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.
Classifies crossings in tangles on surfaces, finding no nontrivial indices.
In this paper we study the chord index of virtual knots, which can be thought of as an extension of the chord parity. We show how to use the chord index to define finite type invariants of virtual knots. The notions of indexed Jones polynomial and indexed quandle are introduced, which generalize the classical Jones pol…
A chord index homomorphism for knots in thickened surfaces is constructed.
New index principle shows indistinguishability of certain knot crossings.
A weak chord index is constructed for self crossing points of virtual links. Then a new writhe polynomial of virtual links is defined by using . is a generalization of writhe polynomial defined in [6]. Based on , three invariants of virtual links are constructed. These invariants can be used to …
The paper defines new homotopy relations on knot projections and classifies certain knot types.
The notion of a braided chord diagram is introduced and studied. An equivalence relation is given which identifies all braidings of a fixed chord diagram. It is shown that finite-type invariants are stratified by braid index for knots which can be represented as closed 3-braids. Partial results are obtained about spann…
Study counts sub-chord diagrams to classify spherical curves.
The paper defines functions from spherical curves and chord diagrams, proving invariance under specific Reidemeister moves.
In this paper we discuss how to define a chord index via smoothing a real crossing point of a virtual knot diagram. Several polynomial invariants of virtual knots and links can be recovered from this general construction. We also explain how to extend this construction from virtual knots to flat virtual knots.
Invariant detects sliceness of virtual knots with specific chord indices.
In this paper we prove an extrinsic one-sided curvature estimate for disks embedded in with constant mean curvature which is independent of the value of the constant mean curvature. We apply this extrinsic one-sided curvature estimate in [24] to prove to prove a weak chord arc type result for these disks…
Study on minimal surfaces with constraints on index and branching order.
Stability of Yang-Mills connections' Morse indices and nullity in 4D.
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic …
The paper shows that knot projections without triple chords can be simplified.
Paper explores relationships between triple chords and a specific homotopy relation in knot theory.
Solves -Gaussian chord Minkowski problem using Gauss curvature flow.
Sharp bounds on weak convergence rate for rough volatility models.
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary cir…
We consider framed chord diagrams, i.e. chord diagrams with chords of two types. It is well known that chord diagrams modulo 4T-relations admit Hopf algebra structure, where the multiplication is given by any connected sum with respect to the orientation. But in the case of framed chord diagrams a natural way to define…
The paper finds at least N orthogonal Finsler geodesic chords in a disk-like manifold.
Paper solves a generalized chord Minkowski problem using Gauss curvature flows.
The study improves inequalities for link diagrams and introduces weak rectangular diagrams.
Enhances Vassiliev knot invariants using chord diagrams.
To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The genus of an oriented chord diagram is the minimal genus of an oriented surface in which it may be realized. Let g_n denote the expected genus o…
In view of the result of Kontsevich, now often called ``the fundamental theorem of Vassiliev theory'', identifying the graded dual of the associated graded vector space to the space of Vassiliev invariants filtered by degree with the linear span of chord diagrams modulo the ``4T-relation'' (and in the unframed case, th…
We propose a novel approach for the generation of polyphonic music based on LSTMs. We generate music in two steps. First, a chord LSTM predicts a chord progression based on a chord embedding. A second LSTM then generates polyphonic music from the predicted chord progression. The generated music sounds pleasing and harm…
It is known that the totally umbilical hypersurfaces in the (n+1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. That is, a compact hypersurface with constant mean curvature, cmc, in S^{n+1}, different from an Euclidean sphere, must have stability index greater than or equa…
Paper develops invariants for spherical curves using chord diagrams.
The study finds at least two short, simple geodesic chords on a disk with convex boundary.
The paper proves the existence and properties of geodesics on convex surfaces.
Vassiliev invariants can be studied by studying the spaces of chord diagrams associated with singular knots. To these chord diagrams are associated the intersection graphs of the chords. We extend results of Chmutov, Duzhin and Lando to show that these graphs determine the chord diagram if the graph has at most one loo…
The paper calculates a specific weight system for chord diagrams with a particular graph structure.
We introduce a new geometric flow called the chord shortening flow which is the negative gradient flow for the length functional on the space of chords with end points lying on a fixed submanifold in Euclidean space. As an application, we give a simplified proof of a classical theorem of Lusternik and Schnirelmann (and…
The study estimates Reeb chords using sheaf theory and persistence.
The paper finds an upper limit for the length of geodesic chords on Riemannian manifolds.
We present a new approach to harmonic analysis that is trained to segment music into a sequence of chord spans tagged with chord labels. Formulated as a semi-Markov Conditional Random Field (semi-CRF), this joint segmentation and labeling approach enables the use of a rich set of segment-level features, such as segment…
For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to t…
Proves Arnol'd's chord conjecture for conormal bundles.
The study proves geodesic loops and chords without intersections for specific metrics.
Study on curve shortening flow with boundary conditions, proving convergence or contraction.
Complete invariant defined for doodles on a sphere.
The paper proves stability of critical points for conformally invariant Lagrangians.
In previous work, we defined the intersection graph of a chord diagram associated with a string link (as in the theory of finite type invariants). In this paper, we look at the case when this graph is a tree, and we show that in many cases these trees determine the chord diagram (modulo the usual 1-term and 4-term rela…
Paper shows how to represent Milnor's triple linking number using chord diagrams and doodle invariants.
This is the first of two papers in which we prove that a cell model of the moduli space of curves with marked points and tangent vectors at the marked points acts on the Hochschild co--chains of a Frobenius algebra. We also prove that a there is dg--PROP action of a version of Sullivan Chord diagrams which acts on the …
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study…