For links with vanishing pairwise linking numbers, the link components bound pairwise disjoint surfaces in . In this paper, we describe the set of genera of such surfaces in terms of the -function, which is a link invariant from Heegaard Floer homology. In particular, we use the -function to give lower bou…
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48 results for “link functions”
ZSPO optimizes RL from unknown link functions using human feedback.
problem Designing RLHF algorithms for unknown link functions.
method Zero-order policy optimization with human preference feedback.
result ZSPO converges to a stationary policy with a polynomial rate.
New link invariants from diagram colorings match link widths.
problem Defining link widths via diagram colorings.
method Colorings of link diagrams to define invariants and prove their equivalence to link widths.
result Invariants of link widths calculated algorithmically.
Formula for arborescent link tails using theta functions.
problem Understanding tails of colored Jones polynomials for arborescent links.
method Explicit formula using theta and false theta functions.
result Numerical evidence for modularity of tails for alternating knots.
We study Heegaard Floer homology and various related invariants (such as the -function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the -function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Fl…
Paper computes link determinants using Fourier-Hadamard transforms.
problem Computing determinants of complex link structures.
method Fourier-Hadamard transforms of Boolean functions.
result Determinant of centrally symmetric links with even components equals zero.
The paper explores fibered and quasi-positive links, introducing new families and invariants.
problem Understanding the structure of -space links and their properties.
method Using the H-function as a concordance link invariant.
result Introduced a subfamily of fibered strongly quasi-positive -space links and an infinite family of non-quasi-positive -space links.
We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient conditions for the local link (respectively the link at infinity) to be fibred.
Multiplicity of non-acyclic -representations and L-functions of the odd-twisted Whitehead linksmath.GT
Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.
problem Understanding the multiplicity of non-acyclic SL2-representations and their L-functions.
method Geometric interpretation of Reidemeister torsion divisors and application to L-functions.
result Prove multiplicity two for odd-twisted Whitehead links.
New tests for VaR and ES forecast encompassing using flexible link functions.
problem Testing forecast encompassing for Value at Risk and Expected Shortfall.
method Flexible link functions for testing convex forecast combinations and nonstandard asymptotic theory for boundary parameters.
result Tests based on new link functions outperform unrestricted linear link functions for one-step and multi-step forecasts.
It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1-jet of the 0-function, and thus cannot be distinguished by the cla…
We give a closed formula for the multivariable Conway potential function of any graph link in a homology sphere. As corollaries, we answer three questions by Walter Neumann about graph links.
The elliptic Hall algebra governs torus link homology.
problem Proving the elliptic Hall algebra's role in torus link homology.
method Developed a rational Shareshian-Wachs involution to prove the symmetry of generating functions.
result Resolved a conjecture by establishing the elliptic Hall algebra's role in torus link homology.
Study on colored Jones polynomial and link complements.
problem Understanding the structure of link complements with arbitrary colors.
method Investigated the potential function of the colored Jones polynomial and established a relationship with hyperbolicity.
result Evidence supports the Chen-Yang conjecture on link complements.
This article is about a natural distance function induced by smooth cobordisms between links. We show that the cobordism distance of torus links is determined by the profiles of their signature functions, up to a constant factor.
Proposes a new model for high-dimensional data analysis with unknown link function.
problem Estimating link function, component functions, and variable interactions in high-dimensional data.
method Generalized Sparse Additive Model with Unknown Link Function (GSAMUL) using B-spline basis and MLP network for link estimation, with -norm regularizer for variable selection.
result Can realize both variable selection and hidden interaction.
An immersed concordance between two links is a concordance with possible self-intersections. Given an immersed concordance we construct a smooth four-dimensional cobordism between surgeries on links. By applying -invariant inequalities for this cobordism we obtain inequalities between the -functions of links, whi…
Geometrically describes the linear and quadratic forms for rational links.
problem Predicting generating functions for colored HOMFLY-PT polynomials of rational links.
method Direct geometric description of linear and quadratic forms in terms of configuration spaces.
result Direct geometric description of forms for rational links.
New method optimizes policies without assuming known link functions between preferences and rewards.
problem Policy alignment with unknown and unrestricted link functions.
method Formulates an -divergence-constrained reward maximization problem, learning policies directly.
result Induces a semiparametric single-index binary choice model for policy alignment.
Multiple Linking Numbermath.GT
Study on multiple linking numbers, extending Gauss diagram formulas.
problem Extending link invariants to more complex diagrams.
method Investigate second Gauss diagram formula involving two arrows.
result Discover two types of multiple linking numbers, one Vassiliev invariant, the other sensitive to Reidemeister moves.
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 …
Link signature limit depends on linking matrix under specific polynomial condition.
problem Limits of Tristam-Levine signature function under precise polynomial conditions.
method Analysis of Alexander polynomial and linking matrix.
result Limit of Tristam-Levine signature at 1 determined by linking matrix under specific polynomial condition.
New polynomial invariants for virtual links are stronger than F-polynomials.
problem Defining new invariants for virtual links.
method Introducing weight functions and a recurrent construction for new invariants.
result New polynomial invariants are stronger than F-polynomials.
Derives FPDE for equity-linked insurance pricing.
problem Calculating prices for insurance policies with complex payment histories.
method Variational techniques in functional Itô calculus.
result Derives a functional partial differential equation.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.
