Papers

Parametric interactions are foundational to superconducting quantum technologies, yet conventional microwave-driven pumping introduces parasitic Kerr nonlinearities and higher-order harmonics that limit device performance. Josephson Photonics (JP) avoids these parasitics by utilizing dc-biased junctions but has remained constrained by high phase noise and the absence of a stable phase reference. Here, we overcome this limitation by integrating a Josephson voltage standard (JVS) to establish a noise-tolerant phase reference, and demonstrate that this reference is coherently transferred to an inelastic Cooper-pair tunneling amplifier (ICTA) via the superconducting order parameter. The resulting low-phase-noise architecture yields a 14-dB enhancement in averaged gain and better quantum-limited noise performance. Critically, the phase reference enables the first observation of phase-sensitive gain and squeezing in a dc-biased amplifier. By reconciling clean, Kerr-free nonlinearities with phase-coherent drive, our architecture establishes a robust platform for high-purity parametric processes in superconducting circuits.

Content Management Systems (CMS), such as WordPress, power a large share of the web (~58%), and their extensibility through third-party plugins is a major source of their popularity as well as of their attack surface. One high-impact weakness that remains understudied is log file exposure by CMS plugins, which create log files for debugging or other purposes. If these files are insufficiently secured, they can disclose sensitive information (e.g. credentials, personal data) which has led to website compromises in the past. In this work, we present an agentic, LLM-based framework that automatically detects potential log file exposures in plugins of the most popular CMS (WordPress). Our agent analyzes each plugin by performing static and dynamic analysis. We evaluated our approach on the 300 most-installed WordPress plugins (about 0.6% of all), which together account for over 250M active installations, i.e. 75% of all active installations in the official plugin ecosystem. We manually validated each finding, reproducing 79 of 81 findings from 62 plugins. We observed that several protective measures appear to be implemented that we classify as creation-control (e.g. manual log activation) and access-control (e.g. deny rules in .htaccess). However, we find that multi-layered protection is required, but not always present. From these results we derive a taxonomy of log file path and protection patterns and deduce a set of best practices for developers to securely handle them. Finally, our study corroborates that agentic LLMs are an useful tool for security analysis.

Precise determination of the partonic structure of real photons has attracted renewed interest in view of ongoing studies of high-energy photon-induced processes in ultraperipheral collisions (UPCs) at the Large Hadron Collider (LHC) and the future Electron-Ion Collider (EIC). Despite being fundamental in their own right and essential for QCD phenomenology of hard processes initiated by resolved photons, the quark and gluon distributions of the photon are poorly known and merit a new analysis employing modern tools of statistical data analysis. We determine new sets of leading-order (LO) and next-to-leading-order (NLO) parton distributions (PDFs) for the real photon, dubbed VALO1.0, by performing a global QCD analysis of the world data on the photon structure function $F_2^{\gamma}$ measured in deep-inelastic scattering (DIS) processes on a real photon target in electron-positron collisions. Our analysis improves on the results available in the literature by providing uncertainties in the form of Monte Carlo replicas and the photon PDFs in the LHAPDF6 format. We observe that while the electron-positron data allow us to determine the singlet quark distribution very well at both LO and NLO, the gluon distribution is constrained to a much lesser degree, especially at LO. For this analysis, we have developed an open-source framework, which extends the pineline framework, developed for the proton, to the photon case and includes the program solving the inhomogeneous scale evolution of photon PDFs, $\gamma$EKO.

Alfvén waves and their nonlinear interactions are ubiquitous in space and astrophysical plasmas, and are thought to play important roles in the dynamics of these systems, yet their nature remains to be fully understood. We describe experiments performed on the Large Plasma Device to study the nature of counter- and co-propagating wave interactions relevant to strong Alfvénic turbulence. Both interactions were found to produce a broad spectrum of nonlinear modes as a result of a dominant quadratic nonlinearity. The counter-propagating interaction can be explained through the standard reduced MHD nonlinearity, and the co-propagating interaction can be explained through a recently-proposed model that includes second-order nonlinear terms from Hall MHD that dominate at large imbalance and scale with the ion inertial length. The predictions of the latter model were tested in both the experiment and in 3D hybrid simulations, where the nonlinear mode growth rate and ion inertial scale dependence were found to be consistent. Finally, at the obtained interaction strengths, energy was seen to be transferred to progressively smaller perpendicular scales, consistent with a local cascade, although not a state of fully-developed turbulence. These results reveal and verify the mechanisms occurring in balanced and imbalanced turbulence (as well as other Alfvénic nonlinear processes), and represent an important step towards the generation of controlled Alfvénic turbulence in the laboratory.

