition hardware. Given the parameters of any elliptic curve in a supported equation form, Locus automatically generates ASIC and FPGA implementations of PADD, enabling systematic exploration of the PADD design space. Using Locus, we conduct the first comprehensive hardware-focused study of PADD designs, exploring trade-offs over 1,000 design points. On a 12nm technology node, our framework produces PADD designs that yield a $2.71\times$ geomean speedup and $3.11\times$ geomean area reduction compared to prior ASICs, $34.67\times$ geomean speedup over CPU, and $3.15\times$ geomean speedup on end-to-end proof generation when integrated into a prior ZKP accelerator at iso-area. Locus is available at https://github.com/cryptolets/cryptolets/tree/locus.

We define high-order discrete differential and integral calculus following the discrete embedding formalism strategy. Using this framework, we define high-order discrete Lagrangian functionals and the corresponding calculus of variations. This provides a new derivation of Galerkin variational integrators.

Multimodal coding agents are expected to turn visual inputs into usable artifacts, and they act through a harness, the layer of tools, context management, and execution environment around the model. Existing evaluations often isolate short tool calls, API traces, or screenshot resemblance, and a low score under these proxies cannot say whether the model saw poorly, planned poorly, or was failed by its harness. We study scientific overview figure reconstruction, an agent task in which a source image must become an editable PowerPoint slide that preserves text, topology, layout, and native document structure. We introduce ReFigBench, a benchmark and evaluation framework built on 1,000 real overview figures retrieved from arXiv papers with full provenance. Coding agents from four model families reconstruct every figure under two workflows, direct code generation and a specialized PPTX workflow, and the strongest model runs inside two commercial harnesses, yielding ten configurations. Evaluation combines deterministic artifact checks, repeated automated scoring by judges from two model families, and blinded human comparisons. Perception remains a bottleneck that iterative rendering only partly repays. Whether workflow effort converts into quality depends on the model together with its harness, since the same model gains from the specialized workflow inside one harness and loses inside the other, and the harness shifts scores even under an identical direct prompt. The specialized workflow erases native connectors in every configuration, human judges still prefer its renderings in most matchups, and even the strongest agent falls short of the rubric ceiling. These results expose the tension between fidelity and editability as the central challenge for practical multimodal document agents.

Polar wide bandgap semiconductors offer the unique capability to manipulate internal electric fields and induce two-dimensional electron gases (2DEG). The emerging orthorhombic {\epsilon}-Ga2O3 is a promising candidate owing to its large spontaneous polarization (Psp). However, exploiting this material is hindered by fundamental ambiguities surrounding its absolute Psp vectors and the inability to govern its epitaxial direction. Here we show the resolution of the absolute Psp vectors in {\epsilon}-Ga2O3 and control of its macroscopic polarity via substrate engineering. By correlating interferometric piezoresponse with atomic configurations, we establish an identification criterion where opposing polarities are assigned through the geometric elevation within an asymmetric four-atom sequence. Guided by this signature, we demonstrate that epitaxy on Al-polar AlN and sapphire yields uniformly Ga-polar (upward Psp) and O-polar (downward Psp) architectures, respectively, whereas deteriorated crystallinity disrupts this registry and triggers mixed-polarity. This atomic-to-macroscopic correlation eliminates long-standing ambiguities regarding absolute polar orientations in non-centrosymmetric oxides. Analogous to mature III-Nitride architectures, this blueprint provides the foundational platform for designing macroscopic polarization discontinuities at heterointerfaces, unlocking {\epsilon}-Ga2O3 for advanced polarization electronics.

