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 algebraic structure for 2-string links and long knots.
Study homotopy groups of spaces of long links and knots, finding new generators.
We extend the state models for Jones and Alexander polynomials of classical links to state models of 2-variable polynomials in the case of singular links. Moreover, we extend both of them to polynomials with d+1 variables for long singular knots with exactly d double points. These extensions can detect non-invertibilit…
The Tong-Yang-Ma representations are extended to string links and welded string links.
We prove the existence of a degree 7 Vassiliev invariant of long (or string) two-component links which is not preserved under the simultaneous change of orientation of both components. The non-invertibility of this invariant can be detected by the standard weight system with values in the tensor square of the universal…
New theorem for 4D links simplifies characterisation problem.
Brunnian links have been known for a long time in knot theory, whereas the idea of n-triviality is a recent innovation. We illustrate the relationship between the two concepts with four short theorems.
Finite Goeritz groups for links with long bridge decompositions.
It has long been known that a Milnor invariant with no repeated index is an invariant of link homotopy. We show that Milnor's invariants with repeated indices are invariants not only of isotopy, but also of self C_k-moves. A self C_k-move is a natural generalization of link homotopy based on certain degree k clasper su…
We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by meaning an analogy with -polynomial for virtual links. A degree of -polynomial estimates a virtual crossing number. We describe some application of -polynomial for the study of m…
We will discuss a method for visual presentation of knotted surfaces in the four space, by examining a number and a position of its Morse's critical points. Using this method, we will investigate surface-knot with one critical point of index 1. Then we show infinitely many mutually distinct surface-knots that has an em…
This paper proposes a paradigm shift in the valuation of long term annuities, away from classical no-arbitrage valuation towards valuation under the real world probability measure. Furthermore, we apply this valuation method to two examples of annuity products, one having annual payments linked to a mortality index and…
Paper develops knot invariants for long knots in a torus.
This paper explains how to compute Khovanov homology of torus links using the Kauffman bracket polynomial.
We partially solve the conjecture by A.Shumakovitch about torsion in the Khovanov homology of prime, non-split links in S^3. We give a size restriction on the Khovanov homology of almost alternating links. We relate the Khovanov homology of the connected sum of a link diagram and the Hopf link with the Khovanov homolog…
We extend knot Floer homology to string links in D^{2} \times I and to d-based links in arbitrary three manifolds, without any hypothesis on the null-homology of the components. As for knot Floer homology we obtain a description of the Euler characteristic of the resulting homology groups (in D^{2} \times I) in terms o…
In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting the weight norm approach. In particular, it is shown how to com…
The surgery unknotting number of a Legendrian link is defined as the minimal number of particular oriented surgeries that are required to convert the link into a Legendrian unknot. Lower bounds for the surgery unknotting number are given in terms of classical invariants of the Legendrian link. The surgery unknotting nu…
Unified Long-Moody and Katz methods for constructing local systems.
In this paper we consider long-run risk sensitive average cost impulse control applied to a continuous-time Feller-Markov process. Using the probabilistic approach, we show how to get a solution to a suitable continuous-time Bellman equation and link it with the impulse control problem. The optimal strategy for the und…
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of the odd writhe polynomial defined by the first author. The relation between this…
Budney recently constructed an operad that encodes splicing of knots. He further showed that the space of (long) knots is generated over this operad by the space of torus knots and hyperbolic knots, thus generalizing the satellite decomposition of knots from isotopy classes to the level of the space of knots. Infection…
The Alexander polynomial is linked to Bott-Cattaneo-Rossi invariants via Chern-Simons theory.
Kernel method estimates long-term effects from short-term data.
We refine the Polyak-Viro Gauss diagram formula for the Vassiliev invariant of order two in a very simple way for the 2-cable of a framed long knot. Surprisingly, the resulting isotopy invariant of framed knots can detect already the non-invertibility of knots. This makes the natural generalization of our invariant for…
In this paper, we propose a stochastic investment model for actuarial use in South Africa by modelling price inflation rates, share dividends, long term and short-term interest rates for the period 1960-2018 and inflation-linked bonds for the period 2000-2018. Possible bi-directional relations between the economic seri…
The performance of trend following strategies can be ascribed to the difference between long-term and short-term realized variance. We revisit this general result and show that it holds for various definitions of trend strategies. This explains the positive convexity of the aggregate performance of Commodity Trading Ad…
The paper analyzes insurance risks using stochastic models.
We use rational formality of configuration spaces and the bar construction to study the cohomology of the space of braids in dimension four or greater. We provide a diagram complex for braids and a quasi-isomorphism to the de Rham cochains on the space of braids. The quasi-isomorphism is given by a configuration space …
The Links-Gould invariant of alternating links has log-concave coefficients.
Medial quandles fail to distinguish certain links, highlighting their limitations.
It has long been known that every quasi-homogeneous normal complex surface singularity with Q-homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called "s…
The web link selection problem is to select a small subset of web links from a large web link pool, and to place the selected links on a web page that can only accommodate a limited number of links, e.g., advertisements, recommendations, or news feeds. Despite the long concerned click-through rate which reflects the at…
This paper provides a theoretical and computational justification of the long held claim that of the similarity of the probit and logit link functions often used in binary classification. Despite this widespread recognition of the strong similarities between these two link functions, very few (if any) researchers have …
A long-standing conjecture due to Michael Freedman asserts that the 4-dimensional topological surgery conjecture fails for non-abelian free groups, or equivalently that a family of canonical examples of links (the generalized Borromean rings) are not A-B slice. A stronger version of the conjecture, that the Borromean r…
Study spaces of knots and links in specific 3-manifolds.
The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphi…
We review recent quantitative results on the approximation of mean field diffusion equations by large systems of interacting particles, obtained by optimal coupling methods. These results concern a larger range of models, more precise senses of convergence and links with the long time behaviour of the systems to be con…
The transport literature is dense regarding short-term traffic predictions, up to the scale of 1 hour, yet less dense for long-term traffic predictions. The transport literature is also sparse when it comes to city-scale traffic predictions, mainly because of low data availability. In this work, we report an effort to …
We introduce a new technique for showing classical knots and links are not slice. As one application we resolve a long-standing question as to whether certain natural families of knots contain topologically slice knots. We also present a simpler proof of the result of Cochran-Teichner that the successive quotients of t…
Researchers develop a formula to calculate rho invariant of Dehn surgeries on links.
The study examines the topology of complements of polytopal skeletons.
New method produces positive colored superpolynomials from four-point functions.
Khovanov homology offers a nontrivial generalization of Jones polynomial of links in R^3 (and of Kauffman bracket skein module of some 3-manifolds). In this chapter (Chapter X) we define Khovanov homology of links in R^3 and generalize the construction into links in an I-bundle over a surface. We use Viro's approach to…
New invariants defined for volume-preserving flows on 3-manifolds.
We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincare polynomial, and Tutte polynomial. We consider basic algebraic properties of such chain complexes, including long-exact sequences associated to deletio…
Develops a bi-variate stochastic framework to model mortality and interest rates with long-range dependence.
New geometric methods solve a conjecture for hyperbolic 3-manifolds.