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.
Study groups with polynomial growth, finding structure and applications.
Study geometric structures and their interactions under different metrics.
A -dimensional Lie group equipped with a left invariant symplectic form $\om^+$ is called a symplectic Lie group. It is well-known that $\om^+$ induces a left invariant affine structure on . Relatively to this affine structure we show that the left invariant Poisson tensor corresponding to $\om^+$ is po…
Graphical notation simplifies complex polynomial constraints in linear models.
Study polynomial structures on generalized tangent bundles and their compatibility with operators.
We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollobás-Riordan polynomial to ribbon graph with this structure. The extended polynomial satisfies the contraction-deletion relations and naturally behaves with respect to the partial duality of ribbon graphs. We construct an arrow ri…
Quantum polynomials are derived from a specific tribracket structure.
New Frobenius manifold structures found on Dicyclic group orbits.
We establish a quadratic identity for the Yamada polynomial of ribbon cubic graphs in 3-space, extending the Tutte golden identity for planar cubic graphs. An application is given to the structure of the flow polynomial of cubic graphs at zero. The golden identity for the flow polynomial is conjectured to characterize …
Origami structures are enumerated and shown to be quantum modular.
Study the relationship between canonical polynomials and elliptic sequences for elliptic singularities.
Study on colored Jones polynomial and link complements.
This article discuss a class of tractable model in the form of polynomial type.
Classifies connected shelves up to order six.
In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we gi…
New polynomials defined for quandle structures, enhancing graph invariants.
Knitted and woven textile structures are examples of doubly periodic structures in a thickened plane made out of intertwining strands of yarn. Factoring out the group of translation symmetries of such a structure gives rise to a link diagram in a thickened torus. Such a diagram on a standard torus is converted into a c…
Continuity of roots of hyperbolic polynomials with smooth coefficients.
New findings on computational limits for estimating hidden structures.
New knot models analyze local entanglement for robust curve analysis.
The study describes a cell structure for multisets in a rectangle.
New formula simplifies interior polynomial calculation.
New invariants for singular knots and links defined using shadow structures.
In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions and low degrees. We provide the tools to calculate simple cubic Poisson structu…
We define a two-variable polynomial invariant of finite quandles. In many cases this invariant completely determines the algebraic structure of the quandle up to isomorphism. We use this polynomial to define a family of link invariants which generalize the quandle counting invariant.
We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special Kähler geometry and the ring of almost-holomorphic modular forms defined on modular curves.
We formulate a conjecture (already proven by A. Kricker) about the structure of Kontsevich integral of a knot. We describe its value in terms of the generating functions for the numbers of external edges attached to closed 3-valent diagrams. We conjecture that these functions are rational functions of the exponentials …
Investigates polynomial solutions to minimal surface equation, proving constraints and structure theorems.
We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the (2,1)-colored HOMFLY polynomials that distinguish a famous mutant pair, Kinoshita-Terasaka and Conway knot.
Two categorifications are given for the arrow polynomial, an extension of the Kauffman bracket polynomial for virtual knots. The arrow polynomial extends the bracket polynomial to infinitely many variables, each variable corresponding to an integer {\it arrow number} calculated from each loop in an oriented state summa…
NO approximates non-Markovian BSDEs with polynomial scaling in 1/ε.
Researchers find Frobenius manifold structures on orbits spaces of finite groups.
New polynomial invariants derived from birack and switch structures.
Novel symmetry found in colored HOMFLY polynomials from superalgebras.
The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designe…
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are us…
The paper studies geometric structures of polynomial spaces.
Recently, it has been shown that the Jones polynomial, in [LS19], and the Alexander polynomial, in [NT18], of rational knots can be obtained by specializing -polynomials of cluster variables. At the core of both results are continued fractions, which parameterize rational knots and are used to obtain cluster variabl…
Compact groups with polynomial growth have specific embeddings.
We study computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded factor size and bounded connectivity can be learned in polynomial time and polynomial number of samples, assuming that the data is generated by a netwo…
Polynomial-time method solves complex combinatorial semi-bandits.
Simpler equations derived for knot polynomials coefficients, forming a ring.
The paper introduces new structures for colored HOMFLY-PT invariants using skein theory.
Holomorphic actions on complex spaces for nilpotent groups.
Infinite dimensional measure-valued processes modeled as polynomial diffusions.
In this note, we consider the problem of constructing knot invariants from Yang-Baxter operators associated to (unitary associative) algebra structures. We first compute the enhancements of these operators. Then, we conclude that Turaev's procedure to construct knot invariants, as modified by Murakami, invariably produ…
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot dependin…
In two previous papers, the author showed how to decompose the Khovanov homology of a link into the algebraic pairing of a type D structure and a type A structure (as defined in bordered Floer homology), whenever a diagram for is decomposed into the union of two tangles. Since Khovanov homol…