Study links in 3-manifolds, linking volume to polynomial coefficients.
problem Understanding the volume of hyperbolic links in 3-manifolds.
method Using Kauffman bracket functions and polynomial invariants, linking volume to polynomial coefficients.
result Coefficients of polynomial provide 2-sided linear bounds on the volume of hyperbolic links.
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 …
Symmetric function lifts torus link homology.
problem Computing the triply-graded Khovanov-Rozansky homology of torus links.
method Defined a symmetric function and showed it satisfies a recursion for torus link homology.
result Triply-graded Khovanov-Rozansky homology of torus links is a specialization of .
The slope invariant is shown to be unchanged by concordance of colored links.
problem Describing the concordance of colored links with a distinguished component.
method Proved the slope invariant is invariant under concordance using C-complexes and generalized Seifert forms.
result The slope invariant is invariant under concordance of links.
Study on singularities of specific polynomial functions.
problem Characterizing the topology of singularities of mixed functions.
method Introduced inner non-degenerate mixed functions and used Newton boundary to characterize links.
result Links of singularities can be completely characterized under certain conditions.
Hasse-Weil zeta functions of SL_2-character varieties of arithmetic two bridge link complementsmath.NT
Hasse-Weil zeta functions of SL_2-character varieties of arithmetic two bridge link groups are determined. Special values of the zeta functions at s=0,1,2 are also investigated.
We show that the twisted signature invariants of boundary link concordance derived from unitary representations of the free group are actually ordinary link concordance invariants. We also show how the discontinuity locus of this signature function is determined by Seifert matrices of the link.
All link types arise from semiholomorphic polynomials.
problem Proving every link type can be represented by semiholomorphic polynomials.
method Constructive proof showing every link type arises from a weakly isolated singularity of a semiholomorphic polynomial.
result Every link type in the 3-sphere arises as the link of a weakly isolated singularity of a semiholomorphic polynomial.
A theory of signatures for odd-dimensional links in rational homology spheres is studied via their generalized Seifert surfaces. The jump functions of signatures are shown invariant under appropriately generalized concordance and a special care is given to accommodate 1-dimensional links with mutual linking. Furthermor…
Legendrian solid-torus linksmath.SG
Differential graded algebra invariants are constructed for Legendrian links in the 1-jet space of the circle. In parallel to the theory for R^3, Poincare-Chekanov polynomials and characteristic algebras can be associated to such links. The theory is applied to distinguish various knots, as well as links that are closur…
We compute different versions of link Floer homology and for any -space link with two components. The main approach is to compute the -function of the filtered chain complex which is determined by the Alexander polynomials of every sublink of the -space link. As an application, Thurst…
Farey Recursive Functionsmath.GT
Paper defines Farey Recursive Functions and explores their properties.
problem Understanding recursive functions on rationals.
method Defined and studied Farey Recursive Functions using Farey graph.
result Farey Recursive Functions naturally connect to 2-bridge knots and links.
New invariant slope for links helps complete signature formula.
problem Signature formula for splice of links.
method Developed slope invariant and computed it using various methods.
result Established close relation to Conway polynomials and Kojima-Yamasaki η-function.
Given an oriented link in the 3-sphere, the Euler characteristic of its link Floer homology is known to coincide with its multivariate Alexander polynomial, an invariant only defined up to a sign and powers of the variables. In this paper, we get rid of this ambiguity by proving that this Euler characteristic is equal …
Complex functional maps link tangent bundles, preserving orientation and angles.
problem Linking tangent bundles for orientation-aware correspondence.
method Endow tangent bundles with complex structures to enable robust transfer of tangent vector fields.
result Establishes orientation-aware correspondence without relying on descriptors or extra regularization.
Corrected a false lemma in Cimasoni's work on linking theory.
problem A false lemma in Cimasoni's geometric construction of the Conway potential function.
method Presented counterexamples and a detailed proof of the corrected lemma.
result The lemma is false and its correction has significant consequences for subsequent works.
RVFL NNs perform well without direct links and output bias for regression.
problem Effect of direct links and output bias on RVFL performance.
method Classical and two new methods for generating hidden nodes' parameters tested.
result Direct links and output bias do not significantly improve RVFL accuracy for typical nonlinear regression problems.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
Paper introduces new link homotopy invariants and applies them to 3-bouquet graphs.
problem Milnor's triple linking number and its applications in link homotopy.
method Developed new integer-valued link homotopy invariants and applied them to 3-bouquet graphs.
result Found new integer-valued invariants derived from four terms summing to Milnor's triple linking number.
It it known that the set of L-space surgeries on a nontrivial L-space knot is always bounded from below. However, already for two-component torus links the set of L-space surgeries might be unbounded from below. For algebraic two-component links we provide three complete characterizations for the boundedness from below…
We compute the Heegaard-Floer link homology of algebraic links in terms of the multivariate Hilbert function of the corresponding plane curve singularities. The main result of the paper identifies four homologies: (a) the Heegaard-Floer link homology of the local embedded link of the germ, (b) the lattice homology asso…
Given a biquandle , a function with certain compatibility and a pair of {\em non commutative cocyles} with values in a non necessarily commutative group , we give an invariant for singular knots / links. Given , we also define a universal group and universa…
Proves a plumbing-multiplicative property of a Links-Gould invariant.
problem Proving a multiplicative property of the Links-Gould invariant.
method Using Laurent polynomials and topological plumbing of surfaces.
result The Links-Gould invariant is monic in the Laurent polynomial ring.