Tootfinder

ExtraGS: Geometric-Aware Trajectory Extrapolation with Uncertainty-Guided Generative Priors
Kaiyuan Tan, Yingying Shen, Haohui Zhu, Zhiwei Zhan, Shan Zhao, Mingfei Tu, Hongcheng Luo, Haiyang Sun, Bing Wang, Guang Chen, Hangjun Ye
https://arxiv.org/abs/2508.15529

ExtraGS: Geometric-Aware Trajectory Extrapolation with Uncertainty-Guided Generative Priors
Synthesizing extrapolated views from recorded driving logs is critical for simulating driving scenes for autonomous driving vehicles, yet it remains a challenging task. Recent methods leverage generative priors as pseudo ground truth, but often lead to poor geometric consistency and over-smoothed renderings. To address these limitations, we propose ExtraGS, a holistic framework for trajectory extrapolation that integrates both geometric and generative priors. At the core of ExtraGS is a novel R…

A note on $\chi$-unbounded classes of geometric graphs
Pegah Pournajafi
https://arxiv.org/abs/2507.14884 https://arxiv.org/pdf/2507.1…

A note on $χ$-unbounded classes of geometric graphs
We show that there exist infinitely many classes of intersection graphs of geometric objects that are not $χ$-bounded -- namely, $d$-CBU graphs for $d\geq 3$ -- and each is incomparable with the class of Burling graphs. This answers a folklore open problem on whether Burling graphs are the sole source of unbounded chromatic number among geometric intersection classes.

Parabolic geometric Eisenstein series and constant term functors
Joakim Faergeman, Andreas Hayash
https://arxiv.org/abs/2507.13930 https://

Parabolic geometric Eisenstein series and constant term functors
We prove a compatibility between parabolic restriction of Whittaker sheaves and restriction of representations under the geometric Casselman-Shalika equivalence. To do this, we establish various Hecke structures on geometric Eisenstein series functors, generalizing results of Braverman-Gaitsgory in the case of a principal parabolic. Moreover, we relate compactified and non-compactified geometric Eisenstein series functors via Koszul duality. We sketch a proof that the spectral-to-automorphic …

Geometric components of representation spaces via robust families of submanifolds
Gabriele Viaggi
https://arxiv.org/abs/2508.14842 https://arxiv.org/pdf/25…

Geometric components of representation spaces via robust families of submanifolds
We introduce robust families of submanifolds for a linear Lie group $G$. We show that they give rise to geometric subspaces of the representation space ${\rm Hom}(Γ,G)$. As an application, we give a unified short proof of results of Beyrer and Kassel and of Benoist and Koszul about the existence of higher Teichmüller components for $G={\rm SO}(p,q+1),{\rm SL}(p+1,\mathbb{R})$. Being based on very general principles, our approach might be suited for finding geometric components in various ${\r…

Dimension-Decomposed Learning for Quadrotor Geometric Attitude Control with Almost Global Exponential Convergence on SO(3)
Tianhua Gao, Masashi Izumita, Kohji Tomita, Akiya Kamimura
https://arxiv.org/abs/2508.14422

Dimension-Decomposed Learning for Quadrotor Geometric Attitude Control with Almost Global Exponential Convergence on SO(3)
This paper introduces a lightweight and interpretable online learning approach called Dimension-Decomposed Learning (DiD-L) for disturbance identification in quadrotor geometric attitude control. As a module instance of DiD-L, we propose the Sliced Adaptive-Neuro Mapping (SANM). Specifically, to address underlying underfitting problems, the high-dimensional mapping for online identification is axially ``sliced" into multiple low-dimensional submappings (slices). In this way, the complex high-di…

A high geometric albedo and small size of the Haumea cluster member (24835) 1995 SM55 from a stellar occultation and photometric observations
J. L. Ortiz, N. Morales, B. Sicardy, F. L. Rommel, F. Braga-Ribas, Y. Kilic, E. Fern\'andez-Valenzuela, J. L. Rizos, B. Morgado, L. Catani, M. Kretlow, J. M. G\'omez-Lim\'on, J. Desmars, P. Santos-Sanz, O. Erece, I. Akoz, K. Uluc, S. Kaspi, A. Marciniak, V. Turcu, D. Moldovan, A. Sonka, E. Petrescu, A. Nedelcu, C. Nehir, R. Morales, R…

A high geometric albedo and small size of the Haumea cluster member (24835) 1995 SM55 from a stellar occultation and photometric observations
Trans-Neptunian objects (TNOs) are among the most ancient bodies of the solar system. Understanding their physical properties is key to constraining their origin and the evolution of the outer regions beyond Neptune. Stellar occultations provide highly accurate size and shape information. (24835) 1995 SM55 is one of the few members of the Haumea cluster and thus of particular interest. We aimed to determine its projected size, absolute magnitude, and geometric albedo, and to compare these with …

Consistent Pose Estimation of Unmanned Ground Vehicles through Terrain-Aided Multi-Sensor Fusion on Geometric Manifolds
Alexander Raab, Stephan Weiss, Alessandro Fornasier, Christian Brommer, Abdalrahman Ibrahim
https://arxiv.org/abs/2508.14661

Consistent Pose Estimation of Unmanned Ground Vehicles through Terrain-Aided Multi-Sensor Fusion on Geometric Manifolds
Aiming to enhance the consistency and thus long-term accuracy of Extended Kalman Filters for terrestrial vehicle localization, this paper introduces the Manifold Error State Extended Kalman Filter (M-ESEKF). By representing the robot's pose in a space with reduced dimensionality, the approach ensures feasible estimates on generic smooth surfaces, without introducing artificial constraints or simplifications that may degrade a filter's performance. The accompanying measurement models are compati…

Real geometric transcendence for Weierstrass elliptic functions
Arshay Sheth, Matteo Tamiozzo
https://arxiv.org/abs/2508.14645 https://arxiv.org/pdf/2508.1…

Real geometric transcendence for Weierstrass elliptic functions
Given a lattice $Λ\subset \mathbb C\simeq \mathbb R^2$ with associated Weierstrass function $\wp_Λ$, we determine the algebraic curves in $\mathbb R^2$ whose image via $\wp_Λ$ is contained in an algebraic curve.

Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method
Junke Zhang, Yiqian Wang
https://arxiv.org/abs/2507.14646

Intermittent--synchronization in non-weakly coupled piecewise linear expanding map lattice: a geometric-combinatorics method
The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework of the Perron-Frobenius operator and mainly focuses on weakly-coupled cases. In this paper, a novel geometric-combinatorics method for for non weakly-coupled CMLs is provided on the dynamical behavior of a two-node CMLs with identical piecewise linear expand…

Towards Geometric and Textural Consistency 3D Scene Generation via Single Image-guided Model Generation and Layout Optimization
Xiang Tang, Ruotong Li, Xiaopeng Fan
https://arxiv.org/abs/2507.14841

Towards Geometric and Textural Consistency 3D Scene Generation via Single Image-guided Model Generation and Layout Optimization
In recent years, 3D generation has made great strides in both academia and industry. However, generating 3D scenes from a single RGB image remains a significant challenge, as current approaches often struggle to ensure both object generation quality and scene coherence in multi-object scenarios. To overcome these limitations, we propose a novel three-stage framework for 3D scene generation with explicit geometric representations and high-quality textural details via single image-guided model ge…

Geometric design of the tangent term in landing algorithms for orthogonality constraints
Florentin Goyens, P. -A. Absil, Florian Feppon
https://arxiv.org/abs/2507.15638

Geometric design of the tangent term in landing algorithms for orthogonality constraints
We propose a family a metrics over the set of full-rank $n\times p$ real matrices, and apply them to the landing framework for optimization under orthogonality constraints. The family of metrics we propose is a natural extension of the $β$-metric, defined on the Stiefel manifold.

