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Andreas Wieser

Publications and source records attributed to Andreas Wieser.

At least 19 recordsLinked to original sources
arXiv2026

Planes in quadratic 4-space and associated shapes of lattices

Let $Q=-x_1^2-x_2^2-x_3^2+x_4^2$ be the standard signature $(1,3)$ quadratic form. To each non-degenerate rational plane $L$ in the four-dimensional quadratic space $(\mathbb{Q}^4,Q)$ we can naturally attach a periodic geodesic on the Bianchi orbifold $\mathrm{SL}_2(\mathbb{Z}[i])\backslash \mathbb{H}^3$ which records the position of $L$ in the Grassmannian up to integer rotations. Moreover, each such plane $L$ defines a CM point and a periodic geodesic on the modular curve through restriction of $Q$ to $L$ and its orthogonal complement. Lastly, the local isomorphism between $\mathrm{SO}_{1,3}(\mathbb{R})$ and $\mathrm{SL}_2(\mathbb{C})$ gives rise to a further periodic geodesic on the Bianchi orbifold. In this article, we exhibit a natural coupling of all the above objects and prove simultaneous equidistribution under a Linnik-type splitting condition. The main ingredient is the classification of joinings of higher-rank diagonalizable actions on homogeneous spaces due to Einsiedler and Lindenstrauss.

math.NT↗
arXiv2026

The TEAMx Observational Campaign

As part of the international research programme TEAMx (multi-scale transport and exchange processes in the atmosphere over mountains - programme and experiment) a one-year long measurement campaign, the TEAMx Observational Campaign (TOC), was conducted between 2024 and 2025 in a north-south transect through the Alps. Building on the dense operational measurement network in the Alps, the TOC was designed to collect long-term atmospheric observations over the highly complex Alpine terrain. During two six-week long Extended Observational Periods, more than 40 research institutions came together to instrument about 30 sites in the four target areas of the TEAMx domain and study different transport processes, from gravity waves to orographic convection, thermally driven flows, and turbulent exchange. In addition to a suite of ground-based in-situ and remote-sensing instruments, observational activities included airborne measurements with up to three research aircraft and multiple UAS. This paper gives an overview of the science goals and the TOC design, together with preliminary analyses that highlight the potential of the collected dataset.

physics.ao-ph↗
arXiv2026

Representations of binary quadratic forms by quaternary quadratic forms

We prove a local-global principle for primitive representations of binary quadratic forms by quaternary quadratic forms. Our method is a variant of Linnik's ergodic method showing density for certain homogenous toral sets. The central ingredient is a measure classification result of Einsiedler and Lindenstrauss for actions of rank two diagonalizable groups on quotients of products of $\mathrm{SL}_2$. This rigidity result together with an application of the Siegel mass formula reduces the density problem to a counting problem on a certain affine variety. We solve that counting problem using the determinant method of Bombieri-Pila and Heath-Brown.

math.NT↗
arXiv2026

Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in epidemiological or survey settings, individuals with certain outcomes may be more likely to be included, resulting in biased prevalence estimates with potentially substantial downstream impact. Classical corrections, such as inverse-probability weighting or explicit likelihood-based models of the selection process, rely on tractable likelihoods, which limits their applicability in complex stochastic models with latent dynamics or high-dimensional structure. Simulation-based inference enables Bayesian analysis without tractable likelihoods but typically assumes missingness at random and thus fails when selection depends on unobserved outcomes or covariates. Here, we develop a bias-aware simulation-based inference framework that explicitly incorporates selection into neural posterior estimation. By embedding the selection mechanism directly into the generative simulator, the approach enables amortized Bayesian inference without requiring tractable likelihoods. This recasting of selection bias as part of the simulation process allows us to both obtain debiased estimates and explicitly test for the presence of bias. The framework integrates diagnostics to detect discrepancies between simulated and observed data and to assess posterior calibration. The method recovers well-calibrated posterior distributions across three statistical applications with diverse selection mechanisms, including settings in which likelihood-based approaches yield biased estimates. These results recast the correction of selection bias as a simulation problem and establish simulation-based inference as a practical and testable strategy for parameter estimation under selection bias.