Scaling laws hold that language models grow more capable with more parameters and more training data. Mixture-of-Experts (MoE) architectures are a remarkable demonstration of these laws, activating only a fraction of an enormous parameter bank for each token. But this success is built on static pretraining data — the facts and corrections supplied by users during live interactions are a significant untapped source of potential improvement for a deployed model, but cannot be exploited by conventional architectures whose weights are frozen after training. Instead, this newfound knowledge must be placed in the context (by instruction or retrieval) and re-read on every request, only to be discarded afterwards. We seek instead to learn from live interactions by dynamically updating model weights. Inspired by MoEs, we propose the Infinite-Parameter LLM. A compact hypernetwork turns the online data into low-rank modulations of a shared base network, so feed-forward weights are generated from live data, not read from static memory. Whereas existing weight generators are held fixed after reading the context once, we form a Bayesian belief over the generator's latent state and update it online, such that the effective weights are re-derived as our belief evolves during the session. Although the model's memory footprint is constant, the feasible space of generated weights is thus effectively infinite. Representing live data in the weights rather than the prompt amortises compute, frees the context window, persists updates across turns, and can generalise better than in-context use. Our evaluation protocol applies this methodology to in-context learning and retrieval.

In this introductory review, we present and compare four algorithms for the numerical integration of the Lindblad equation for one-dimensional quantum lattice systems. All four methods are based on Matrix Product State representations and can be viewed as extensions of the Time-Evolving Block Decimation (TEBD) algorithm to open quantum systems. Two approaches directly integrate the vectorized Lindblad equation, one of them explicitly enforcing the positivity of the density matrix. The other two rely on stochastic unravelings of the Lindblad equation, namely the quantum trajectory and quantum state diffusion approaches. We discuss the principles, numerical implementation, accuracy, and computational efficiency of the different methods, and benchmark them against an exactly solvable free fermion model.

In this paper, we investigate the existence of maximal algebraic two-sided ideals in nonunital $C^*$-algebras. We formulate singular-distribution estimates in terms of lower semicontinuous $2$-quasitraces and introduce a novel criterion, which we call an admissible compact quasitracial triple set. These tools allow us to control membership in algebraic ideals and to prove the nonexistence of maximal ideals in nonunital $C^*$-algebras under a closed finite-scale face condition. This nonexistence result applies to a broad class of simple $C^*$-algebras including simple separable stable AF algebras, and nonunital, simple, separable, stably finite, $\mathcal Z$-stable $C^*$-algebras $A$ that admit an approximate identity consisting of increasing projections $(p_n)$ and for which the simplex $\operatorname{QT}_2^1(A,p_1)$ of normalized traces at $p_1$ has finitely many extreme points. Moreover, we construct a simple AF algebra whose finite-scale face is dense but not closed and which nevertheless has a maximal dense algebraic ideal. This example yields a negative resolution to a question raised by Ozawa, asking whether every maximal algebraic two-sided ideal in a $C^*$-algebra must be closed.

The rise of large satellite constellations and Distributed Space Systems (DSS) demands generalized frameworks that enable fault-tolerant, autonomous distributed space applications. Conventional ground-centric command and control does not scale to systems of tens or hundreds of satellites, motivating the adoption of distributed computing. This paper introduces a conceptual distributed computing framework for satellite swarms, covering distributed state, command and control, and scientific mission. As a first validation step, a strongly eventually consistent distributed state service is designed and implemented using Conflict-free Replicated Data Types (CRDT), specifically a Last-Write-Wins Register-based key-value store. The service is evaluated in the context of Space Situational Awareness catalog dissemination across a simulated 66-satellite constellation emulated with GoNetEm. Results show that the CRDT-based approach reduces ground-to-satellite communication from 66 messages to a single uplink per update, with tree traversal matching the total message count of direct uplink. Under concurrent updates, sub-linear inter-satellite message growth is observed as nodes discard outdated versions, further reducing network overhead. These results demonstrate the viability of a CRDT-based distributed state as a scalable and fault-tolerant foundation for satellite swarm applications.

We consider $m$-dimensional currents in $\mathbb{R}^{m+1}$ that almost minimize an anisotropic energy whose integrand is continuous in the space variable and $C^{2,{\rm Dini}}$ in the normal variable. We prove that if the boundary of such a current is differentiable, then the current admits a flat blowup at every boundary point.