We present a supersymmetric extension of the Hull-Lambert-Sen chiral boson model. The two-metric formulation developed by Hull provides a powerful and tractable framework for the quantization of chiral bosons, and we demonstrate that it admits a natural supersymmetric generalization. We construct the theory explicitly on the two-torus and analyze its coupling to external sources.

Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysis and design. However, constructing accurate surrogates for realistic aircraft configurations remain challenging due to complex geometries, multiple flow regimes, and limited training data. This work presents the methodology that achieved first place in the ONERA CRM Wall Distribution Regression Challenge, which focuses on predicting pressure and skin-friction coefficient distributions over the NASA Common Research Model wing-body-pylon-nacelle configuration under different operating conditions. The proposed approach formulates the problem as a conditional neural field mapping spatial coordinates, surface normals, and operating conditions to aerodynamic wall quantities. Fourier feature encoding, a relative squared error objective aligned with the challenge metric, ensemble learning, and $k$-fold cross-validation are progressively introduced to improve prediction accuracy and exploit the limited training data. Beyond presenting the final methodology, the paper documents the successive model design choices that led to the winning solution through a comprehensive ablation study and discusses several alternative approaches that were investigated but ultimately discarded. On the hidden competition test set, the proposed methodology achieves an overall score of 8.81, outperforming the strongest organizer-provided baseline, which achieved a score of 8.64, while requiring approximately three orders of magnitude fewer trainable parameters. These results illustrate that carefully designed coordinate-based neural fields constitute an efficient and robust framework for aerodynamic surrogate modeling on complex geometries under limited-data conditions.

The chemical compositions of planets and their hosts stars are intrinsically linked, having formed from the same protostellar material. Characterising this relationship provides key constraints on the processes governing planetary formation and evolution. Focusing on host stars with near-solar chemical abundances limits our understanding of how planetary composition varies across a broader chemical parameter space. Expanding the sample to include stars with compositions markedly different from the Sun is therefore essential for building a complete picture of star–planet compositional connections. Here, we focus specifically on iron-poor hosts since they are more likely to be alpha-enhanced and represent some of the most chemically distinct stars relative to the Sun (i.e., thick disc stars). We present a sample of 45 stars hosting 64 planets across the super-Earth and sub-Neptune regimes, for which we homogeneously obtain new stellar parameters including abundances, re-derive planetary mass and radius, and model the bulk interior compositions of their planetary companions. No statistically significant evidence for a correlation between stellar and planetary composition was found in our sample. We suggest that this null result is primarily driven by the large uncertainties inherent to both compositional proxies, which may obscure an underlying relationship. Quantifying these uncertainties is therefore a critical step that previous studies have not fully addressed. Furthermore, even with improved precision, uncovering such a relation may require a higher-dimensional treatment that accounts for additional parameters such as planetary equilibrium temperature.

We investigate Empirical Bayes (EB) methods in the context of compound adaptive experiments, where the arm distribution in each experiment follows a normal distribution with an unknown mean that we seek to estimate. There are two main EB strategies: $g$-modeling, which estimates the prior by maximizing the marginal likelihood, and $f$-modeling, which derives posterior means directly from the empirical distribution of the observations. We show that $g$-modeling continues to be a valid EB procedure even when it incorrectly assumes that data are collected exogenously; its validity does not depend on the particular sampling algorithm or on whether sample sizes are endogenous. In practice, one can apply standard $g$-modeling techniques by acting as though the data were exogenously sampled. We extend regret guarantees from exogenous sampling to adaptively generated data. By contrast, naively applying the Tweedie formula based on the marginal density of the observed data, as in standard $f$-modeling, can produce biased rules under adaptive sampling. We corroborate the robustness of $g$-modeling through simulations with widely used adaptive algorithms and demonstrate its applicability using a real-world dataset consisting of multiple sequential experiments.

