Papers

Sparse Gaussian processes achieve $O(N)$ inference by replacing the kernel with an appropriate expansion in a fixed basis $\{\phi_j\}$ on the input space. Given a compute budget $M \ll N$, practitioners conventionally truncate the basis to its first $M$ entries. Nothing in the formalism, however, prevents one from selecting only those $M$ basis functions that matter for the data at hand. This would avoid spending budget on basis functions where there is no signal, but it requires a criterion for ranking the candidates. We propose three such criteria derived from an information-theoretic view of the basis-function selection problem. Each criterion matches a different state of knowledge at selection time: a no-data state, a no-prior state, and an in-between state. We then study the performance of truncation versus selection strategies on six UCI regression benchmarks across three basis families: Hilbert-space Gaussian processes (HSGP), variational Fourier features (VFF), and variational inducing spherical harmonics (VISH). We observe that the no-data criterion is a safe default, matching or improving on truncation for HSGP, VFF and VISH, with substantial gains for VISH and improvements over a recently developed selection heuristic for that basis family. The data-aware no-prior and in-between criteria provide substantial gains over truncation specifically for HSGP, which is the most broadly used of the three families in practice.

Diffusion-based synthetic data generation offers a promising route for sharing medical imaging data without releasing sensitive patient records. However, generative models face a fundamental tension between privacy and fairness: they may memorize rare training samples, leading to privacy risks, or fail to reproduce underrepresented features, resulting in unfair synthetic distributions. While prior work has largely focused on either memorization or fairness in isolation, their interaction remains insufficiently understood. In this work, we introduce a data-interventional framework to systematically analyze privacy and fairness in diffusion models. We discuss synthetic anatomical fingerprints (SAFs), rare and manually injected image features, as controlled probes to study whether models generalize sensitive attributes across identities, memorize training samples, or suppress rare signals entirely. Across multiple conditioning modalities, we observe a consistent behavior: models either forget these fingerprints or memorize the entire image in which they appear, but do not generalize them to novel images. To support large-scale auditing where explicit sample extraction is infeasible, we further introduce the indicator metric t', which estimates a model's susceptibility to memorization by exploiting the internal structure of the diffusion process. By comparing conditioning signals of varying surprisal, we reveal a clear relationship between conditioning rarity and memorization behavior. Highly surprising conditioning signals act as retrieval keys that amplify memorization, whereas low-surprisal conditioning signals systematically suppress rare features, even when these appear repeatedly in the training data. Our findings provide actionable insights and concrete mitigation strategies for safe and fair synthetic medical data sharing. Code is available at https://github.com/MischaD/Privacy.

This paper studies both stability and maximal regularity of the diffusion equation on an unbounded surface without any assumptions on the curvature. We show that the surface diffusion system admits a unique global-in-time strong solution satisfying $L^2$-asymptotic stability when the slope of the surface is gentle. We also derive maximal $L^2$-regularity of the solution when the exterior force satisfies both surface divergence form and tangential condition. Moreover, we investigate the Hölder continuity with respect to time of the solution. The key idea of showing our stability and maximal regularity results is to apply nice properties of both Laplace and weighted Laplace-Beltrami operators in order to derive the properties of the Laplace-Beltrami operator on the unbounded surface.

Greedy decoding from large language models is commonly treated as deterministic. We show it is not precision-invariant: the same model, prompt, and decoding algorithm produce different outputs in BF16 versus FP16 on identical hardware. Across our evaluations of six models (1.1B-7B parameters, four families; divergence additionally characterised at 12B) and three benchmarks, 49-100% of prompts diverge; a single token flip often cascades into trajectory-level divergence. We develop an empirical error-propagation analysis and find that 22 layers of accumulated body error do not distinguish flipping from non-flipping steps; the outcome depends primarily on the top-two logit margin at the LM head relative to the directional perturbation between the top-two candidates. The analysis makes five testable predictions about intervention outcomes, including that applying more FP32 compute (broader scope) makes agreement worse. The experiments match all five predictions. The best-performing low-overhead intervention we evaluate, selective FP32 LM head recomputation, triggered only when the margin falls below a threshold, delivers +22-36 pp exact agreement on A10G (+12-21 pp on L4 and A100) at less than 4% latency overhead in low-batch (batch size <=4) single-stream inference. We map the applicability boundary across six models and four batch sizes, and hypothesise that training-time precision stability is a determining factor. The method is a partial mitigation rather than a universal determinism guarantee: its benefit vanishes when body-originated error dominates, including at batch size >=8 and under end-to-end FP8 in our tests.