On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective
Stephen Maguire
https://arxiv.org/abs/2509.15445 https://arxiv.org/pdf/250…

On the Invariant Theory of Unipotent Groups Actions from a Geometric Perspective
This paper is a generalization of a previous paper by the author to connected unipotent linear algebraic groups. The notion of an $ α$-pair answers when an open $ G $-stable, affine, sub-variety $ D(H) $ is a trivial bundle over $ G \backslash \backslash D(H) $ in the Zariski topology, or whether there is an fppf topology $ ϕ: U \to D(H) $ such that $ U $ is a trivial bundle over $ G \backslash \backslash U $ and such that the fibres $ ϕ^{-1}(x) \cong \ker(α) $. We also describe a generaliz…

Stoquasticity is not enough: towards a sharper diagnostic for Quantum Monte Carlo simulability
Arman Babakhani, Armen Karakashian
https://arxiv.org/abs/2508.14382 https://

Stoquasticity is not enough: towards a sharper diagnostic for Quantum Monte Carlo simulability
Quantum Monte Carlo (QMC) methods are powerful tools for simulating quantum many-body systems, yet their applicability is limited by the infamous sign problem. We approach this challenge through the lens of Vanishing Geometric Phases (VGP) \cite{Hen_2021}, introducing it as a `geometric' criterion for diagnosing QMC simulability. We characterize the class of VGP Hamiltonians, and analyze the complexity of recognizing this class, identifying both hard and efficiently identifiable cases. We furth…

Systems-Level Analysis of Multisite Protein Phosphorylation: Mathematical Induction, Geometric Series, and Entropy
Iman Tavassoly, Adel Mehrpooya, Parsa Mirlohi, Zahra Abbaspourasadollah
https://arxiv.org/abs/2507.15050

Systems-Level Analysis of Multisite Protein Phosphorylation: Mathematical Induction, Geometric Series, and Entropy
Multisite protein phosphorylation plays a pivotal role in regulating cellular signaling and decision-making processes. In this study, we focus on the mathematical underpinnings and informational aspects of sequential, distributive phosphorylation systems. We first provide rigorous steady-state solutions derived using geometric series arguments and formal mathematical induction, demonstrating that the distribution of phosphorylation states follows a geometric progression determined by the kinase…

Functional Liftings of Restricted Geometric Inequalities
Andreas Malliaris, James Melbourne, Cyril Roberto, Michael Roysdon
https://arxiv.org/abs/2508.15247 https://

Functional Liftings of Restricted Geometric Inequalities
We investigate what we term ``generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from the special case of indicator functions corresponding to a geometric inequality. As consequences we derive a Borell-Brascamp Lieb inequality for the Gaussian Brunn-Minkowski inequality and give a functional analog of the log-Brunn-Minkowski conjecture. We also show that Barthe's reverse Brascamp-Lieb inequality is equi…

Well-posed geometric boundary data in General Relativity, III: conformal-volume boundary data
Zhongshan An, Michael T. Anderson
https://arxiv.org/abs/2507.15567

Well-posed geometric boundary data in General Relativity, III: conformal-volume boundary data
In this third work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations in general relativity with twisted DIrichlet boundary conditions on a finite timelike boundary. The boundary conditions consist of specification of the pointwise conformal class of the boundary metric, together with a scalar density involving a combination of the volume form of the bulk metric restricted to the boundary together with the volume form of the boundary metric itse…

Generalizable Geometric Image Caption Synthesis
Yue Xin, Wenyuan Wang, Rui Pan, Ruida Wang, Howard Meng, Renjie Pi, Shizhe Diao, Tong Zhang
https://arxiv.org/abs/2509.15217 http…

Generalizable Geometric Image Caption Synthesis
Multimodal large language models have various practical applications that demand strong reasoning abilities. Despite recent advancements, these models still struggle to solve complex geometric problems. A key challenge stems from the lack of high-quality image-text pair datasets for understanding geometric images. Furthermore, most template-based data synthesis pipelines typically fail to generalize to questions beyond their predefined templates. In this paper, we bridge this gap by introducing…

Analysis on fibred cusp spaces
Daniel Grieser, \'Alvaro S\'anchez-Hern\'andez, Boris Vertman
https://arxiv.org/abs/2507.15467 https://

Analysis on fibred cusp spaces
We give a survey of a number of analytic and geometric results on `fibred cusp spaces'. These results cover topics in spectral geometry, in particular analytic torsion and index theory, and boundary value problems. The underlying tools include a careful microlocal analysis of the resolvent and the heat kernel. We include an exposition of the geometric and analytic foundations and sketch the ideas of the proofs of the main theorems.

Geometric Analogues of Mie Scattering
S. Subedi, T. Curtright
https://arxiv.org/abs/2507.14821 https://arxiv.org/pdf/2507.14821

Geometric Analogues of Mie Scattering
Cross-sections for particles scattered from selected spatial geometries exhibit many of the same interesting features as Mie scattering.

Isotropic Remeshing with Inter-Angle Optimization
Hanbing Zheng, Chenlei Lv
https://arxiv.org/abs/2507.13641 https://arxiv.org/pdf/25…

Isotropic Remeshing with Inter-Angle Optimization
As an important metric for mesh quality evaluation, the isotropy property holds significant value for applications such as texture UV-mapping, physical simulation, and discrete geometric analysis. Classical isotropy remeshing methods adjust vertices and edge lengths, which exhibit certain limitations in terms of input data sensitivity, geometric consistency control, and convergence speed. In this paper, we propose an improved isotropy remeshing solution with inter-angle optimization during mesh…

Series B, Episode 08 - Hostage
SERVALAN: Have your decoded It?
VOICE: Not yet.
SERVALAN: What is the origin of the message?
VOICE: Unspecified. No Federation code sign was given.
SERVALAN: Decode at once.
VOICE: And Counsellor Joban is here.
https://blake.torpidity.net/m/208/192

On chain polynomials of geometric lattices
Petter Br\"and\'en, Leonardo Saud Maia Leite
https://arxiv.org/abs/2508.13810 https://arxiv.org/pdf/250…

On chain polynomials of geometric lattices
Athanasiadis and Kalampogia-Evangelinou recently conjectured that the chain polynomial of any geometric lattice has only real zeros. We verify this conjecture for families of geometric lattices including perfect matroid designs, Dowling lattices, and for a class of geometric lattices that contains all lattices of flats of paving matroids. We also investigate how the conjecture behaves with respect to certain operations such as direct products, ordinal sums and single-element extensions.

