U-Net style networks are commonly utilized in unsupervised image registration to predict dense displacement fields in the full-resolution spatial domain. For high-resolution volumetric image data, this process is, however, resource-intensive and time-consuming. To address this challenge, we propose Fourier-Net+, an image-domain deformable registration framework that operates on real-valued images for broad modality compatibility. Fourier-Net+ uses deterministic Fourier-domain band-limiting for efficient down- and up-sampling and employs a parameter-free, model-driven decoder to learn a band-limited, low-dimensional representation of the displacement field; all learnable network layers are real-valued. In addition, to enhance the registration performance and encourage diffeomorphism, we propose the cascaded and diffeomorphic versions of Fourier-Net+. We evaluate the proposed methods on five datasets, including two brain MRI, one 3-D cardiac MRI (3-D-CMR), one abdominal CT-MR dataset, and one noisy ultrasound cardiac dataset, comparing them against various state-of-the-art approaches. Our Fourier-Net+ and its variants achieve comparable results with these approaches while exhibiting faster training and inference speeds with a lower memory footprint and fewer multiply add operations (mult-adds). For example, on the 3-D-CMR dataset, our Diff-Fourier-Net+ significantly outperforms strong baselines such as TransMorph, TransMatch, and SACB-Net in Dice and HD, as well as in clinical metrics including end-diastolic (ED) volume and ejection fraction estimation, while using substantially less memory and computational cost. This efficiency enables large-scale 3-D registration training on low-VRAM GPUs.

Inverse rendering is an ill-posed problem. Previous work has sought to resolve this by focussing on priors for object or scene shape or appearance. In this work, we instead focus on a prior for natural illuminations. Current methods rely on spherical harmonic lighting or other generic representations and, at best, a simplistic prior on the parameters. This results in limitations for the inverse setting in terms of the expressivity of the illumination conditions, especially when taking specular reflections into account. We propose a conditional neural field representation based on a variational auto-decoder and a transformer decoder. We extend Vector Neurons to build equivariance directly into our architecture, and leveraging insights from depth estimation through a scale-invariant loss function, we enable the accurate representation of High Dynamic Range (HDR) images. The result is a compact, rotation-equivariant HDR neural illumination model capable of capturing complex, high-frequency features in natural environment maps. Training our model on a curated dataset of 1.6K HDR environment maps of natural scenes, we compare it against traditional representations, demonstrate its applicability for an inverse rendering task and show environment map completion from partial observations. We share our PyTorch implementation, dataset and trained models.

Vision as looking and seeing through a bottleneck.

What are the functions of primary visual cortex (V1)?

We present a new class of solvers for direct data-driven mechanical problems based on a sparse basis representation of equilibrium stress fields. Our first contribution is an efficient algorithm for computing the required sparse null-space basis on tetrahedral meshes. Only a single QR decomposition is needed to compute a small remaining set of dense basis vectors associated with boundary conditions and topological holes which can be handled efficiently via a partitioned Cholesky factorization. Building on this, we demonstrate how standard iterative solvers-such as the Newton-Raphson method-can be applied to direct data-driven formulations. The proposed approach is particularly valuable for challenging problems with complex data distributions requiring systematic exploration of the space of equilibrium stress fields. To this end, we introduce an algorithm that constructs a hierarchical solution set through an eigenvalue decomposition in the joint space of equilibrium stress and compatible strain fields. We demonstrate the proposed methodology with a numerical example involving brittle fracture with probabilistic tensile strength. The resulting family of failure patterns offers valuable insights for uncertainty quantification and design decision-making.