stat.ML↗
arXiv2026

Seifert surfaces in the four-ball and composition of binary quadratic forms

We use composition of binary quadratic forms to systematically create pairs of Seifert surfaces that are non-isotopic in the four-ball. Our main topological result employs Gauss composition to classify the pairs of binary quadratic forms that arise as the Seifert forms of pairs of disjoint Seifert surfaces of genus one. The main ingredient of the proof is number-theoretic and of independent interest. It establishes a new connection between the Bhargava cube and the geometric approach to Gauss composition via planes in the space of two-by-two matrices. In particular, we obtain a geometric recipe that given any two binary quadratic forms finds a Bhargava cube that gives rise to their composition.

math.GT↗
arXiv2026

Dense 3D Displacement Estimation for Landslide Monitoring via Fusion of TLS Point Clouds and Embedded RGB Images

Landslide monitoring is essential for understanding geohazards and mitigating associated risks. Existing point cloud-based methods, however, typically rely on either geometric or radiometric information and often yield sparse or non-3D displacement estimates. In this paper, we propose a hierarchical partitioning-based coarse-to-fine approach that integrates 3D point clouds and co-registered RGB images to estimate dense 3D displacement vector fields. Patch-level matches are constructed using both 3D geometry and 2D image features, refined via geometric consistency checks, and followed by rigid transformation estimation per match. Experimental results on two real-world landslide datasets demonstrate that the proposed method produces 3D displacement estimates with high spatial coverage (79% and 97%) and accuracy. Deviations in displacement magnitude with respect to external measurements (total station or GNSS observations) are 0.15 m and 0.25 m on the two datasets, respectively, and only 0.07 m and 0.20 m compared to manually derived references, all below the mean scan resolutions (0.08 m and 0.30 m). Compared with the state-of-the-art method F2S3, the proposed approach improves spatial coverage while maintaining comparable accuracy. The proposed approach offers a practical and adaptable solution for TLS-based landslide monitoring and is extensible to other types of point clouds and monitoring tasks. The example data and source code are publicly available at https://github.com/gseg-ethz/fusion4landslide.

cs.CV↗
arXiv2025

Representations of binary forms by quaternary quadratic forms

We prove a local-global principle for representations of binary by quaternary quadratic forms. One of the main ingredients is a recent measure rigidity result of Einsiedler and Lindenstrauss for diagonalizable actions on quotients of products of $\mathrm{SL}_2$'s. Based on this, it suffices to show that limits of the uniform measures on the associated rank one adelic toral packets have more entropy than one half of the maximal entropy. The latter is proved using the Siegel mass formula and the determinant method as developed by Bombieri and Pila as well as Heath-Brown.

math.NT↗
arXiv2025

A uniform Linnik basic lemma and entropy bounds

We prove a version of Linnik's basic lemma uniformly over the base field using theta-series and geometric invariant theory in the spirit of Khayutin's approach (Duke Math. J., 168(12), 2019). As an application, we establish entropy bounds for limits of invariant measures on homogeneous toral sets in GL(4) of biquadratic, cyclic, or dihedral type.

math.NT↗
arXiv2025

Cross-modal feature fusion for robust point cloud registration with ambiguous geometry

