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arXiv2026

Engineering Quantum-Enhanced Transport by Supertransfer

Collective behaviour of the components of a quantum system can significantly alter the rates of dynamical processes within the system. A paradigmatic collective effect is superradiance, the enhancement in the rate that radiation is emitted by a group of emitters relative to that emitted by independent emitters. Less studied are collective effects in energy transport, notably supertransfer, the enhancement of the rate of energy transfer from donors to acceptors due to delocalised excitations. Despite its generality as a collective enhancement mechanism in transport, there has been no direct experimental detection of supertransfer because, in most physical platforms where delocalisation arises naturally, delocalisation cannot be turned on and off to evaluate its effect on energy transfer. Here, we show that supertransfer could be directly observed using a quantum device based on a superconducting circuit. The programmability and control offered by an engineered device would allow controllable delocalisation of quantum states, giving full tunability over supertransfer. Our guidelines for engineering supertransfer could inform the design of future quantum-enhanced devices.

quant-ph↗
arXiv2026

A Multiscale Eulerian Vlasov-Rosenbluth-Fokker-Planck Algorithm for Thermonuclear Burning Plasmas

Accurate treatment of energetic fusion byproducts in laboratory plasmas often requires a kinetic description, owing to their large birth kinetic energy and long mean free paths compared with the characteristic system scale lengths. For example, alpha particles produced by deuterium-tritium fusion reactions are born at high energies (\qty{3.5}{MeV}) and predominantly slow down through interactions with electrons traveling at comparable speeds. As an alpha particle slows, its distribution collapses near the background ion-thermal speed, forming a sharp structure in velocity space. Such sharp features pose numerical challenges in grid-based Eulerian methods: capturing the full alpha-particle energies demands a large velocity domain, while resolving the near-thermal region requires a sufficiently fine mesh. Inspired by the work of Peigney \textit{et al.}~[\textit{J.\ Comput.\ Phys.} \textbf{278} (2014)], we present a two-grid approach that splits the alpha-particle distribution into energetic (suprathermal) and ash (thermal) components. A Gaussian-based sink term transfers particles from the energetic population to the ash population as they slow to the thermal regime, and a conservative projection scheme ensures that mass, momentum, and energy of the slowing energetic alpha population are conserved when it is remapped onto the ash grid. Unlike the formulation of Peigney \textit{et al.}, our method does not require a strict asymptotic separation of velocity scales, which can, in principle, be arbitrary. We demonstrate the robustness of this approach on challenging multiscale problems, including a surrogate for an igniting inertial confinement fusion capsule.

physics.plasm-ph↗
arXiv2026

Multi-FPGA Synchronization and Data Communication for Quantum Control and Measurement

Quantum computing has grown from novel physics experiments with a few qubits controlled by a single controller to systems with qubit counts that require multiple controllers working in concert. While a few expensive multi-board commercial solutions exist, most open-source solutions are limited to single-board radio frequency system-on-chip (RFSoC). The essential requirements for a multi-board solution are clock synchronization among multiple boards and the ability to transfer data with low latency for performing real-time feedback. In this work, we design a clock synchronization framework to distribute deterministic clock and synchronize the clock counters across multiple RFSoC boards to generate time-aligned radio frequency (RF) pulses used to control qubits. We also develop a data communication system over a fiber link to transfer quantum measurement data among multiple field-programmable gate arrays (FPGAs). This clock synchronization and data communication module has been integrated into the open-source quantum control system, QubiC, to enable the execution of quantum algorithms across multiple boards. We validate the design through bench tests and qubit experiments on a superconducting quantum processor. Qubit coherence experiments driven by two clock-synchronized boards show no measurable degradation compared to single-board operation. The data communication link, built directly on raw gigabit transceivers with a minimal custom protocol, achieves a one-way board-to-board latency of 71.2 $\pm$ 2.6 ns and enables a real-time cross-board conditional bit-flip experiment, demonstrating mid-circuit measurement and feed-forward across multiple boards well within the qubit coherence time.