Near-field propagation between finite apertures can support multiple spatial channels, while far-field transmission is effectively single mode and follows the Friis transmission formula. This letter establishes a direct connection between these two regimes through the mutual shadow area between the transmitting and receiving apertures. The mutual shadow determines the asymptotic number of spatial degrees of freedom and, in the paraxial regime, leads to a simple beamforming distance that provides a characteristic scale for the transition from multimode to effectively single-mode propagation. The channel singular-value sum rule further shows that, below this distance, increasing separation primarily reduces the number of supported spatial channels while their average normalized strength remains approximately constant. Beyond the transition, the remaining channel strength decreases according to the conventional free-space quadratic power law, recovering the Friis transmission formula. Numerical results for circular apertures demonstrate the transition, the scaling with aperture size, and the dependence on the transmitter and receiver apertures. The mutual-shadow formulation also extends the description beyond the paraxial regime.

A surveillance system that detects an anomaly often has to repair the footage as well, yet the two tasks are studied in isolation: training-free anomaly detectors stop at a score or a label, while training-free video editing answers to a user prompt rather than to a detector. This paper proposes AVR (Anomaly-aware Video Restoration), which closes that gap with frozen pretrained models alone and generates content only where the clip offers no evidence to copy. Motion evidence first gates open-vocabulary proposals into spatio-temporal masks. A background prior computed from the clip then fills every pixel the anomaly ever uncovers, leaving diffusion to synthesize only what no frame showed, and a frozen verifier decides per clip whether to trust a classical, a prior-anchored, or a background-conditioned restorer. Extensive experiments on three surveillance datasets, under both full-reference anomaly injection and real anomalies, show that AVR leads full-frame fidelity under oracle masks, matches three trained video inpainters inside the edited region, and outperforms a detect-then-generate pipeline on the masks it produces itself, while suppressing both the residual anomaly and the flicker of free diffusion.

We establish a degree-independent bound on spectral independence for log-concave Holant problems on simple graphs. As a corollary, we obtain relaxation-time bounds for Glauber dynamics of $O_\lambda(m)$ for the monomer-dimer model at activity $\lambda$ and $O_{b,\lambda}(m)$ for $b$-matchings at fugacity $\lambda>0$, where $m$ is the number of edges. For uniform $b$-matchings, the relaxation-time bound improves to $O(bm)$. The main proof ideas were found using GPT-5.6 Sol.

We prove that any finite-time collapsing Kähler-Ricci flow on compact Kähler surfaces develops a Type I singularity. Together with the previous results, this implies that any finite time singularity of the Kähler-Ricci flow on compact Kähler surfaces is of Type I.

Random walks are a standard tool for search problems in which a state can be updated locally and tested for being marked. When updating the state and checking whether it is marked have different costs, two classical strategies optimize different parts of the cost: checking after every step is optimal in the number of updates, while repeatedly checking only after mixing is optimal in the number of checks. For a single marked state $m$ and a walk started from its stationary distribution $\pi$, Dohotaru and Høyer stated that both guarantees can be matched simultaneously, for a walk that checks after blocks of a fixed length; their argument is sketched through quantum walks, and they observe that they know of no classical proof. We give a short and self-contained classical proof of such a tradeoff, for arbitrary irreducible Markov chains. The algorithm replaces the original transition matrix $P$ by the averaged walk $ \overline P_\tau = \frac{1}{\tau}\sum_{k=1}^{\tau} P^k, $ where $\tau$ is of order $\pi(m)HT(m)$. Using a coupling with the original walk and Kac's lemma, we prove directly that the averaged walk hits the marked state in $O(1/\pi(m))$ checks in expectation. The resulting search cost is \[ S + O(HT(m))U + O(1/\pi(m))C \] in expectation, where $S$, $U$, and $C$ denote setup, update, and checking costs.