Paleo-detectors provide a unique avenue to reconstruct the multi-million-year history of cosmic-ray (CR) flux, preserving signatures of transient high-energy events such as nearby supernovae. This technique aims to use natural minerals as particle detectors, looking at the persistent damage tracks created by CR-induced nuclear recoils, accumulated over the minerals' geological lifespan, offering a geological archive of past particle fluxes. Building on our study of Messinian Salinity Crisis evaporites, which demonstrated that minerals with specific geological histories may enable the detection of primary CR flux variations, we have now expanded to diverse terrestrial records. This contribution presents our recent publication proposing olivine xenoliths from Auvergne, France, where eruption chronosequences could allow for the differentiation of CR flux scenarios over the last 50 kyr. This phenomenological work is supported by the INFN-funded PRImuS experiment, which aims to prove the efficacy of high-throughput optical microscopy and plasma etching to analyze these mineral targets. By validating theoretical track-length spectra and refining the estimates of experimental effects, PRImuS's goal is to establish paleo-detectors as a powerful tool for very-long-range time-domain astrophysics.

Laboratory simulations of meteor ablation provide a critical quantitative link between the chemical composition of meteoroids and their observed spectral features. In this work, we analyzed high-resolution Echelle spectra (wavelength range 380-780 nm) of 22 diverse meteorites from the dataset presented in our previous work (Matlovič et al., 2024), representing the largest collection of laboratory meteor analogs to date. Using a radiative transfer model assuming local thermodynamic equilibrium (LTE) and accounting for self-absorption in optically thick plasma, we derived plasma parameters and elemental abundances for both major (Fe, Mg, Cr, Mn, Si, Na, Ni, Li, and K) and minor (Co, Cu, and V) species. Comparison with known bulk meteorite compositions allowed us to validate the modeling approach and assess chemical biases resulting from laboratory-induced ablation. Our analysis suggested plasma temperatures between 5220 and 5810 K and revealed systematic discrepancies in the elemental abundances compared to the original chemical composition. Specifically, we observed a significant enhancement of volatile species (Na, K) relative to Fe, accompanied by a depletion of the moderately volatile element Mg, while refractory elements (Al, Ca, Ti) remained undetected in the plasma radiation. These trends are consistent with the equilibrium vaporization model and demonstrate that under the simulated entry conditions ($\sim$12 km/s at $\sim$80 km altitude), the ablation process is dominated by incomplete and fractional vaporization. We conclude that while laboratory spectra of plasma from ablated meteorites do not fully reflect the original bulk composition, radiative transfer modeling effectively characterizes the state of the radiating plasma, offering a more robust approach for interpreting compositional properties from meteor observations.

The Proton Improvement Plan-II (PIP-II) project is under construction to provide the Fermilab Accelerator Complex with a new H$^-$ superconducting radiofrequency (SRF) linac and beam transfer line delivering 800 MeV protons at Booster injection at double energy and double intensity (6.7x10$^{12}$ protons per 20 Hz pulse) in comparison with the present Linac. The design goals of PIP-II Linac will be described, including delivering 1.2 kW beam power on Long Baseline Neutrino Facility (LBNF) target, continuous wave (CW) operation compatibility and future upgrades. The progress of the Linac construction and the development of the Commissioning Plan will be presented. Finally, the challenges of operating the SRF Linac to drive the Fermilab Booster will be addressed.

Spectral Turán-type problems ask how the absence of prescribed subgraphs constrains the spectral radius of a matrix associated with a graph. Given a family of graphs $\mathcal{F}$, a graph is called $\mathcal{F}$-free if it contains no member of $\mathcal{F}$ as a subgraph. The theta graph $\theta(l_1,\ldots,l_k)$ consists of $k$ internally disjoint paths of lengths $l_1,\ldots,l_k$ with two common end vertices. In this paper, we study two spectral Turán-type extremal problems for the signless Laplacian spectral radius. First, among all $\{C_3,C_4\}$-free graphs of fixed order with no pendant vertices, we determine the maximum signless Laplacian spectral radius and uniquely characterize the extremal graph attaining it. The extremal structure exhibits a parity phenomenon: odd and even orders give rise to two distinct graph families. These results, in particular, sharpen a recent general upper bound for this class given by Liu and Wang (2026). Next, we obtain the corresponding extremal results for all $\{\theta(1,2,2),\theta(1,2,3)\}$-free graphs of fixed size with no pendant vertices when the size is congruent to $1$ modulo $3$ and $2$ modulo $3$, again obtaining unique but structurally different maximizing graphs in the two cases. Together with the previously known result for sizes congruent to $0$ modulo $3$ by Liu and Wang (2026), this completes the fixed-size problem across all three congruence classes modulo $3$.

