Ray marching method visualizes flat surfaces efficiently.
problem Efficient visualization of flat surfaces.
method Ray marching approach for intuitive exploration.
result Effective visualization of translation surfaces and polyhedra.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “ray marching”
Ray-marching method visualizes 8 Thurston geometries in real-time.
problem Accurately rendering and visualizing Thurston geometries in real-time.
method Ray-marching algorithms with theoretical framework for non-Euclidean geometries.
result Accurate interactive real-time views of Thurston geometries achieved.
Paper proves March's criterion for transience on symmetric manifolds.
problem Determining transience on rotationally symmetric manifolds.
method Analyzes bounded non-constant harmonic functions and Dirichlet problem at infinity.
result March's criterion is necessary and sufficient for transience.
This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on ?" This unsolved mathematical question was the subject of the Conference "MAM 1 (Non-)Existence of Complex Structures on ", which took place at Philipps-Universität Marburg, Germany, between M…
Study extends geodesic ray transform results to orientable surfaces.
problem Characterize and stabilize mixed and transverse ray transforms on surfaces.
method Algebraic arguments applied to various geometries and ray transforms.
result Characterization of kernel and stability for mixed and transverse ray transforms on orientable surfaces.
ObSuRF converts a single image into a 3D model with NeRFs.
problem Creating a 3D model from a single image with object segmentation.
method Unsupervised volume segmentation using Neural Radiance Fields (NeRFs).
result ObSuRF can segment a 3D scene into objects from a single image.
The Ray-Singer torsionmath.DG
Ray-Singer torsion is a mathematical concept with applications in physics.
problem No specific problem stated in the abstract.
method No specific method stated in the abstract.
result No specific key result stated in the abstract.
In this paper we review the well-known fact that the only spheres admitting an almost complex structure are S^2 and S^6. The proof described here uses characteristic classes and the Bott periodicity theorem in topological K-theory. This paper originates from the talk "Almost Complex Structures on Spheres" given by the …
Lecture notes from the Third International School on Geometry and Physics at the Centre de Recerca Matematica in Barcelona, March 26--30, 2012.
We show that any grafting ray in Teichmüller space is (strongly) asymptotic to some Teichmüller geodesic ray. As an intermediate step we introduce surfaces that arise as limits of these degenerating Riemann surfaces. Given a grafting ray, the proof involves a Teichmüller ray with a conformally equivalent limit, and bui…
Survey on broken ray transforms and open problems.
problem Understanding broken ray transforms and their applications.
method Survey of recent developments and open problems.
result Discussion of open problems in broken ray transforms.
We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the …
We study rays and co-rays in the Wasserstein space () whose ambient space is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability measures concentrated on the set of rays in the ambient spac…
Three disjoint rays in euclidean 3-space form Borromean rays provided their union is knotted, but the union of any two components is unknotted. We construct infinitely many Borromean rays, uncountably many of which are pairwise inequivalent. We obtain uncountably many Borromean hyperplanes.
Infinite clique of rays in plane minus Cantor set.
problem Understanding the mapping class group of plane minus Cantor set.
method Using a graph of loops and cliques of high-filling rays.
result Construction of an infinite clique of high-filling rays.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
problem Analyzing light ray transform in pseudo-Euclidean space.
method Investigate normal operator, derive inversion formula, analyze as Fourier Integral Operator.
result Derive an inversion formula and prove stability estimates.
Unique geodesics selected by energy minimization in Teichmüller space.
problem Finding a unique geodesic between points in Teichmüller space.
method Energy minimization of harmonic map rays, extending Thurston boundary.
result Selection of a unique Thurston geodesic through points in Teichmüller space.
The article recovers tensor fields from partial data using weighted divergent ray transforms.
problem Recovering tensor fields from partial data.
method Weighted divergent ray transforms, unique continuation property of fractional Laplacian, explicit reconstruction formulas.
result Recovery of symmetric -tensor fields and unique continuation for vector fields and symmetric 2-tensor fields.