We classify isolated singularities of classical solutions to the capillary equation with negative gravity, \[ \operatorname{div}\frac{Du}{\sqrt{1+|Du|^2}}=-u \qquad\text{in }B_R\setminus\{0\}\subset\mathbb R^n, \qquad n\ge2, \] without a priori assumptions on symmetry, sign, one-sided boundedness, or blow-up rate. Every such solution is either bounded near the puncture or tends uniformly to $+\infty$ or $-\infty$. In the bounded case, the solution extends across the puncture as a $W^{1,1}_{\mathrm{loc}}$ distributional solution; this extension has a unique continuous representative when $2\le n\le7$. In the unbounded case, for some $\varepsilon\in\{-1,1\}$, \[ u(x)=\varepsilon\left(\frac{n-1}{|x|} -\frac{n+3}{2(n-1)^2}|x|^3\right)+O(|x|^5), \] uniformly in the angular variable. In every fixed smaller ball, all sufficiently high level sets of $\varepsilon u$ are connected, smooth, strictly convex hypersurfaces enclosing the puncture. The corresponding pressure-rescaled graphs converge smoothly with multiplicity one to the round cylinder $\partial B_{n-1}\times\mathbb R$. Nonradial examples form infinite-dimensional families that agree with the radial pole to every algebraic order, so the complete asymptotic expansion does not determine the singular solution germ. The proof of the classification combines critical tail estimates and logarithmic $BV$ compactness with level-set rigidity and the translation identities of the capillary equation. The critical two-dimensional case requires an additional finite-height analysis to exclude a translation defect.

Many examples of integrable sigma models admit families of integrable deformations that involve coupling the undeformed “seed” theory to auxiliary fields with algebraic equations of motion. In this work, we apply this paradigm to the case where the seed theory is the lambda model, which interpolates between the Wess-Zumino-Witten model and the non-Abelian T-dual of the principal chiral model. We present an auxiliary field deformation of the lambda model and exhibit a Lax connection whose flatness is equivalent to the remaining equations of motion after imposing the algebraic field equations. We also carry out a Hamiltonian analysis of the deformed theory, verifying that it obeys the assumptions of theorems in arXiv:2605.18213 which guarantee both (i) that the model enjoys the Maillet structure that ensures involution of its conserved charges, and (ii) that the theory possesses a classical Yangian. Thus, as in other cases, the auxiliary field deformation of the lambda model changes its classical dynamics while leaving the integrable structure essentially unchanged.

This work reports on the computation of the ghost-gluon vertex for the pure Yang-Mills SU(3) gauge group, using lattice simulations and the Landau gauge. The simulations access only one of the form factors that describes the vertex. The form factor is estimated using large statistical ensembles of gauge configurations, with two different lattice spacings and two different volumes to check for finite size effects. Moreover, the calculation shows the importance of using lattice perturbation theory, instead of its continuum version, to correct for the breaking of rotational symmetry. The measured bare lattice form factors are compatible, within errors, for all the ensembles. The form factor has a maximum at momentum $\sim 1$ GeV, is suppressed in the infrared and is compatible with a constant behaviour at high momenta, in good agreement with the corresponding lattice estimations for the SU(2) gauge group.

We study state-adversarial Markov decision processes (SA-MDPs) as games of observation-space attacks: at each step, an agent selects an action from a received observation while an adversary$\unicode{x2014}$who knows the true state the agent is in$\unicode{x2014}$chooses a perturbed observation within a state-dependent proximity set. While existing work focuses on Markovian policies, we develop a solution concept and computational approach for SA-MDPs under history dependence. History dependence can materially change equilibrium outcomes and can force both the agent and the adversary to adapt their strategies. First, we prove the non-existence of universal (agnostic of the initial state distribution) history-dependent equilibrium policies. Our main result presents the first algorithmic route to computing $\epsilon$-approximations of initial-state dependent equilibria. We do so by reducing SA-MDPs to a strategically equivalent constrained zero-sum one-sided partially observable stochastic game. We test our algorithm on small analytically verifiable games and show that it scales to larger, more realistic benchmarks, including Atari Freeway rollouts with a 12-period ahead horizon.

We present a complete calculation of the next-to-leading order (NLO) electroweak corrections to the loop-induced gluon-fusion process $gg\to\gamma\gamma$ at the LHC, including the full third-generation quark and the Higgs boson contributions for the first time. To efficiently evaluate the large number of multi-scale two-loop Feynman integrals, we employ a numerical approach based on differential equations with an optimized basis. Our results show that, although the NLO electroweak corrections to the phase-space-integrated cross section remain at the sub-percent level, they can reach about $-10\%$ in the tails of the diphoton invariant-mass and photon transverse-momentum distributions. Moreover, the diphoton invariant-mass distribution exhibits rich and intriguing structures, including a dip-bump structure in the Higgs-threshold region and a mild enhancement near the top-quark pair threshold. These features make the electroweak corrections indispensable for future precision studies of diphoton production at the LHC.

