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.
Study shows how optimal transport behaves in higher dimensions.
Geometric optics describes wave behavior near convex obstacles.
Solves open problem on simple surfaces with novel twistor correspondence.
The paper studies ray transforms on surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.
It is shown that curvature-dimension bounds CD(N, k) for a metric measure space (X,d,m) in the sense of Sturm imply a weak L^1- Poincare-inequality under some symmetry assumption on the choice of transport rays in the cut locus of (X,d). This condition is satisfied if (X,d) has m-almost surely no branching points.
Researchers find Busemann functions in Wasserstein space, enabling efficient projections and distances.
Study improves Calderón problem for systems, uniquely determining connections and potentials.
Study solves inverse problems for real principal type operators using unique data sets and ray transforms.
We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of th…
Study geodesic X-ray transform and streaking artifacts on simple surfaces or spaces of constant curvature.
We prove a quantitative version of Obata's Theorem involving the shape of functions with null mean value when compared with the cosine of distance functions from single points. The deficit between the diameters of the manifold and of the corresponding sphere is bounded likewise. These results are obtained in the genera…
Study proves solenoidal injectivity for tensor fields on curved manifolds with low regularity.
For homeland and transportation security applications, 2D X-ray explosive detection system (EDS) have been widely used, but they have limitations in recognizing 3D shape of the hidden objects. Among various types of 3D computed tomography (CT) systems to address this issue, this paper is interested in a stationary CT u…
To improve the performance of classical generative adversarial network (GAN), Wasserstein generative adversarial networks (W-GAN) was developed as a Kantorovich dual formulation of the optimal transport (OT) problem using Wasserstein-1 distance. However, it was not clear how cycleGAN-type generative models can be deriv…
On a Riemannian manifold with a positive lower bound on the Ricci tensor, the distance of isoperimetric sets from geodesic balls is quantitatively controlled in terms of the gap between the isoperimetric profile of the manifold and that of a round sphere of suitable radius. The deficit between the diameters of the mani…
Bayesian calibration for BCP self-assembly models using image data and measure transport.
Study extends geodesic ray transform results to orientable surfaces.
Ray-Singer torsion is a mathematical concept with applications in physics.
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.
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.
New surfaces with conjugate points have global blow-down maps in their TT spaces.
Infinite clique of rays in plane minus Cantor set.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
Unique geodesics selected by energy minimization in Teichmüller space.
The article recovers tensor fields from partial data using weighted divergent ray transforms.
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
Local X-ray transform works well near boundaries in hyperbolic spaces.
Paper shows invertibility of tensor X-ray transform on certain manifolds.
New proofs of Donaldson-Uhlenbeck-Yau theorem using geodesic rays.
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…
We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral geometry question of some attenuated geodesic ray transform through a pseudolinear…
Study proves uniqueness for ray transform on surfaces with obstacles.
The study examines the asymptotic behavior of extremal length in Teichmüller space.
Local invertibility of ray transforms on convex manifolds.
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.
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.
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…
Injectivity result for light ray transform on Lorentzian manifolds.
New methods model gamma-ray data to better understand Galactic emissions.
New Teichmüller geodesic rays found with unique 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 …