Photographic composition aims to provide visual guidance for improving the framing, viewpoint, and spatial arrangement of an image. Early methods primarily rely on image cropping to enhance composition, which is restricted to the viewpoint and spatial arrangement of the input image. Recent methods have explored image understanding and editing to improve composition, but they mainly focus on instruction following and aesthetic quality, overlooking the importance of 3D scene geometry consistency for photographic composition. In this work, we propose GeoComposer, a novel geometry-grounded photographic composition framework that analyzes the composition of a given image to generate textual guidance and synthesizes a visual exemplar that enhances the composition of the given image. To promote geometry-grounded composition, we propose a geometry-aware representation learning mechanism that leverages geometric priors from a visual geometry foundation model to shape the intermediate representations of the composition editing model. This mechanism preserves both global structural relationships and local fine-grained correspondences for geometry-grounded composition. Furthermore, we propose a reinforcement learning strategy guided by a hybrid reward that jointly optimizes instruction following, aesthetic quality, and geometric consistency. This enables the model to generate visual exemplars that faithfully follow the composition instructions while remaining visually appealing and geometrically consistent. Extensive experiments show the superiority of our approach over state-of-the-art methods, highlighting its effectiveness in generating visually appealing and geometrically consistent composition.

We study geometric inverse problems for finite sets $A\subset \mathbb{Z}^d$ whose Fourier $L^1$ norm, or Wiener norm, \begin{align*} \|A\|:=\int_{\mathbb{T}^d}\Big|\sum_{a\in A}e(a\cdot t)\Big|dt \end{align*} is subpolynomial in $|A|$. In particular, we show a variety of geometric phenomena are incompatible with small Fourier $L^1$ norm. Our principal application concerns spherical Freiman models. Suppose $\|A\|=|A|^{o(1)}$ and $D\subseteq A$ is Freiman isomorphic to a set $S$ of lattice points on a sphere; then, $|D|/|A|$ must be polynomially small in $|A|$. Moreover, if $|D|/|A|$ is not too small, almost all of $S$ lies in a small number of spherical caps, and almost all caps have rich additive structure. The proof uses a new mechanism for studying additive structure across subsets of $A$, along with decoupling results of Bourgain-Demeter.

End-to-end (E2E) driving policies have advanced rapidly on open-loop (OL) benchmarks, yet OL evaluation cannot reveal whether a policy can withstand compounding errors, recover from failures, or interact safely with surrounding actors. We introduce NavSafe-$\infty$, a photorealistic closed-loop (CL) benchmark comprising 280 scenarios spanning 28 event types, each with success and failure criteria defined within a structured traffic-safety taxonomy, yielding category-level capability scores for Traffic Crashes, Vulnerable Road User Crashes, Traffic Violations, and Traffic Incidents. After evaluating 20 E2E policies, we find that OL gains do not reliably transfer to CL safety. Analysis of two common remedies reveals that (1) passive demonstration perturbation helps mainly when CL rollouts stay near their perturbed training states, and (2) OL reinforcement-learning fine-tuning exhibits reward hacking by trading safety margin for ego progress, which CL feedback amplifies into compounding safety-critical errors. Together, these results demonstrate the blind spot of OL benchmarks indicating CL safety success. The benchmark and an extensible toolbox for customizable event curation and policy diagnosis will be open-sourced to facilitate future research.