Low signal-to-noise ratio (SNR) data is a core challenge of online Data-Driven Predictive Control (DPC) for linear, time-varying systems. This paper proposes a Bayesian, online DPC framework based on autoregressive models with exogenous inputs (ARX) that uses an externally-provided prior, which encodes inductive bias such as smooth system dynamics and stability, to safeguard performance when SNR is low. The posterior estimate of the ARX parameter is propagated forward in time using a Kalman filter with a state equation defined by an adaptation-rate hyperparameter, which is adjusted online to track the rate at which the underlying system dynamics evolve. The Kalman filter's posterior mean and covariance determine the DPC's Final Control Error cost function, which is the posterior expectation of the quadratic cost function. Critically, the Kalman filter's process equation is chosen so that, regardless of the hyperparameter adaptation, the prior distribution is invariant over time. Thus, while old data is forgotten, the prior is not. DPC tracking experiments on a time-varying second-order system demonstrate the efficacy of the proposed method.

External magnetic fields, through their coupling to orbital and spin motion, complicate the correlated electronic states and impose coordinate-dependent phases on the wavefunction, thereby making accurate electronic structure calculations substantially more demanding. Recently, neural network-based quantum Monte Carlo (NNQMC) has emerged as a highly accurate approach to study nucleus-free systems in magnetic fields. For molecular systems, however, things get more complicated as the magnetic field would introduce a rapidly varying phase in the region far from the gauge origin. Here we introduce a gauge-including phase factor that acts directly on the full many-electron wavefunction and accounts for the prescribed magnetic phase, leaving a smoother correlated residual for the network to learn. This factor greatly improves molecular translation consistency and size consistency, providing a route for studying systems in magnetic fields with NNQMC. Upon this approach, we reproduce weak-field magnetizabilities and strong-field bond contraction in \ce{H2}. We further apply the method to selected transitions in the \ce{CN} red and \ce{C2} Swan systems at magnetic fields relevant to white dwarfs. The \ce{CN} transition exhibits a much larger field-induced shift than its \ce{C2} counterpart, suggesting its potential as a probe of white-dwarf magnetic fields.

Background: Molecular testing for NPM1 and FLT3-ITD mutations guides critical early treatment decisions in acute myeloid leukemia (AML), but results can take weeks, long after these decisions must be made. Flow cytometry, already performed within hours of admission as part of routine care, may carry enough signal to predict these mutations directly, without added cost or delay. Methods: We developed an interpretable multi-instance learning classifier based on a decision tree, in which each patient sample is modeled as a collection of individual cells and mutation status is inferred from cell-level predictions. The model was benchmarked against a random forest trained on clinical variables and a deep convolutional neural network adapted for multitube flow cytometry data. Performance was assessed by cross-validation on a discovery cohort of 197 patients and tested on an independent cohort of 161 patients, using the area under the receiver operating characteristic curve (AUROC) and positive predictive value. Results: In cross-validation on the discovery cohort, the MIL model achieved mean AUROCs of 0.96 (SD=0.05) for NPM1 and 0.86 (SD=0.10) for FLT3-ITD, outperforming the clinical baseline and matching deep learning approaches. The model then successfully generalized to the independent test cohort of 161 patients, reaching AUROCs of 0.90 (NPM1) and 0.82 (FLT3-ITD), with positive predictive values of 0.87 and 0.68, respectively. Cell-level interpretation recovered established immunophenotypic signatures (CD33${}^{+}$ /CD34___ for NPM1-mutated cases, CD33${}^{+}$ /low side-scatter for FLT3-ITD), directly linking model predictions to known biology. Conclusions: These results show that an interpretable model applied to data already collected in routine care can predict AML molecular status within hours, offering a practical route to earlier, biology-informed treatment decisions.