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[1/2]:
- G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model
Gao, Pi, Zhang, Ye, Zhong, Wang, Hong, Han, Xu, Li, Kong

Intrinsic Linear Response from Zeeman Quantum Geometry in 2D Unconventional Magnets
Neelanjan Chakraborti, Sudeep Kumar Ghosh, Snehasish Nandy
https://arxiv.org/abs/2508.14745 h…

Intrinsic Linear Response from Zeeman Quantum Geometry in 2D Unconventional Magnets
Unconventional magnets with zero net magnetization yet momentum-dependent spin splitting constitute a newly identified class of materials that provide a rich platform for quantum-geometry-driven transport phenomena. Exploiting the interplay between momentum translation and spin rotation, we uncover a distinct linear transport response governed by a generalized quantum geometric tensor, the Zeeman quantum geometric tensor (ZQGT). We show that the ZQGT drives a linear intrinsic gyrotropic magneti…

Geometric Image Synchronization with Deep Watermarking
Pierre Fernandez, Tom\'a\v{s} Sou\v{c}ek, Nikola Jovanovi\'c, Hady Elsahar, Sylvestre-Alvise Rebuffi, Valeriu Lacatusu, Tuan Tran, Alexandre Mourachko
https://arxiv.org/abs/2509.15208

Geometric Image Synchronization with Deep Watermarking
Synchronization is the task of estimating and inverting geometric transformations (e.g., crop, rotation) applied to an image. This work introduces SyncSeal, a bespoke watermarking method for robust image synchronization, which can be applied on top of existing watermarking methods to enhance their robustness against geometric transformations. It relies on an embedder network that imperceptibly alters images and an extractor network that predicts the geometric transformation to which the image w…

On the Invariant Theory of $ \mathbb{G}_{a} $-Actions from a Geometric Perspective
Stephen Maguire
https://arxiv.org/abs/2509.15438 https://arxiv.org/pdf/2…

On the Invariant Theory of $ \mathbb{G}_{a} $-Actions from a Geometric Perspective
In this paper we give a strict classification of $ \mathbb{G}_{a} $-representations. This is done through the notion of a $ c(t) $-pair. Namely if $ \operatorname{Spec}(A) $ is a $ \mathbb{G}_{a} $-variety with action $ β$, then a $ c(t) $-pair is a pair of elements $ (g,h) $ such that $ g(t_{0} \ast x) = g(x)+c(t_{0}) h(x) $. This allows us to describe exactly when an affine, $ \mathbb{G}_{a} $-stable, sub-variety $ D(h) $ is a trivial bundle over $ D(h)//\mathbb{G}_{a} $. If $ \operatorname{…

MorphIt: Flexible Spherical Approximation of Robot Morphology for Representation-driven Adaptation
Nataliya Nechyporenko, Yutong Zhang, Sean Campbell, Alessandro Roncone
https://arxiv.org/abs/2507.14061

MorphIt: Flexible Spherical Approximation of Robot Morphology for Representation-driven Adaptation
What if a robot could rethink its own morphological representation to better meet the demands of diverse tasks? Most robotic systems today treat their physical form as a fixed constraint rather than an adaptive resource, forcing the same rigid geometric representation to serve applications with vastly different computational and precision requirements. We introduce MorphIt, a novel algorithm for approximating robot morphology using spherical primitives that balances geometric accuracy with comp…

A novel geometric predictive algorithm for assessing Compressive Elastic Modulus in MEX additive processes, based on part nonlinearities and layers stiffness,validated with PETG and PLA materials
J. M. Mercado Colmenero, C. Martin Donate
https://arxiv.org/abs/2508.13164

A novel geometric predictive algorithm for assessing Compressive Elastic Modulus in MEX additive processes, based on part nonlinearities and layers stiffness,validated with PETG and PLA materials
The paper presents an innovative methodology based on the use of a new predictive algorithm created by the researchers capable of obtaining the elastic modulus of a plastic material manufactured with MEX and its mechanical behaviour in the elastic zone under compressive loads. The predictive algorithm only needs as input the compressive elastic modulus of the isotropic plastic material filament and the manufacturing parameters of the MEX process. The smart developed algorithm calculates the sti…

Differentiable Acoustic Radiance Transfer
Sungho Lee, Matteo Scerbo, Seungu Han, Min Jun Choi, Kyogu Lee, Enzo De Sena
https://arxiv.org/abs/2509.15946 https://

Differentiable Acoustic Radiance Transfer
Geometric acoustics is an efficient approach to room acoustics modeling, governed by the canonical time-dependent rendering equation. Acoustic radiance transfer (ART) solves the equation through discretization, modeling the time- and direction-dependent energy exchange between surface patches given with flexible material properties. We introduce DART, a differentiable and efficient implementation of ART that enables gradient-based optimization of material properties. We evaluate DART on a simpl…

Holographic Extended Thermodynamics of deformed AdS-Schwarzschild black hole
Kamal L. Panigrahi, Balbeer Singh
https://arxiv.org/abs/2508.14873 https://arx…

Holographic Extended Thermodynamics of deformed AdS-Schwarzschild black hole
We investigate the thermodynamics and phase structure of a deformed AdS-Schwarzschild black hole, generated via the gravitational decoupling (GD) method as a minimal geometric deformation. In the bulk canonical ensemble, our results exhibit a van der Waals-type first-order phase transition in addition to the Hawking-Page transition, in the suitable parameter regime. Further, we compute the critical exponents characterising the bulk transition, confirming their consistency with mean-field theory…

Optics in spiral dislocation spacetime: Torsion as a geometric waveguide and frequency-filtering mechanism
Semra Gurtas Dogan, Omar Mustafa, Abdullah Guvendi, Hassan Hassanabadi
https://arxiv.org/abs/2507.14865

Optics in spiral dislocation spacetime: Torsion as a geometric waveguide and frequency-filtering mechanism
We present an exact analytical investigation of null trajectories and scalar wave propagation in a $(2+1)$-dimensional spacetime containing a spiral dislocation-a topological defect characterized by torsion in the absence of curvature. For null rays, the torsion parameter $β$ modifies the affine structure, enforcing a finite turning radius $r_{\min} = \sqrt{b^2 - β^2}$ and inducing a torsion-mediated angular deflection that decreases monotonically with increasing $β$. The photon trajectory d…

Replaced article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Fuzzy simplicial sets and their application to geometric data analysis
Barth, Fahimi, Joharinad, Jost, Keck, Mikhail

Equivalence of mutually unbiased bases via orbits: general theory and a $d=4$ case study
Amit Te'eni, Eliahu Cohen
https://arxiv.org/abs/2508.15412 https://

