Papers

Multimodal Aspect-Based Sentiment Analysis (MABSA) infers fine-grained sentiment polarity toward specific aspects by jointly modeling text and images. Despite progress in cross-modal fusion, two challenges remain in multi-aspect settings: (1) multimodal noise, where aspect-irrelevant content distracts sentiment learning; and (2) weak cross-modal sentiment alignment, as visual evidence can be ambiguous and textual–visual sentiments may conflict, limiting multimodal complementarity. To address these issues, we propose a Gated Noise-filtered Sentiment-Relevance Interaction (GNSRI) framework. It employs a gated noise-filtering module to suppress sentiment-irrelevant features and enhance aspect-aware sentiment cues, and a sentiment-relevance interaction module to capture consistent and conflicting cross-modal signals at micro and macro levels. Finally, a learnable decision fusion mechanism adaptively combines predictions from textual, visual, and cross-modal branches at the aspect level. Experiments on public MABSA benchmarks show that GNSRI outperforms state-of-the-art methods, improving accuracy by 1.94% and 2.06% on Twitter-2015 and Twitter-2017, respectively.

Phase-field trajectories governed by the Allen–Cahn equation determine the effective force $G=F'/\eps^2$, but not the free-energy potential $F$ and interfacial scale $\eps$ separately. We introduce surface-tension-calibrated Allen–Cahn identification (STAC), a two-step method that resolves this ambiguity using an independently supplied surface tension. First, space–time weak moments produce a linear inverse problem without differentiating the measured field. A Bernstein representation with positive coefficients enforces two stable pure phases and a single central energy maximum. Second, the surface tension fixes the remaining scale algebraically. We prove scale equivalence of the forward model, uniqueness of the calibrated pair within this class, and finite perturbation bounds that remain valid when the potential vanishes at the pure phases. Experiments with resolved synthetic phase fields separate the effects of the structural constraint, ridge regularization, and constitutive approximation error. Across 80 shared noisy records, unconstrained degree-five regression produces six potentials with an incorrect well structure. Positivity combined with ridge regularization eliminates these violations and reduces the mean force error from 8.70% to 5.66%. Lower-degree models are nevertheless more accurate in some tests, and an admissible law outside the positive Bernstein family shows how the constraint can introduce approximation bias. STAC thus recovers a structurally admissible, physically scaled potential while making explicit which information comes from the observed dynamics and which comes from the independent surface-tension datum.

Motivated by the progress in the physics of two-dimensional materials and the recent two-dimensional generalization of the Fröhlich model, we study the formation of bipolarons in polar monolayers. Because of very special nonlocal dielectric screening in two dimensions, this setting differs qualitatively from the conventional Fröhlich model. In monolayers, (i) long wavelength LO phonons acquire a nontrivial dispersion; (ii) the Fröhlich electron-phonon vertex becomes momentum-dependent and regular at small momenta; and (iii) direct repulsion between charge carriers takes the Keldysh-Rytova form. Using the Feynman path-integral variational approach, we show that the region in the parameter space where stable bipolarons exist is strongly modified compared to the usual quasi-two-dimensional model with dispersionless phonons. Specifically, in the most favorable limit, when the ratio $\sigma_0$ of the static polarizability to the high-frequency polarizability tends to infinity, the lower critical coupling, sufficient for the formation of bipolarons, can be made arbitrarily small. More surprisingly, we demonstrate that no stable bipolarons can exist in the strong coupling limit: in the isolated monolayer the stability region is always confined to a finite range of coupling constants. In general, the stability region is strongly shifted toward large values of the polarizability ratio $\sigma_0$, well beyond the parameter regimes in representative crystals, which indicates that polar monolayers do not favor bipolarons.

Audio inpainting aims to restore missing segments in an audio waveform, as encountered in dropouts and packet losses. This paper revisits the autoregressive (AR) interpolation method proposed by Etter, which combines forward and backward AR prediction through a structured linear system, yet lacks a widely used full implementation for audio signals. We provide an open implementation and propose two practical extensions: A formulation that allows high-order AR models even when the gap length is shorter than the model order, and a causal variant tailored to packet loss concealment. The method is evaluated on musical excerpts with gaps up to 80 ms, using SNR and perceptually motivated objective difference grades, complemented by a listening test. The results show that Etter inpainting matches the performance of most AR- and sparsity-based baseline methods, with the exception of the iterative, gap-wise Janssen approach.

