New theorem for 4D links simplifies characterisation problem.
problem Long-standing open problem in link characterisation.
method Reidemeister Theorem for solid ribbon torus links.
result Complete characterisation of a related class of links.
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48 results for “link problem”
Problems on region choices for knot and link diagrams solved using Alexander numbering.
problem Existence of solutions for region choice problems on knot and link diagrams.
method Alexander numbering for regions, alternative proofs, necessary and sufficient conditions.
result Existence of solutions for region choice problems on link diagrams.
We show that three natural decision problems about links and 3-manifolds are computationally hard, assuming some conjectures in complexity theory. The first problem is determining whether a link in the 3-sphere bounds a Seifert surface with Thurston norm at most a given integer; this is shown to be NP-complete. The sec…
Paper simplifies link classification in 3-sphere using braids and templates.
problem Classify links in the 3-sphere.
method Simplified braid description, generalised T-links, bunch algorithm.
result Established upper volume bound for 3-manifolds.
New examples show limits of physical link isotopies.
problem Limits of physical link isotopies in thick and thickly embedded links.
method Construction of specific examples of thick and thickly embedded links.
result Explicit examples of links that cannot be split through thick homotopies.
FakeEdge tackles dataset shift in link prediction tasks.
problem Dataset shift between training and testing sets in link prediction.
method Model-agnostic technique to mitigate graph topological gap.
result Extensive experiments show FakeEdge's superiority on multiple datasets.
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…
In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic knots to hyperbolic links, and confirm it for an infinite family of hyperbolic 2…
New proof shows a link problem is hard without complex links.
problem Deciding if a link contains a trivial sublink is hard.
method Reduces from Independent Set Problem, avoiding Brunnian links.
result The Trivial Sublink Problem is NP-hard due to mod 2 linking.
Polynomial algorithm found for alternating link equivalence.
problem Link equivalence of alternating links in 3-space.
method Tait flyping conjectures, observations from graph theory, and topological graph theory.
result Alternating link equivalence has a polynomial algorithm.
An explicit polynomial in the linking numbers and Milnor's triple linking numbers on six component links is shown to be a well-defined finite type link-homotopy invariant. This solves a problem raised by B. Mellor and D. Thurston. An extension of our construction also produces a finite type link invar…
We study the effect of Nielsen moves and their geometric counterparts, handle slides, on good boundary links. A collection of links, universal for 4-dimensional surgery, is shown to admit Seifert surfaces with trivial Lagrangian. They are good boundary links, with Seifert matrices of a more general form than in known c…
New obstructions show links with vanishing Milnor invariants may not be concordant to homology boundary links.
problem Understanding links with vanishing Milnor invariants and their concordance properties.
method Developing new obstructions and examples within the solvable filtration framework.
result Existence of links with vanishing Milnor invariants that are not concordant to homology boundary links.
Survey of Turk's head knots and links properties.
problem Characterize Turk's head knots and links.
method Discussion of various results in the mathematical literature.
result Turk's head links are alternating, fibered, hyperbolic, invertible, non-split, periodic, and prime.
We study the problem of defining maps on link Floer homology induced by unoriented link cobordisms. We provide a natural notion of link cobordism, disoriented link cobordism, which tracks the motion of index zero and index three critical points. Then we construct a map on unoriented link Floer homology associated to a …
In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy …
Finite type invariants separate PL links in 3D space.
problem If two PL links are isotopic, are they PL isotopic?
method Proved PL isotopic links are indistinguishable by finite type invariants.
result Finite type invariants separate PL links in 3D space if and only if certain conjectures hold.
The fundamental n-quandles of links are residually finite for n ≥ 2.
problem Residual finiteness of fundamental n-quandles of oriented links.
method Investigation of residual finiteness and subquandle separability of quandles; use of Winker's work on 3-sphere branched covers.
result Fundamental n-quandles of oriented links are residually finite for each n ≥ 2.
Link prediction in a graph is the problem of detecting the missing links that would be formed in the near future. Using a graph representation of the data, we can convert the problem of classification to the problem of link prediction which aims at finding the missing links between the unlabeled data (unlabeled nodes) …
Polynomial bound on Reidemeister moves for each link type.
problem Recognizing whether a given link diagram represents a specific link type.
method Showed existence of a polynomial such that any two diagrams of a link type differ by at most Reidemeister moves.
result The problem of recognising a link type is in NP and can be completed in exponential time.
Extends Milnor's invariants to 3-manifolds, solving an open problem.
problem Extract transfinite Milnor invariants for 3-manifolds.
method Develops a theory of transfinite invariants for 3-manifold groups.
result Realizes nontrivial values of transfinite Milnor invariants.
Study on Gehring link problem and width of bands in curved manifolds.
problem Width of bands in positively curved manifolds.
method Same idea applied to focal radius and rigidity of hypersurfaces.
result Sphere theorem for hypersurfaces in involving focal radius and rigidity of Clifford hypersurface.
