All knots are fused isotopic to the unknot via a process known as virtualization. We extend and adapt this process to show that, up to fused isotopy, classical links are classified by their linking numbers.
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48 results for “Link Adaptation”
We affirmatively address the question of whether the proposed link homotopy invariant of Li is well-defined. It is also shown that if one wishes to adapt the homotopy invariant of Schneiderman-Teichner to a link homotopy invariant of link maps, the result coincides with .
We introduce a new method for computing triply graded link homology, which is particularly well-adapted to torus links. Our main application is to the (n,n)-torus links, for which we give an exact answer for all n. In several cases, our computations verify conjectures of Gorsky et al relating homology of torus links wi…
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 describe a correspondence between Turaev surfaces of link diagrams on and special Heegaard diagrams for adapted to links.
We use foams to give a topological construction of a rational link homology categorifying the slN link invariant, for N>3. To evaluate closed foams we use the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that for any link our homology is isomorphic to Khovanov and Rozansky's.
Adapts scanning algorithm for odd Khovanov homology.
problem Computing odd Khovanov homology efficiently.
method Uses mapping cone construction instead of tensor product.
result Determines odd Khovanov homology of 3-strand torus links.
We consider the task of few shot link prediction on graphs. The goal is to learn from a distribution over graphs so that a model is able to quickly infer missing edges in a new graph after a small amount of training. We show that current link prediction methods are generally ill-equipped to handle this task. They canno…
Ozsvath and Szabo proved that knot Floer homology determines the genera of knots in S^3. We will generalize this deep result to links in homology 3-spheres, by adapting their method. Our proof relies on a result of Gabai and some constructions related to foliations. We also interpret a theorem of Kauffman in the world …
Paper predicts interference for better LA in URLLC.
problem Improving LA for URLLC with strict latency and reliability.
method Exploits time correlation of interference for prediction.
result Predicted interference improves LA for URLLC.
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 show that quasi-alternating links arise naturally when considering surgery on a strongly invertible L-space knot (that is, a knot that yields an L-space for some Dehn surgery). In particular, we show that for many known classes of L-space knots, every sufficiently large surgery may be realized as the two-fold branch…
The paper confirms a conjecture and extends arrow polynomial to twisted links.
problem Extending classical invariants to virtual and twisted links.
method Checkerboard framings, cut points, and normalized arrow polynomial.
result The normalized arrow polynomial is an invariant for twisted links.
Online learners track optimal solutions with constant step-size.
problem Tracking optimal solutions in online learning settings.
method Established a link between steady-state performance and tracking performance using analogies with adaptive filters.
result Inferred tracking performance from steady-state expressions directly.
Wireless systems perform rate adaptation to transmit at highest possible instantaneous rates. Rate adaptation has been increasingly granular over generations of wireless systems. The base-station uses SINR and packet decode feedback called acknowledgement/no acknowledgement (ACK/NACK) to perform rate adaptation. SINR i…
The paper proposes DEA to make graph neural networks fairer in link prediction.
problem Graph neural networks can unfairly prioritize certain social groups in link prediction.
method Drop Edges and Adapt (DEA) fine-tuning strategy with covariance constraints.
result DEA improves fairness and accuracy in link prediction tasks.
A new method predicts links better across various networks.
problem Adaptive link prediction for diverse network types.
method MOLI method using local information from neighbors of different distances.
result MOLI outperforms other link prediction algorithms.
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 …
Study categorizes knots and links as rigid or shaky based on Reidemeister moves.
problem Classifying knots and links as rigid or shaky based on adaptability to Reidemeister moves.
method Categorization of hard diagrams as rigid or shaky, investigation of rigid and shaky hard diagrams for specific knots and links.
result Every link has a rigid hard diagram, and there is an upper limit for the number of crossings in such diagrams.
Multi-agent models have been used in many contexts to study generic collective behavior. Similarly, complex networks have become very popular because of the diversity of growth rules giving rise to scale-free behavior. Here we study adaptive networks where the agents trade ``wealth'' when they are linked together while…
An invariant of Legendrian and transverse links from open book decompositions of contact 3-manifoldsmath.GT
We introduce a generalization of the Lisca-Ozsváth-Stipsicz-Szabó Legendrian invariant to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link in a contact 3-manifold with a diagram , given by an open book decomposition …
The virtual flyping theoremmath.GT
The flyping theorem is extended to virtual links and surfaces.
problem Proving the flyping theorem for virtual links and surfaces.
method Adapting geometric proof for thickened surfaces and using diagrammatic correspondence.
result Established an isomorphism between Gordon-Litherland pairing and 4-manifold intersection form.
State-of-the-art link prediction utilizes combinations of complex features derived from network panel data. We here show that computationally less expensive features can achieve the same performance in the common scenario in which the data is available as a sequence of interactions. Our features are based on social vec…
Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev link invariant construction to tangles with a flat connection in a principal G-bundle over the complement of the tangle. The purpose of this paper is to adapt and renormalize their construction to define invariants of G-links using the semi-cyc…
Kernelized bandit algorithm tackles adaptive contextual bandits with single-index models.
problem Adaptive contextual bandits with single-index models and unknown link functions.
method Kernelized ε-greedy algorithm combining Stein-based index estimation and kernel ridge regression for reward functions.
result Unified framework for simultaneous learning and inference in single-index contextual bandits.