Point cloud registration has seen significant advancements with the application of deep learning techniques. However, existing approaches often overlook the potential of integrating radiometric information from RGB images. This limitation reduces their effectiveness in aligning point clouds pairs, especially in regions where geometric data alone is insufficient. When used effectively, radiometric information can enhance the registration process by providing context that is missing from purely geometric data. In this paper, we propose CoFF, a novel Cross-modal Feature Fusion method that utilizes both point cloud geometry and RGB images for pairwise point cloud registration. Assuming that the co-registration between point clouds and RGB images is available, CoFF explicitly addresses the challenges where geometric information alone is unclear, such as in regions with symmetric similarity or planar structures, through a two-stage fusion of 3D point cloud features and 2D image features. It incorporates a cross-modal feature fusion module that assigns pixel-wise image features to 3D input point clouds to enhance learned 3D point features, and integrates patch-wise image features with superpoint features to improve the quality of coarse matching. This is followed by a coarse-to-fine matching module that accurately establishes correspondences using the fused features. We extensively evaluate CoFF on four common datasets: 3DMatch, 3DLoMatch, IndoorLRS, and the recently released ScanNet++ datasets. In addition, we assess CoFF on specific subset datasets containing geometrically ambiguous cases. Our experimental results demonstrate that CoFF achieves state-of-the-art registration performance across all benchmarks, including remarkable registration recalls of 95.9% and 81.6% on the widely-used 3DMatch and 3DLoMatch datasets, respectively...(Truncated to fit arXiv abstract length)

cs.CV↗
arXiv2025

Effective equidistribution of semisimple adelic periods and representations of quadratic forms

We prove an effective equidistribution theorem for semisimple closed orbits on compact adelic quotients. The obtained error depends polynomially on the minimal complexity of intermediate orbits and the complexity of the ambient space. The proof uses dynamical arguments, property $(τ)$, Prasad's volume formula, an effective closing lemma, and a novel effective generation result for subgroups. The latter in turn relies on an effective version of Greenberg's theorem. We apply the above to the problem of establishing a local-global principle for representations of integral quadratic forms, improving the codimension assumptions and providing effective bounds in a theorem of Ellenberg and Venkatesh.

math.NT↗
arXiv2024

Birkhoff generic points on curves in horospheres

Let $\{a_t: t \in \mathbb{R}\}< SL_{d}(\mathbb{R})$ be a diagonalizable subgroup whose expanding horospherical subgroup $U < SL_{d}(\mathbb{R})$ is abelian. By the Birkhoff ergodic theorem, for any $x \in SL_{d}(\mathbb{R})/SL_{d}(\mathbb{Z})$ and for almost every point $u \in U$ the point $ux$ is Birkhoff generic for $a_t$ when $t \to \infty$. We prove that the same is true when $U$ is replaced by any non-degenerate analytic curve in $U$. This Birkhoff genericity result has various applications in Diophantine approximation. For instance, we obtain density estimates for Dirichlet improvability along typical points on a curve in Euclidean space. Other applications address approximations by algebraic numbers and best approximations (in the sense of Lagarias).

math.DS↗
arXiv2024

Long-range and dead-zone free dual-comb ranging for the interferometric tracking of moving targets

Dual-comb ranging has emerged as an effective technology for long-distance metrology, providing absolute distance measurements with high speed, precision, and accuracy. Here, we demonstrate a dual-comb ranging method that utilizes a free-space transceiver unit, enabling dead-zone-free measurements and simultaneous ranging with interchanged comb roles to allow for long-distance measurements even when the target is moving. It includes a GPU-accelerated algorithm for real-time signal processing and a free-running single-cavity solid-state dual-comb laser with a carrier wavelength $λ_c \approx$ 1055 nm, a pulse repetition rate of 1 GHz and a repetition rate difference of 5.06 kHz. This combination offers a fast update rate and sufficient signal strength to reach a single-shot time-of-flight precision of around 0.1 $μ$m (i.e. $< λ_c/4$) on a cooperative target placed at a distance of more than 40 m. The free-running laser is sufficiently stable to use the phase information for interferometric distance measurements, which improves the single-shot precision to $<$20 nm. To assess the ranging accuracy, we track the motion of the cooperative target when moved over 40 m and compare it to a reference interferometer. The residuals between the two measurements are below 3 $μ$m. These results highlight the potential of this approach for accurate and dead-zone-free long-distance ranging, supporting real-time tracking with nm-level precision.

physics.optics↗
arXiv2024

Effective equidistribution of orbits under semisimple groups on congruence quotients