Understanding how particles such as microplastics and plankton spread, or accumulate in localized regions below the ocean surface is crucial both for the development of sea pollutant control strategies and for marine ecology. Yet the role of vertically inhomogeneous turbulence, due to the vertical structure of density stratification in the ocean, remains poorly understood. We study, by means of direct numerical simulations, the dynamics of weakly inertial, quasi-neutrally buoyant particles in an idealized two-layer fluid model aimed to represent the ocean convective mixed layer and the more stably stratified upper thermocline beneath. We find that particles eventually rise at the surface if their density matches the mean value of the fluid at a selected depth within the mixed layer. Interestingly, however, for all other values of density, they accumulate around their neutral-buoyancy depth within the thermocline, where stratification hinders vertical transport. Our analysis shows that the thickness of the accumulation layer results from the competition between buoyancy-driven confinement, internal-wave motions, and turbulent fluctuations penetrating from the mixed layer. Smaller particles, which respond more rapidly to flow fluctuations, form broader layers; layers also broaden as their equilibrium depth approaches the mixed layer. We then derive a reduced stochastic model that explains the dependence on particle inertia and reference depth of such spreading around the equilibrium position. These results show how the coupled action of stratification and decaying mixed-layer turbulence controls subsurface particle-layer formation, which may be relevant to ocean-biology oriented studies and to improve the sampling of plastic pollution in the sea.

Identifying isolated points is important in image processing applications such as medical imaging, astronomy and quality control management. Other domains, such as cybersecurity, also present challenges that can be framed as image processing problems. One example of particular interest is the identification of anomalous single nodes in spatially organised networks where groups of nodes in different regions share similar feature values. This task can involve both binary and more complex grayscale images. However, existing methods face limitations: template matching is infeasible for grayscale images, while 2nd order derivative based methods are highly sensitive to noise and require user-specified thresholds. To overcome these issues, a novel method is proposed for detecting meaningful single-pixel deviations in images. This approach modifies and extends a neuron model, originally designed for anomaly detection, to operate on spatially diameter limited receptive fields that incorporate excitatory and inhibitory regions. The result is a method that is free from user-specified thresholds and parameters, and can be applied to both binary and grayscale images, providing an effective, robust and efficient solution.

Altermagnetism is conventionally understood in a spin-conserving framework, where symmetry-enforced momentum-dependent spin splitting emerges in collinear magnets with vanishing net magnetization. Here, we show that its defining signatures persist in nanomagnet arrays coupled exclusively by dipolar interactions, despite the intrinsic breaking of spin conservation. Using a macrospin theory of dipolar-coupled ferromagnetic nanoislands, corroborated by micromagnetic simulations, we demonstrate that arrays engineered with altermagnetic symmetries exhibit spin-split magnon bands whose eigenstates can partially remain strongly spin polarized. The resulting spin expectation value displays the characteristic $d$-wave pattern throughout the Brillouin zone, establishing a mesoscopic realization of altermagnetic magnons beyond the conventional spin-conserving paradigm. As a consequence, spin-wave propagation becomes strongly direction dependent, providing a highly tunable platform for anisotropic magnon transport and synthetic altermagnetic functionality.

In this paper we study the genome rearrangements done by translocation events. Genome rearrangements were used to measure evolutionary distance between organisms since 1936 (Dobzhansky and Sturtevant). The chromosomes are represented as strings of DNA and the translocation operation is defined as the exchange of prefixes between two strings. This operation results in the creation of two new strings (chromosomes) that can then be utilized in subsequent translocations. A translocation is referred to as contiguous if the new strings are produced in a single copy, so each of them can be used in only one subsequent operation. When the words produced by a translocation operation are considered to have an infinite number of copies, the translocation is referred to as non-contiguous. If the exchanged prefixes are of equal length, the translocation is called uniform. Otherwise, the translocation is termed non-uniform. The translocation distance between two sets of strings, termed the input set and the target set, represents the minimum number of translocations necessary to obtain all the strings in the target set via translocation operations. We prove that both the non-uniform contiguous and the non-uniform non-contiguous translocation distance problems are NP-hard over arbitrary finite alphabets, where the alphabet is part of the input. For the case in which the target set consists of a single string, we give a fixed-parameter tractable algorithm parameterized by the length of the target string.

