Papers

This paper considers an inverse shape problem for recovering an unknown impenetrable clamped obstacle in two dimensions from near-field point source and dipole measurements for the biharmonic Helmholtz equation in the frequency domain. The measured data consist of the scattered field and its normal derivative on a closed measurement curve surrounding the obstacle. Since the associated near-field operator does not directly admit the symmetric factorization required by the factorization method, we introduce a far-field transformation. This transformation is defined independently of the obstacle and augments the near-field operator into the associated far-field operator which does admit a symmetric factorization. This yields a rigorous complete characterization of the obstacle by the factorization method theory and leads to a practical reconstruction algorithm based on the spectral data of the transformed operator. Numerical experiments are presented to demonstrate the effectiveness of the proposed method, with synthetic near-field data generated using the method of fundamental solutions. We also consider reconstructions using only scattered-field measurements generated by point sources, demonstrating the potential for reduced the amount of measured data.

We analyze polarization data streamed from a commercial coherent transponder, used in MedNautilus link, during 2023 Turkey earthquakes. We show how earthquake features and cable geometry fundamentally govern the optical polarization response, taking the first steps for detailed interpretation in designing fiber-based seismic sensing systems.

We present a multiconfigurational, relativistic embedded-cluster study of the local electronic structure of ruthenium dioxide ($\mathrm{RuO_2}$), a candidate altermagnetic material. Starting from free $\mathrm{Ru}$ ions, we progressively build up the local environment through a $\mathrm{Ru+Q_6}$ electrostatic model, a bare $\mathrm{[RuO_6]^{8-}}$ ligand model, and finally a high-accuracy $\mathrm{RuO_6}$@CTEP embedded cluster that reproduces the crystalline surroundings. All systems are treated at the SA-CASSCF and NEVPT2+SOC levels of theory to capture strong electron correlation and spin-orbit coupling on an equal footing. While the formal local site symmetry of the $\mathrm{Ru}$ sites in $\mathrm{RuO_2}$ is orthorhombic ($D_{2h}$), we find that the calculated $4d$-orbital energy spectrum and its splitting pattern behave much closer to the higher tetragonal ($D_{4h}$) symmetry, preserving a strong quasi-degeneracy among the relevant $4d$ orbitals. Since the local $xy$ quadrupolar order responsible for altermagnetic spin splitting in independent-particle models relies on this symmetry reduction, its suppression by orbital quasi-degeneracy offers a natural explanation for why altermagnetism is not observed in bulk $\mathrm{RuO_2}$ experiments, in contrast to the robust altermagnetic signatures reported in strained thin films.

Fluctuation-response relations (FRRs) connect the linear response of a system to an external perturbation with properties of spontaneous fluctuations in the unperturbed system. We provide a simple derivation of FRRs for non-stationary dynamics following an almost standard way based on introducing a variable conjugated to perturbation (a dynamic conjugate). The derivation relies solely on the Markovianity of the underlying dynamics, with the only additional assumption that the transition PDF of the process is differentiable with respect to the strength of a constant, time- independent perturbation. The structure of this conjugate variable is however unusual: it is a two-time one, and reduces to a usual single-time conjugate in stationary situations. We show how several known results follow from this approach.

Rigid-body interpenetration frequently occurs in procedurally assembled and generated scenes and must be removed before downstream applications such as physical simulation. We present S4R (Scaling for Rigid-Body Interpenetration Resolution), a scale-continuation method for static interpenetration repair. S4R first uniformly shrinks each body about a fixed reference center to a small initial scale, at which the layout is penetration-free, and then restores full scale through a sequence of minimum-norm convex contact quadratic programs (QPs) that target the linearized separation margin during continuation. Resolution thereby replaces one deep correction with a sequence of shallow-contact subproblems. A conservative scale-event bound and frozen-witness gap predictions cut the number of exact mesh queries; the continuation then ends with a full-scale evaluator check and bounded tail refinement. We evaluate S4R on Kubric, HY3D-Bench, and Thingi10K using a shared mesh-level evaluator and a unified per-scene timing protocol. In the main comparisons on all three benchmarks, up to N=5000 bodies, S4R reaches zero reported penetration with displacement that stays small and nearly independent of scene size, and at the lowest wall time within each hardware tier among the compared methods. A GPU implementation extends these results to large-scale scenes. Our code and data can be found on our project page: https://frank-zy-dou.github.io/projects/S4R/index.html.

