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.
Enhances biquandle counting invariant using finite type enhancements.
The aim of this survey is to give an overview on the geometry of Einstein maximal globally hyperbolic 2+1 spacetimes of arbitrary curvature, conatining a complete Cauchy surface of finite type. In particular a specialization to the finite type case of the canonicla Wick rotation-rescaling theory, previously developed b…
New invariants define the rational and real homotopy types of closed manifolds.
We define enhancements of the quandle counting invariant for knots and links with a finite labeling quandle Q embedded in the quandle of units of a Lie algebra \mathfrak{a} using Lie ideals. We provide examples demonstrating that the enhancement is stronger than the associated unenhanced counting invariant.
Enhanced Saito duality connects group rings and equivariant Euler characteristics.
Enhances power of covariance matrix tests for high-dimensional data.
Enhances knot counting invariant using skew braces.
We study Coxeter racks over and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are stronger than the unenhanced rack counting invariants.
Enhances knot invariants using bilinear forms on vector spaces.
Enhances knot counting invariant using biquasile Boltzmann weights.
The paper improves PCS approximation for ranking and selection under limited simulation budgets.
We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effe…
Survey of quantum enhancements in knot theory.
New quantum enhancements for biquandle colored links.
Enhances knotoid counting invariants using biquandle brackets.
Abstract: New invariants for links and three-manifolds from finite groups.
Enhanced Yang-Baxter operators give rise to invariants of oriented links. We expand the enhancing method to generalized Yang-Baxter operators. At present two examples of generalized Yang-Baxter operators are known and recently three types of variations for one of these were discovered. We present the definition of enha…
The column group is a subgroup of the symmetric group on the elements of a finite blackboard birack generated by the column permutations in the birack matrix. We use subgroups of the column group associated to birack homomorphisms to define an enhancement of the integral birack counting invariant and give examples whic…
Enhanced Black-Scholes model for option pricing with stochastic volatility and interest rate variability.
Category theory generalizes finite type invariants using diagrams systems.
New invariant stops certain types of geometric transformations.
Birack modules are modules over an algebra Z[X] associated to a finite birack X. In previous work, birack module structures on Z mod n were used to enhance the birack counting invariant. In this paper, we use birack modules over Laurent polynomial rings Z_n[q,1/q] to enhance the birack counting invariant, defining a cu…
Enhanced DFO using adaptive batch-based FD estimates.
We introduce a modified rack algebra Z[X] for racks X with finite rack rank N. We use representations of Z[X] into rings, known as rack modules, to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide computations and examples to show that the new invariants are stric…
The study identifies helicoids and spheres as the only finite III-type ruled and quadric surfaces.
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite t…
Submanifolds of coordinate finite-type were introduced in HV1. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of Δ. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for g…
Finite-type surfaces have a topological Hopf property.
The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo the birack rank of the labeling birack. In this first of an anticipated series …
Defines finite type Multivalued Shape using hyperspaces.
Enhanced neural networks detect thin boundaries between different types of anomalies.
New invariant fully describes finite type invariants of knots in homology 3-spheres.
Finite type curves are asymptotic lines of plane fields, with examples.
A birack is an algebraic structure with axioms encoding the blackboard-framed Reidemeister moves, incorporating quandles, racks, strong biquandles and semiquandles as special cases. In this paper we extend the counting invariant for finite racks to the case of finite biracks. We introduce a family of biracks generalizi…
Compact manifolds with boundary have finite type mapping class groups.
We observe that most known results of the form "v is not a finite-type invariant" follow from two basic theorems. Among those invariants which are not of finite type, we discuss examples which are "ft-independent" and examples which are not. We introduce (n,q)-finite invariants, which are generalizations of finite-type…
Homotopy classes of nanowords and nanophrases are combinatorial generalizations of virtual knots and links. Goussarov, Polyak and Viro defined finite type invariants for virtual knots and links via semi-virtual crossings. We extend their definition to nanowords and nanophrases. We study finite type invariants of low de…
Paper shows 3D hyperbolic manifolds are uniquely identified by their finite groups.
2L-FUSE enhances feature sparsity through kernel learning.
Enhanced Kauffman bracket invariant in polynomial rings.
Changes in collateralization have been implicated in significant default (or near-default) events during the financial crisis, most notably with AIG. We have developed a framework for quantifying this effect based on moving between Merton-type and Black-Cox-type structural default models. Our framework leads to a singl…
Finite type invariants separate PL links in 3D space.
Enhances CEV model pricing with high-order scheme and adaptive time stepping.
Paper explores hyperbolic groups with unique subgroup properties.
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the `cubic' point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In …
GAIF enhances online multiple testing with feedback, improving statistical power.
A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for manifolds with large first betti number, encompassing much of the complexity of Ohtsuki'…
Proofs for Gauss map properties on surfaces with finite geometric type.