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.
New quasi-geodesics for Stiefel manifold simplify complex computations.
New formulas for geodesics on Stiefel and flag manifolds using trust-region method.
Geodesic algorithms extended to arbitrary ellipsoids.
Bounds on geodesic distances on Stiefel manifold derived from new metrics.
In this paper we present the full details of the construction of a Morse-Floer type homology related to the super-quadratic perturbation of the Dirac-geodesic model. This homology is computed explicitly using a Leray-Serre type spectral sequence and this computation leads us to several existence results of Dirac-geodes…
GEORCE computes geodesics quickly and accurately.
Study geodesic curves on Heisenberg group, classify them, and compute first step of quadrature.
Convex optimization is a vibrant and successful area due to the existence of a variety of efficient algorithms that leverage the rich structure provided by convexity. Convexity of a smooth set or a function in a Euclidean space is defined by how it interacts with the standard differential structure in this space -- the…
New method to bound Laplacian eigenvalues of geodesic balls.
We compute curvatures of a three-manifold formed by a Weil-Petersson geodesic in Teichmuller space.
The curve graphs are not locally finite. In this paper, we show that the curve graphs satisfy a property which is equivalent to graphs being uniformly locally finite via Masur--Minsky's subsurface projections. As a direct application of this study, we show that there exist computable bounds for Bowditch's slices on tig…
We give an algorithm to compute the stable lengths of pseudo-Anosovs on the curve graph, answering a question of Bowditch. We also give a procedure to compute all invariant tight geodesic axes of pseudo-Anosovs. Along the way we show that there are constants such that the minimal upper bound on `slices' of …
In this paper we study 1/k geodesics, those closed geodesics that minimize on all subintervals of length , where is the length of the geodesic. We develop new techniques to study the minimizing properties of these curves on doubled polygons, and demonstrate a sequence of doubled polygons whose closed geodesics…
Geodesic envelopes stay uniformly bounded in specific Teichmüller spaces.
New method for geodesics of multivariate normals, derived from a Toda lattice.
Study geodesic curvature of logarithmic spirals on curved surfaces.
We describe a polynomial-time algorithm to compute a (tight) geodesic between two curves in the curve graph. As well as enabling us to compute the distance between a pair of curves, this has several applications to mapping classes. For example, we can use these geodesics to compute the asymptotic translation length, Ni…
We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.
Researchers compute de Rham cohomology of geodesic flow foliations on hyperbolic surfaces.
Study geodesic complexity in homogeneous Riemannian manifolds.
Study compact Willmore surfaces without complex structure convergence, computing energy loss and geodesic lengths.
This paper aims to systematically and comprehensively initiate a foundation for using concepts from computational differential geometry as instruments for power flow computing and research. At this point we focus our discussion on the static case, with power flow equations given by quadratic functions defined on voltag…
New upper bound for geodesic complexity derived from cut locus decompositions.
Estimates barycenter in geodesic spaces with finite sample bounds.
We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmueller geodesic flow restricted to the hyperelliptic connected components, settling a question of Farb. We stress that all proofs a…
Dissertation tackles geodesic ray transform on Riemannian manifolds.
Geodesically equivalent Finsler metrics share invariant volume forms and first integrals.
We consider equitorsion second type almost geodesic mappings of a non-symmetric affine connection space in this article. Using different computational methods, we obtained some invariants of these mappings. Last generalized Thomas projective parameter and Weyl projective tensor as invariants of a second type almost geo…
Researchers find geodesics on K3 surfaces using electrostatics.
Study magnetic geodesics on odd spheres, computing critical energy values.
We give an algorithm for determining the distance between two vertices of the complex of curves. While there already exist such algorithms, for example by Leasure, Shackleton, and Webb, our approach is new, simple, and more effective for all distances accessible by computer. Our method gives a new preferred finite set …
New method calculates winding of geodesics on surfaces.
We compute the number of systoles, the shortest simple closed geodesics and 2-systoles, the second shortest simple closed geodesics on hyperbolic surfaces homeomorphic to once-punctured torus and four-punctured sphere.
Given a space it is easy to obtain the system of geodesic equations on it. In this paper the inverse problem of reconstructing the space from the geodesic equations is addressed. A procedure is developed for obtaining the metric tensor from the Christoffel symbols. The procedure is extended for determining if a second …
The paper calculates the volume growth of hyperbolic surfaces with short geodesics.
Study geodesics on compact Lorentzian solvmanifolds, finding conditions for closedness.
Totally geodesically embeddings of infinitely many closed 7-manifolds into 13-dimensional positively curved closed Riemannian manifolds are constructed. The problems of computing pinching constants and existence of other totally geodesical embeddings are discussed.
We compute the asymptotics, as R tends to infinity, of the number of closed geodesics in Moduli space of length at most R, or equivalently the number of pseudo-Anosov elements of the mapping class group of translation length at most R.
In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the cost function. The first proposed problem is control for positive definite Hermiti…
Super efficient geodesics have a unique vertex in the complex of curves.
We show that the geodesic period spectrum of a Riemannian 2-orbifold all of whose geodesics are closed depends, up to a constant, only on its orbifold topology and compute it. In the manifold case we recover the fact proved by Gromoll, Grove and Pries that all prime geodesics have the same length. In the appendix we pa…
The paper computes special values of combinatorial zeta functions to reveal topological properties of manifolds.
Neural solver computes Wasserstein geodesics and velocity fields efficiently.
New data-driven Cartan connection tracks complex vascular structures.
A new snake model improves segmentation of SEM images.
Researchers compute contact structures for null geodesics on specific spacetimes.
Generalizes Rips' result on hyperbolic spaces to metric spaces, showing collapses for tree metrics.
GeONet learns the Wasserstein geodesic without mesh discretization.