Quantum communication underpins secure information processing and scalable quantum networks. In particular, remote state preparation (RSP) enables efficient quantum state transfer, but accurately estimating target states under complex noise remains challenging. Here, we propose a Transformer-based Quantum State Characterizer (TQSC) model for noisy RSP experiments. Our model reconstructs experimentally prepared pure and mixed photonic polarization states from noisy measurements in complex scattering environments, while its attention patterns provide physically grounded insights into correlations among the measured observables. The method achieves a mean estimator-target fidelity exceeding 99.999% under complex scattering and dynamic Gaussian noise, while its robustness and generalization are further examined using Qiskit-simulated Bloch-ball states. Furthermore, in a practical MNIST image transmission task with held-out states, the decoded bit error rate is reduced from 50.34% to zero after TQSC post-processing. The TQSC model enables accurate tomographic characterization under dynamic noise and provides physically grounded post-hoc insights, holding promise for intelligent quantum information processing applications.

By introducing new ergodic-theoretic techniques in nilsystems, we determine which infinite sumset configurations occur in $U^k(\Phi)$-uniform and Nil-Bohr sets. To be more precise, our first result associates the degree $k$ of a $U^k(\Phi)$-uniform set with the variety of sumsets it contains, solving a conjecture of Kra, Moreira, Richter and Robertson. Restricting to Nil-Bohr sets we show the existence of infinite sumsets with summands in the shifted primes $\mathbb{P}-1$. As a consequence, we show that for any real polynomial $Q(n)$ with leading irrational coefficient of degree $k$, and any natural numbers $\ell_1, \cdots, \ell_k$ there is an infinite set $P\subset \mathbb{P}$ such that \begin{equation*} Q\Big(\sum_{p \in I} p\Big) \in U \pmod 1 \quad \text{ for all } I \subset P , |I| = \ell_1, \ldots, \ell_k. \end{equation*}

The rank of a semigroup is the cardinality of a smallest generating set. In this paper, we introduce iterated wreath products of transformation semigroups. We determine the rank of iterated wreath products of full transformation monoids and symmetric groups.

We prove sharp spectral-norm bounds and construct a mean-fitting regularization procedure for sparse random tensors of fixed order $k$. For an $n\times\cdots\times n$ tensor with independentBernoulli$(p)$ entries, the centered norm is $O(\sqrt{np})$ with polynomially high probability whenever $np\ge c\log n$. This removes the logarithmic loss in Zhou and Zhu (2021). We also determine the expected centered norm at every sparsity level: for every $0<p\le1/2$, it has order $\min\{n^kp,\sqrt{d_{\mathrm{eff}}}\}$, where $d_{\mathrm{eff}}$ is an effective degree accounting for unusually large fiber counts. The upper bounds extend to tensors with deterministic entrywise weights and unequal sampling probabilities. Analogous two-sided bounds hold for the Friedman–Wigderson model at every degree; its expected centered norm has order $\sqrt{d_{\mathrm{eff}}}$. We also give an all-sparsity regularization procedure for independent Bernoulli tensors with unknown, possibly unequal means in $[0,p]$. Our light-fitting regularization estimates the original mean with minimax expected spectral-norm error of order $\min\{\sqrt{np},pn^{k/2}\}$ for every known $0\le p\le1$. The procedure fits light multilinear residuals under an entrywise constraint on the candidate mean, rather than deleting high-degree fibers.

As coding agents move from supervised code completion to unattended, around-the-clock exploration, their work expands from isolated predictions into long trajectories of reasoning, tool use, and feedback. Token efficiency therefore becomes important for scaling recursive self-improvement. We take an RSI-inspired approach at the harness layer, scaling auto-research loops across increasingly numerous and diverse environments for harness rollouts. At this scale, the process yields reusable improvements that transfer beyond their development setting, moving automated harness discovery toward production-level outcomes. Four mechanisms survive selection and form SoL-Pi, spanning action execution, context compaction, observation handling, and delegated reading. On the 51-task EdgeBench evaluation, SoL-Pi achieves performance comparable to Pi across GPT-5.6 Sol and Opus 5 while reducing recorded token traffic by 44.7-49.0% and API cost by about one third. In other words, estimated hourly savings are \$8.75-\$13.50 relative to native Codex and Claude Code harnesses, and \$4.36-\$5.71 relative to Pi.

Ventricular Assist Devices (VADs), particularly rotary Left Ventricular Assist Devices (LVADs), are essential for patients with advanced heart failure who are ineligible for transplantation. Despite advances in cardiovascular modeling and control, clinical translation of proposed LVAD control methods remains limited. This review examines the evolution of LVAD modeling and control and argues that the gap results not from insufficiently sophisticated algorithms, but from mismatches between modeling assumptions, sensing limitations, and real-world cardiovascular variability. A systematized review of more than 100 peer-reviewed studies covers mathematical cardiovascular models, lumped-parameter and reduced-order representations, classical and advanced control strategies, and emerging data-driven and machine learning approaches. The literature is synthesized using a problem-driven framework linking modeling and control choices to clinical challenges, including physiological observability, parameter identifiability, patient variability, and prevention of adverse events such as ventricular suction and thrombosis. The analysis shows that high-fidelity models and intelligent controllers can perform well in simulation, but their dependence on unmeasurable states, extensive parameter tuning, and dense sensing limits clinical implementation. Simpler control approaches often provide greater robustness under clinical constraints. Adaptive and data-driven techniques may help bridge this gap, but only if they account for implantable sensing limitations and interpretability requirements. By identifying structural barriers to adoption, this review synthesizes LVAD modeling and control paradigms and outlines research directions for physiologically adaptive, clinically implementable, and patient-safe LVAD systems.

We show that the sharp Euclidean isoperimetric inequality holds for domains in complete simply connected Riemannian $n$-manifolds of nonpositive sectional curvature, $3\leq n\leq9$, which establishes the Cartan-Hadamard conjecture in these dimensions. The main step is a sharp inequality for constant-mean-curvature hypersurfaces, proved via integrals over pairs of boundary points, together with estimates for Jacobi fields along geodesic chords of the boundary. The weights in these integrals depend on the length of the chord and its angles with the boundary, and are chosen dimension by dimension, with a Green function pole. The inequality persists for boundaries of isoperimetric regions trapped in geodesic balls, whose mean curvature is constant only on the free part and which may have singularities. The isoperimetric-profile argument of Kleiner and Ghomi-Spruck completes the proof.

In this paper, we explore group invariants arising from combinatorial structures associated with finite groups, including the functional graphs of power maps and the well-studied power graphs. These invariants induce equivalence relations (and hence partitions) on the set of isomorphism classes of finite groups, which we classify from the finest to the coarsest. Surprisingly, all but three of these partitions turn out to coincide; for the subclass of nilpotent groups, all but two coincide. Furthermore, we introduce a broad class of nilpotent groups and show that, within this class, all but one of these partitions agree. Our proofs draw on tools and ideas from Combinatorics and Number Theory, while requiring only basic notions from Group Theory. In particular, we construct a general framework that may prove useful in contexts similar to those considered in this paper. Finally, we propose some open questions that emerge from our results.

We show that the ACC conjecture for minimal log discrepancies holds for both bounded generalized sub-pairs in arbitrary dimension and bounded threefolds with arbitrary boundaries.