The absorbed dose in Boron Neutron Capture Therapy (BNCT) arises from various radiation components, each contributing differently to the overall biological effect. These effects depend not only on the absorbed dose but also on the type and energy of the involved secondary charged particles. Current dosimetric models convert absorbed dose into an equivalent photon dose using radiation-specific weighting factors that account for some differences in radiation type. However, these models generally neglect the energy dependence of biologicaleffectiveness. To evaluate the relevance of incorporating the energy dependence of secondary charged particles into BNCT dosimetry, and to assess its impact on dose calculations and clinical outcomeestimations. The photon isoeffective dose formalism was extended by reformulating the mathematical model for in terms of the secondary particle fields rather than dose components in BNCT. Tissue-specific radiobiological (RB) parameters and were introduced as functions of Linear Energy Transfer (LET), as predicted by the BIANCA biophysical model for normal skin and head and neck tumor tissues. Recoil proton spectra were analyzed at superficial and deep locations in tissues to evaluate their effectiveness relative to 583keV protons from the (n,p) reaction. Four approaches to , with varying levels of detail regarding energy and radiation fields representation, were evaluated across three scenarios. The analysis moved from a simplified geometry using a cylindrical phantom irradiated with epithermal neutrons, to progressively more realistic clinical scenarios, including a head and neck cancer treatment planning case and a retrospective study of a cutaneous melanoma case treated with BNCT at the RA-6 reactor inArgentina. Recoil protons were found to have lower than 583keV protons from (n,p) reactions, indicating that assuming equal effectiveness leads to overestimated doses in photon-equivalent units. In the phantom, detailed LET-based modeling proved essential in low-to-moderate boron concentration or superficial tissue scenarios, where simplified models showed deviations up to 30%. In contrast, boron-rich or deep tissue conditions tolerated simplifications with minimal loss of accuracy. In the head and neck case, simplified models led to skin overdoses up to 13%, increasing NTCP from negligible ( ) to high values ( ), thus raising the potential radiotoxicity risk. An apparent gain in TCP resulted from overestimating the required treatment time due to oversimplified modeling. In the retrospective melanoma case irradiated with the RA-6 mixed thermal-epithermal beam, simplified models underestimated the skin dose by 8% to 12%, potentially compromising dose-responseinterpretations. Beyond treatment planning, accurate dose modeling is also key for outcome assessment and meaningful comparisons with photon radiotherapy. Incorporating detailed LET-dependent RB modeling is especially important in scenarios involving low-to-moderate boron concentration levels or superficial tissues, where recoil protons dominate the dose composition. In contrast, simplified models may be acceptable in boron-rich, high-LET contexts, particularly when constrained by limited radiobiological data or computational resources. These findings support the development of a flexible photon isoeffective dose formalism that can evolve alongside advances in BNCT technologies and RBdata.

In recent years, there has been increasing interest in developing machine and deep learning models capable of annotating clinical documents with semantically relevant labels. However, the complex nature of these models often leads to significant challenges regarding interpretability and transparency. This study aims to improve the interpretability of transformer models and evaluate the explainability of a deep learning-based annotation of coded clinical documents derived from death certificates. Specifically, the focus is on interpreting and explaining model behavior and predictions by leveraging calibrated confidence, saliency maps, and measures of instance difficulty applied to textualized representations coded using the International Statistical Classification of Diseases and Related Health Problems (ICD). In particular, the instance difficulty approach has previously proven effective in interpreting image-based models. We used disease language bidirectional encoder representations from transformers, a domain-specific bidirectional encoder representations from transformers model pretrained on ICD classification-related data, to analyze reverse-coded representations of death certificates from the US National Center for Health Statistics, covering the years 2014 to 2017 and comprising 12,919,268 records. The model inputs consist of textualized representations of ICD-coded fields derived from death certificates, obtained by mapping codes to the corresponding ICD concept titles. For this study, we extracted a subset of 400,000 certificates for training, 100,000 for testing, and 10,000 for validation. We assessed the model's calibration and applied a temperature scaling post-hoc calibration method to improve the reliability of its confidence scores. Additionally, we introduced mechanisms to rank instances by difficulty using Variance of Gradients scores, which also facilitate the detection of out-of-distribution cases. Saliency maps were also used to enhance interpretability by highlighting which tokens in the input text most influenced the model's predictions. Experimental results on a pre-fine-tuned model for predicting the underlying cause of death from reverse-coded death certificate representations, which already achieves high accuracy (0.990), show good out-of-the-box calibration with respect to expected calibration error (1.40), though less so for maximum calibration error (30.91). Temperature scaling further reduces expected calibration error (1.13) while significantly increasing maximum calibration error (42.17). We report detailed Variance of Gradients analyses at the ICD category and chapter levels, including distributions of target and input categories, and provide word-level attributions using Integrated Gradients for both correctly classified and failure cases. This study demonstrates that enhancing interpretability and explainability in deep learning models can improve their practical utility in clinical document annotation. By addressing reliability and transparency, the proposed approaches support more informed and trustworthy application of machine learning in mission-critical medical settings. The results also highlight the ongoing need to address data limitations and ensure robust performance, especially for rare or complex cases.

Abstract Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak{g}$ to be rectangular and completely classify faithful rectangular representations. As an application, we obtain new $\lambda $-independence results on the algebraic monodromy groups of compatible systems of $\lambda $-adic Galois representations of number fields.