Clinical decision making heavily relies on predicting the disease progression trajectory by seeking to understand patient's health status which is characterised by multimodal medical data. AI holds great potential for learning useful representations from multimodal medical data to predict disease progression and aid clinical decision making. However, development of predictive AI models is constrained by missing modalities and incomplete tabular data frequently occurring in medical datasets. In addition, disease labels alone may only provide limited supervisory signals for learning representations from high-dimensional multimodal data. Here, we present MMAP, a novel Multimodal Missing-aware Alignment Pretraining method for learning image-tabular representations from incomplete data. An image encoder is pretrained with efficient sigmoid contrastive learning combined with generative reconstruction. A tabular encoder is built upon a tabular foundation model. A missing token generator enables the two encoders to take incomplete data as input, enabling the model to be robust against missing modalities, either with missing images or missing tabular data. We evaluate the clinical usefulness of the learnt multimodal representations on two challenging longitudinal clinical tasks for Alzheimer's disease: predicting disease stage conversion and predicting amyloid status. The proposed method outperforms strong multimodal and unimodal baselines.

Distributed Filesystems (DFS) are a crucial component of modern computing environments, and their performance is critical to the success of all the facilities that rely on them. However, predicting the DFS I/O performance solely based on the storage system hardware is not trivial. In this paper, we address this challenge by presenting an empirical method that tries to quantitatively assess how hardware configuration choices influence the performance of a DFS using Ceph as a case study. We investigate the influence of three hardware parameters-number of CPU cores, amount of RAM, and disk bandwidth. To control these variables, we relied on the Linux hotplug interface and Cgroups, avoiding additional software overhead. Our results reveal that for the analyzed workloads, decreasing hardware resources does not always yield proportional performance losses. This method offers practical insights for designing cost-effective distributed storage systems, remaining general enough to be applied to other filesystems.

In sparse random matrices, spectral outliers (eigenvalues and singular values located away from the bulk) emerge due to degree fluctuations: high degrees inflate the operator norm, while low column degrees reduce the least singular value. As proved by Feige and Ofek (2005) and Le, Levina, and Vershynin (2017), degree regularization enforces concentration at the expected norm scale. However, precise bounds incorporating the cutoffs remain unexplored and challenging since regularization introduces dependencies among entries. For the first time in the literature, we provide variance- and cutoff-dependent bounds for extreme singular values and eigenvalues of regularized inhomogeneous random matrices. In the absence of regularization, our lower bound for the least singular value matches the same leading constant obtained by Brailovskaya and van Handel (2024). Moreover, our error term vanishes under the milder condition $d/\log N\to\infty$, as opposed to their stronger requirement $d/(\log N)^4\to\infty$. A key ingredient is to extend spectral radius bounds for nonbacktracking matrices to the dependent setting. We build on approaches for independent cases established by Benaych-Georges, Bordenave, and Knowles (2020), as well as Dumitriu and Zhu (2024), and carefully handle edges traversed only once. Our proof framework separates deterministic spectral comparisons from probabilistic estimates: once Loewner inequalities and columnwise variance controls are established, the remaining probabilistic analysis boils down to verifying the graph moment conditions formulated in this paper. We hope this framework can be extended to handle general random matrices with more complex dependencies.

Normal-conducting radiofrequency (rf) cavities for muon-collider ionization cooling must operate at high accelerating gradients in strong solenoidal magnetic fields, where rf breakdown can be enhanced by the magnetic focusing of field-emitted electrons. In this work, field-emitted electrons were tracked in the realistic field maps of rectilinear cooling-lattice cavities to test the validity of the previously developed localized-bombardment picture with simplified field maps. Under comparable reduced-field assumptions, the tracking results show good agreement with previous results. The full rf eigenmode fields and nonuniform solenoidal fields modify the idealized beamlet structure, producing rf phase dependent centroid shifts and broadened impact distributions from solenoid fringe fields. Nevertheless, the original model remains a useful framework for estimating limits on operating gradients. The thermal response is evaluated analytically using this model, with material properties varied to assess the coupled effects of heat transport and thermomechanical damage threshold. These results can inform cavity testing in strong solenoidal fields, muon ionization cooling channel designs, and other applications requiring high-gradient rf operation in magnetic fields.