Let $(X,\tau)$ be metrizable and let $F=\{a_1,\ldots,a_k\}\subseteq X$, where $2\le k<\infty$. We represent all metrizable topologies $\sigma\subseteq\tau$ agreeing with $\tau$ on $X\setminus F$ by compatible systems of continuous gauges $s_i:X\to[0,1]$ with $s_i^{-1}(0)=\{a_i\}$. The condition $\inf_X\max\{s_i,s_j\}>0$ for $i\ne j$ is equivalent to both Hausdorffness and metrizability of the prescribed gauge topology. A normalized product map into the standard simplex gives an explicit metric; its triangle inequality follows from a simplex slack inequality. This metric is complete whenever the auxiliary bounded compatible metric is complete. For two compatible systems, their coordinatewise minimum describes the intersection topology. It is compatible exactly when the two coarsenings have a common Hausdorff lower bound; in that case the intersection is metrizable and is their meet. Otherwise every common lower topology is non-Hausdorff. A closed-discrete construction produces such an obstructed pair for every noncompact metrizable space and every finite exceptional set with at least two points. Consequently, for these exceptional sets, the family is downward directed, or is a lattice, if and only if $(X,\tau)$ is compact, in which case it consists only of $\tau$.

The analytic minimal model program proposed in \cite{SongTianSingularities, JST} seeks to describe the birational transitions and fibre collapsing of the Kähler–Ricci flow through the geometry of its singularities. A fundamental conjecture of \cite{JST} predicts Type I bounds for the scalar curvature and diameter of every fibre contratced by the limiting cohomological class at the finite singular time. This paper is a continuation of \cite{Splitting} that establishes the Type I conjecture for collapsing solutions on Fano bundles with arbitrary smooth Fano fibres. If the fibre admits a smooth Kähler-Einstein metric, the Type I bound holds for the full curvature tensor.

We construct a symmetric operad $\mathfrak{C}$ on the class of all multivariate copulas, where operadic composition is given by Sklar substitution. We prove that the absolutely continuous subclass $\mathfrak{C}^{ac}$—which coincides with the $L^1$ class of copula densities—forms a suboperad; under composition, the density of the composite copula is given by the explicit Sklar substitution density formula $g(v)=\phi\big(\Psi_1(v^{(1)}),\dots,\Psi_n(v^{(n)})\big)\prod_{k=1}^{n}\psi_{k}(v^{(k)})$. Furthermore, we show that copulas with finite copula entropy—identified with the $L\log L$ class of copula densities—are closed under substitution and hence constitute a suboperad $\mathfrak{C}^{L\log L}$. On this suboperad, copula entropy is strictly additive: $H(\gamma(\Phi;\Psi_{1},\ldots,\Psi_{n}))=H(\Phi)+\sum_{k=1}^{n}H(\Psi_{k})$.

We study length inflation in on-policy distillation (OPD), where student responses can become excessively long and even exhaust the generation budget. We identify termination-token mismatch between base students and post-trained teachers as an important source of this behavior. Across Qwen3, Llama, and Gemma, the two models can place their stopping probability on different EOS tokens, even when their declared stopping sets are identical. This mismatch can suppress the student's preferred termination action without reliably transferring the teacher-preferred alternative. We show that aligning the decoding stopping set alone is insufficient, while treating functionally equivalent EOS tokens as a shared semantic stopping action substantially mitigates mismatch-induced length inflation across all three model families. To further understand how termination behavior evolves over training, we study OPD across different K2-Horizon training stages. This stage-wise analysis shows that termination preferences can shift substantially during training, while also revealing a distinct length inflation late in the OPD run that persists beyond termination alignment. Together, these results identify termination mismatch as an important, but not exhaustive, source of OPD length dynamics. We release an implementation incorporating the proposed termination-handling corrections.

Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.

For art historians, goldsmith marks play a critical role in the identification and dating of artifacts. In practice, experts must manually compare a query mark against hundreds of documented examples, a process that is both tedious and highly dependent on specialist knowledge. To address this, we present an AI-assisted retrieval pipeline that combines mark localization with metric-learning fine-tuning across three backbone architectures: an ImageNet-pretrained ResNet-50, a supervised ViT-S/16, and a self-supervised DINOv2 ViT-S/14. We conduct a systematic evaluation of cropping strategies, where we measure the impact of no cropping, manual ground-truth cropping, and learned detection-based cropping, and assess their interaction with each backbone. Our strongest configuration, DINOv2 ViT-S/14 with manual crop and metric-learning fine-tuning, achieves an mAP of 62.63% and a Top-1 accuracy of 73.74%. Our experiments show that self-supervised pretraining and mark localization are the two most impactful factors, with learned cropping recovering the majority of the gain from manual cropping without requiring ground-truth annotations at inference time. To enable reproducibility and adoption in the digital humanities, we release our manually annotated dataset and codebase, and deploy the system via a public web interface.

E-commerce livestreams have emerged as an important channel for presenting products to online consumers, often featuring multiple products with relevant information distributed across different moments. This poses significant challenges for downstream product understanding applications, such as product-centric livestream clipping, where models need to identify the product and its relevant segments for information gathering. However, existing benchmarks for general product understanding typically evaluate product retrieval and temporal localization in isolation, leaving the critical correspondence between product identity and temporal evidence largely unassessed. To address this limitation, we introduce GPUB, a large-scale benchmark comprising 3,000 real-world e-commerce livestream instances with quality-controlled multi-moment temporal annotations and a catalog of over 31K fashion products. GPUB supports three evaluation tasks: given a livestream video and a candidate product set, the main task Grounded Product Understanding (GPrU) requires jointly identifying the product being presented and localizing its supporting moments; Product Retrieval and Product Moment Localization serve as two complementary subtasks. Evaluation of existing multimodal models shows that GPrU remains highly challenging, with the best-performing off-the-shelf baseline achieving only 10.13% Pair mAP@.3. To narrow the performance gap, we further develop UniPro, a unified product understanding model that derives product-aligned and temporally structured representations from shared multimodal encoding, improving Pair mAP@.3 to 24.58% while achieving 38.81% Joint R@1@.3 on GPrU.

Micro- and nano-plastic particles (MPs/NPs) are ubiquitous environmental contaminants whose increasing abundance and potential health impacts have created an urgent need for rapid, label-free detection methods. As particle size decreases to the low-micrometer range, conventional optical and spectroscopic techniques become increasingly challenging because of limited throughput and/or complex sample preparation. In this work, we present a machine learning (ML)-assisted radio-frequency (RF) dielectric spectroscopic cytometry (DiSC) platform for the label-free detection and classification of MPs. Eight types of $ 10 $ {\mu}m nominal-diameter MP particles suspended in deionized (DI) water were characterized at four frequencies spanning $ 0.2\text{-}9\text{ GHz} $. The measured alterations in RF scattering parameters (S-parameters), referenced to the carrier medium, were used to train supervised ML models for material classification, including the identification of MPs in mixed samples and saline-water environments. For eight MP classes suspended in DI water, the proposed method achieved macro-average F1-score, precision, and recall values exceeding $ 0.71 $. Furthermore, PET classification performance was largely maintained in saline carrier media containing $3.3\% $ and $ 6.6\% $ sea salt. These results demonstrate the feasibility of ML-assisted RF DiSC for rapid, single-particle MP classification in aqueous environments. Future work will focus on improving classification performance through enhanced RF calibration, increased spectral coverage, larger training datasets, and validation using environmentally aged and biologically contaminated microplastics.