Virtual sensing, the estimation of hard-to-measure quantities from available sensor measurements, is a critical enabler for control and monitoring in cyber-physical systems. However, when sensors fail, learning-based predictors can produce physically implausible estimates that propagate to system-level failures. We argue that real-world deployment demands robustness and introduce MuViS-C, the first multi-domain benchmark of robustness against common sensor failures in learning-based virtual sensing. Building on an existing nominal-performance benchmark and established corruption taxonomies, it covers ten sensor failure modes, from subtle drifts to catastrophic signal dropouts, at multiple severities. These are paired with complementary robustness measures capturing average error under corruption, relative degradation, and worst-case fragility. Across nine datasets from six domains, we benchmark six architectures spanning gradient-boosted trees and the major inductive biases for sequence modeling: convolution, recurrence, attention, and MLP-mixing. On the attention-based architecture, we further probe three robustification strategies. We find that (i) every model degrades substantially under corruption, becoming worse than a naïve predictor on at least one corruption setting, (ii) gradient-boosted tree ensembles achieve strong robustness, and (iii) dedicated robustification closes the gap between the attention-based architecture and the most robust models, though each strategy hurts nominal performance. The benchmark's multi-domain design proves essential, as model rankings shift across datasets, and no single domain captures the full robustness picture. MuViS-C is open-source and extensible to new datasets, failure modes, measures, and models.

Policies for robotic manipulation are produced by training on large teleoperated datasets. These datasets typically consist of free-space trajectories, making them difficult to transfer to test-time environments with obstacles. Previous methods for closing this gap have largely fallen into two groups. Dataset augmentation addresses it at training time but needs obstacle geometry in advance, whereas steering an existing checkpoint at inference time avoids that requirement but is limited in flexibility. Our method draws from both areas without inheriting either drawback. DetAug applies an obstacle-blind augmentation scheme to the transit phases of a free-space dataset, leaving object interactions untouched, and records the augmentation parameters as an explicit conditioning label. At inference it samples a batch of labels and executes the trajectory with the lowest collision cost. On the SafeLIBERO benchmark DetAug achieves a collision-free success rate more than 20pp above the next best method, and selecting over the label space outperforms guidance on the same policy by 26pp. On real hardware, inference-time steering methods collapse on tasks requiring large detours, while DetAug matches or exceeds an obstacle-conditioned baseline without ever seeing obstacles in training.

We report the results of a Turing Test conducted in Finland in the Finnish language. Because languages and cultural contexts are unevenly represented in LLM training data, we expected the model (ChatGPT 5.2) to perform worse in a Finnish-language Turing Test than in previously studied English-language US contexts. We also present model-generated role prompting as a replicable technique for conducting comparative LLM-based Turing Tests designed to improve construct validity. Contrary to our expectations, the LLM passed the Finnish Turing Test. A prominent source of error was participants' reliance on linguistic cues, particularly colloquial Finnish, as markers of human authorship. We reframe the Turing Test from a test of intelligence to a comparative method for examining whether an AI system can display credible membership in a particular social world. Because its outcome reflects model capabilities, prompted identity, insider competence among human participants, and their AI literacy, the method provides a useful probe of the human-machine boundary across domains.

Conditioning a video generator on multiple images requires preserving appearance while associating each reference with its intended role. We present MSR (Multiple Subject Reference), a slot-aware conditioning scheme for LTX-based video generation. Each reference image is independently encoded as a static clip and represented by a separate latent-token group. A compact Fourier-feature multilayer perceptron adds a numeric slot embedding, while slot-dependent temporal offsets modify the group's rotary coordinates. The reference groups are prepended to noisy target tokens and serve as clean context during target-only flow-matching training. We implement this scheme through low-rank adaptation and release the resulting weights and inference workflows. Qualitative examples demonstrate compositions containing distinct characters and referenced environments in realistic and stylized scenes. Development observations suggest reduced reference confusion relative to an earlier continuous-reference baseline, while similar clothing, complex garments, and viewpoint changes remain challenging. We describe the conditioning mechanism, the retained training configuration, and the observed strengths and limitations of the released system. A supplementary audio-reference experiment adds voice conditioning while keeping the visual parameters frozen.

Vision-language-action models (VLAs) have trans- formed the field of robotic manipulation in recent years by combining the semantic understanding of LLMs with the precise control of flow-matching policies. Advantage conditioning is a recent technique that iteratively improves VLAs by training a value function on deployment data and using this to train an advantage-conditioned policy. Previous works have only applied simple, low-information success/failure rewards, which leave the value function unable to distinguish states of differing quality beyond how far along the task they appear. Motivated by an exploration of out-of-distribution (OOD) detection methods, we introduce Distance-based Advantage Learning (DistAL), which, by using an embedding space distance as a reward, produces a more informative value function and subsequently a higher downstream task success rate. We validate our method on a series of simulation benchmarks and dexterous bi-manual manipulation tasks on real hardware.