Photorenewable polymer adsorbents, aimed at reducing the low density lipoproteins (LDLs) level, are reported experimentally. Previously we developed a mesoscale model for this setup with uniformly grafted chains, and examined the role played by chains length and grafting density [Ilnytskyi, et al., Processes, 2023, 11, 2913]. The analysis is extended here to the cases of bunch-like and grid-like grafting micropatterns. The bunch-like arrangement is the most efficient one displaying low- and high-density peaks for adsorbing effectiveness. The former peak is twice higher compared with uniform grafting, as a consequence of a match between LDLs dimensions and the micropattern pitch. Adsorption isotherms are fitted well by either Langmuir or logistic growth forms, indicating a higher growth rate compared with uniform grafting. The high-density peak exists only for this micropattern and extends the applicability of an adsorbent. At the highest LDL concentration, adsorption is hampered by self-assembly of LDLs into a packed cubic phase.

This work develops a reduced order observer framework of monocular visual-inertial odometry (VIO). The key idea consists in considering the gravity vector in the body-frame as an additional state and constructing an appropriate output that relates the monocular bearing measurements and their time derivatives to the body-frame velocity. This eliminates the need for the estimation of the landmark positions, leading to a six-dimensional linear time-varying (LTV) observer for the body-frame velocity and gravity, endowed with uniform global exponential stability guarantees. These estimates are subsequently used to recover the orientation almost globally, up to an unknown constant yaw offset, and the position up to an unknown constant translation. The mixed-bearing framework is further extended to account for the inertial measurement unit (IMU) biases, yielding a twelve-dimensional LTV observer endowed with local exponential stability guarantees. Numerical simulations are provided to illustrate the effectiveness of the proposed observers.

Astrophysical sources of ultra-high-energy cosmic rays (UHECRs) remain unidentified, and no nearby cosmic accelerators are established even for the highest-energy events. In addition, puzzling correlations of a fraction of UHECR flux with distant blazars were found by HiRes and, recently, Telescope Array experiments. Here we propose that dark matter can provide a mechanism to effectively transfer UHECRs from distant sources: dark-matter particles are boosted by UHECRs near the source and pass their momentum to baryons close to the observer. The probability of this relay is not negligible because of the growth of dark-matter-baryon cross section with energy. We demonstrate that the effect is observable for fermionic dark matter of mass $m_{\mathrm{DM}} \sim 25$ MeV and discuss possible observational signatures of this mechanism.

Despite their outstanding performance on many NLP tasks, LLMs face serious challenges related to semantic abstraction. In this study, we are interested in understanding how LLMs leverage abstract semantic knowledge in natural language inference (NLI), which requires sophisticated linguistic capabilities to interpret implicit meanings, contextual conceptual relationships, and semantic connections between words and phrases. To this end, we propose a methodological framework for constructing new semantic knowledge at a higher level of abstraction, which we define under the notions of semantic compatibility and incompatibility for NLI. In this framework, the meaning of the lexical-semantic relations between the premise and the hypothesis is reconfigured to achieve a more flexible semantic network that induces different reasoning paths in LLMs. These new pathways show a consistent pattern of responses that allows agreement on a single response. The results demonstrate that our proposal allows to discover and compensate for LLMs' semantic knowledge gaps in NLI, achieving significant improvements in accuracy, exceeding 10% for some models, and in particular for the non-entailment class. It is essential to note that LLMs need structured knowledge and not just more data to bridge reasoning gaps. Our hybrid approach directs attention to overlooked word relationships, allowing models to synthesize missing information. We believe that the future lies not in increasing model size, but in creating a semantic scafolding that mimics the flexibility of human thinking. Hopefully, our proposal will enable the development of more robust agents and interpretable reasoning, guiding AI toward reliable language understanding.