We introduce d-minimal and b-minimal extensions, two weakenings of minimality based respectively on eventual domination and infinitely often domination. We prove that the generic extensions obtained by the full Mathias forcing and by Mathias forcing relative to Ramsey ultrafilters are d-minimal, whereas Hechler extensions are b-minimal. We also construct a d-minimal extension that is weakly $\omega^\omega$-bounding but neither minimal nor $\omega^\omega$-bounding, and realize every constellation of these properties compatible with their natural implications.

Vision Transformers (ViTs) are central to most modern vision models, yet obtaining input attributions that are fine-grained, faithful, and stable remains challenging. Layer-wise Relevance Propagation (LRP) has been adapted to transformer attention, but in ViTs it often produces noisy, unfaithful explanations. We show that the missing ingredient is the treatment of residual connections: cancellation effects in residual pathways lead to attribution explosion. Moreover, we find that these cancellations are substantially stronger in ViTs than in language transformers. To address this issue, we introduce Residual-aware Layer-wise Relevance Propagation (ResLRP), a simple extension of LRP whose propagation rules explicitly account for cancellations in residual branches, are exactly conservative, and provably bound relevance explosion. Causal channel-wise interventions confirm that residual cancellation, not a generic regularization effect, drives the instability. ResLRP substantially improves attribution quality across faithfulness and localization, evaluated on ViT architectures spanning supervised, self-supervised, contrastive, hierarchical, and multimodal families, as well as on the ground-truth-controlled FunnyBirds benchmark. The largest gains arise in modern Vision Language Models (VLMs), with +27-29% localization and up to 3.4x faithfulness scores. Beyond benchmarks, ResLRP localizes Sparse Autoencoder (SAE) features in input space, and our residual amplification measure serves as an architecture-level diagnostic predicting where attribution degrades.

Over the last twenty years, particle-in-cell simulations with Monte Carlo collisions (PIC-MCC) have given the low-temperature plasma community much of what it knows about electron heating in RF discharges, sheaths and secondary emission, striations, and the instabilities of magnetised plasmas. But these results remain in papers, and in codes that only their authors can run. JC-PIC is a free Windows program: a one-dimensional, three-velocity (1D3V) electrostatic PIC-MCC code with a parallel Fortran engine (OpenMP) and a complete graphical interface. It is built around a library of about one hundred ready-to-run cases, each documented, referenced and explained. About half of them reproduce a published result under the original conditions; the others compare the code with a classical analytical result. This overview presents the program, its companion book, and six of the cases from the physics point of view: Langmuir waves from Landau damping to electron trapping, the heating-mode transition in argon RF discharges, the electrical asymmetry effect, the Franck-Hertz experiment treated as a swarm, the striations of a positive column, and the ExB drift instability of Hall thrusters.

We present a claim-relative evidence/reference framework for hybrid quantum-classical workflow integrity. Observational indistinguishability yields structural blind regions, distinct from finite-batch statistical misses. Within the declared lattice, a trusted same-batch scalar $R_0$ suffices for conclusion integrity, aggregate $M_0$ for aggregate plus conclusion integrity, and item-aligned binding for item identity. In 3,600 label interventions, feature/prediction views realize exact label-path invariance; all 764 geometry-aligned aggregate-blind rows equal their paired-clean responses, giving zero attack-only increment. For statistical response, the geometry-aligned construction detects 343/2,700 conclusion-changing ($\tau \to 0^+$) label interventions with the conformal rule and 1,183/2,700 with the uncorrected union; the original frozen same-item geometry yields 11/2,617 and 43/2,617, respectively. The executed conformal clean false-action rates are 0.048–0.059 descriptively; its finite-sample guarantee requires exchangeability, which the overlapping-draw design violates. The cluster-preserving adaptive stress test (Gate A) reduces response versus matched controls in 25–40 of 40 environment/split cells while retaining conclusion changes. A bounded 165-design-cell ideal-statevector and finite-shot-emulation branch directly instantiates semantic, estimated and observed kernel transitions. The fixed equal-weight design estimates neither deployment prevalence nor QPU, provider or deployed-service assurance.