quant-ph↗
arXiv2026

Conditioned stochastic stability of equilibrium states on uniformly hyperbolic sets

We establish the conditioned stochastic stability of equilibrium states for Hölder potentials on uniformly hyperbolic sets. While standard stochastic stability characterises measures on attractors, we analyse the statistics of transient dynamics on non-attracting sets by conditioning small random perturbations of the dynamics to not escape from our regions of interest. We prove that as the noise intensity vanishes, the quasi-ergodic measure of the $e^ϕ$-weighted process generated by $\e$-small random perturbations of the deterministic dynamics converges to the unique equilibrium state associated with the potential $ϕ- \log \left|\det \left. D T\right|_{E^u}\right|$. The results are obtained via perturbative spectral analysis of transfer operators acting on anisotropic Banach spaces and topological hyperbolic dynamics arguments. Furthermore, we extend this framework globally to Axiom A diffeomorphisms with multiple basic sets using dynamical filtrations. This work provides a rigorous characterisation of natural measures on uniformly hyperbolic repellers, which are fundamental in the context of transient chaos. Our results have been formalised in Lean~4.

math.DS↗
arXiv2026

Diffusion-Based Hypothesis Testing and Change-Point Detection

Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we extend the score-based hypothesis test and change-point detection stopping rule into their diffusion-based analogs. Additionally, we theoretically quantify the performance of these diffusion-based algorithms and study scenarios where optimal performance is achievable. We propose a method of numerically optimizing the weight matrix and present numerical simulations to illustrate the advantages of diffusion-based algorithms.

stat.ML↗
arXiv2026

Uniform ergodicity and spectral gap of importance-tempered MCMC with heavy-tailed targets

We study the importance-tempered random-walk Metropolis (RWM) algorithm on $\mathbb{R}^d$, which targets the tempered density $π_β(x) \propto π(x)^β$ with $β\in (0,1)$ and corrects for the resulting bias by importance weighting. The dynamics of this sampler can be described by a continuous-time Markov chain whose embedded chain is the tempered RWM. We prove that when the tails of $π$ decay at rate $\|x\|^{-γ}$, this continuous-time chain is uniformly ergodic if and only if $d/γ< β< (γ- 2)/γ$. Further, the global spectral gap of this chain can be controlled via the spectral gap of the chain restricted to a ball with radius growing polynomially in $d$. Our theory and simulation studies show that, with a suitable choice of $β$, importance tempering can substantially reduce sensitivity to initialization and significantly improve efficiency over the standard RWM.

stat.CO↗
arXiv2026

Diophantine Equations over $\mathbb Z$: Universal Bounds and Parallel Formalization

This paper explores multiple closely related themes: bounding the complexity of Diophantine equations over the integers and developing mathematical proofs in parallel with formal theorem provers. Hilbert's Tenth Problem (H10) asks about the decidability of Diophantine equations and has been answered negatively by Davis, Putnam, Robinson and Matiyasevich. It is natural to ask for which subclasses of Diophantine equations H10 remains undecidable. Such subclasses can be defined in terms of universal pairs: bounds on the number of variables $ν$ and degree $δ$ such that all Diophantine equations can be rewritten in at most this complexity. Our work develops explicit universal pairs $(ν, δ)$ for integer unknowns, focused on reducing the number of unknowns to $ν= 11$. This achieves new bounds that cannot be obtained by naive translations from known results over $\mathbb{N}$. In parallel, we have conducted a formal verification of our results using the proof assistant Isabelle. While formal proof verification has traditionally been applied a posteriori to known results, this project integrates formalization into the discovery and development process. In a final section, we describe key insights gained from this approach and its implications for mathematical practice. Our work contributes both to the study of Diophantine equations and to the broader question of how mathematics is conducted in the 21st century.