We prove the sharp two-disk comparison conjectured by Langford and Laugesen for the second positive Neumann eigenvalue under an upper Gaussian-curvature bound, and strengthen it to a shifted reciprocal inequality. Let $\Omega\subset\mathbb{C}$ be bounded, simply connected and Lipschitz, with $g=\omega|dz|^2$, where $\omega$ is continuous and positive on $\overline{\Omega}$ and $\Delta\log\omega+2K\omega\ge0$ in distributions. Write $A=|\Omega|_g$ and enumerate the spectrum by $0=\lambda_0<\lambda_1\le\lambda_2\le\cdots$. If $KA<4\pi$ when $K>0$, then $\frac{1}{\lambda_2}+\frac{1}{\lambda_3}>\frac{2}{\lambda_1(D_K(A/2))}$ and $\lambda_2<\lambda_1(D_K(A/2))$, where $D_K(A/2)$ is the constant-curvature disk of area $A/2$. The same conclusions hold for disk-type Lipschitz domains in smooth surfaces. In the subcritical regime, both bounds are sharp, as witnessed by an extremizing sequence of smooth connected domains of exact area and curvature whose Neumann eigenvalues converge, at every fixed index, to those of two disjoint equal model disks. At $KA=4\pi$ we obtain the sharp non-strict bounds $\lambda_2\le2K$ and $\lambda_2^{-1}+\lambda_3^{-1}\ge K^{-1}$. The proof combines two-pole Green coordinates, positive-kernel comparison, and simultaneous centering. We also establish a global quadratic deficit for the model area split.

The choice of probe state is essential to achieving ultimate precision in quantum metrology. For a single parameter, an equal superposition of eigenstates associated with the largest and smallest generator eigenvalues is optimal. This simple construction does not directly extend to multiple parameters, since different parameters can favor different probes. We address this difficulty through a geometric construction of optimal probes for multiparameter estimation in distributed quantum sensing. In this setting, the generators commute and share a common eigenbasis, so each common eigenstate defines a vector of generator eigenvalues. We show that the minimal enclosing balls and ellipsoids of these vectors determine the maximal total quantum Fisher information and the minimum weighted covariance, respectively. In both cases, the boundary of the convex body identifies the common eigenstates that can contribute to an optimal probe, and its center and shape specify the conditions that their populations must satisfy. Our results provide a systematic approach to designing optimal probe states, linking the structure of the parameter generators directly to the attainable precision in multiparameter quantum metrology.

In this paper, we prove an Erdős-Ko-Rado characterisation of maximum intersecting families of blocks in Steiner $2$-designs arising from Desarguesian maximal arcs. This answers a recent question of Goryainov and Konstantinova, and implies that, among the known Steiner $2$-designs, only finitely many admit a maximum intersecting family that is neither canonical nor associated with a subdesign. We also perform a computational study of $2$-$(120,8,1)$ designs and find strong counterexamples to a problem of Godsil and Meagher. Finally, we give a parametric generalisation of $2$-$(66,6,1)$ designs with tight dual arcs as non-canonical maximum intersecting families.

We provide a model for the nested optimisation problem of market making and rebate design problems in option markets and find optimal strategies. A single market maker trades multiple European call options in a local-stochastic volatility option market with both make and take strategies, modeled, respectively, as continuous and impulse controls. Her objective is to maximize, over all admissible make-take strategies, net profit of option portfolio value and cumulative rebate revenue, subject to a penalty on residual portfolio delta and vega. In addition, we demonstrate how an exchange can incentivize a market maker to improve market liquidity by setting suitable fee rebates, thereby resolving its own liquidity attraction problem. To this end, we propose a three-step rebate design scheme with flexibility to accommodate specific liquidity targets imposed by an exchange. Numerical results are provided to validate the effectiveness of the proposed scheme.

Foundation model embeddings of screening mammograms may encode pre-diagnostic tissue change without task-specific adaptation. We tested whether embeddings move faster along a data-derived "cancer direction" in women later biopsied for cancer than in matched screen-negative controls, and whether this depends on pretraining domain. We studied 1,773 biopsied women (785 malignant, 988 biopsy-negative) and 1,773 matched controls, each with at least two annual screening exams before their index exam. An identical pipeline was applied to four 2D models: Mammo-CLIP (MC, out-of-distribution mammography), HOPPR (in-distribution mammography), MedImageInsight (MII, general medical imaging), and BiomedCLIP (biomedical vision-language pretraining on literature figures). Breast-level embeddings quantified longitudinal movement along the cancer direction. We compared cases and controls using a between-patient design with complementary mixed-effects analysis, and biopsied versus healthy contralateral breasts within patients. Under matched modality in MII embedding space, malignant cases drifted significantly faster than controls in the first two screening intervals preceding the index exam; biopsy-negative cases showed significance only in the first. MC differences were significant in the first interval for both biopsy groups. Within-patient comparisons showed a broadly similar pattern, with MC significance extending to the second interval in both groups and HOPPR showing significance at interval 1. BiomedCLIP showed no significant differences in either design or biopsy group. Overall, directional embedding velocity emerges as a property of clinically grounded rather than general biomedical pretraining, showing that foundation model embeddings can encode pre-diagnostic mammographic change without task-specific adaptation.