This thesis consists of three self-contained chapters. The first two concern quantum invariants of links and three manifolds and the third contains results on the word problem for link groups. In chapter 1 we relate the tree part of the Aarhus integral to the mu-invariants of string-links in homology balls thus general…
NPGNN improves graph link prediction by adapting to new graphs.
problem Inductive link prediction in graphs with limited training data.
method Meta-learning with graph neural networks (NPGNN).
result NPGNN outperforms state-of-the-art models in real-world graphs.
We consider the link prediction problem in a partially observed network, where the objective is to make predictions in the unobserved portion of the network. Many existing methods reduce link prediction to binary classification problem. However, the dominance of absent links in real world networks makes misclassificati…
GEN tackles few-shot out-of-graph link prediction in evolving multi-relational graphs.
problem Predicting links between unseen nodes in evolving multi-relational graphs with few edges per node.
method Transductive meta-learning framework (GEN) for inductive and transductive inference.
result GEN significantly outperforms relevant baselines for out-of-graph link prediction tasks.
Constructs universal link invariants from intersections in configuration spaces.
problem Globalise topologically all coloured Jones polynomials and ADO polynomials.
method Defines new link invariants from graded intersections in configuration spaces.
result Recover all coloured Jones polynomials and ADO polynomials for links.
We numerically study an Asset Liability Management problem linked to the decommissioning of French nuclear power plants. We link the risk aversion of practitioners to an optimization problem. Using different price models we show that the optimal solution is linked to a de-risking management strategy similar to a concav…
The aim of this article is to detect new classes of quasi-alternating links. Quasi-alternating links are a natural generalization of alternating links. Their knot Floer and Khovanov homology are particularly easy to compute. Since knot Floer homology detects the genus of a knot as well as whether a knot is fibered, as …
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.
The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T+1? If our da…
Optimizes the conformal capacity of linked curves in .
problem Finding the minimum conformal capacity of linked curves in .
method Analyzes the standard Hopf link under the assumption that each component lies on a different side of a conformal image of the Clifford torus.
result Proves the Hopf link is a local minimizer in a strong sense.
This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and…
In the present paper, we construct the generalized Kuperberg bracket for two-component links with one component fibred. We consider a new geometrical complexity for such links and establish minimality of diagrams in a strong sense.
It is an open problem whether Kirk's invariant is the complete obstruction to a link map being link homotopically trivial. With the objective of constructing counterexamples, Li proposed a link homotopy invariant that is defined on the kernel of and also obstructs link nullhomotopy. We …
The A-B slice problem is a reformulation of the topological 4-dimensional surgery conjecture in terms of decompositions of the 4-ball and link homotopy. We show that link groups, a recently developed invariant of 4-manifolds, provide an obstruction for the class of model decompositions, introduced by M. Freedman and X.…
DEAL model predicts links for new nodes with only attribute info.
problem Predicting links for new nodes with only attribute info.
method DEAL model with two encoders and alignment mechanism.
result DEAL significantly outperforms existing methods on inductive link prediction.
We prove that, for any ordinary sense slice 1-link , we can define the Arf invariant and Arf(L)=0. We prove that, for any m-component 1-link L_1, there exists a 3m-component ordinary sense slaice 1-link L_2 of which L_1 is a sublink.
Study of Legendrian links using Floer theory and cluster varieties.
problem Understanding exact Lagrangian fillings of positive braid Legendrian links.
method Floer-theoretic approach and exact Lagrangian cobordisms.
result Proves that positive braid Legendrian links admit infinitely many exact Lagrangian fillings.
New heuristics for predicting links in multiplex networks.
problem Link prediction in networks with multiple types of connections.
method Proposed a general framework and three families of heuristics.
result Significantly outperformed baseline heuristics for ordinary networks.
This paper constructs Koszul duals for Heegaard Floer Dehn surgery formulas.
problem Computational problems involving link surgery formulas.
method Described Koszul duals of an associative algebra encoding Heegaard Floer Dehn surgery formulas.
result Proved several equivalences of categories using dualizing bimodules.
Proposes a novel tensor-based approach for multi-level link prediction.
problem Inferring potential links from observed networks.
method Tensor-based joint network embedding capturing pairwise and hyperlinks.
result Improves hyperlink and pairwise link prediction accuracy.
"Slicing" the Hopf linkmath.GT
A link in the 3-sphere is called (smoothly) slice if its components bound disjoint smoothly embedded disks in the 4-ball. More generally, given a 4-manifold M with a distinguished circle in its boundary, a link in the 3-sphere is called M-slice if its components bound in the 4-ball disjoint embedded copies of M. A 4-ma…
New model for links uses meander diagrams and combinatorics.
problem Modeling and analyzing random links.
method Random meander model based on meander diagrams and graphs, proving properties using combinatorics.
result Trivial links are unlikely, and there's a lower bound on non-isotopic knots.
We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in $\sp^3$ and . We prove the thickness of a nontrivial knot or link in $\sp^3$ is no more than , the thickness of a Hopf link. We also give arguments and evidence supporting the conject…
Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to their simplicity, interpretability, and for some of them, scalability. However, ev…
Graph-based multi-label classifier extends CULP for multi-label data.
problem Solving multi-label classification problems.
method Extends CULP algorithm to handle multi-label data.
result Competitive results compared to cutting-edge multi-label classifiers.
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.