High-quality light field (LF) acquisition involves a trade-off between spatial and angular resolution. Hybrid camera systems offer a practical solution but present challenges for dense reconstruction due to sparse angular sampling and complex occlusions. To address these issues, this paper proposes a geometry-aware implicit neural representation (INR) framework for LF reconstruction. Distinct from traditional discrete representations or generic ray-space embeddings, we introduce a compact, continuous representation that combines a radiance field with a geometry module, where scalar disparity provides an ideal geometric interpretation and a ray-displacement field serves as the practical realization for occlusion-aware reconstruction. This framework leverages the global epipolar geometry of the 2D LF grid while utilizing the displacement field to correct local geometric inconsistencies caused by occlusions and non-Lambertian effects. By coupling these fields with a radiance network, our method enables end-to-end differentiable optimization from sparse, multi-resolution inputs without relying on large-scale external training datasets. Experiments on hybrid camera data fusion and spatial-angular super-resolution tasks demonstrate that our approach preserves high-frequency details and geometric consistency.

We introduce Motion2VecSets, a 4D diffusion model for dynamic surface mesh generation from various ambiguous observations, including a sequence of RGB images, sparse and partial point clouds, and low-resolution voxel grids. While recent methods using neural field representations have shown success in modeling non-rigid objects, conventional feed-forward architectures struggle with noisy, partial, or sparse observations due to their deterministic nature. To address the inherent one-to-many mapping problem, we introduce a diffusion model that explicitly learns the shape and motion distribution of non-rigid objects through an iterative denoising process of compressed latent representations. The diffusion-based priors provide more plausible and diverse reconstructions under ambiguous conditions. Instead of relying on global latent codes, we represent 4D dynamics using latent sets. This novel 4D representation captures local shape and deformation patterns, leading to more accurate non-linear motion capture and significantly improving generalization capacity to unseen motions and identities. For temporally coherent tracking, we jointly denoise latent sets across frames and enable cross-frame information exchange. To reduce computational cost, we design an interleaved spatial-temporal attention block that alternately aggregates deformation latents along spatial and temporal dimensions. Extensive experiments on datasets of humans, animals, and articulated objects demonstrate that Motion2VecSets outperforms prior methods in reconstructing and tracking non-rigid deformations from various imperfect observations. Our implementation is available at https://vveicao.github.io/projects/Motion2VecSets/.

On the accuracy of implicit neural representations for cardiovascular anatomies and hemodynamic fields.

This paper presents a comprehensive theoretical and computational study on the sequential representation of arrays within the algebraic framework of Galois Fields (GF), with a primary focus on GF(7). By employing modular arithmetic, symmetry principles, and binary encoding techniques, the work demonstrates how discrete array elements can be systematically mapped to finite field structures to achieve efficient and fault-tolerant data representation. The proposed methodology integrates sequential indexing with field operations to ensure closure, invertibility, and predictable algebraic transformations. Through detailed mathematical formulations and computational simulations, the study validates that array differences and mappings preserve the cyclic structure intrinsic to GF(7). Furthermore, the research highlights the applicability of this representation in several domains, including digital communication systems, cryptographic primitives, coding theory, and error-resilient computation. Sequential binary encodings derived from modular residues provide an additional layer of structure suitable for hardware-level implementation and secure data processing pipelines. The study also connects these representations to Perfect Difference Sets (PDS) and Perfect Difference Networks (PDN), illustrating how modular differences support highly symmetric interconnection topologies. Overall, the framework provides a unified perspective on finite-field-based array representation, offering both analytical clarity and practical relevance for modern computational architectures and secure information systems.

Abstract. In order to study the behaviour of cloud droplets at the cloud-clear interface, the “Solving The Entrainment Puzzle” (STEP) project examined a droplet stream in the Turbulent Leipzig Aerosol Cloud Interaction Simulator (LACIS-T). LACIS-T comprises two particle free air streams, that are turbulently mixed, and during the experiment one air stream was resembling in-cloud conditions, whereas the other air stream was set to out-of-cloud conditions. A droplet stream was injected by a droplet generator into the mixing plane of the two air streams. Droplet size distributions were observed with a phase Doppler anemometer at various levels in the measurement section of LACIS-T, corresponding to different residence times of the droplets in the turbulent environment. Additionally, observations were made using different flow speeds in the two air streams to create shear flows in the wind tunnel. The experiment was accompanied by computational fluid dynamics simulations to provide a full 3D representation of meteorological fields and turbulence parameters. This manuscript provides a description of the laboratory settings and instrumentation, the experimental design, the simulations, and a general overview of the data. We invite the scientific community for joint data analysis and numerical studies using the data which is freely available from the Eurochamp Data Centre, see Table 2 in the Data availability section for details.