Equivalence of mutually unbiased bases via orbits: general theory and a $d=4$ case study
In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct the space of its orthonormal bases as a discrete quotient of the complete flag manifold. We introduce a metric on this space, which corresponds to the "MUBness" distance. This allows us to describe equivalence between sets of mutually unbiased bases in terms of…

Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Marian Gidea, Rafael de la Llave, Tere M-Seara
https://arxiv.org/abs/2508.14794

Geometric, topological and dynamical properties of conformally symplectic systems, normally hyperbolic invariant manifolds, and scattering maps
Conformally symplectic diffeomorphisms $f:M \rightarrow M$ transform a symplectic form $ω$ on a manifold $M$ into a multiple of itself, $f^* ω= ηω$. We assume $ω$ is bounded, as some of the results may fail otherwise. We show that there are deep interactions between the topological properties of the manifold, the dynamical properties of the map, and the geometry of invariant manifolds. We show that, when the symplectic form is not exact, the possible conformal factors $η$ are related …

Geometric spectral properties of electromagnetic waveguides
Philippe Briet (EPSILON), Maxence Cassier (EPSILON), Thomas Ourmi\`eres-Bonafos (I2M), Michele Zaccaron (EPSILON)
https://arxiv.org/abs/2508.13591

Geometric spectral properties of electromagnetic waveguides
Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide is straight, the spectrum of the associated self-adjoint Maxwell operator with a constant twist (which may be zero) lies on the real line and is symmetric with respect to zero and exhibits a spectral gap around the origin. Moreover, the spectrum is purely essential, and contains 0 which is an eigenvalue of infinite mu…

FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale
Boris Bonev, Thorsten Kurth, Ankur Mahesh, Mauro Bisson, Jean Kossaifi, Karthik Kashinath, Anima Anandkumar, William D. Collins, Michael S. Pritchard, Alexander Keller
https://arxiv.org/abs/2507.12144…

FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale
FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting. The approach is designed to respect spherical geometry and to accurately model the spatially correlated probabilistic nature of the problem, resulting in stable spectra and realistic dynamics across multiple scales. FourCastNet 3 delivers forecasting accuracy that surpasses leading conventional ensemble models and rivals the best diffusion-ba…

On a Generalization of the Christoffel Tree: Epichristoffel Trees
Abhishek Krishnamoorthy (Madras Christian College), Robinson Thamburaj (Madras Christian College), Durairaj Gnanaraj Thomas (Madras Christian College)
https://arxiv.org/abs/2507.15313

On a Generalization of the Christoffel Tree: Epichristoffel Trees
Sturmian words form a family of one-sided infinite words over a binary alphabet that are obtained as a discretization of a line with an irrational slope starting from the origin. A finite version of this class of words called Christoffel words has been extensively studied for their interesting properties. It is a class of words that has a geometric and an algebraic definition, making it an intriguing topic of study for many mathematicians. Recently, a generalization of Christoffel words for an …

Exact $\ell^\infty$-separation radius of Sobol' sequences in dimension 2
Kosuke Suzuki
https://arxiv.org/abs/2508.14803 https://arxiv.org/pdf/2508.1480…

Exact $\ell^\infty$-separation radius of Sobol' sequences in dimension 2
Quasi-uniformity is a fundamental geometric property of point sets, crucial for applications such as kernel interpolation, Gaussian process regression, and space-filling experimental designs. While quasi-Monte Carlo methods are widely recognized for their low-discrepancy characteristics, understanding their quasi-uniformity remains important for practical applications. For the two-dimensional Sobol' sequence, Sobol' and Shukhman (2007) conjectured that the separation radius of the first $N$ poi…

A Hidden Pulse: Uncovering a New Timing Signal in Cygnus X-1 with AstroSat
Sandeep K. Rout, Federico Garcia, Mariano Mendez, Abhay Kumar, Santosh Vadawale, David M. Russell, Pei Jin
https://arxiv.org/abs/2507.13884

A Hidden Pulse: Uncovering a New Timing Signal in Cygnus X-1 with AstroSat
The study of fast variability properties in X-ray binaries advances our understanding of the physical processes and geometric properties of the accretion flow around the compact object. In this work, we study the evolution of the timing properties of Cygnus X-1 with AstroSat/LAXPC, during the transition of the source from the hard to soft state in 2017. We use a novel frequency-segmented technique to fit simultaneously the cross spectra and part of the power spectra and coherence function with …

Cactus, Pascal, and Pappus Point-Line Configurations: An Algebraic-Geometric Perspective
Lisa Vandebrouck
https://arxiv.org/abs/2508.14141 https://arxiv.or…

Cactus, Pascal, and Pappus Point-Line Configurations: An Algebraic-Geometric Perspective
We study point-line configurations and their associated matroid and circuit varieties. We aim to find a finite set of defining equations for matroid varieties and an irreducible decomposition for circuit varieties. To solve the former problem, we use some classical techniques from algebraic geometry, including the Grassmann-Cayley algebra and the liftability technique. From this, we can respectively derive the Grassmann-Cayley ideal, introduced by Sidman, Traves and Wheeler, and the lifting i…

A geometric approach to constructing quasi-isodynamic fields
G. G. Plunk, E. Rodr\'iguez
https://arxiv.org/abs/2508.12820 https://arxiv.org/pdf/2508.12…

A geometric approach to constructing quasi-isodynamic fields
The near-axis theory for quasi-isodynamic stellarator equilibria is reformulated in terms of geometric inputs, to allow greater control of the ``direct construction'' of quasi-isodynamic configurations, and to facilitate understanding of the space of such equilibria. This includes a method to construct suitable magnetic axis curves by solving Frenet-Serret equations, and an approach to controlling magnetic surface shaping at first order (plasma elongation), which previously has required careful…

Series B, Episode 13 - Star One
DURKIM: Why would I want to do that?
SERVALAN: 'Why' is always the most difficult question. At the moment I am more concerned with 'how'.
DURKIM: Is she involved?
SERVALAN: You know her?
https://blake.torpidity.net/m/213/116 B…

On the distance between mean and geometric median in high dimensions
Richard Schwank, Mathias Drton
https://arxiv.org/abs/2508.12926 https://arxiv.org/pdf/…

On the distance between mean and geometric median in high dimensions
The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are very close in high dimensions when the dependence between the distribution components is suitably controlled. Concretely, we find an upper bound on the distance that vanishes with the dimension asymptotically, and derive a rate-matching first order expansion o…

The effect of fiber plasticity on domain formation in soft biological composites -- Part II: An imperfection analysis
Dimitris Iordanidis, Fernanda F. Fontenele, Konstantinos Poulios, Michalis Agoras, Nikolaos Bouklas
https://arxiv.org/abs/2507.14764

The effect of fiber plasticity on domain formation in soft biological composites -- Part II: An imperfection analysis
The main objective of this work is to numerically investigate the effect of geometric imperfections on the macroscopic response and domain formation in soft biological composites that exhibit plasticity in the stiff (fiber) phase.This work builds on the corresponding bifurcation analysis in Part I of this study for simple laminates with perfectly flat layers under plane strain, nonmonotonic loading conditions, aligned with the layer direction. The post-bifurcation solution obtained in Part I fo…

Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations
Viacheslav Yusupov, Maxim Rakhuba, Evgeny Frolov
https://arxiv.org/abs/2508.11978 https://

Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical insights to improve representation learning and increase computational stability at the same time. We reformulate the notion of hyperbolic distances to unlock additional representation capacity over conventional Euclidean space and learn more expressive user and …

Predictive models for strain energy in condensed phase reactions
Baptiste Martin, Shukai Yao, Chunyu Li, Anthony Bocahut, Matthew Jackson, Alejandro Strachan
https://arxiv.org/abs/2508.15592

Predictive models for strain energy in condensed phase reactions
Molecular modeling of thermally activated chemistry in condensed phases is essential to understand polymerization, depolymerization, and other processing steps of molecular materials. Current methods typically combine molecular dynamics (MD) simulations to describe short-time relaxation with a stochastic description of predetermined chemical reactions. Possible reactions are often selected on the basis of geometric criteria, such as a capture distance between reactive atoms. Although these simu…

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Limiting Sets for Digital Cones and Suspensions
Laurence Boxer
https://

LeanGeo: Formalizing Competitional Geometry problems in Lean
Chendong Song, Zihan Wang, Frederick Pu, Haiming Wang, Xiaohan Lin, Junqi Liu, Jia Li, Zhengying Liu
https://arxiv.org/abs/2508.14644

LeanGeo: Formalizing Competitional Geometry problems in Lean
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 …

Approximate Fiber Products of Schemes and Their \'Etale Homotopical Invariants
Dongfang Zhao
https://arxiv.org/abs/2509.15616 https://arxiv.org/pdf/250…

Approximate Fiber Products of Schemes and Their Étale Homotopical Invariants
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $ϕ: X \to S$ and $ψ: Y \to S$, coincide exactly. This condition of strict equality, however, is insufficient for describing the geometric structure of semantic spaces in modern large language models, whose foundational architecture is the Transformer. The token spaces of these models are fundamentally arithmetic, and recent work has revealed complex geometric sing…

Multiple-Noise-Resilient Nonadiabatic Geometric Quantum Control of Solid-State Spins in Diamond
Si-Qi Chen, Qi-Tao Duan, Chengxian Zhang, He Lu
https://arxiv.org/abs/2508.12221 …

Multiple-Noise-Resilient Nonadiabatic Geometric Quantum Control of Solid-State Spins in Diamond
Reliable and robust control lies at the core of implementing quantum information processing with diamond nitrogen-vacancy (NV) centers. However, control pulses inevitably introduce multiple errors, leading to decoherence and hindering scalable applications. Here, we experimentally report an experiment-friendly multiple-noise-resilient nonadiabatic geometric quantum gate~(MNR-NGQG) that can significantly improve conventional dynamical gate in both robustness and coherence. Notably, even when the…

Seeing 3D Through 2D Lenses: 3D Few-Shot Class-Incremental Learning via Cross-Modal Geometric Rectification
Xiang Tuo, Xu Xuemiao, Liu Bangzhen, Li Jinyi, Li Yong, He Shengfeng
https://arxiv.org/abs/2509.14958

Seeing 3D Through 2D Lenses: 3D Few-Shot Class-Incremental Learning via Cross-Modal Geometric Rectification
The rapid growth of 3D digital content necessitates expandable recognition systems for open-world scenarios. However, existing 3D class-incremental learning methods struggle under extreme data scarcity due to geometric misalignment and texture bias. While recent approaches integrate 3D data with 2D foundation models (e.g., CLIP), they suffer from semantic blurring caused by texture-biased projections and indiscriminate fusion of geometric-textural cues, leading to unstable decision prototypes a…

Iterated integrals on the Legendre family of elliptic curves
Eisuke Otsuka
https://arxiv.org/abs/2507.13790 https://arxiv.org/pdf/250…

Iterated integrals on the Legendre family of elliptic curves
K.T. Chen showed that iterated integrals give comparison isomorphisms between the cohomologies of bar complexes and fundamental group rings. This led to the development of an algebraic-geometric approach to studying periods given by iterated integrals. In this paper we consider an analogue of this comparison isomorphism theorem for iterated integrals on the Legendre family.

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts
Norihiro Iizuka, Akihiro Miyata, Mitsuhiro Nishida
https://arxiv.org/abs/2507.15262 https://

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts
The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap c…

Series C, Episode 02 - Powerplay
CALLY: More survivors from the battle?
NURSE: Just one, apparently. We picked up a voice signal a couple of hours ago. We're homing in on it now. It will be a quick touchdown and immediate lift-off. The local inhabitants are hostile, apparently. Ah, let's see how your burns are healing.
https://

Spin(7)-Orbifold Resolutions
Viktor F. Majewski
https://arxiv.org/abs/2509.16057 https://arxiv.org/pdf/2509.16057…

Spin(7)-Orbifold Resolutions
We establish a general analytic and geometric framework for resolving Spin(7)--orbifolds. These spaces arise naturally as boundary points in the moduli space of exceptional holonomy metrics, and smooth Gromov--Hausdorff resolutions can be viewed as paths from the boundary to the interior of the moduli space. Our construction combines algebraic and symplectic techniques with analytic gluing methods: singular strata are replaced by families of adiabatic torsion--free, asymptotically conical fibre…

A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar
https://arxiv.org/abs/2508.13235 https://arxiv.org/pdf/2508…

A proof of the reverse isoperimetric inequality using a geometric-analytic approach
We present the first proof of the reverse isoperimetric inequality for black holes in arbitrary dimension using a two-pronged geometric-analytic approach. The proof holds for compact Riemannian hypersurfaces in AdS space and seems to be a generic property of black holes in the extended phase space formalism. Using Euclidean gravitational action, we show that, among all hypersurfaces of given volume, the round sphere in the $D$-dimensional Anti-de Sitter space maximizes the area (and hence the e…

A generalized canonical metric for optimization on the indefinite Stiefel manifold
Dinh Van Tiep, Duong Thi Viet An, Nguyen Thi Ngoc Oanh, Nguyen Thanh Son
https://arxiv.org/abs/2509.16113

A generalized canonical metric for optimization on the indefinite Stiefel manifold
Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian metric, preparing geometric tools such as orthogonal projections, formulae for Riemannian gradient, retraction and then extending an unconstrained optimization algorithm on the Euclidean space to the established manifold. The choice for the metric undoubtedly has…

Replaced article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- Tautological Tuning of the Kostant-Souriau Quantization Map with Differential Geometric Structures
Tom McClain

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Infinite Ideal Polyhedra in Hyperbolic 3-Space: Existence and Rigidity
Huabin Ge, Hao Yu, Puchun Zhou

The Rectilinear Marco Polo Problem
Ofek Gila (University of California, Irvine), Michael T. Goodrich (University of California, Irvine), Zahra Hadizadeh (University of Rochester), Daniel S. Hirschberg (University of California, Irvine), Shayan Taherijam (University of California, Irvine)
https://arxiv.org/abs/2508.14820