Thioacetaldehyde (CH3CHS), recently detected in TMC-1, has an abundance approximately 36 times lower than its oxygen analog, acetaldehyde (CH3CHO). This makes the CH3CHS/CH3CHO pair the one with the largest column density difference among the detected oxygen/sulfur analogue pairs in this cloud. We investigate the hydrogenation pathways of CH3CHS to address two chemical dichotomies in the ISM: (i) the differenciation between CH3CHS and CH3CHO, and (ii) the apparent absence of both CH3CHS in the G+0.693-0.027 molecular cloud and ethyl mercaptan (CH3CH2SH), in TMC-1. Our results reveal a complex scheme that involves multiple competing reactions, highlighting an efficient sequence of consecutive hydrogenations that can lead to CH3CH2SH. This finding suggests that the high S/O ratio observed for thioacetaldehyde in TMC-1 (~36), and even more pronounced in G+0.693-0.027 ($\geq$112), may result from its conversion via hydrogenation on the ice surface, contrary to the case of CH3CHO, which is more resistant to that chemical process. The straightforward hydrogenation of CH3CHS on ices, which can also take place even in the gas-phase at 150 K, provides a reliable explanation for its non-detection in G+0.693-0.027, where grain-surface chemistry is expected to play an important role, favoring the conversion of CH3CHS into CH3CH2SH, which is indeed detected in G+0.693-0.027. In contrast, TMC-1 represents a more pristine gas-phase environment, where grain-surface chemistry has a lower impact. Under these conditions, CH3CHS can persist, while CH3CH2SH remains undetected. Overall, our results show the entirely different reactivity that contributes to the chemical complexity of two of the largest interstellar sulfur factories.

One conjectures that all integers greater than 14 are the sum of an odd prime and two positive squares. We prove that all integers $n$ with $14<n<10^{26}$ can be represented in this manner. Along the way, we investigate sums of a prime and one square and then “bootstrap” to get our results on sums of a prime and two squares. We also show that all integers between $308$ and $10^{16}$ can be represented as the sum of an odd prime and two positive cubes. Our methods require the determination of the integral points on various elliptic curves.

FarmerChat is Digital Green's AI-powered agricultural advisory assistant for smallholder farmers, who access it in their own language through text, voice, or photographs. Voice is a critical channel for this population, yet field-recorded speech is challenging for general-purpose automatic speech recognition (ASR) because recordings frequently contain machinery noise, background media, competing speakers, and domain-specific agricultural vocabulary. These conditions disproportionately affect crop, pest, chemical, and quantity terms that carry the meaning of a farmer's query. We present a modular, model-agnostic pipeline for improving ASR quality in FarmerChat without fine-tuning or replacing the underlying ASR model. The pipeline combines gated audio enhancement, speaker diarization and target-speaker selection, ASR, domain-aware correction using a weighted agricultural lexicon, and a quality gate for detecting unreliable transcripts. Only the diarization stage is fine-tuned; all other stages use off-the-shelf models behind common interfaces. We evaluate the pipeline on human-annotated FarmerChat recordings in Hindi, Telugu, and Odia using word error rate (WER) and a domain-weighted error rate that gives greater importance to agricultural terminology. The largest improvements occur on multi-speaker recordings, where target-speaker selection prevents competing speech from entering the transcript. Across the full corpus, the pipeline reduces WER by 16-23% relative on three cloud ASR models and by 5% on an on-device model. On multi-speaker recordings, the reductions are 32-42% for the cloud models and 16% for the on-device model. All reported reductions are statistically significant. These results show that targeted preprocessing, speaker selection, and domain-aware post-processing can substantially improve agricultural speech transcription while preserving the underlying ASR model.

Understanding how collective ion transport emerges from equilibrium fluctuations is central to electrolyte statistical mechanics. Finite-volume fluctuations provide an accessible route to this information, but their interpretation is complicated because they mix wave numbers and collective fields. Here, we extend the finite-volume counting framework for inferring collective ion diffusion by combining the exact window projection with an inertial independent-particle reference, and apply it to a symmetric 1:1 solvent primitive model. The growth of ion-number fluctuations between the ballistic and plateau regimes appears nearly ideal, but this apparent ideality results from compensation between negative structural and positive dynamical excess contributions. The coupled ion-number–solvent relaxation further reveals a signed redistribution between solvent-associated and solvent-orthogonal projections that is largely hidden in the total response. The inferred collective diffusion depends on observation length and dynamical closure: measured structure alone does not systematically improve the estimate, whereas the coupled-field description reduces the high-concentration discrepancy. These results provide a basis for analyzing more realistic electrolytes with mutually coupled ion-number, charge, and solvent fluctuations.