Software supply-chain security requires accurate identification of third-party components and an understanding of how they evolve from development to execution. Existing software composition analysis (SCA) approaches examine manifests, build environments, release artifacts, containers, or runtime states, but typically produce only stage-specific views of software composition. As dependencies are resolved, removed, repackaged, and transformed across lifecycle stages, a single snapshot cannot capture both where a component originates and where it ultimately ends up. Combining snapshots from multiple stages still leaves their cross-stage relationships unresolved. We present SCA-Agent, an agent-based approach to lifecycle-aware SCA that reconstructs evidence-backed component lifecycle traces across Code, Build, Release, Deploy, and Runtime. SCA-Agent adaptively explores project-specific analysis paths, gathers stage-specific evidence, and correlates observations across stages to recover component identities, versions, introduction paths, propagation relationships, and final lifecycle states. We evaluate SCA-Agent on 105 real-world projects from the Java, JavaScript, and Python ecosystems. SCA-Agent achieves the highest component detection F1 across all lifecycle stages and ecosystems. For vulnerability exposure assessment, it reaches an F1 score of 96.69%, exceeding the best traditional SCA tool by 18.76 percentage points. These results show that lifecycle-aware SCA supports traceable component provenance and more accurate software supply-chain risk assessment.

AI-powered medical scribes are increasingly used to transcribe doctor-patient conversations and automate clinical documentation. However, large-scale real-world consultation datasets are scarce due to the sensitivity of clinical conversations, leading developers to rely on simulated and LLM-generated synthetic consultations. While scalable, these alternatives may fail to capture culturally situated patterns of clinical interaction. We introduce interactional cultural markers, measurable patterns of doctor-patient interaction grounded in cross-cultural clinical communication, and use them to compare real, simulated, and synthetic consultations from Indian and US clinical contexts. We find distinct patterns of participation and control: Indian consultations involve greater patient participation but stronger doctor control, while US consultations exhibit balanced participation and open-ended discussion. Synthetic Indian consultations often fail to reproduce these patterns, instead converging toward US-like interaction. We identify additional synthetic signatures, including excessive doctor explanation and formulaic patient responses. We conclude by discussing implications for generating culturally grounded synthetic clinical conversations.

Random-batch methods accelerate molecular dynamics by replacing full interaction sums with stochastic force estimators. In Langevin simulations, however, random-batch force errors can cause artificial heating and distort equilibrium and dynamical observables, especially for small batch sizes or under weak thermostat coupling. Moreover, the magnitude of these errors can vary across particles. We introduce moment-informed force rescaling for random-batch list (Mi-RBL) and random-batch Ewald (Mi-RBE) methods. A lagged average of each particle's sampled-force intensity sets an isotropic gain before the current batch is sampled, changing the random-batch force magnitude without changing its direction. The formal finite-time analysis quantifies the bias–variance tradeoff, and an estimate of the steady-state kinetic-temperature error predicts the scaling of the kinetic error with time step and thermostat friction. In the coexistence, binary-mixture, and electrolyte tests, Mi-RBL and Mi-RBE reduce kinetic errors and more closely reproduce the mean-square displacement, radial distribution function, and charge density profiles of the reference solutions. Mi-RBE also reduces the growth rate of the kinetic error with the time step by more than half and retains the predicted dependence on thermostat friction. The tested rescaling strength decreases with increasing batch size, and the particlewise update retains $O(N)$ complexity for fixed batch size.

Large language models are increasingly trained on GPUs distributed across multiple regions, but geo-distributed training is challenging in practice. Real clusters often contain GPUs with different speeds and memory capacities, and they communicate over slow wide-area networks. Our analysis shows that this creates serious problems: existing synchronous methods preserve stable updates, but fast GPUs wait up to 20.9% of their runtime for slower ones, and all workers spend, on average, 65.8% of their runtime on synchronization. Recent asynchronous methods reduce waiting time but worsen the model accuracy due to stale updates. To address the problems, we present GeoMesh, a synchronous geo-distributed training framework for heterogeneous GPUs. GeoMesh balances per-worker workloads by assigning each GPU a suitable batch size and number of inner steps, so faster GPUs do more useful work instead of waiting. It also reduces communication volume by nearly 32x by exchanging compressed sign-based pseudo-gradients with lightweight magnitude and token count. Across heterogeneous GPUs and Azure-derived WAN, GeoMesh reduces time-to-target perplexity by up to 70.2% over representative baselines and lowers straggler- and WAN-induced GPU idle by up to 8.0x and 5.6x, respectively, while preserving comparable zero-shot accuracy.