The Rectilinear Marco Polo Problem
We study the rectilinear Marco Polo problem, which generalizes the Euclidean version of the Marco Polo problem for performing geometric localization to rectilinear search environments, such as in geometries motivated from urban settings, and to higher dimensions. In the rectilinear Marco Polo problem, there is at least one point of interest (POI) within distance $n$, in either the $L_1$ or $L_\infty$ metric, from the origin. Motivated from a search-and-rescue application, our goal is to move a …

Reduced basis solvers for unfitted methods on parameterized domains
Nicholas Mueller, Santiago Badia, Yiran Zhao
https://arxiv.org/abs/2508.15320 https://a…

Reduced basis solvers for unfitted methods on parameterized domains
In this paper, we present a unified framework for reduced basis approximations of parametrized partial differential equations defined on parameter-dependent domains. Our approach combines unfitted finite element methods with both classical and tensor-based reduced basis techniques -- particularly the tensor-train reduced basis method -- to enable efficient and accurate model reduction on general geometries. To address the challenge of reconciling geometric variability with fixed-dimensional sna…

Replaced article(s) found for cs.RO. https://arxiv.org/list/cs.RO/new
[1/1]:
- Automatic Geometric Decomposition for Analytical Inverse Kinematics
Daniel Ostermeier, Jonathan K\"ulz, Matthias Althoff

Zak Phase Dislocations in Trimer Lattices
Tileubek Uakhitov, Abdybek Urmanov, Serik E. Kumekov, Anton S. Desyatnikov
https://arxiv.org/abs/2509.15894 https://

Zak Phase Dislocations in Trimer Lattices
Wave propagation in periodic media is governed by energy-momentum relation and geometric phases characterizing band topology, such as Zak phase in one-dimensional lattices. We demonstrate that in the off-diagonal trimer lattices Zak phase carries quantized screw-type dislocations winding around degeneracies in parameter space. If the lattice evolves in time periodically, as in adiabatic Thouless pump, corresponding closed trajectory in parameter space is characterized by a Chern number equal th…

Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs
Edward Phillips, Sean Wu, Soheila Molaei, Danielle Belgrave, Anshul Thakur, David Clifton
https://arxiv.org/abs/2509.13813

Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs
Large language models demonstrate impressive results across diverse tasks but are still known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy for hallucination detection, but no existing black-box approach provides estimates for both global and local uncertainty. The former attributes uncertainty to a batch of responses, while the latter attributes uncertainty to individual responses. Current loca…

Event2Vec: A Geometric Approach to Learning Composable Representations of Event Sequences
Antonin Sulc
https://arxiv.org/abs/2509.12188 https://arxiv.org/p…

Event2Vec: A Geometric Approach to Learning Composable Representations of Event Sequences
The study of neural representations, both in biological and artificial systems, is increasingly revealing the importance of geometric and topological structures. Inspired by this, we introduce Event2Vec, a novel framework for learning representations of discrete event sequences. Our model leverages a simple, additive recurrent structure to learn composable, interpretable embeddings. We provide a theoretical analysis demonstrating that, under specific training objectives, our model's learned rep…

Chirally Frustrated Superradiant Phases in a Jaynes-Cummings Trimer
Lin-Lin Jiang, Xuan Xie, Lin Tian, Jin-Feng Huang
https://arxiv.org/abs/2507.13800 http…

Chirally Frustrated Superradiant Phases in a Jaynes-Cummings Trimer
We investigate the emergence of frustrated quantum phases in a Jaynes-Cummings (JC) trimer with complex hopping amplitudes between the cavities, which represents the smallest frustrated unit in light-matter systems. The complex hopping amplitudes that can be engineered via synthetic gauge fields introduce chiral effects and geometric frustration into the system.We obtain analytic solutions in the semiclassical limit and map out the phase diagram of this model, featuring one normal and three dis…

Leveraging Geometric Visual Illusions as Perceptual Inductive Biases for Vision Models
Haobo Yang, Minghao Guo, Dequan Yang, Wenyu Wang
https://arxiv.org/abs/2509.15156 https://…

Leveraging Geometric Visual Illusions as Perceptual Inductive Biases for Vision Models
Contemporary deep learning models have achieved impressive performance in image classification by primarily leveraging statistical regularities within large datasets, but they rarely incorporate structured insights drawn directly from perceptual psychology. To explore the potential of perceptually motivated inductive biases, we propose integrating classic geometric visual illusions well-studied phenomena from human perception into standard image-classification training pipelines. Specifically, …

Series B, Episode 01 - Redemption
CALLY: In range.
BLAKE: Force wall.
AVON: [Tries to activate force wall but it just burbles] Primary malfunction. Force wall won't activate.
BLAKE: Leave it. Hit it, Jenna, all the power we've got. Hang on!
https://blake.torpidity.net/m/201/113

Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications
Huaian Diao, Hongyu Liu, Qingle Meng, Li Wang
https://arxiv.org/abs/2507.14779

Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement), spectral geometry of transmission eigenfunctions, and geometric characterization of invisibility phenomena and inverse shape problems in wave scattering. We uncover and rigorously characterize a novel local pattern formation, establishing a sharp quantitative re…

An exotic Springer correspondence for $F_4$
Jonas Antor
https://arxiv.org/abs/2508.14199 https://arxiv.org/pdf/2508.14199

An exotic Springer correspondence for $F_4$
We investigate the structure of the `exotic nilcone' of $F_4$ which is defined by exploiting certain characteristic two phenomena. We show that there are finitely many orbits on this nilcone and construct an associated Springer correspondence. Further to that, we show that all corresponding `exotic Springer fibers' admit an affine paving. We also deduce from this a geometric classification of certain simple modules for the affine Hecke algebra with unequal parameters of type $F_4$.

Neural-GASh: A CGA-based neural radiance prediction pipeline for real-time shading
Efstratios Geronikolakis, Manos Kamarianakis, Antonis Protopsaltis, George Papagiannakis
https://arxiv.org/abs/2507.13917

Neural-GASh: A CGA-based neural radiance prediction pipeline for real-time shading
This paper presents Neural-GASh, a novel real-time shading pipeline for 3D meshes, that leverages a neural radiance field architecture to perform image-based rendering (IBR) using Conformal Geometric Algebra (CGA)-encoded vertex information as input. Unlike traditional Precomputed Radiance Transfer (PRT) methods, that require expensive offline precomputations, our learned model directly consumes CGA-based representations of vertex positions and normals, enabling dynamic scene shading without pr…

Crosslisted article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Non-negative curvature on certain product manifolds
Wen Shen
https://

Integer continued fractions for complex numbers
Cormac O'Sullivan
https://arxiv.org/abs/2508.15078 https://arxiv.org/pdf/2508.15078

Integer continued fractions for complex numbers
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation.

$Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory
Saebyeok Jeong, Norton Lee
https://arxiv.org/abs/2507.15450 https://

$Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory
We study the quantization of the moduli space of multiplicative Higgs bundles through the lens of five-dimensional $\mathcal{N}=1$ supersymmetric gauge theories in $Ω$-background. We extend the 4d $\mathcal{N}=2$ gauge theoretical construction of key geometric and representation-theoretic structures, established in earlier works, to the five-dimensional uplift. We construct and analyze the $Q$-operators and $q$-opers associated with the canonical codimension-two defect: the $Q$-operators are d…

Holomorphic parabolic geometries on smooth projective varieties
Benjamin McKay
https://arxiv.org/abs/2507.15691 https://arxiv.org/pdf…

Holomorphic parabolic geometries on smooth projective varieties
We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety model of any holomorphic parabolic geometry on that variety. Along the way, we uncover foliations and fibrations on smooth projective varieties that admit holomorphic parabolic geometries.

Mag-Match: Magnetic Vector Field Features for Map Matching and Registration
William McDonald, Cedric Le Gentil, Jennifer Wakulicz, Teresa Vidal-Calleja
https://arxiv.org/abs/2508.15300

Mag-Match: Magnetic Vector Field Features for Map Matching and Registration
Map matching and registration are essential tasks in robotics for localisation and integration of multi-session or multi-robot data. Traditional methods rely on cameras or LiDARs to capture visual or geometric information but struggle in challenging conditions like smoke or dust. Magnetometers, on the other hand, detect magnetic fields, revealing features invisible to other sensors and remaining robust in such environments. In this paper, we introduce Mag-Match, a novel method for extracting an…

Dirac monopole magnets in non-Hermitian systems
Haiyang Yu, Tao Jiang, Li-Chen Zhao
https://arxiv.org/abs/2508.15186 https://arxiv.org/pdf/2508.15186

Dirac monopole magnets in non-Hermitian systems
We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation $Δϕ_d = Δϕ_g$, which quantifies how cumulative…

Geometric Stability Analysis for Differential Inclusions Governed by Maximally Monotone Operators
Hassan Saoud, Michel Th\'era, Minh N. Dao
https://arxiv.org/abs/2507.13000

Geometric Stability Analysis for Differential Inclusions Governed by Maximally Monotone Operators
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a normal cone. However, the resulting dynamics are often difficult to analyze directly due to the absence of Lipschitz selections and boundedness. To overcome these challenges, we introduce a regularized system based on a fixed Lipschitz approximation of the co…

Nonvanishing results for K\"ahler varieties
Andreas H\"oring, Vladimir Lazi\'c, Christian Lehn
https://arxiv.org/abs/2508.14634 https://arxiv…

Nonvanishing results for Kähler varieties
Nonvanishing theorems play a central role in birational geometry, since they derive geometric consequences from numerical information and constitute a crucial step towards abundance and semiampleness problems. General nonvanishing statements remain rare, especially in the Kähler setting. We present two types of nonvanishing results for compact Kähler varieties. First, on non-uniruled varieties with nonzero Euler-Poincaré characteristic, we prove nonvanishing for adjoint bundles of numerica…

Self-Supervised Cross-Modal Learning for Image-to-Point Cloud Registration
Xingmei Wang, Xiaoyu Hu, Chengkai Huang, Ziyan Zeng, Guohao Nie, Quan Z. Sheng, Lina Yao
https://arxiv.org/abs/2509.15882

Self-Supervised Cross-Modal Learning for Image-to-Point Cloud Registration
Bridging 2D and 3D sensor modalities is critical for robust perception in autonomous systems. However, image-to-point cloud (I2P) registration remains challenging due to the semantic-geometric gap between texture-rich but depth-ambiguous images and sparse yet metrically precise point clouds, as well as the tendency of existing methods to converge to local optima. To overcome these limitations, we introduce CrossI2P, a self-supervised framework that unifies cross-modal learning and two-stage reg…

Replaced article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Rigidity of Kleinian groups via self-joinings: measure theoretic criterion
Dongryul M. Kim, Hee Oh

Centralizers in Hecke Algebras of Any Coxeter Group
Haiyu Chen
https://arxiv.org/abs/2508.14473 https://arxiv.org/pdf/2508.14473

Centralizers in Hecke Algebras of Any Coxeter Group
We study the centralizer of a parabolic subalgebra in the Hecke algebra associated with an arbitrary (possibly infinite) Coxeter group. While the center and cocenter have been extensively studied in the finite and affine cases, much less is known in the indefinite setting. We describe a basis for the centralizer, generalizing known results about the center. Our approach combines algebraic techniques with geometric tools from the Davis complex, a CAT(0)-space associated to the Coxeter group. As …

't Hooft Anomalies and Defect Conformal Manifolds: Topological Signatures from Modulated Effective Actions
Christian Copetti
https://arxiv.org/abs/2507.15466

't Hooft Anomalies and Defect Conformal Manifolds: Topological Signatures from Modulated Effective Actions
Symmetry breaking of continuous symmetries by extended dynamical defects entails the existence of continuous families of defects, which form conformal manifolds in a critical setup. In the presence of bulk 't Hooft anomalies, defects are in fact required to break the symmetry: defect conformal manifolds are anomaly-enforced. We show that, by coupling the system to a modulated deformation parameter, the geometric structure of the conformal manifold is sensible to the 't Hooft anomaly. This leads…

Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordstr\"om AdS Black Holes
Y. Sekhmani, G. G. Luciano, S. N. Gashti, A. Baruah
https://arxiv.org/abs/2508.14953

Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordström AdS Black Holes
We present a unified topological and geometric analysis of charged Anti-de Sitter (AdS) black holes immersed in a quintessence field, incorporating infrared gravitational corrections arising from the Extended Uncertainty Principle (EUP). The latter modifies the standard Heisenberg uncertainty relation by introducing a minimal momentum/maximal length scale, which effectively captures long-wavelength quantum gravitational effects relevant to black hole thermodynamics in curved spacetimes. We deri…

Crosslisted article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- $c_{\rm eff}$ from Resurgence at the Stokes Line
Griffen Adams, Ovidiu Costin, Gerald V. Dunne, Sergei Gukov, O\u{g}uz \"Oner

Global Regulation and Excitation via Attention Tuning for Stereo Matching
Jiahao Li, Xinhong Chen, Zhengmin Jiang, Qian Zhou, Yung-Hui Li, Jianping Wang
https://arxiv.org/abs/2509.15891

Global Regulation and Excitation via Attention Tuning for Stereo Matching
Stereo matching achieves significant progress with iterative algorithms like RAFT-Stereo and IGEV-Stereo. However, these methods struggle in ill-posed regions with occlusions, textureless, or repetitive patterns, due to a lack of global context and geometric information for effective iterative refinement. To enable the existing iterative approaches to incorporate global context, we propose the Global Regulation and Excitation via Attention Tuning (GREAT) framework which encompasses three attent…

Crosslisted article(s) found for math.GT. https://arxiv.org/list/math.GT/new
[1/1]:
- Pseudo-Anosov Flows: A Plane Approach
Thomas Barthelm\'e, Kathryn Mann