Knowledge spillovers have largely been studied as unintended externalities diffusing through geographic proximity, while deliberate interregional networks have been examined mostly through co-inventor ties rather than the scientific layer carried by co-authored publications. This study asks whether spillovers from interregional AI-related co-publications increase regional AI patenting, and whether the ownership composition of regional R&D shapes the capacity to capitalize on them. Using a network-econometric approach across 26 Chinese provincial-level regions from 2006 to 2020, we find that co-publication spillovers foster AI patenting, but the returns concentrate almost entirely in regions where privately owned enterprises dominate R&D, reinforcing regional divergence.

Hierarchical latent communication improves the generalization of a power-flow model, shared across three grids, to new operating scenarios. The module exchanges information through two reduced graphs inside the corrective network of GENCO, replacing two of its local correction steps. We compare Kron-derived transports, a same-anchor Quotient construction and the flat GENCO Base architecture, all trained under one protocol of our own with about a hundred times fewer optimizer updates per grid than GENCO's reference training: 200 epochs on three grid topologies, fewer than 1,900 training scenarios per grid and three initialization seeds per model. Evaluation uses 200 newly generated, preselected scenarios per grid. On the training topologies, Kron reaches a macro family-balanced voltage error of $0.851\pm0.110$, 51.3% below a per-bus mean fitted on training solutions (1.747). Kron is below this reference on 98.5% of the 600 fresh scenarios, and both hierarchical models outperform it on every training topology in all three seeds. The flat baseline reaches $5.660\pm0.899$ and does not outperform the reference on any training topology, so Kron's 85.0% reduction relative to it compares architectures within our training regime. Kron is also 31.0% below Quotient ($1.235\pm0.225$). These results demonstrate generalization across operating scenarios within the studied topologies, with one set of learned parameters shared across grids. On two topologies unseen in training, the current models do not yet outperform the fitted reference in calibrated transfer; extrapolation to new topologies is the next development objective.

Motivation: The Multiple Longest Common Subsequence (MLCS) problem for an arbitrary number of sequences is an NP-hard problem in sequence analysis. Existing exact algorithms based on dynamic programming or MLCS-DAG pruning rapidly exhaust memory as sequence lengths and set sizes grow, while heuristic and hyper-heuristic approaches compromise solution quality and require heavy parameter tuning, respectively. Results: This paper presents the ARP heuristic that, for a given primary sequence, performs three key actions: (i) Adding-$\Delta$s, which incrementally builds a solution by adding subsequences, called $\Delta$s, of the primary sequence to an initial solution; (ii) Replacing-Subsequences, which enhances the diversity of the solution set via targeted replacement of subsequences common to all solutions; and (iii) Prioritizing groups of characters from the primary sequence that are likely to appear together in longer common subsequences. ARP allows the user to configure the degree of Replacements and Prioritization actions for carrying out quality-runtime tradeoff. Empirical evaluations on both synthetic and biological sequence sets demonstrate that ARP's fastest configuration AOnly finds significantly longer common subsequences than the BNMAS classical heuristic and its aggressive configuration attains solution quality comparable to state-of-the-art hyper-heuristic (UB-HH) while running 1.1$\times$-1.7$\times$ faster.