Local existence and uniqueness of smooth solutions are established for the three-dimensional compressible primitive equations with constant viscosity and a physical vacuum free boundary. We employ a Nash-Moser approach to address two distinct derivative losses, one arising from the free boundary geometry in the transformed viscosity and the other from the diagnostic reconstruction of the vertical velocity. We handle the first through Alinhac's good velocity unknown and the second through a modified height. Combining these two corrections with weighted energy estimates adapted to the vacuum degeneracy yields the tame estimates required for the iteration.

We investigate the ground-state properties of a two-component attractive Fermi gas confined to a spherical surface. In the strongly attractive regime, the system forms a Bose-Einstein condensate (BEC) of tightly bound dimers, yielding a gap and chemical potential that approach flat-space results with leading-order geometric corrections. As the attraction decreases, the system crosses over into a Bardeen-Cooper-Schrieffer (BCS) regime, the sphere radius $R$ constrains the Cooper pair size and shell effects emerge. For closed shells, corresponding to magic particle numbers set by the single-particle spectrum, pairing is suppressed above the scattering length $a^*=4R$, whose value is universal in the spherical geometry in contrast with box-trapped fermionic gases. Our results highlight a fundamental interplay among geometry, quantum statistics, and interactions, motivating future experiments with shell-trapped ultracold fermions and inspiring geometry-controlled condensed matter devices.

Emotions are an essential aspect of human communication, particularly on social media, where authors frequently combine text and images to convey their emotions. Yet prior work on emotion analysis of social media posts has overlooked two important aspects in regard to measuring how well readers can reconstruct the authors' intent: (1)~the image modality, with most work focusing solely on text, and (2)~the real-world events that trigger the expressed emotions, and their relationship to the post content. We therefore study the relation between (a) the author's experience of the event that caused them to write a social media post and (b) the content of the post, with a focus on readers' capability to reconstruct that emotion expression. To do that, we introduce the Multimodal Multi-Emotion-Model dataset Mult2EMo, created by collecting annotations from both authors and readers on the posts and their triggering events. We find that reconstruction is possible but challenging for both human readers and computational models. We show that understanding the triggering event is crucial for accurate reconstruction, and that reconstruction is particularly challenging when posts rely heavily on the image to express emotion.

We present a robust benchmark for measuring cultural value orientation in large language models on the two Inglehart-Welzel axes over several domains and roles (hence GYROval - Gridded Yielding of Robust value Orientation), together with the results of administering it to twenty models. Items are binary contrastive scenarios in the sense introduced by CDEval: both options are legitimate courses of action, neither is correct, there is no answer key, and a model's score on an axis is the proportion of its responses falling on the counted pole. Eleven of the twenty models were additionally administered a paired Russian translation of the identical items and a second sampling temperature. The instrument is publicly released in both languages. Stability was assessed by treating the vignette as the unit of analysis, ranking the models within the levels of each perturbation factor, and summarising the agreement between levels by tie-corrected Kendall's W against an empirical permutation null.

We report Geant4-based simulations of cosmic-ray muon backgrounds in models reproducing the geometries of the five-arm and six-arm e+e- pair spectrometers operated by the Atomki group at Debrecen. Full detector geometries are implemented for both setups, including position-sensitive detectors and plastic scintillators. In both configurations, cosmic muons generating two-arm coincidences produce statistically significant excesses in the opening-angle distribution whose positions are determined by the discrete azimuthal arrangement of detector arms and the plastic scintillators dimensions: in the six-arm spectrometer a peak appears near 140 degrees when the scintillator energy sum is selected in the 8Be transition window (16-20 MeV) and is suppressed for energy-asymmetric pairs, while a distinct peak near 120 degrees emerges in the 4He window (18-22 MeV), with no comparable enhancement in the respective background energy region. These angles, asymmetry dependences, and background characteristics show behaviours similar to those reported by the Atomki group as evidence for a 17 MeV boson. For the five-arm setup, a 140-degree excess is also reproduced at 8Be energies, and normalizing internal pair conversion events and cosmic coincidences to typical Atomki running conditions yields a cosmic-to-IPC ratio above unity in the signal window, indicating that the cosmic background is a leading contribution to the event rate at the energies and angles of interest. While they do not settle the question of the origin of the Atomki excesses, these results highlight the critical importance of a robust cosmic-ray treatment in this type of measurements, and call for a detailed description of the beam-off studies supporting the search for anomalies in the opening-angle vs. energy-sum distribution around the signal region.