math.NT↗
arXiv2026

Convergence of the Birkhoff spectrum for nonintegrable observables

We consider interval maps with countably many full branches and observables with polynomial tails. We show that the Birkhoff spectrum is real analytic and that its convergence to the Hausdorff dimension of the repeller is governed by the polynomial tail exponent. This result extends previous work by Arima on more regular observables and demonstrates how the tail behaviour influences the structure of the Birkhoff spectrum. Our proof relies on techniques from thermodynamic formalism and tail estimates for the observable and our applications are to natural observations on Gauss maps, Lüroth transformations as well as to a the first return time for a class of induced Manneville-Pomeau maps.

math.DS↗
arXiv2026

Few-shot Classification as Multi-instance Verification: Effective Backbone-agnostic Transfer across Domains

We investigate cross-domain few-shot learning under the constraint that fine-tuning of backbones (i.e., feature extractors) is impossible or infeasible---a scenario that is increasingly common in practical use cases---and show how representing few-shot classification as a series of multiple instance verification (MIV) tasks enables competitive classification performance using the static embeddings produced by frozen, "black-box" backbones. More specifically, based on this novel representation, we introduce a new approach to few-shot domain adaptation named the "MIV-head": a classification head that is backbone-agnostic and computationally efficient. We show that the core components of the MIV-head, when trained on few-shot data from a target domain, collectively yield strong performance on test data from that domain. Importantly, they do so without fine-tuning the backbone, requiring only the "meta-testing" phase. In experiments under various settings on an extension of the Meta-Dataset benchmark for cross-domain few-shot image classification, using representative off-the-shelf convolutional neural network and vision transformer backbones pretrained on ImageNet1K, we demonstrate that the MIV-head achieves highly competitive accuracy when compared to state-of-the-art "adapter" (or "partial fine-tuning") methods applied to the same backbones, while incurring substantially lower adaptation cost. Moreover, compared to our approach, well-known "classification head" approaches achieve a substantially lower level of accuracy. We share our code at: https://github.com/xxweka/MIV-head.

cs.CV↗
arXiv2026

A simple formalization of alpha-equivalence

While teaching untyped $λ$-calculus to undergraduate students, we were wondering why $α$-equivalence is not directly inductively defined. In this paper, we demonstrate that this is indeed feasible. Specifically, we provide a grounded, inductive definition for $α$-equivalence and show that it conforms to the specification provided in the literature. The work presented in this paper is fully formalized in the Rocq Prover.

cs.LO↗
arXiv2026

A Decision Procedure for Probabilistic Kleene Algebra with Angelic Nondeterminism

In Ong et al.~(2025), a new finite automaton model with probabilistic and nondeterministic transitions was introduced, along with a corresponding regular expression language. The key difference from previous approaches is that nondeterminism is formalized in terms of multisets instead of powersets. Automata and expressions are interpreted over the space of probability distributions over multisets of strings with finite multiplicities. The main result of that paper was a full Kleene theorem showing that the two formalisms are equally expressive. In this paper we give a decision procedure for the semantic equivalence of two automata or expressions. The algorithm is based on polyomial algebra and makes use of Gröbner basis techniques for ideal membership testing.

cs.FL↗
arXiv2026

Meta-learning of Gibbs states for many-body Hamiltonians with applications to Quantum Boltzmann Machines

