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 approach to rotational Weingarten surfaces using geometric momentum.
New groups from strand diagrams show polycyclic subgroups are virtually abelian and undistorted.
Extends harmonic map theory to arbitrary surfaces.
New perspective on Heegaard splittings using square complexes and combinatorial measurements.
Simplifies convolutions using tensor networks and einsum for efficient second-order methods.
We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are exactly characterized b…
The paper studies Einstein metrics on homogeneous supermanifolds.
We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrat…
The paper refines transformations of lattice diagrams and introduces dotted diagrams.
This note explains how to transform Heegaard diagrams into framed link diagrams.
New minimal link diagrams found, including torus links and homogeneous ones.
We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of curvature is a second order system of partial differential equations which we sho…
Algorithm converts Kirby diagrams to trisection diagrams for 4-manifolds.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering …
Study categorizes knots and links as rigid or shaky based on Reidemeister moves.
Twisted graph diagrams are virtual graph diagrams with bars on edges. A bijection between abstract graph diagrams and twisted graph diagrams is constructed. Then a polynomial invariant of Yamada-type is developed which provides a lower bound for the virtual crossing number of virtual graph diagrams.
We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals consid…
The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with comput…
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Problems on region choices for knot and link diagrams solved using Alexander numbering.
Table of symmetric diagrams for knots up to 10 crossings.
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we provide a framework for working with subknots inside of knot diagrams via knotoid dia…
Proves minimal crossing diagrams for specific spatial graphs.
Rectangular diagrams help analyze foliations in 3-sphere.
Bankwitz characterized an alternating diagram representing the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize an almost alternaing diagram representing the trivial knot. As a corollary we determine an unknotting number one alter…
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the original knot diagram has a small number of crossings, thus outperforming the famous…
The paper explores when specific knot operations simplify diagrams.
Study on positive solutions of Yamabe-type equation on spheres.
Gauss diagrams' properties can change with Hamiltonian cycle choice.
New estimate of semimeander complexity for knots with more than 10 crossings.
Paper proves link diagrams can be realized for some but not all types of links.
GridPyM handles grid diagrams for knot theory.
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While every plane graph arises as a Tait graph of a unique link diagram, not every embedd…
The study improves inequalities for link diagrams and introduces weak rectangular diagrams.
In this paper, a link diagram is said to be minimal if no Reidemeister move I or II can be applied to it to reduce the number of crossings. We show that for an arbitrary diagram D of a link without a trivial split component, a minimal diagram obtained by applying Reidemeister moves I and II to D is unique. The proof al…
By using the cohomology theory of quandles, quandle cocycle invariants and shadow quandle cocycle invariants are defined for oriented links and surface-links via broken surface diagrams. By using symmetric quandles, symmetric quandle cocycle invariants are also defined for unoriented links and surface-links via broken …
Standard trisection diagrams found for Mazur type 4-manifolds.
Algorithm for recognizing and performing Reidemeister moves in Gauss diagrams.
Minimal grid diagrams for 12-crossing prime knots identified.
The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.
Complete criterion for VoI in multi-decision influence diagrams established.
A virtual link diagram is called mod almost classical if it admits an Alexander numbering valued in integers modulo , and a virtual link is called mod almost classical if it has a mod almost classical diagram as a representative. In this paper, we introduce a method of constructing a mod almost class…
Study minimum ribbonlength of immersed flat knots and links.
Algorithm constructs Kirby diagrams for 4D open books.
For an oriented virtual link, L.H. Kauffman defined the f-polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which the diagram can be embedded. In this paper we show that the span of the f-polynomial of an alternating virtual link L is determined by the nu…
Study shows that splitting links requires an arbitrarily large number of extra crossings.