Gauge theoretic descriptions of 2D quantum magnets are defined on a restricted physical Hilbert space by imposing Gauss's law. In this work, we study an unconstrained compact lattice QED$_{2+1}$ coupled to bond phonons, in which local Gauss operators are conserved, but their eigenvalues are not a priori fixed. Using exact auxiliary-field quantum Monte Carlo simulations at $N_f = 2$, we investigate how the physical Gauss sector becomes energetically favourable, and how this process is connected to confinement and symmetry breaking. We identify an orthogonal semimetallic (OSM) phase, in which fermions striped off their gauge charge and form a Dirac liquid. This phase mixes various Gauss sectors, and becomes unstable when Gauss's law is explicitly enforced. Upon the imposition of Gauss's law, compactness allows for monopole excitations carrying antiferromagnetic (AFM) and valence-bond-solid (VBS) quantum numbers. Gauge field fluctuations and spinon-phonon coupling tune between the competition of such monopoles and generate a phase diagram with OSM, AFM and VBS orders. The transitions out of the OSM phase coincide with the dynamical generation of Gauss's law, while the competition between AFM and VBS charged monopoles produces a transition consistent with deconfined quantum criticality. Thus our results establish that upon the projection to the physical Hilbert space, deconfinement in compact lattice QED$_{2+1}$ is always unstable towards either AFM or VBS order.

Federated learning trains a shared model from private client data. In practice, data-generating distributions may differ, and the true mixture across clients is often unknown, making the underlying group distribution difficult to specify. Existing approaches address cross-client mixture uncertainty by optimizing against the worst-case mixture, yet assume accurate client-wise distribution estimates. However, these estimates can be unreliable when based on finite samples. To handle both cross-client mixture uncertainty and within-client distributional ambiguity, we construct a global ambiguity set as the union of admissible mixtures of local ambiguity sets. The construction allows client-specific ambiguity radii and admits a client-wise separable reformulation. Leveraging this structure, we establish a high-probability out-of-sample performance guarantee. We further develop a federated algorithm for a penalty-based reformulation and prove its convergence under milder regularity conditions. Simulations validate the algorithm's effectiveness.

We review recent advances in particle physics enabled and motivated by the rapid progress of quantum technologies. The continued development of quantum computing toward large-scale, fault-tolerant systems has the potential to address dynamical problems that remain extremely challenging for classical computational approaches, opening new avenues for studying nonperturbative dynamical processes. Tabletop detectors and quantum-enhanced technologies have reached unprecedented sensitivities, enabling novel searches for ultralight particles, gravitational waves, and other physics beyond the Standard Model in parameter regimes previously inaccessible to conventional instrumentation. Taken together, these developments highlight a rapidly evolving landscape in which quantum technologies are beginning to reshape fundamental physics. We aim to synthesize recent progress and illuminate the opportunities they present for advancing particle physics in the coming years.

The paper presents a numerical approach for the end-effector trajectory smoothing of a parallel robot designed for minimally invasive pancreatic surgery. The approach is tailored for real-time master-slave control architecture and uses a 3D space mouse for command input for velocity control. The trajectory smoothing is achieved by generating S-curves in the end-effector velocity fields, thus controlling the accelerations, which in turn reduces tissue trauma in the minimally invasive procedures. Real-time control is enabled by segmenting the S-curves based on the command inputs from the 3D space mouse. A special case is considered where the acceleration time is constant for all command inputs. Numeric results demonstrate stable transitions (without abrupt changes) in both the end-effector parameter space and in the active joints parameters, thereby validating the proposed approach. Further work aims to test the approach on an experimental model and integrate it into AI-based training modules.