The preparation of quantum Gibbs states is a fundamental challenge in quantum computing, essential for applications ranging from modeling open quantum systems to quantum machine learning. Building on the Meta-Variational Quantum Eigensolver framework proposed by Cervera-Lierta et al. and a problem-driven ansatz design, we introduce two meta-learning algorithms: Meta-Variational Quantum Thermalizer (Meta-VQT) and Neural Network Meta-VQT (NN-Meta VQT) for efficient thermal state preparation of parametrized Hamiltonians on Noisy Intermediate-Scale Quantum (NISQ) devices. Meta-VQT utilizes a fully quantum ansatz, while NN Meta-VQT integrates a quantum--classical hybrid architecture. Both use collective optimization over a finite set of training parameter values to prepare approximate Gibbs states at held-out parameter values within the sampled parameter domain. We validate our methods on Transverse Field Ising Models (TFIM) with up to eight qubits and on a two-qubit Heisenberg model with all field terms. Within these finite-size benchmarks, the trained models accurately prepare thermal states at test points inside the training interval. For the six and eight qubit cases of TFIM, meta-learned parameters when combined with appropriately designed ansatz serve as warm-start initializations, significantly outperforming random initializations in the optimization tasks. Furthermore, a 3 qubit Kitaev ring example showcases our algorithm's effectiveness across finite-temperature crossover regimes. Finally, we apply our algorithms to train a Quantum Boltzmann Machine (QBM) on a 2-qubit Heisenberg model with all field terms, achieving enhanced training efficiency, improved Gibbs state accuracy, and a 30-fold runtime speedup over existing techniques such as variational quantum imaginary time (VarQITE)-based QBM highlighting the practicality of meta-algorithm-based QBMs.

quant-ph↗
arXiv2026

Automatic Fine-grained Segmentation-assisted Report Generation

Reliable end-to-end clinical report generation has been a longstanding goal of medical ML research. The end goal for this process is to alleviate radiologists' workloads and provide second opinions to clinicians or patients. Thus, a necessary prerequisite for report generation models is a strong general performance and some type of innate grounding capability, to convince clinicians or patients of the veracity of the generated reports. In this paper, we present ASaRG (\textbf{A}utomatic \textbf{S}egmentation-\textbf{a}ssisted \textbf{R}eport \textbf{G}eneration), an extension of the popular LLaVA architecture that aims to tackle both of these problems. ASaRG proposes to fuse intermediate features and fine-grained segmentation maps created by specialist radiological models into LLaVA's multi-modal projection layer via simple concatenation. With a small number of added parameters, our approach achieves a +0.89\% performance gain ($p=0.012$) in CE F1 score compared to the LLaVA baseline when using only intermediate features, and +2.77\% performance gain ($p<0.001$) when adding a combination of intermediate features and fine-grained segmentation maps. Compared with COMG and ORID, two other report generation methods that utilize segmentations, the performance gain amounts to 6.98\% and 6.28\% in F1 score, respectively. ASaRG is not mutually exclusive with other changes made to the LLaVA architecture, potentially allowing our method to be combined with other advances in the field. Finally, the use of an arbitrary number of segmentations as part of the input demonstrably allows tracing elements of the report to the corresponding segmentation maps and verifying the groundedness of assessments. Our code will be made publicly available at a later date.

cs.CV↗
arXiv2026

Extremal Lyapunov exponents in random and simultaneous dynamics

In this manuscript, we consider finitely many maps, all of which are defined on a compact probability space, with at least one map in the collection having degree strictly bigger than 1. Working with two different, however related, dynamics generated by this setting, we obtain an expression for the extremal Lyapunov exponents, that characterise the instability of typical orbits, as the limit of the averages of the logarithm of the operator norm of linear cocycles of generic orbits. We obtain this as a consequence to the Kingman's ergodic theorem for a subadditive sequence of measurable functions, which naturally generalises the Birkhoff's ergodic theorem, in each of the cases.

math.DS↗
arXiv2026

Comparing the face rings of a boolean complex and its barycentric subdivision

We consider the relationship between the Stanley--Reisner ring (a.k.a. face ring) of a simplicial or boolean complex $Δ$ and that of its barycentric subdivision. These rings share a distinguished parameter subring. S. Murai asked if they are isomorphic, equivariantly with respect to the automorphism group $\operatorname{Aut}(Δ)$, as modules over this parameter subring. We show that, in general, the answer is no, but for Cohen--Macaulay complexes in characteristic coprime to $|\operatorname{Aut}(Δ)|$, it is yes, and we give an explicit construction of an isomorphism. To give this construction, we adapt a pair of tools introduced by A. Garsia in 1980. The first one transfers bases from a Stanley--Reisner ring to closely related rings of which it is a Gröbner degeneration, and the second identifies bases to transfer.