Molecular dynamics (MD) simulations are a powerful tool for characterizing membrane-protein dynamics, yet their predictive accuracy critically depends on the choice of force field and membrane representation. Here, we present a systematic benchmark of the AMBER 14SB and CHARMM 36 m force fields across multiple bilayer sizes, using human aquaporin-7 (aquaglyceroporin-7; hAQP7) as a representative membrane protein system. Both force fields maintained global structural integrity, but differed markedly in their dynamic profiles: CHARMM 36 m sampled a broader conformational space and produced more hydrated pore profiles, whereas AMBER 14SB favored conformations closer to the crystallographic structure. Lipid organization and packing also diverged, with CHARMM generating more compact bilayers and AMBER yielding larger areas per lipid. The membrane size exerted minimal influence on the structural or functional descriptors, supporting the use of smaller, computationally efficient membrane patches for equilibrium simulations. The hAQP7 monomers functioned independently, without detectable cooperativity under the simulated conditions. Collectively, these results highlight the substantial impact of force-field selection on aquaporin dynamics and provide practical guidance for designing accurate MD simulations of transmembrane protein channels.

This conceptual understanding article is part of a series where we analyze the recognition and conversion of representations of the electric field concept; in this article, we present the case of algebraic notation. We conducted a study with introductory and upper-division physics students taking electricity and magnetism courses in a large private Mexican university to learn how students recognize the electric field’s main characteristics in the algebraic notation of the field and how they convert to and from different representations. We refer to the theory of registers of semiotic representations as a theoretical framework and use a phenomenographic approach to analyze data. We explored students’ recognition and conversion abilities through interpretation and construction tasks for the electric field’s algebraic notation. We found that the main difficulties of interpreting and constructing the algebraic notation are related to separating the mathematical expression from the situation’s physical meaning. Sometimes, students referred only to the physical meaning without using algebraic notation. In other cases, they construct algebraic notation without explicitly describing the physical meaning. Another source of difficulty is the treatment process because some students make mistakes or misinterpretations that they carry throughout. We recommend that introductory and upper-division electricity and magnetism instructors and physics education researchers in higher education be aware of the difficulties that some interpretation and construction tasks may present to students learning the electric field concept.

Aerial remote sensing efficiently surveys large areas, but accurate direct object-level measurement remains difficult in complex natural scenes. Advancements in 3D computer vision, particularly radiance field representations such as NeRF and 3D Gaussian splatting, can improve reconstruction fidelity from posed imagery. Nevertheless, direct aerial measurement of important attributes like tree diameter at breast height (DBH) remains challenging. Trunks in aerial forest scans are distant and sparsely observed in image views; at typical operating altitudes, stems may span only a few pixels. With these constraints, conventional reconstruction methods have inaccurate breast-height trunk geometry. TreeDGS is an aerial image reconstruction method that uses 3D Gaussian splatting as a continuous scene representation for trunk measurement. After SfM–MVS initialization and Gaussian optimization, we extract a dense point set from the Gaussian field using RaDe-GS’s depth-aware cumulative-opacity integration and associate each sample with a multi-view opacity reliability score. Then, we isolate trunk points and estimate DBH using opacity-weighted solid-circle fitting. Evaluated on 10 plots with field-measured DBH, TreeDGS reaches 4.79 cm RMSE (about 2.6 pixels at this GSD) and outperforms a LiDAR baseline (7.66 cm RMSE). This shows that TreeDGS can enable accurate, low-cost aerial DBH measurement.

ABSTRACTThe medial subdivision of the inferior pulvinar (PIm) has been implicated in motion processing, visuomotor integration, and residual visual function, yet a comprehensive account of its cortical inputs remains unresolved. Previous studies often relied on indirect cortical injections or tracer deposits spanning multiple pulvinar subdivisions, limiting anatomical specificity. Here, we used MRI-guided, cytoarchitectonically restricted retrograde tracer injections to selectively target PI in the common marmoset (Callithrix jacchus) and systematically map its cortical afferents.Across four cases, retrogradely labeled neurons were widely distributed throughout occipital, temporal, parietal, and cingulate cortices, with a strong predominance in layer V, consistent with driver-like corticothalamic projections. Early and middle-tier visual areas (V1, V2, V3, V3A, V4, V6/DM) contributed substantial input, with labeling patterns corresponding to peripheral visual field representations. The middle temporal complex (MT, MTc, MST, FST) represented one of the densest sources of cortical projections. Prominent inputs also arose from posterior parietal regions, including LIP, MIP, VIP, AIP, and inferior parietal areas (e.g., PFG, OPt), linking PIm to visuospatial and action-related networks. Semi-quantitative analyses indicated that occipital cortex and the MT complex together accounted for approximately 60% of total cortical input, while parietal cortex contributed roughly 20%. Additional projections from retrosplenial and posterior cingulate cortices were observed.These findings identify PIm as a central integrative node embedded within distributed visual and visuomotor networks. Rather than functioning as a restricted visual relay, PIm appears positioned to coordinate motion, spatial, and action-relevant signals within cortico-thalamocortical circuits supporting adaptive visually-guided behavior.