In this paper, we study local and global properties of positive solutions to the equation $-\Delta u=u^p|\nabla u|^q$ in a domain $\Omega$ of $\mathbb R^N$, where $p$ and $q$ are parameters. We introduce a linear operator to construct the differential inequality to obtain gradient estimates, and further establish Liouville-type theorems. As an application, we derive universal estimates for local solutions. Some of our results are new, as we extend the condition $p+q<(N+3)/(N-1)$ considered by He, Hu and Wang [Math. Z. 313 (2026), No. 6] to a wider range of parameters.

We construct relative Du Bois and relative intersection Du Bois complexes for smooth-factorizable morphisms to a smooth complex base using relative de Rham complexes of mixed Hodge modules and Grothendieck duality. For a smooth morphism, these complexes recover the relative Kähler differentials. Comparisons with the relative Du Bois complexes of Kovács and Ning remain open. We construct finite filtrations on the absolute Du Bois and intersection Du Bois complexes whose graded pieces are the corresponding relative complexes tensored with differential forms from the base. We also study restriction to fibers and its relation to symbolic $m$-Du Bois and weak $m$-rational singularities.

Autonomous racing confronts significant challenges in safely overtaking Opponent Vehicles (OVs) that exhibit uncertain trajectories, stemming from unknown driving policies. To address these challenges, this study proposes heterogeneous kernel metrics for Deep Kernel Learning (DKL), designed to robustly capture the diverse driving policies of OVs, and carry out precise trajectory predictions along with the associated uncertainties. A key virtue of the proposed kernel metrics lies in their ability to align similar driving policies and disjoin dissimilar ones in an unsupervised manner, given the observed interactions between the Ego Vehicle (EV) and OVs. The efficacy of the proposed method is substantiated through experimental studies on a 1/10th scale racecar platform, demonstrating improved prediction accuracy and thereby safely overtaking against OVs. Furthermore, our method is computationally efficient for onboard computing units, affirming its viability in fast-paced racing environments. The video and source code can be found at https://github.com/HMCL-UNIST/OpponentPredictionWithKMDKL.git.

We study an optimal intervention problem for linear threshold models. This is a popular class of dynamical network systems whereby a number of agents, identified with the nodes of a graph, strategically change their binary action (0 or 1) according to a threshold rule. Specifically, an agent adopts action 1 if and only if the fraction of its neighbors in the interaction graph that do so is greater than or equal to a prescribed threshold. Assuming that a planner can modify the agents' thresholds at a cost equal to the aggregate threshold increase, we study the minimum intervention cost needed to ensure global convergence to the all-1 configuration. Our main contribution is the introduction of a new graph-theoretic quantity, called oriented path number, that is the minimum number of disjoint paths needed to cover the graph that can be oriented to form a directed acyclic graph. When thresholds are all equal to 1/2, the optimal cost is shown to coincide with the oriented path number, whereas, in the general case, it turns out to be the main ingredient of a bound on the optimal intervention cost.

In this paper, we study 3D LiDAR scan alignment in challenging scenarios with degeneracies, such as straight corridors or flat fields, where the alignment solution is not unique and compromises localization and mapping accuracy. Existing degeneracy detection methods that neglect the potential for reassociating data points are prone to being sensitive to noise and complex degeneracies. Therefore, we propose LiLi - a novel method that leverages Lie theory to identify the full set of degenerate transformations within the SE(3) Lie group of rigid transformations. The method employs perturbations of the optimized solution and compares the resulting optimized poses to ensure robust detection of degeneracies. By leveraging generators from the Lie algebra se(3), the method provides a systematic approach to describing the set of degenerate transformations. Quantitative evaluations on synthetic data show significant improvement over the state-of-the-art Hessian-based method, reducing alignment error by 50%, with more significant improvements for datasets featuring noise. In the real-world degenerate datasets, the proposed method integrated into LiDAR-based odometry yields superior localization performance compared to the reference solution based on the Hessian-based degeneracy detector on a 260 m long trajectory, and succeeds on a 430 m long round-trip tunnel trajectory where the reference fails.