We introduce a new finite element discretization for a mixed formulation of the two-dimensional incompressible Stokes equations with symmetric viscous stresses. The method is based on a mass-conserving stress-yielding formulation (Gopalakrishnan, Lederer, Schöberl; A mass conserving mixed stress formulation for the Stokes equations; IMA J. Numer. Anal., Vol 40, 2020) with symmetric stresses, with the key novelty that the symmetry of the stress tensor is enforced exactly as an intrinsic property of the discrete space. This space is constructed on the Clough–Tocher macroelement split and consists of matrix-valued functions whose normal-tangential components across macroelement interfaces are continuous. Since the exact symmetry is enforced via local polynomial bubble functions on the subelements, which can be eliminated via static condensation, the number of globally coupled degrees of freedom coincide with those of the original mass-conserving stress-yielding formulation. The resulting pressure-robust method is stable without requiring any additional enrichment. We establish optimal convergence rates for all the variables and present numerical experiments that confirm the theoretical results.

Despite their high accuracy on point-wise metrics, machine learning weather forecasting models can exhibit different failure modes such as blurring, periodic irregularities, and other unphysical spatial artifacts. This has motivated a variety of metrics to detect known failure cases. Existing metrics fix a representation or transformation in advance, and that choice limits the artifacts they can detect. We propose to train a discriminator for separating reference data from the model's output, and using its output logit to obtain a divergence-like realism score. The discriminator learns whatever separates the model's fields from real weather, adapting to whichever failure mode that model exhibits. We compare our learned atmospheric critic to existing metrics using various synthetic corruptions applied to ERA5 reanalysis data. Our method successfully identifies the corruptions and ranks their severity, while existing metrics fail on at least one corruption. Additionally, we evaluate forecasts from real weather models, and find that the realism score degrades with longer lead times and the metric generally assigns higher realism to numerical models than to machine learning models.

The cocyclic development of Hadamard matrices has recently been extended from groups to loops by means of a cohomology theory that incorporates associativity obstructions. Over the finite field $\mathbb F_2$, the resulting loop-cocycles can be computed as solutions of homogeneous linear systems, making the framework suitable for exact computation. In this paper, we investigate multidimensional Hadamard matrices arising from finite loops. We introduce the notion of $\delta$-compatible pairs of $2$-cochains over a loop $L$ as a natural extension of the usual $2$-cocycle identity, which allows the use of two distinct $2$-cochains. They form a vector space naturally isomorphic to the direct product of the space of $2$-cocycles and the space of $1$-cochains. This yields a generalization of the classical cocyclic construction of multidimensional Hadamard matrices from groups to arbitrary loops, while preserving the computational advantages of the cocyclic approach. The obtained decomposition shows that the determination of Hadamard equivalence classes can be reduced from the full space of $\delta$-compatible pairs to the smaller space of ordinary $2$-cocycles, eliminating a redundant factor of $2^n$ from the search space. Computational results for all groups of orders $4$ and $8$, together with a non-associative loop of order $8$, show that the proposed three-dimensional construction refines the classical cocyclic Hadamard classification. While all examples collapse into a single equivalence class in dimension two, they split into several distinct classes in dimension three. In particular, the non-associative loop produces a three-dimensional Hadamard class that does not arise from any of the groups considered, showing that the multidimensional construction detects structural information that is invisible at the cocyclic matrix level.