Animals and humans rely on optic flow to navigate cluttered and unknown environments. While most previous studies have focused on how organisms achieve self-motion perception through optic flow information, biological neural networks for navigation based on optic flow remain unexplored. Here, we propose a biologically plausible neural network model for optic flow-based reactive navigation. The model incorporates a primary visual cortex, which is responsible for generating a cortical representation of the optic flow field; a higher-order cortex, which calculates the focus of expansion (FOE) of the optic flow field; and a cerebellum, which generates motor commands. A feedback inhibitory pathway from V1 layer VI to layer IV is introduced, enhancing heading sensitivity and enabling rapid adaptation in dynamic environments. To achieve precise obstacle localization, we propose a dual encoding strategy that combines optic flow with depth maps derived from the optic flow field, FOE, and control acceleration. This strategy mitigates distortions in depth estimation near the expansion center and ensures more reliable obstacle representation. The cerebellum outputs motor commands for heading direction and speed control based on the output of the visual cortex. Simulations and real-world experiments with an intelligent vehicle confirm that the proposed model enables collision-free navigation across diverse scenarios and outperforms classical optic flow balance strategies in complex environments. These findings demonstrate that biologically inspired neural networks provide a feasible solution for visual reactive navigation in autonomous agents.

The upper atmospheric microwave sounding channels data are important for atmospheric data assimilation and retrieval. However, radiative transfer simulation accuracy is constrained by the precise characterization of the Zeeman splitting effect. This study investigates key influencing factors in upper-atmospheric microwave radiance simulations, focusing on the geomagnetic field parameters and the Zeeman splitting absorption coefficients. A three-dimensional (3D) atmosphere-magnetic coupling dataset is constructed using the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) version 2.0 Level 2A atmospheric profiles and the International Geomagnetic Reference Field (IGRF-13) as input for the microwave Line-by-Line (LBL) model. Observations from Special Sensor Microwave Imager/Sounder (SSMIS) channels 19 and 20 are used to quantitatively compare the effects of 2D and 3D geomagnetic fields on simulations and evaluate the impact of updated Zeeman splitting coefficients. Quantitative analysis reveals that the average vertical attenuation rate of geomagnetic field strength between 50 and 0.001 hPa is 2.98%, and using 3D magnetic field parameters improves the observation and simulation bias (O-B) for SSMIS channels 19 and 20 by approximately 3.67% and 3.52%, respectively. The updated microwave LBL model, incorporating molecular self-spin interactions and higher-order Zeeman effects, reduces the mean absolute error (MAE) and root mean square error (RMSE) of the SSMIS channel 20 by approximately 2.7% and 2.25%, respectively. Experimental results indicate that the 7+ line within a 2 MHz frequency shift is sensitive to moderate magnetic field strength (0.35–0.55 Gauss), while the 1− line is sensitive to strong magnetic fields (0.5–0.7 Gauss). This study demonstrates that optimizing geomagnetic field representation and Zeeman splitting coefficients can improve upper atmospheric microwave radiance simulation accuracy by detailed comparison with observations.

Abstract The electron density distribution in the lunar ionosphere has been characterized by only a few tens of vertical profiles of detectable electron density. Reported density values are highly variable: observed vertical profiles of electron density have maximum values that differ by a factor of 100. Here we report ionospheric results from five two‐way S‐band radio occultation observations performed by the Danuri spacecraft. The observations were implemented successfully and suitable raw data were acquired, but the initial versions of the derived frequency residuals and corresponding electron density profiles contain undesirable systematic features. We hypothesize that these undesirable features may be associated with the coarse representation of the lunar gravity field (degree and order of 100 × 100) that was used to reconstruct the Danuri trajectory. Simulations using different representations of the lunar gravity field suggest that improving the resolution to 400 × 400 can change the reconstructed spacecraft trajectory enough to account for the undesirable systematic features in the frequency residuals and corresponding electron density profiles. It will be important to assess how results of single frequency radio occultation observations that were processed with a relatively coarse representation of the lunar gravity field are changed if they are reprocessed with an improved representation of the lunar gravity field. Such changes may be significant. If this issue is addressed, then it may improve understanding of the lunar ionosphere.