Intelligent reflecting surface (IRS)-assisted mobile Internet of Things uplinks require joint control of channel aging, costly cascaded channel state information (CSI) acquisition, and coupled IRS/radio resources. This investigation develops a unified prediction-aware deterministic framework for partitioned IRS-assisted massive multiple-input multiple-output (mMIMO) uplinks. Direct channels are recursively tracked, whereas cascaded channels are selectively refreshed by differential semi-blind acquisition reusing the same unknown data block across a minimum-reflection baseline and DFT-coded IRS states. Moreover, finite-block acquisition covariances initialize reduced-order beam-domain prediction, which propagates only unit-beam means online and retrieves age-dependent covariances from precomputed tables. A mixed-integer nonconvex formulation captures net throughput, fairness, outage, uncertainty, switching cost, and sliding-window IRS service. The causal controller integrates covariance-floor actionability, feasible equal-size granularity, residual-feasible ownership, isolated-beam one-sweep refinement, same-block fresh-payload accounting, and service-first allocation using recomputed uncertainty-aware ZF rates and bidirectional receiver-consistent risk. Analysis establishes service-feasibility preservation, effective-channel error bounds, distribution-free reliability, and polynomial online scaling. In unseen environments, the predicted acquisition floor matches the practical semi-blind error, actionable recalibration reduces the mean recalibration rate by 31.5%, and IRS-assisted control achieves a 14.09% mean net-rate gain over direct-only transmission. Receiver-consistent allocation improves realized rate, while ablations support equal-size partitioning and single-sweep refinement; zero post-action service violations occur under nominal, mobility, and load-stress conditions.

We study scaling limits of $\mathbb R^d$-valued branching random walks (BRWs for short) in the following setting: indexing-trees are Galton-Watson trees with critical offspring distribution which are assumed, when appropriately rescaled, to converge to a critical $\psi$-Lévy tree; conditional on the indexing tree, the jumps of the BRW may exhibit dependence within the same sibling group, but distinct sibling groups are independent, and their distributions are centered but may vary (and for instance depend on the whole indexing tree), with a typical value of the walk nevertheless remaining within the domain of attraction of a mixture of Gaussian distributions. Under these assumptions and a necessary additional assumption, which we call the discrete Sheu assumption, we show that rescaled discrete snakes converge functionally to the $\psi$-Brownian snake introduced by Le Gall & Le Jan (1998) and D.~& Le Gall (2002). The method uses a coupling result for BRWs of independent interest. An application is given concerning the scaling limits of the range of BRWs that take their values in the $\mathtt b$-ary tree to the reflected $\psi$-Brownian cactus which is a variant of the Brownian cactus introduced by Curien, Le Gall & Miermont (2013).

The dynamics of gauge theories is of fundamental interest, with low-dimensional systems displaying a rich phenomenology beyond the rapid thermalization typical of QCD and non-Abelian theories. In particular, recent quantum simulation experiments have reported robust and unexpected signatures of slow relaxation in generic regimes and at large volumes in one-dimensional U(1) lattice gauge theories (LGTs), whose origin remains poorly understood. Here, we present a framework that provides a unified perspective on such slow dynamics and establishes a new route for exploring subdiffusive fractonic hydrodynamics in Rydberg experiments. The backbone of our theory is an exact analytical mapping from U(1) LGTs with a topological $\theta$ angle to non-local kinetically constrained fermionic models with an emergent linear Stark potential. In the absence of the $\theta$ term, this framework interprets the non-thermal dynamics reported in recent experiments as prethermal behavior arising from proximity to an integrable free-fermion model. For non-zero $\theta$, the emergent Stark potential instead explains the freezing dynamics observed in other recent experiments. We argue that this correspondence could also lead to subdiffusive transport due to emergent conservation laws. We predict that these phenomena arise in a much broader class of models, and support this prediction with numerical simulations and proposals for future experiments.

The future 6G networks are expected to incorporate a proliferation of wireless services in diverse environments, which presents a significant challenge for information security. Conventionally optimization always requires recalculation and learning strategy often suffers poor generalization, which are thus incapable for the security provisioning with wide scenario coverage. In this paper, we propose an adaptive and robust learning framework that leverages a mixture-of-experts (MoE) architecture to achieve cross-scenario physical layer security guarantee. Specifically, we first select a few representative scenarios and establish the scenario-specific generative diffusion model (GDM)-based experts for secure transmission beamforming with artificial noise. The diffusion nature of experts learns the overall probability distribution of security strategy solution landscape and the Transformer-based denoising process enhances the ability to generalize across varying network configurations. Then, a lightweight gating network is constructed to identify the scenarios by engineering the channel features and select the most relevant experts. Finally, an attention-based combiner is introduced to synthesize the security proposals from the top-rated experts to produce a high-fidelity security strategy to cover the unseen scenarios. Simulation results demonstrate that the proposed GDM-based MoE framework can accurately recognize the scenarios and properly select the experts, maintaining near-optimal secrecy rates across a continuum of wireless scenarios and outperforming traditional single-model paradigms.

We establish sharp variance asymptotics and limiting distributions for the quadratic optimal matching cost between the uniform measure and an empirical measure counterpart on the flat torus $\mathbb T^d$ in dimensions $d=2,3,4$. More precisely, let $\mu$ be Haar probability measure and $\mu_n$ the empirical measure of $n$ independent samples drawn from $\mu$. Then, for $d=2,3$, $$ \begin{aligned} n\bigl(W_2^2(\mu_n,\mu)-\mathbb E[W_2^2(\mu_n,\mu)]\bigr) &\xrightarrow{\mathrm d} L_d,\\ n^2\operatorname{Var}(W_2^2(\mu_n,\mu)) &\longrightarrow \frac{1}{8\pi^4} \sum_{k\in\mathbb Z^d\setminus\{0\}}\frac{1}{|k|^4}, \end{aligned} $$ where $L_d$ is an explicit non-Gaussian weighted sum of independent centered exponential random variables. In dimension four, $$ \frac{n}{\sqrt{\log n}} \bigl(W_2^2(\mu_n,\mu)-\mathbb E[W_2^2(\mu_n,\mu)]\bigr) \xrightarrow{\mathrm d} N\left(0,\frac{1}{16\pi^2}\right). $$ The main idea of the proof is to rely on a Hoeffding decomposition of the optimal transport cost, which turns out to be asymptotically equivalent to U-statistics of order 2.

We study Hamiltonian learning for $k$-local Hamiltonians at large step size, using only forward time evolution at integer multiples of a fixed time interval. For this task, our new technique, which we call eigenphase engineering, achieves Heisenberg-limited learning with a step size that is optimal up to logarithmic factors. For an unknown $s$-sparse Hamiltonian with fixed locality $k$ and $\|H\|_{\mathrm{op}}\leq\Lambda$, our algorithm recovers its Pauli coefficients to $\ell_2$ error $\varepsilon$ in total evolution time $\widetilde{O}(s/\varepsilon)$, matching the best known scaling while allowing a near-maximal step size $\widetilde{\Theta}(1/\Lambda)$. As an independent contribution, we strengthen the evolution-time lower bound to $\Omega_k(s^{1-1/(2k)}/\varepsilon)$, placing our algorithm within a factor $\widetilde{O}(s^{1/(2k)})$ of being optimal. Eigenphase engineering departs from approaches based on dynamical approximation or iteratively canceling the unknown Hamiltonian. It encodes energy expectation differences in the perturbative response of eigenphases of the actual controlled evolution, then extracts them through phase estimation and high-order extrapolation. This avoids the need for polynomially shorter evolution steps as the target precision improves. A version using only single-qubit operations retains the same step size with a $\sqrt n$ overhead in $\ell_2$ learning time for $n$ qubits. The method also enables tolerant Hamiltonian certification and estimation of a specified Pauli coefficient, the latter without locality or sparsity assumptions. These results establish eigenphase engineering as a versatile approach to extracting Hamiltonian information with infrequent control.

Let X1,...,Xn be independent exponential random variables with arbitrary positive, not necessarily equal, rates, and let Y1,\ldots,Yn be independent and identically distributed exponential random variables. We prove that, for every order statistic, the homogeneous order statistic is smaller than its heterogeneous counterpart in the convex transform order. Our results show that, relative to the homogeneous benchmark, heterogeneity stretches upper quantiles more strongly than lower quantiles, while the homogeneous order statistic ages faster in the convex-transform sense. We further extend the comparison to a proportional-hazards family that includes Weibull, Lomax, and Burr XII distributions. We give explicit conditions under which the comparison is preserved and show that the shape restriction is sharp within the Weibull family. These results characterize how component heterogeneity changes the distributional shape of order statistics beyond effects on location or scale.