The ray graph is a Gromov hyperbolic graph on which the mapping class group of the plane minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the ray graph in terms of cliques of long rays on the plane minus a Cantor set. As a consequence, we prove that the Gromov boundary of the ray g…
Regularity results for geodesic X-ray transform on nonsmooth manifolds
problem Geodesic X-ray transform on nonsmooth simple manifolds
method Symbol smoothing arguments and pseudodifferential operators with low regularity symbols
result Improved injectivity results for functions
Local X-ray transform works well near boundaries in hyperbolic spaces.
problem Injectivity of X-ray transform near boundaries for hyperbolic metrics.
method Local injectivity proof for geodesic X-ray transform on asymptotically hyperbolic manifolds.
result Local injectivity near a boundary point for X-ray transform in dimensions 3 and higher, up to .
Paper shows invertibility of tensor X-ray transform on certain manifolds.
problem Invertibility of tensor X-ray transform on asymptotically conic manifolds.
method Used 1-cusp pseudodifferential operator algebra and modified solenoidal gauge condition.
result Invertibility of tensor X-ray transform up to natural obstruction.
New proofs of Donaldson-Uhlenbeck-Yau theorem using geodesic rays.
problem Donaldson-Uhlenbeck-Yau theorem implications
method Geodesic rays of Hermitian metrics
result New proofs of the theorem
We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a function is determined by its integrals over broken geodesic rays that reflect on the boundary of th…
Study proves uniqueness for ray transform on surfaces with obstacles.
problem Uniqueness of functions and 1-forms on surfaces with reflecting obstacles.
method Broken ray transform on twisted geodesics with nonpositive curvature and reflecting boundary.
result Proves uniqueness result for sums of functions and 1-forms.
The study examines the asymptotic behavior of extremal length in Teichmüller space.
problem Understanding the asymptotic behavior of extremal length along Teichmüller rays.
method Analyzing the limit of extremal length and deriving formulas for limiting Teichmüller distance and detour metric.
result An explicit formula for the limiting Teichmüller distance and a necessary and sufficient condition for Teichmüller rays to be asymptotic.
Local invertibility of ray transforms on convex manifolds.
problem Invertibility of ray transforms on compact Riemannian manifolds with strictly convex boundary.
method Local invertibility results for transverse and mixed ray transforms of 1 and 1+1 tensors.
result Local invertibility of ray transforms near boundary points, leading to global results.
This article contains a detailed study, in the toric case, of the test configuration geodesic rays defined by Phong-Sturm. We show that the `Bergman approximations' of Phong-Sturm converge in C^1 to the geodesic ray and that the geodesic ray itself is C^{1,1} and no better. The \kahler metrics associated to the geodesi…
The natural topological, differentiable and geometrical structures on the space of light rays of a given spacetime are discussed. The relation between the causality properties of the original spacetime and the natural structures on the space of light rays are stressed. Finally, a symplectic geometrical approach to the …
Study on Teichmüller rays' asymptotic behavior and distances.
problem Understanding the asymptotic behavior of Teichmüller rays.
method Explicit formula derivation for limiting Teichmüller distance under specific conditions.
result Two Teichmüller rays are asymptotic if their vertical measured foliations are modularly equivalent and their limit surfaces coincide.
In this paper, we consider the asymptotic behavior of two Teichmüller geodesic rays determined by Jenkins-Strebel differentials, and we obtain a generalization of a theorem in \cite{Amano14}. We also consider the infimum of the asymptotic distance in shifting base points of the rays along the geodesics. We show that th…
Study shows stability in X-ray transform on specific hyperbolic manifolds.
problem Stability of X-ray transform on asymptotically hyperbolic manifolds.
method Constructed a parametrix for the normal operator in 0-pseudodifferential calculus.
result Showed a stability estimate for the X-ray transform.
On the broken ray transformmath.DG
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is injective. We employ four different methods to approach this question, and each o…
These are lecture notes mainly aimed at graduate students on selected aspects of generalized geometry: in particular generalized complex and Kaehler structures and generalized holomorphic bundles. They are based on lectures given in March 2010 at the Chinese University of Hong Kong.