Let $\mathcal{S}^ r$ denote the Schatten–von Neumann class and let $S_{\Psi_{f,\lambda}}$ be the Schur–Hadamard multiplier whose symbol is the divided-difference matrix of $f$ along $\lambda$. Let $0<\alpha,r<\infty$, let $f\in C^1([-1,1])$ satisfy $f(0)=0$, $|f'(t)|\lesssim |t|^\alpha$, and let $\lambda\in\ell^r$ be real with $\|\lambda\|_{\ell^\infty}\leq1$. We determine the pairs $0<p,q\leq\infty$ for which $S_{\Psi_{f,\lambda}}:\mathcal{S}^ q\to\mathcal{S}^ p$ is bounded for every such $f$ and $\lambda$. Our principal new positive estimates treat $q=\infty,1$ and $0<p<1$. Precisely, we show that the boundedness holds exactly when \[ \frac1p\leq\frac{\alpha}{r} +\min\!\left\{1,\frac1q\right\}. \] In particular, this resolves the untreated cases in [Arazy, PAMS, 1982] and [Potapov, Sukochev, Tomskova, Adv. Math., 2015]. Our method also delivers a new proof of the main results in just cited papers.

We develop a theory of Orlicz and Lorentz–Zygmund sequence spaces. We study in detail elementary properties of both structures. In particular, we characterize the values of governing parameters for which the corresponding spaces satisfy the axioms of rearrangement-invariant Banach sequence spaces, we evaluate the asymptotic behavior of their fundamental functions, and we characterize their associate spaces. In our main result, we characterize all cases in which a Lorentz–Zygmund sequence space coincides with some Orlicz sequence space.

We establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into a projective variety and a family of hypersurfaces in subgeneral position. The above bound of the total defect obtained from our result is better than that of the previous results. Moreover, in our result, the truncation level of the counting functions is estimated explicitly and independently of the number of hypersurfaces. Especially, we do not need the assumption that the family of hypersurfaces must satisfy the Bezout properties as imposed in some earlier studies, but only a weak Bezout property.

Traversability prediction is a critical component of autonomous navigation in unstructured environments, where complex and uncertain robot-terrain interactions pose significant challenges such as traction loss and dynamic instability. Despite recent progress in learning-based traversability prediction, these methods often fail to adapt to novel terrains. Even when adaptation is achieved, retaining experience from previously trained environments remains a challenge, a problem known as catastrophic forgetting. To address this challenge, we propose a continual learning framework for traversability prediction that incrementally adapts to new terrains using a generative experience recall model. A key virtue of the proposed framework is two folds: i) retain prior experience without storing past data; and ii) incorporate the uncertainty of the generated samples from the recall model, enabling uncertainty-aware adaptation. Real-world experiments with a skid-steering robot validate the effectiveness of the proposed framework, demonstrating its ability to adapt across a series of diverse environments while mitigating catastrophic forgetting.

Whereas the effect of monotonically decaying memory kernels on reaction dynamics has been studied extensively, the effect of oscillatory memory, observed for widely different systems, is much less explored. We analyze non-Markovian barrier-crossing dynamics in the presence of a single exponentially decaying oscillatory friction memory kernel by simulations and analytical theory. We identify three scaling regimes: two in which the mean first-passage time $\tau_{\mathrm{MFP}}$ scales quartically and linearly with the memory kernel decay time $\tau_{\mathrm{o}}$, respectively, and a third in which $\tau_{\mathrm{MFP}}$ scales quartically with the oscillation period $\tau_\varphi$ of the memory kernel. Our results are relevant to a broad class of many-body dynamical systems such as dihedral isomerization processes and chemical reactions in solvents.

Chen and Ngo showed that the Hitchin morphism for Higgs bundles on a projective manifold $X$ factors through a closed subscheme of the Hitchin base called the spectral base, and the induced map is called the spectral morphism. In this paper, we investigate local Cohen-Macaulay obstructions to the surjectivity of spectral morphisms via a refined spectral correspondence. We show that every affine normal variety with a local ring that admits no rank one maximal Cohen-Macaulay modules can be geometrically realized as a local obstruction to the surjectivity of spectral morphisms, and that these local obstructions can be compactified via the Kawamata covering trick. As an application of these constructions, we provide counterexamples to the Chen-Ngo conjecture on the surjectivity of spectral morphisms for $GL_r$-Higgs bundles in dimensions $n\geq 9$. Moreover, we construct counterexamples to the Chen-Ngo conjecture for $SL_2$-Higgs bundles in every dimension $n\geq 2$ and for semistable $GL_3$-Higgs bundles on a smooth projective surface.

