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.
The paper characterizes sigma-adequacy of link diagrams using Tutte polynomials.
This paper continues our study, initiated in [arXiv:1108.3370], of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolic links, we show that the geometric type of these surfaces in the Thurston trichotomy is completely determined by a simple gr…
We bound the hyperbolic volumes of a large class of knots and links, called homogeneously adequate knots and links, in terms of their diagrams. To do so, we use the decomposition of these links into ideal polyhedra, developed by Futer, Kalfagianni, and Purcell. We identify essential product disks in these polyhedra.
Khovanov homology is simplified for plumbing operations.
The twisting technique creates infinite links.
Every Kauffman state σof a link diagram D(K) naturally defines a state surface S_σwhose boundary is K. For a homogeneous state σ, we show that K is a fibered link with fiber surface S_σif and only if an associated graph G'_σis a tree. As a corollary, it follows that for an adequate knot or link, the second and next-to-…
We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius co…
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the `quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the -quaternionic manifolds. Moreover, …
Within the framework of maximum entropy principle we show that the finite-size long-range Ising model is the adequate model for the description of homogeneous credit portfolios and the computation of credit risk when default correlations between the borrowers are included. The exact analysis of the model suggest that w…
Proves trivial tail homology for non -adequate links.
This article presents a proof of the existence of Bertrand-Nash equilibrium prices with multi-product firms and under the Logit model of demand that does not rely on restrictive assumptions on product characteristics, firm homogeneity or symmetry, product costs, or linearity of the utility function. The proof is based …
Study shows crossing numbers of cable knots are larger than previously thought.
A link is adequate and has Turaev genus one if its Jones polynomial span is one less than its crossing number.
We show that the head and tail functions of the colored Jones polynomial of adequate links are the product of head and tail functions of the colored Jones polynomial of alternating links that can be read-off an adequate diagram of the link. We apply this to strengthen a theorem of Kalfagianni, Futer and Purcell on the …
The class of +adequate links contains both alternating and positive links. Generalizing results of Tanaka (for the positive case) and Ng (for the alternating case), we construct fronts of an arbitrary +adequate link A so that the diagram has a ruling, therefore its Thurston-Bennequin number is maximal among Legendrian …
Jones polynomial bounds and crossing numbers of knots.
We provide a diagrammatic criterion for semi-adequate links to be hyperbolic. We also give a conjectural description of the satellite structures of semi-adequate links. One application of our result is that the closures of sufficiently complicated positive braids are hyperbolic links.
It is known that the colored Jones polynomial of a -adequate link has a well-defined tail consisting of stable coefficients, and that the coefficients of the tail carry geometric and topological information on the -adequate link complement. We show that a power series similar to the tail of the colored Jones poly…
Jones slopes characterize adequate knots under the Strong Slope conjecture.
Characterizes adequate links using Jones polynomial and crossing number.
The paper develops a theory of skein adequate links in thickened surfaces and proves Tait conjectures.
Survey updates knowledge on homogeneous Einstein spaces.
Refines virtual link equality criterion for diagrams with one virtual crossing.
The extreme degrees of the colored Jones polynomial of any link are bounded in terms of concrete data from any link diagram. It is known that these bounds are sharp for semi-adequate diagrams. One of the goals of this paper is to show the converse; if the bounds are sharp then the diagram is semi-adequate. As a result,…
Jacobi operators on certain naturally reductive spaces have constant coefficient ODEs.
Study analyzes data breach reporting patterns and frequency across U.S. states, finding increasing trends after 2020.
The paper simplifies multi-agent RL dynamics in finite-state Markov games using homogenization.
Using computer calculations and working with representatives of pretzel tangles we established general adequacy criteria for different classes of knots and links. Based on adequate graphs obtained from all Kauffman states of an alternating link we defined a new numerical invariant: adequacy number, and computed adequac…
The paper defines a new homotopy type for colored links and proves stabilization behavior.
Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.
Garoufalidis conjectured a relation between the boundary slopes of a knot and its colored Jones polynomials. According to the conjecture, certain boundary slopes are detected by the sequence of degrees of the colored Jones polynomials. We verify this conjecture for adequate knots, a class that vastly generalizes that o…
A homogeneous knot is a generalization of alternating knots and positive knots. We determine the Rasmussen invariant of a homogeneous knot. This is a new class of knots such that the Rasmussen invariant is explicitly described in terms of its diagrams. As a corollary, we obtain some characterizations of a positive knot…
The paper extends a classical result to positively curved homogeneous spaces.
Proposes a multi-state model for evaluating life insurance conversion options.
We study the behavior of the degree of the colored Jones polynomial and the boundary slopes of knots under the operation of cabling. We show that, under certain hypothesis on this degree, if a knot satisfies the Slope Conjecture then a -cable of satisfies the conjecture, provided that is not a Jon…
Continuous state spaces and stochastic, switching dynamics characterize a number of rich, realworld domains, such as robot navigation across varying terrain. We describe a reinforcementlearning algorithm for learning in these domains and prove for certain environments the algorithm is probably approximately correct wit…
The goal of this paper is to address A. Shumakovitch's conjecture about the existence of -torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs which provides a link between the link homology and well-developed theory of Hochschild ho…
C. Armond, S. Garoufalidis and T.Le have shown that a unicolored Jones polynomial of a B-adequate link has a stable tail at large colors. We categorify this tail by showing that Khovanov homology of a unicolored link also has a stable tail, whose graded Euler characteristic coincides with the tail of the Jones polynomi…
In this paper, we show that the volumes for a family of A-adequate closed braids can be bounded above and below in terms of the twist number, the number of braid strings, and a quantity that can be read from the combinatorics of a given closed braid diagram. We also show that the volumes for many of these closed braids…
Improved price bounds for financial derivatives using time-homogeneous stock movements.
New algorithm optimizes complex model selection for non-homogeneous hidden Markov models.
New risk measures adjust for tail risk inadequacies.
SNORE applies denoiser only on images with noise of adequate level for image restoration.
Extends Gaussian process regression for non-Gaussian data.
For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.
In this paper we define alternating Kauffman states of links and we characterize when the induced state surface is a fiber. In addition, we give a different proof of a similar theorem of Futer, Kalfagianni and Purcell on homogeneous states.
New bounds on HOMFLY polynomial for homogeneous links.
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms. Graded bundles are graded manifolds in the sense that we can choose an atlas whose…