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 mappings on closed manifolds can't be broken down easily.
Study shows pooling scores for conformal prediction distorts group coverage.
Vertex distortion measures how far lattice knots deviate from straight lines.
Develops a unified framework for computing n-dimensional quasi-conformal mappings.
Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular distortion. Conformal registrations are beneficial since it preserves the local ge…
Efficiently samples conformal boundaries in high dimensions using flows.
A neural network method tackles high-dimensional diffeomorphic mapping problems.
Develops a method for conformal parameterization of point clouds without fixed boundaries.
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the…
Polyconvex energies with conformal invariance have smooth stationary points outside a discrete set.
QC-SPHARM detects Alzheimer's Disease early using hippocampal surface geometry.
New framework for better mapping of surfaces onto ellipsoids.
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichmüller map between Riemann surfaces of finite type are theoretically guaranteed [1]. Rece…
A robust method for decomposing spectral peaks robust to distortion and interference.
We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circ…
Method determines asset prices in incomplete markets to optimize portfolios.
A general criterion in terms of the Schwarzian derivative is given for global univalence of the Weierstrass--Enneper lift of a planar harmonic mapping. Results on distortion and boundary regularity are also deduced. Examples are given to show that the criterion is sharp. The analysis depends on a generalized Schwarzian…
Motivation: Proteins are known to undergo conformational changes in the course of their functions. The changes in conformation are often attributable to a small fraction of residues within the protein. Therefore identification of these variable regions is important for an understanding of protein function. Results: We …
This paper presents a method to compute the {\it quasi-conformal parameterization} (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain onto a punctured disk associated with a given Beltrami differential. The Beltrami differential, which me…
We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero surfaces that minimizes this energy. We then prove that the energies of the minimizing …
Vertex distortion detects if a knot is unknot.
Algorithm finds optimal affine transformation to minimize overall distortion.
We consider the problem of distortion minimal morphing of -dimensional compact connected oriented smooth manifolds without boundary embedded in . Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
Most distortion correction methods focus on simple forms of distortion, such as radial or linear distortions. These works undistort images either based on measurements in the presence of a calibration grid, or use multiple views to find point correspondences and predict distortion parameters. When possible distortions …
Study distortion risk measures for step-weighted distributions.
The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we prove that any nontrivial tame knot has distortion at least 5pi/3; examples show that distortion under 7.16 suffices to build a trefoil kno…
Computed distortion coefficients for the α-Grushin plane.
Study on risk measures using distorted Choquet integrals with random distortions.
Develops spherical density-equalizing maps for closed surfaces.
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
Registration, which aims to find an optimal one-to-one correspondence between different data, is an important problem in various fields. This problem is especially challenging when large deformations occur. In this paper, we present a novel algorithm to obtain diffeomorphic image or surface registrations with large def…
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical imaging, computer graphics and computer vision. Existing computational QC theor…
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, ha…
The distortion of a curve is the supremum, taken over distinct pairs of points of the curve, of the ratio of arclength to spatial distance between the points. Gromov asked in 1981 whether a curve in every knot type can be constructed with distortion less than a universal constant C. Answering Gromov's question seems to…
Euler and Delisle developed a map method for the Russian Empire, which is now outperformed by the Lambert conformal conical projection.
The study shows exponential distortion in virtually special groups containing free subgroups.
Estimates rate-distortion function for large datasets using neural networks.
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.
New coding theorem shows achievable rate matches theoretical limit.
Paper proposes a new black-box attack approach to minimize visual distortion.
Sharp bounds for distortion risk metrics under uncertain distributions.
Study stability of rigid motions and Möbius transformations on spheres, proving new rigidity estimates.
Study dynamic risk measures and performance indices using distortion functions.
New bounds on knot distortion and Seifert surface properties.
In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is …
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…
New method tests risk measures for various distortions.