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group. This extends previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work with Lindenstrauss, Margulis, Mohammadi, and Shah.

math.DS↗
arXiv2024

Equidistribution of rational subspaces and their shapes

To any $k$-dimensional subspace of $\mathbb Q^n$ one can naturally associate a point in the Grassmannian ${\rm Gr}_{n,k}(\mathbb R)$ and two shapes of lattices of rank $k$ and $n-k$ respectively. These lattices originate by intersecting the $k$-dimensional subspace with the lattice $\mathbb Z^n$. Using unipotent dynamics we prove simultaneous equidistribution of all of these objects under a congruence conditions when $(k,n) \neq (2,4)$.

math.NT↗
arXiv2024

The TEAMx-PC22 Alpine field campaign -- Objectives, instrumentation, and observed phenomena

The multi-scale transport and exchange processes in the atmosphere over mountains -- programme and experiment (TEAMx) wants to advance the understanding of transport and exchange processes over mountainous terrain as well as to collect unique multi-scale datasets that can be used, e.g., for process studies, model development and model evaluation. The TEAMx Observational Campaign (TOC) is planned to take place between 2024 and 2025. In summer 2022 a TEAMx pre-campaign (TEAMx-PC22) was conducted in the Inn Valley and one of its tributaries, the Weer Valley, to test the suitability and required logistics of measurement sites, to evaluate their value for the main campaign, and to test new observation techniques in complex terrain. Scientifically, this campaign focused on resolving the mountain boundary layer and valley wind systems on multiple scales. Through the combined effort of six institutions the pre-campaign can be deemed successful. A detailed description of the setup at each sub-target area is given. Due to the spatial distribution of instruments and their spatio-temporal resolution, atmospheric processes and phenomena like valley winds have been investigated at different locations and on different scales. Furthermore, scale interactions were detected and are discussed in detail in two example cases. Additionally, observational gaps were determined which should be closed for the TOC. Data of the pre-campaign are publicly available online and can be used for process studies, demonstrating the utility of new observation methods, model verification, and for data assimilation.

physics.ao-ph↗
arXiv2023

DEFLOW: Self-supervised 3D Motion Estimation of Debris Flow

Existing work on scene flow estimation focuses on autonomous driving and mobile robotics, while automated solutions are lacking for motion in nature, such as that exhibited by debris flows. We propose DEFLOW, a model for 3D motion estimation of debris flows, together with a newly captured dataset. We adopt a novel multi-level sensor fusion architecture and self-supervision to incorporate the inductive biases of the scene. We further adopt a multi-frame temporal processing module to enable flow speed estimation over time. Our model achieves state-of-the-art optical flow and depth estimation on our dataset, and fully automates the motion estimation for debris flows. The source code and dataset are available at project page.

cs.CV↗
arXiv2022

Dynamic 3D Scene Analysis by Point Cloud Accumulation

Multi-beam LiDAR sensors, as used on autonomous vehicles and mobile robots, acquire sequences of 3D range scans ("frames"). Each frame covers the scene sparsely, due to limited angular scanning resolution and occlusion. The sparsity restricts the performance of downstream processes like semantic segmentation or surface reconstruction. Luckily, when the sensor moves, frames are captured from a sequence of different viewpoints. This provides complementary information and, when accumulated in a common scene coordinate frame, yields a denser sampling and a more complete coverage of the underlying 3D scene. However, often the scanned scenes contain moving objects. Points on those objects are not correctly aligned by just undoing the scanner's ego-motion. In the present paper, we explore multi-frame point cloud accumulation as a mid-level representation of 3D scan sequences, and develop a method that exploits inductive biases of outdoor street scenes, including their geometric layout and object-level rigidity. Compared to state-of-the-art scene flow estimators, our proposed approach aims to align all 3D points in a common reference frame correctly accumulating the points on the individual objects. Our approach greatly reduces the alignment errors on several benchmark datasets. Moreover, the accumulated point clouds benefit high-level tasks like surface reconstruction.

cs.CV↗