math.AC↗
arXiv2026

On buoyancy in disperse two-phase flow and its impact on the well-posedness of two-fluid models

The Maxey--Riley--Gatignol equation for the flow around a sphere at low particle Reynolds number tells us that the fluid-particle interaction force decomposes into a contribution from the local flow disturbance caused by the particle's boundary---consisting of the drag, virtual-mass, and history forces, and their Faxén corrections---and another contribution from the stress of the background flow, termed generalized-buoyancy force. There is also a consensus that, for general disperse two-phase flow, the interfacial force density, coupling the average fluid phase and dispersed-phase momentum balances, decomposes in a like manner. However, there has been a long-standing controversy about the physical closure separating the generalized-buoyancy from the interfacial force density, especially whether or not pseudo-stresses, such as the Reynolds stress, should be attributed to the background flow. Furthermore, most existing propositions for this closure involve small-particle approximations. Here, we show that all existing buoyancy closures are inconsistent with particle-resolving numerical simulations and/or at least one of two simple thought experiments designed to determine the roles of pseudo-stresses and small-particle approximations. We then derive the unique consistent closure. It requires no approximation and implies that all stresses and pseudo-stresses in the average fluid phase momentum balance, except the Reynolds stress, fully contribute to the background flow responsible for buoyancy. Remarkably, it exhibits a low-pass filter property, attenuating buoyancy at short wavelengths, that prevents it from causing Hadamard instabilities, constituting a first-principles-based solution to the long-standing ill-posedness problem of two-fluid models. When employing the derived closure, even simplistic two-fluid models are linearly well-posed.

physics.flu-dyn↗
arXiv2026

ArtSeek: Deep artwork understanding via multimodal in-context reasoning and late interaction retrieval

Analyzing digitized artworks requires both visual interpretation and deep artistic, contextual, and historical knowledge. We introduce ArtSeek, a multimodal framework for art analysis that combines multimodal large language models with retrieval-augmented generation. Unlike prior work, our pipeline relies only on image input, so it applies to artworks without links to Wikidata or Wikipedia, common in most digitized collections. ArtSeek integrates three components: a late-interaction multimodal retrieval module, a contrastive multitask network predicting artist, genre, style, media, and tags, and an agentic reasoning strategy enabled through in-context examples. Central to this approach is WikiFragments, a dataset of image-text fragments extracted from the entire English Wikipedia to support knowledge-grounded multimodal reasoning. Our multimodal query encoding raises retrieval NDCG@5 from 33.9 to 44.9 over encoding the full image-text query, and fixed-budget token pooling keeps late-interaction search practical over millions of fragments at under 7% of the cost of full multi-vector retrieval. ArtSeek sets a new state of the art in artwork attribute classification, with +8.4% F1 in style classification over GraphCLIP, and gains +7.1 BLEU@1 on ArtPedia captioning. On five knowledge-grounded question answering benchmarks graded by an LLM judge from a different model family, retrieval helps where the answer is documented in our index or lies inside the classifier's label space (+0.19 mean correctness on two of them) and is neutral where it is not; what separates the two regimes is how much of a benchmark our knowledge base covers. The gain transfers to two non-Qwen backbones (+0.22 to +0.28). A blind human study and a qualitative analysis of successes and failures corroborate this picture and expose where retrieval still misleads. Data and code: https://cilab.di.uniba.it/artseek/

cs.CV↗
arXiv2026

Semi-infinite parabolic IC-sheaf II: the Ran space version

This paper is a sequel to arXiv:2310.0638. Let G be a split reductive group. We define the parabolic semi-infinite category on the Ran version of the affine Grassmanian Gr_{G,Ran}. We study the semi-infinite parabolic IC-sheaf in this category. We provide several descriptions of this object, one as certain colimit, another as an intermediate extension in certain category. We relate the global and local semi-infinite categories of sheaves. We also relate the intersection cohomology sheaf of the Drinfeld compactification of Bun_P with the semi-infinite parabolic IC-sheaf.

math.RT↗