Injectivity result for light ray transform on Lorentzian manifolds.
problem Injectivity of light ray transform on Lorentzian manifolds.
method Explicit relationship between geodesic and magnetic vector fields.
result Injectivity up to natural obstruction under certain conditions.
New methods model gamma-ray data to better understand Galactic emissions.
problem Uncertain diffuse Galactic gamma-ray emissions bias data interpretation.
method Gaussian processes and variational inference for flexible modeling.
result More robust interpretation of gamma-ray sky, especially dark matter signals.
New Teichmüller geodesic rays found with unique foliations.
problem Capturing generic directions in Teichmüller space.
method Using Chaika-Masur-Wolf and Durham-Zalloum work.
result First sublinearly-Morse geodesic rays with minimal non-uniquely ergodic foliations.
We construct symplectic and Kähler ray reduced spaces and discuss their relation with the Marsden-Weinstein (point) reduction. This Kähler reduction is well defined even when the momentum value is not totally isotropic. The compatibility of the ray reduction with the cone construction and the Boothby-Wang fibration is …
These are lecture notes on scale calculus and M-polyfolds written for a graduate course at UNICAMP March-June 2018 and an advanced mini-course given during the biannual meeting of Brazilian mathematicians, CBM-32, at IMPA in August 2019.
Ray tracing sampler improves neural network sampling efficiency and resilience.
problem Sampling neural network posterior distributions efficiently and robustly.
method Markov Chain Monte Carlo using ray tracing through likelihood space.
result Significantly higher resilience to gradient heating compared to HMC.
An Entropy-Based Test and Development Framework for Uncertainty Modeling in Level-Set Visualizationscs.HC
The study evaluates different probability models for uncertainty visualization using entropy calculations.
problem Choosing the right probability model affects memory use, run time, and accuracy in uncertainty visualization.
method Entropy calculation on ensemble data to compare various probability models (uniform, Gaussian, histogram, quantile).
result Models matching the ensemble data distribution have the lowest entropy, indicating better accuracy.
Optical interpretation of Euler's angle problem for caustics of light rays.
problem Euler's angle problem for caustics of light rays.
method Optical interpretation of intrinsic equations and study of caustics.
result Characterization of curves under specific conditions and novel pantograph equations.
Symplectic manifold rays can be removed without changing the manifold's structure.
problem Removing parametrized rays from a symplectic manifold without altering its structure.
method Using a specific vector field condition to ensure symplectomorphism.
result Symplectic manifolds and their subsets remain symplectomorphic after removing parametrized rays.
Characterizes closures of test configurations and algebraic singularity types.
problem Understanding closures of test configurations and algebraic singularity types.
method Analyzes metric spaces of geodesic rays and characterizes closures of singularity types.
result Arithmetic and non-pluripolar volumes coincide for algebraic singularity types, and equality holds on their closure.
Injective X-ray transform on Heisenberg group for regular functions.
problem Injectivity of X-ray transform on sub-Riemannian manifolds.
method Group Fourier Transform and analysis of taming metrics.
result Sufficiently regular functions on Heisenberg group are determined by their line integrals.
Paper proves injectivity of non-abelian X-ray transform on certain spaces.
problem Injectivity of non-abelian X-ray transform on asymptotically hyperbolic spaces.
method Gauge equivalence for unitary connections and skew-Hermitian Higgs fields.
result Injectivity result for non-abelian X-ray transform over skew-Hermitian Higgs fields.
We show that the diameter of the skinning map of an acylindrical hyperbolic 3-manifold M is bounded on thick Teichmueller geodesic rays by a constant depending only on the thickness of the ray and the topological type of the boundary of M.
New metric spaces for geodesic rays in cohomology classes.
problem Constructing geodesic rays in cohomology classes with finite energy.
method Introduced a chordal metric and proved geodesic properties.
result Found a characterization of geodesic rays in terms of test curves.