Covering Complete Geometric Graphs by Monotone Paths
Adrian Dumitrescu, J\'anos Pach, Morteza Saghafian
https://arxiv.org/abs/2507.10840 https://

Covering Complete Geometric Graphs by Monotone Paths
Given a set $A$ of $n$ points (vertices) in general position in the plane, the \emph{complete geometric graph} $K_n[A]$ consists of all ${n\choose 2}$ segments (edges) between the elements of $A$. It is known that the edge set of every complete geometric graph on $n$ vertices can be partitioned into $O(n^{3/2})$ noncrossing paths (or matchings). We strengthen this result under various additional assumptions on the point set. In particular, we prove that for a set $A$ of $n$ \emph{randomly} sele…

Geometric optimization for quantum communication
Chengkai Zhu, Hongyu Mao, Kun Fang, Xin Wang
https://arxiv.org/abs/2509.15106 https://arxiv.org/pdf/2509.1…

Geometric optimization for quantum communication
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the phenomenon of superadditivity. This work develops Riemannian optimization methods to establish significantly tighter, computable two-sided bounds on these fundamental quantities. For upper bounds, our method systematically searches for state and channel extensions th…

C-DOG: Training-Free Multi-View Multi-Object Association in Dense Scenes Without Visual Feature via Connected {\delta}-Overlap Graphs
Yung-Hong Sun, Ting-Hung Lin, Jiangang Chen, Hongrui Jiang, Yu Hen Hu
https://arxiv.org/abs/2507.14095

C-DOG: Training-Free Multi-View Multi-Object Association in Dense Scenes Without Visual Feature via Connected δ-Overlap Graphs
Multi-view multi-object association is a fundamental step in 3D reconstruction pipelines, enabling consistent grouping of object instances across multiple camera views. Existing methods often rely on appearance features or geometric constraints such as epipolar consistency. However, these approaches can fail when objects are visually indistinguishable or observations are corrupted by noise. We propose C-DOG, a training-free framework that serves as an intermediate module bridging object detecti…

The non-orientable spacetime of the eternal black hole
Ovidiu Racorean
https://arxiv.org/abs/2508.15005 https://arxiv.org/pdf/2508.15005

The non-orientable spacetime of the eternal black hole
We derive the metric of the BTZ black hole for the special case of interchanging the characteristics of space and time coordinates. We maximally extend the geometry of this interior solution and show that the line element is similar to its exterior solution counterpart. Thus, we assign the thermofield double state dual to this interior geometric construction. As a result, we have two independent thermofield double states corresponding to the BTZ metric: one dual to the exterior solution and one…

Enhancing Novel View Synthesis from extremely sparse views with SfM-free 3D Gaussian Splatting Framework
Zongqi He, Hanmin Li, Kin-Chung Chan, Yushen Zuo, Hao Xie, Zhe Xiao, Jun Xiao, Kin-Man Lam
https://arxiv.org/abs/2508.15457

Enhancing Novel View Synthesis from extremely sparse views with SfM-free 3D Gaussian Splatting Framework
3D Gaussian Splatting (3DGS) has demonstrated remarkable real-time performance in novel view synthesis, yet its effectiveness relies heavily on dense multi-view inputs with precisely known camera poses, which are rarely available in real-world scenarios. When input views become extremely sparse, the Structure-from-Motion (SfM) method that 3DGS depends on for initialization fails to accurately reconstruct the 3D geometric structures of scenes, resulting in degraded rendering quality. In this pap…

#Blakes7 Series D, Episode 10 - Gold
PILOT: [V.O., over comm.] There's no doubt in your mind that she'll die, Doctor?
DOCTOR: [V.O., over comm.] None at all, Captain.
PILOT: [V.O.] Aborting the trip is out of the question, I'm afraid.

Geometric phase in dissipative quantum batteries
Camila Cristiano, Ludmila Viotti, Paula I. Villar
https://arxiv.org/abs/2509.11313 https://arxiv.org/pdf/2…

Geometric phase in dissipative quantum batteries
We study the geometric phase accumulated during non-adiabatic charging of different driven open quantum systems serving as quantum battery models. We provide a full numerical analysis of dy- namics under different type of noises typically reported in superconducting circuits implementations. We complement the study with analytic results derived in the limiting case of no noise (i.e. isolated systems). We compute the non-unitary geometric phase acquired by the quantum batteries during the transi…

[2025-08-22 Fri (UTC), 5 new articles found for math.GT Geometric Topology]
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[2025-08-21 Thu (UTC), 8 new articles found for math.GT Geometric Topology]
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RoboEye: Enhancing 2D Robotic Object Identification with Selective 3D Geometric Keypoint Matching
Xingwu Zhang, Guanxuan Li, Zhuocheng Zhang, Zijun Long
https://arxiv.org/abs/2509.14966

RoboEye: Enhancing 2D Robotic Object Identification with Selective 3D Geometric Keypoint Matching
The rapidly growing number of product categories in large-scale e-commerce makes accurate object identification for automated packing in warehouses substantially more difficult. As the catalog grows, intra-class variability and a long tail of rare or visually similar items increase, and when combined with diverse packaging, cluttered containers, frequent occlusion, and large viewpoint changes-these factors amplify discrepancies between query and reference images, causing sharp performance drops…

[2025-09-22 Mon (UTC), 2 new articles found for math.GT Geometric Topology]
toXiv_bot_toot

BEVUDA : Geometric-aware Unsupervised Domain Adaptation for Multi-View 3D Object Detection
Rongyu Zhang, Jiaming Liu, Xiaoqi Li, Xiaowei Chi, Dan Wang, Li Du, Yuan Du, Shanghang Zhang
https://arxiv.org/abs/2509.14151

BEVUDA++: Geometric-aware Unsupervised Domain Adaptation for Multi-View 3D Object Detection
Vision-centric Bird's Eye View (BEV) perception holds considerable promise for autonomous driving. Recent studies have prioritized efficiency or accuracy enhancements, yet the issue of domain shift has been overlooked, leading to substantial performance degradation upon transfer. We identify major domain gaps in real-world cross-domain scenarios and initiate the first effort to address the Domain Adaptation (DA) challenge in multi-view 3D object detection for BEV perception. Given the complexit…

Unified Knowledge Distillation Framework: Fine-Grained Alignment and Geometric Relationship Preservation for Deep Face Recognition
Durgesh Mishra, Rishabh Uikey
https://arxiv.org/abs/2508.11376

Unified Knowledge Distillation Framework: Fine-Grained Alignment and Geometric Relationship Preservation for Deep Face Recognition
Knowledge Distillation is crucial for optimizing face recognition models for deployment in computationally limited settings, such as edge devices. Traditional KD methods, such as Raw L2 Feature Distillation or Feature Consistency loss, often fail to capture both fine-grained instance-level details and complex relational structures, leading to suboptimal performance. We propose a unified approach that integrates two novel loss functions, Instance-Level Embedding Distillation and Relation-Based P…