Square jigsaw reassembly requires recovering the spatial arrangement of shuffled fragments from their visual content and pairwise relationships. While recent studies have made substantial progress, existing benchmarks typically assume that all fragments are provided upright, reducing reassembly to a permutation problem. We study the generalized problem in which each fragment may also have gone through an unknown rotation. For this setting we establish a gauge-unobservability theorem: the minimum of the weighted least-squares objective is exactly invariant under a uniform global rotation of arbitrary magnitude, so no residual-based criterion can recover the global orientation. The theorem further identifies how the issue of global orientation can be resolved: an orientation anchor estimated from the content of a single fragment, lying outside its scope, suffices. To address the above, we propose JigSync, which attains 63.8% and 31.8% absolute accuracy (AA) on GAP-3 and GAP-5, respectively, the highest reported on both, while additionally recovering a rotation per piece that neither benchmark requires. We release JigSync, a degradation protocol that sweeps shape, erosion, photometry, grid size, and rotation independently.

We establish the eventual monotonicity of the Willmore deficit \( \int_{\Sigma}H^2\,d\mu-16\pi \) along the mean curvature flow of smooth closed embedded strictly convex surfaces in \( \mathbb R^3 \), thereby complementing Huisken's exponential convergence with an eventual monotonicity property. As a consequence, the Hawking mass is eventually nondecreasing along the contracting mean curvature flow, in contrast with the usual inclusion monotonicity expected of the Hawking mass. We also discuss totally umbilical solutions in three-dimensional space forms, where the monotonicity directions of the Willmore energy and the Hawking mass depend on the sign of the ambient sectional curvature.

We investigate a stationary and axisymmetric power law Kalb-Ramond geometry, obtained as a rotating extension of the asymptotically flat static solution. We reconstruct the exact inverse Einstein source supporting the geometry and determine its energy conditions and curvature properties. We characterize the horizon and stationary limit configurations and quantify the outer ergoregion through its angular dependent radial thickness plus its coordinate and proper spatial volumes. We derive the unstable spherical photon region and show that the Kalb-Ramond deformation shifts the prograde photon orbit into the ergoregion at lower spin, while the retrograde region remains outside throughout the entire domain. From the unstable photon region, we construct the exact vacuum critical curve and analyze its area equivalent diameter and displacement, including comparisons with M87$^\ast$ and Sgr~A$^\ast$ within the asymptotically admissible domain. We further examine the fixed-$J$ geometric behavior and rotational energy extraction, with emphasis to rotating weak deflection and two dimensional weak lensing, commenting the physical consequences of our solution in terms of observable outcomes.

Wide-field mid-infrared photothermal (MIP) imaging enables high-speed, chemically specific imaging at sub-micrometer spatial resolution through several possible contrast mechanisms, including scattering change, fluorescence modulation, and phase change. Each mechanism offers distinct advantages, yet existing wide-field MIP instruments have typically been limited to a single contrast mechanism so far, requiring a dedicated instrument for each. Here, we introduce a switchable multi-contrast wide-field MIP microscope that allows the photothermal readout mechanism (based on scattering-, fluorescence-, or quantitative phase imaging (QPI)) to be matched to the sample and imaging conditions. We characterize the spectral fidelity and signal-to-noise (SNR) ratio of each mechanism using 5 \mu m polystyrene (PS) beads, and the effective spatial resolution using 300 nm PS beads. Scattering- and fluorescence-based detection achieved a sub-500 nm measured point spread function full width at half maximum, while QPI-based detection reached approximately 900 nm but provided up to 26-fold higher SNR than scattering. We further demonstrate imaging across a range of samples, including A549 cells in buffer, mouse lung tissue section, bacteria, and SU8 polymer at 1.4 and 5 \mu m thickness, with a field of view exceeding 200 \mu m. Comparison across these samples shows that each contrast mechanism offers distinct trade-offs in resolution, sensitivity, and applicability, guiding readout-strategy selection by sample type. These results establish a flexible, switchable multi-contrast platform for wide-field MIP imaging, with broad applicability across polymer and biological samples.

Gaussian Whittle-Matérn fields form a flexible class of Gaussian processes on compact metric graphs, where spatial dependence is governed by the geometry and connectivity of the network through a fractional-order stochastic partial differential equation. This paper develops a new bridge representation of these fields in the case of half-integer smoothness parameters, when the fields have Markov properties. This representation decomposes the field into a finite-dimensional graph component and independent Whittle-Matérn bridge processes on the individual edges. The resulting decomposition leads to efficient likelihood evaluation, kriging prediction, and simulation methods. We show that this improves numerical stability and can greatly reduce computation time compared to previous methods. A simulation study on a Chicago street-network graph illustrates the computational efficiency of the sampling method and an application to Madrid traffic intensity data demonstrates the practical gains for likelihood-based inference and prediction. The methods are implemented in the R package MetricGraph.