Geospatial foundation models provide reusable representations of satellite imagery that support downstream mapping with limited task-specific modelling. We evaluate whether annual AlphaEarth embeddings support binary cultivated-versus-non-cultivated mapping in Maine, USA, using 192 spatially separated patches and labels derived from the USDA Cropland Data Layer (CDL). Without fine-tuning the foundation model, a lightweight classifier reaches 93.7% overall accuracy and 90.8% balanced accuracy on held-out patches. Logistic regression is within 0.3 percentage points of a gradient-boosted ensemble, while a nearest-class-centroid rule, which uses class centroids but fits no parameters, reaches 90.2%. A balanced sample of 60,000 labelled pixels is within 1.3 percentage points of the full pool of 8.6 million pixels; because pixels are spatially autocorrelated, this result concerns pixel-sample efficiency rather than 60,000 independent annotation sites. In a same-region transfer experiment, classifiers trained in one year remain accurate across 2018 to 2023. Against a blind, two-interpreter consensus at 385 randomly sampled points in one contiguous 2023 block, the AlphaEarth-plus-random-forest map agrees at 95.3% ($\kappa=0.82$), compared with 91.7% for the CDL ($\kappa=0.72$; exact two-sided McNemar $p=0.0161$). This local result is consistent with partial smoothing of CDL label noise, but it does not establish statewide correction of the reference product. On the same points, the difference from a fine-tuned TerraMind segmentation model is not statistically significant (95.3% versus 93.5%; $p=0.14$), and the experiment is not a controlled comparison of computational cost. These results support frozen geospatial embeddings as a low-compute candidate for regional cropland mapping, subject to the limits of a single-state study, a 30 m-derived training reference, and a one-block human validation.

We reconstruct a spatially varying material coefficient in a scalar elliptic equation from finitely many boundary excitations, each producing a full Dirichlet trace. To mitigate the ill-posedness and the cost of repeated PDE solves, we restrict the coefficient to a low-dimensional family, specified analytically or learned from samples, and solve the inverse problem in its latent coordinates. We consider a \(C^1\) parametrization with \(m\) latent coordinates and full-rank derivative at a reference point. If the continuous linearized Neumann-to-Dirichlet map is injective on the corresponding tangent space, at most \(m\) excitations suffice for local injectivity and Lipschitz stability. Convergence of the coefficient sensitivities then transfers this stability to conforming finite element discretizations. For sufficiently fine meshes, the stability constant and neighborhood can be chosen independently of the mesh size. Under a local residual-comparison condition, uniform accuracy of the surrogate forward map yields coefficient-error bounds separating representation error, data noise, finite element error, and surrogate error. Derivative accuracy additionally preserves the surrogate's own local stability. All stability statements are local to a reference coefficient. Two-dimensional numerical experiments combine analytic and learned representations of inclusions and crack-like coefficients with neural forward surrogates. They illustrate latent-space reconstruction, reduced online cost, and further improvement from optional FEM-based refinement.

In 1989, Dimitrić showed that any pseudo-umbilical biharmonic submanifold in a Euclidean space is minimal when the dimension of the submanifold is different from four. However, the four-dimensional case has remained open for nearly four decades. This difficulty comes from the fact that the tangential part of the biharmonic equation vanishes identically in dimension four. Therefore, we consider biminimal submanifolds, whose defining equation generalizes the normal part of the biharmonic equation. In this paper, we show that any connected pseudo-umbilical 0-biminimal submanifold of codimension two and dimension at least three in a Riemannian manifold of constant sectional curvature $c$ has constant mean curvature. Furthermore, when $c$ is non-positive, we prove that it is minimal. As a corollary, we show that any four-dimensional pseudo-umbilical biharmonic submanifold in a six-dimensional Riemannian manifold of non-positive constant sectional curvature is minimal. These results also provide partial affirmative answers to Chen's conjecture, generalized Chen's conjecture for non-positive constant sectional curvature, and the Balmuş-Montaldo-Oniciuc conjecture.