To a link L in the 3-sphere, we associate a spectral sequence whose E^2 page is the reduced Khovanov homology of L and which converges to a version of the monopole Floer homology of the branched double cover. The pages E^k for k > 1 depend only on the mutation equivalence class of L. We define a mod 2 grading on the sp…
TTT improves model adaptation to test data, especially for nonlinear models.
problem Improving model performance in adapting to test data, especially for nonlinear models.
method Combining Test-time Training (TTT) with In-context Learning (ICL) for nonlinear models.
result TTT enables models to adapt to both feature vector and link function shifts, improving performance.
Bayesian models for networks are often misspecified, leading to overconfident inference.
problem Real-world networks violate assumptions of geometry and link function in latent space models.
method Proposes a generalized posterior framework for random geometric graphs, using Link-Sequential R-SafeBayes to adaptively tune posterior regularization.
result Improved calibration and better link prediction performance demonstrated on synthetic and real-world networks.
Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the overall consensus process. Second, they generally lack the ability to incorpora…
We model GitHub interactions as a temporal knowledge graph for software engineering questions.
problem Insufficient performance of existing temporal models on extrapolated queries and time prediction.
method Introduced an extension to current temporal models using relative temporal information.
result Improved performance on extrapolated queries and time prediction.
M-FISHER detects and adapts to streaming data shifts with statistical validity and stability.
problem Detecting and adapting to distributional shifts in streaming data.
method Constructs an exponential martingale from non-conformity scores and applies Ville's inequality for detection. Fisher-preconditioned updates for adaptation.
result Establishes M-FISHER as a principled approach for robust, anytime-valid detection and geometrically stable adaptation.
Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is di…
New findings link causal models to strategic classification, improving robustness and alignment.
problem Strategic adaptation by users in classification tasks.
method Causal models to bound worst-case out-of-distribution risk.
result Causal classification optimizes classification error after adaptation under certain noise conditions.
We introduce a natural-valued complexity c(X) for pairs X=(M,L), where M is a closed orientable 3-manifold and L is a link contained in M. The definition employs simple spines, but for well-behaved X's we show that c(X) equals the minimal number of tetrahedra in a triangulation of M containing L in its 1-skeleton. Slig…
The paper connects linking numbers to Biot-Savart kernels on compact manifolds.
problem Linking numbers and Biot-Savart kernels on compact manifolds.
method Asymptotic approximation of solutions to the heat equation and exterior derivative equation.
result The differential linking form coincides with the kernel of the Biot-Savart operator in \(\mathbb{R}^3\).
Study on Jones polynomials and their roots in the unit circle and complex plane.
problem Understanding the roots of Jones polynomials for knots and links.
method Analyzing solutions of the equation for double-twist knots and links.
result The set of solutions to is dense in the unit circle and complex plane.
In many machine learning applications, one needs to interactively select a sequence of items (e.g., recommending movies based on a user's feedback) or make sequential decisions in a certain order (e.g., guiding an agent through a series of states). Not only do sequences already pose a dauntingly large search space, but…
FAST improves fast and stable task adaptation in DNNs.
problem Catastrophic forgetting in fine-tuned pretrained models.
method Introducing FAST, an easy-to-implement fine-tuning algorithm.
result FAST learns target tasks faster and retains source knowledge longer.
Framework learns dynamic graph attributes and links co-evolution.
problem Forecasting change of node attributes and link formation in dynamic graphs.
method CoEvoGNN framework with temporal self-attention and joint optimization.
result Framework outperforms baselines on predicting unseen graph snapshots.
Adaptive Margin Ranking Loss for Knowledge Graph Embeddings via a Correntropy Objective Functioncs.CL
Translation-based embedding models have gained significant attention in link prediction tasks for knowledge graphs. TransE is the primary model among translation-based embeddings and is well-known for its low complexity and high efficiency. Therefore, most of the earlier works have modified the score function of the Tr…
Unified approach compares ERGM, GCN, and Word2Vec+MLP for collaboration network link prediction.
problem Link prediction in collaboration networks.
method ERGM, GCN, and Word2Vec+MLP models.
result Machine learning models outperform traditional ERGM in large networks.
High fidelity behavior prediction of intelligent agents is critical in many applications. However, the prediction model trained on the training set may not generalize to the testing set due to domain shift and time variance. The challenge motivates the adoption of online adaptation algorithms to update prediction model…
New method shows certain group presentations are trivial.
problem Proving certain group presentations are trivial.
method 4-manifold trisections
result Certain group presentations are Andrews-Curtis trivial.
Optimal transport aligns source and target distributions for linear regression in 2D.
problem Domain adaptation for linear regression in 2D with limited target data.
method Combining K-means and optimal transport for estimating geometric transformations.
result Optimal transport recovers geometric transformations like rotations, translations, and homotheties.
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…
AGE improves graph embedding by smoothing features and iteratively enhancing node embeddings.
problem Challenges in attributed graph embedding, especially in preserving optimal low-pass characteristics and robustness.
method AGE, a novel framework combining Laplacian smoothing and adaptive encoding, addresses these issues.
result AGE consistently outperforms state-of-the-art methods on node clustering and link prediction tasks.
New methods improve neural directed link prediction across all sub-tasks.
problem Directed link prediction requires handling edge directionality and bidirectionality, not just edge existence.
method Proposes three strategies: Multi-Class Framework, Multi-Objective, and Scalarized approaches.
result Improved performance across all three sub-tasks of directed link prediction.
ABO extends RLS for online learning in non-stationary time-series, improving accuracy and speed.
problem Online learning in non-stationary time-series with overparameterized models.
method QR-based exponentially weighted RLS algorithm with orthogonal-triangular updates.
result ABO maintains bounded residuals and stable condition numbers while achieving speed improvements.