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.
MSA compares neural representations' intrinsic geometry for better understanding.
Minimal surfaces help compare geometric shapes.
A framework compares image representations based on local geometry.
A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated enveloping algebra. The corresponding curvatures are also compared.
We discuss some basic concepts of semi-Riemannian geometry in low-regularity situations. In particular, we compare the settings of (linear) distributional geometry in the sense of L. Schwartz and nonlinear distributional geometry in the sense of J.F. Colombeau.
We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is comparable to its flat length times the flat size of the subsurface.
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are invoked and compared.
In this paper we give an axiomatization of differential geometry comparable to model categories for homotopy theory. Weil functors play a predominant role.
Study compares geometric approaches for shape and deformation statistics.
It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manif…
A new geometry for comparing signals, overcoming traditional limitations.
In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.
Derived geometry can be defined as the universal way to adjoin finite homotopical limits to a given category of manifolds compatibly with products and glueing. The point of this paper is to show that a construction closely resembling existing approaches to derived geometry in fact produces a geometry with this universa…
The paper compares spectral geometry in hyperbolic and spherical manifolds.
We construct a canonically defined affine connection in sub-Riemannian contact geometry. Our method mimics that of the Levi-Civita connection in Riemannian geometry. We compare it with the Tanaka-Webster connection in the three-dimensional case.
Study compares bundles with connections to prehomogeneous geometries.
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
A novel method compares 3D point clouds using information geometry.
Study the Hessian geometry of an ideal gas in a centrifuge.
The study examines Lipschitz normally embedded Hölder triangles in 4D space.
New symmetries found in Riemann-Cartan geometries.
Geodesic currents on surfaces have comparable metrics in thick regions.
Study compares spectral properties of a specific tensor in geometry.
New method uses Riemannian geometry to quantify molecular shapes.
Felix Klein's so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The given translation was made in 1892 by Dr. M. W. Haskell and transcribed by N. C. Rug…
Constructs Cartan geometries from automorphism behaviors.
Study compares metrics from negative curvature and quasi-Fuchsian representations.
MKA incorporates manifold geometry into kernel alignment for more robust representation comparison.
I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume element, some information on the topology and metric is encoded in the partial or…
A new method compares unaligned datasets using log-Euclidean signatures of SPD matrices.
New discrepancy function compares discrete probability measures considering space geometry.
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential g…
Proposes GDTW for aligning time series on different, incomparable spaces.
We compare existence and equivariance phenomena for weak moment maps and homotopy moment maps in multisymplectic geometry.
Paper proposes a method to compare vector fields across surfaces, useful for analyzing brain folding patterns.
Study of Riemannian geometry on quaternionic unit ball linked to Sp(1,1) group.
New method uses Riemannian geometry to describe molecular shapes.
A new method integrates autoencoders with geometry regularization for manifold learning.
We show how to compute tensor derivatives and curvature tensors using affine connections. This allows for all computations to be obtained without using coordinate systems, in a way that parallels the computations appearing in classical Riemannian Geometry. In particular, we obtain Bianchi identities for the curvature t…
The paper uses geometric methods to classify medical data histograms.
Enhances knowledge graph completion with mixed geometry tensor factorization.
In our [Higher-order preconnections in synthetic differential geometry of jet bundles, Beiträge zur Algebra und Geometrie, 45 (2004), 677-696] we have established the affine bundle theorem in the synthetic approach to jet bundles in terms of infinitesimal spaces Dⁿ's. In our succeeding [Synthetic differential geo…
This article investigates the complex symplectic geometry of the deformation space of complex projective structures on a closed oriented surface of genus at least 2. The cotangent symplectic structure given by the Schwarzian parametrization is studied carefully and compared to the Goldman symplectic structure on the ch…
Study -flows reducing to complex geometry flows, focusing on -anomaly and -Laplacian coflow.
We discuss some properties of Jacobi fields that do not involve assumptions on the curvature endomorphism. We compare indices of different spaces of Jacobi fields and give some applications to Riemannian geometry.
The study compares lamplighter graphs up to quasi-isometry using coarse topology.
The paper matches features in images using centro-affine invariants and heat flow.
Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret…