A knot in a thickened surface is a smooth embedding , where is a closed, connected, orientable surface. There is a bijective correspondence between knots in and knots in , so one can view the study of knots in thickened surfaces as an extension of classic…
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48 results for “Fox--Milnor relations”
New results on algebraic knots with Brieskorn polynomials.
problem Understanding cobordisms of algebraic knots defined by Brieskorn polynomials.
method Analyzing Fox--Milnor type relations, decomposing algebraic cobordism classes, and studying cyclic suspensions.
result Spherical algebraic knots associated with Brieskorn polynomials have infinite order in the knot cobordism group.
Study on equivariant Q-sliceness for strongly invertible knots.
problem Understanding Q-sliceness for strongly invertible knots.
method Constructive and obstructive approaches using Fox-Milnor condition and equivariant concordance.
result Klein amphichiral knots are equivariant Q-slice in a single Q-homology 4-ball.
For knots in , it is well-known that the Alexander polynomial of a ribbon knot factorizes as for some polynomial . By contrast, the Alexander polynomial of a ribbon -knot is not even symmetric in general. Via an alternative notion of ribbon -knots, we give a topological condition on a $…
We define a generalization of virtual links to arbitrary dimensions by extending the geometric definition due to Carter et al. We show that many homotopy type invariants for classical links extend to invariants of virtual links. We also define generalizations of virtual link diagrams and Gauss codes to represent virtua…
We introduce Tristram-Levine signatures of virtual knots and use them to investigate virtual knot concordance. The signatures are defined first for almost classical knots, which are virtual knots admitting homologically trivial representations. The signatures and -signatures are shown to give bounds on the topologic…
We define a generalization of virtual links to arbitrary dimensions by extending the geometric definition due to Carter et al. We show that many homotopy type invariants for classical links extend to invariants of virtual links. We also define generalizations of virtual link diagrams and Gauss codes to represent virtua…
Defines a new homomorphism for strongly invertible knots, proving equivariant algebraic concordance.
problem Equivariant algebraic concordance of strongly invertible knots.
method Defining a homomorphism from equivariant concordance group to a new equivariant algebraic concordance group, proving it lifts known homomorphisms and provides new obstructions.
result Obtains a new obstruction to equivariant sliceness and novel lower bounds on equivariant slice genus.
Research classifies knots based on sliceness and amphichirality.
problem Classifying odd-stranded Turk's head knots based on sliceness and amphichirality.
method Constructing commuting pairs of ambient involutions and analyzing the equivariant Fox-Milnor square condition.
result Established a sharp parity dichotomy for equivariant rational sliceness and Klein amphichirality of odd-stranded Turk's head knots.
Defines relations between Dirac structures and spinors using Courant algebroid relations.
problem Defines relations between Dirac structures and spinors using Courant algebroid relations.
method Uses Courant algebroid relations to define relations between Dirac structures and spinors.
result Proves existence results for T-dual structures and demonstrates compatibility with Type II supergravity equations.
Method discovers nonlinear relations from time series data.
problem Identifying directional relations from nonlinear interactions in time series.
method Minimum predictive information regularization method for deep learning.
result Substantially outperforms other methods for learning nonlinear relations.
Unsupervised relation discovery aims to discover new relations from a given text corpus without annotated data. However, it does not consider existing human annotated knowledge bases even when they are relevant to the relations to be discovered. In this paper, we study the problem of how to use out-of-relation knowledg…
Abstractor enhances Transformers for relational reasoning, improving sample efficiency and performance.
problem Improving sample efficiency and performance in relational tasks.
method Introduces Abstractor module with relational cross-attention to enable explicit relational reasoning.
result Dramatic improvements in sample efficiency and performance on various relational tasks.
New method improves graph neural networks by considering different types of relations in sampling.
problem Current graph neural networks ignore relation types in biomedical graphs, leading to suboptimal performance.
method Proposes relation-dependent sampling for multi-relational graphs to balance relation frequency and importance.
result State-of-the-art graph neural networks achieve better accuracy and efficiency with relation-dependent sampling.
Temporal networks are ubiquitous and evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Although many relational datasets contain temporal information, the majority of existing techniques in relational learning focus on static snapshots and ignore the temporal dynamics. We propose…
Bayesian meta-learning on relation graphs improves few-shot relation extraction.
problem Predicting relations in sentences with limited labeled examples.
method Bayesian meta-learning on a global relation graph, using graph neural networks and Langevin dynamics.
result Framework effectively learns and generalizes to new relations.
Study improves CI tests for relational data to robustly discover causal structures.
problem Learning causal relationships from relational data.
method Conduct CI tests against relational data to robustly recover causal structure.
result Effective approach demonstrated through experiments.
One-relator hierarchiesmath.GR
Proves one-relator groups with negative immersions are hyperbolic and virtually special.
problem One-relator groups with negative immersions.
method Refinement of Magnus--Moldavanskii hierarchy and introduction of Z-stable HNN-extensions and hierarchies.
result One-relator groups with negative immersions are hyperbolic and virtually special, resolving a conjecture.
HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.
problem Modeling noisy, sparse, and heterogeneous relational data.
method Hierarchical Chinese restaurant process and Dirichlet process mixture for clustering and modeling relation values.
result HIRM generalizes standard models and discovers relational structure in real-world datasets.
Introduces Relational Privacy (RP) to control relation memorization in question answering models.
problem Relation memorization in question answering models can lead to privacy issues.
method Formalizes Relational Privacy (RP) and Differential Relational Privacy (DrP), providing bounds on relation memorization.
result DrP allows effective learning of general properties of underlying concepts while preventing relation memorization.
Proposes a new method for predicting missing relations in knowledge graphs.
problem Predicting missing relations between entities in knowledge graphs.
method Relational message passing method considering only edge features without entity IDs.
result PathCon method outperforms state-of-the-art methods significantly.
Enhances social spam detection using multi-level dependency of relational sequences.
problem Social spam detection in multi-relation social networks.
method Developed the Multi-level Dependency Model (MDM) to exploit long-term and short-term dependencies in user relational sequences.
result MDM improves social spam detection accuracy on a real-world multi-relational social network.
The paper explores the pentagon relation and its algebraic forms.
problem Exploring the pentagon relation and its various forms.
method Starting with geometric form, then algebraic form as a family of equations, deriving equivalent forms using 6j-symbols, and extracting solutions from modular categories.
result Extracting a solution of the pentagon relation from any modular category.
In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which capture the relations among inputs. In many cases, more than two maps are strongly…
This paper proposes an attention module augmented relational network called SARN(Sequential Attention Relational Network) that can carry out relational reasoning by extracting reference objects and making efficient pairing between objects. SARN greatly reduces the computational and memory requirements of the relational…
Extends coherence results to one-relator products of locally indicable groups.
problem Coherence in one-relator products of locally indicable groups.
method Developed new methods to extend results of Helfer, Wise, Louder, Wilton, and Brodsky.
result New proof of a theorem by Brodsky.
Existing relation classification methods that rely on distant supervision assume that a bag of sentences mentioning an entity pair are all describing a relation for the entity pair. Such methods, performing classification at the bag level, cannot identify the mapping between a relation and a sentence, and largely suffe…
Despite their impressive performance in many tasks, deep neural networks often struggle at relational reasoning. This has recently been remedied with the introduction of a plug-in relational module that considers relations between pairs of objects. Unfortunately, this is combinatorially expensive. In this extended abst…
This work proposes a method to compose visual relations more faithfully.
problem Composing relations between objects in images is challenging due to their entanglement.
method Represent each relation as an unnormalized density (energy-based model) to compose relations factorizedly.
result The proposed method generates and edits scenes with multiple sets of relations more faithfully.
A new quantum relation connects exceptional Lie algebras and knots.
problem Understanding the relationship between exceptional Lie algebras and quantum invariants of knots.
method Developed a two-parameter skein relation on trivalent graphs that specializes to exceptional Lie algebras.
result Found a new quantum exceptional polynomial that agrees with classical computations for knots and links.
Traditional sequential multi-object attention models rely on a recurrent mechanism to infer object relations. We propose a relational extension (R-SQAIR) of one such attention model (SQAIR) by endowing it with a module with strong relational inductive bias that computes in parallel pairwise interactions between inferre…
Relation extraction aims to extract relational facts from sentences. Previous models mainly rely on manually labeled datasets, seed instances or human-crafted patterns, and distant supervision. However, the human annotation is expensive, while human-crafted patterns suffer from semantic drift and distant supervision sa…
RelEx explains relational models without gradient access.
problem Lack of explainability for relational models like GNNs and SRL.
method Model-agnostic explainer for relational models using only outputs.
result Comparable or better performance compared to GNN-Explainer.
Improves neural relational inference for dynamic multi-agent trajectories.
problem Limited accuracy of NRI in short output sequences for relational inference in multi-agent trajectories.
method Proposes DYnamic multi-AgentRelational Inference (DYARI) model to handle changing interactions over time.
result DYARI model outperforms NRI in dynamic relational inference tasks.
Method learns relational features for Gaifman models from knowledge bases.
problem Structure learning for Gaifman models.
method Relational tree distances to learn relational features.
result Empirical evaluation shows superiority over classical rule-learning.
Study super cluster algebras from super Plücker and Ptolemy relations.
problem Developing super cluster algebra structure in super Grassmannians.
method Analyzing super Plücker and Ptolemy relations, developing super cluster structure.
result New simple form of super Plücker relations for $\Gr_{r|1}(n|1)$.
Proves a categorified relation in Khovanov homology.
problem None explicitly stated; focuses on categorification of a relation.
method Categorified analogue of Kontsevich's 4T relation on Khovanov homology.
result Proof of categorified 4T relation in Khovanov homology.
Introduces new algebraic structures for relational groupoids and proves a reduction theorem.
problem Developing algebraic tools for relational groupoids.
method Introduces relational groupoids and convolution algebras, provides examples, and proves a reduction theorem.
result Establishes a reduction theorem recovering the usual convolution of Lie groupoids.
We investigate Relational Graph Attention Networks, a class of models that extends non-relational graph attention mechanisms to incorporate relational information, opening up these methods to a wider variety of problems. A thorough evaluation of these models is performed, and comparisons are made against established be…
Relation extraction models suffer from limited qualified training data. Using human annotators to label sentences is too expensive and does not scale well especially when dealing with large datasets. In this paper, we use Auxiliary Classifier Generative Adversarial Networks (AC-GANs) to generate high-quality relational…
Bayesian weight priors improve neural network learning of identity relations.
problem Neural networks struggle to learn abstract and systematic relations, especially identity relations.
method Extended RBP approach using Bayesian weight priors as a regularization term.
result Bayesian weight priors lead to perfect generalization for identity relations and do not hinder standard neural network learning.
Proves divisibility relations for symplectic curve polynomials.
problem Divisibility relations for symplectic curve polynomials.
method New proofs of divisibility relations for Oka and Alexander polynomials of symplectic curves.
result Proves Libgober's divisibility relations for symplectic curves.
Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large-scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our a…
The study classifies polynomial relation tubular surfaces in 3-spaces.
problem Classifying tubular surfaces with polynomial curvature relations.
method Analyzing polynomial relations between Gaussian and mean curvatures in Euclidean, hyperbolic, and Lorentzian 3-spaces.
result Determination of sets of polynomial relations for tubular surfaces.
Relational Structural Causal Models enable causal reasoning about unseen object combinations.
problem Developing a model that can reason about causal and combinatorial aspects of unseen object combinations.
method Relational Structural Causal Models extend structural causal models to include relational variables and define identification criteria.
result Proposed relational neural causal models outperform non-relational baselines on simulated traffic scenes.
The paper extends graph embedding models to handle multiple relations.
problem Link prediction in multi-relational networks.
method Generalized pseudo-Riemannian embedding models to multi-relational networks, considering relations as submanifolds.
result Validation of the approach in link prediction tasks, including knowledge graph completion and biological domain analysis.
We propose Macau, a powerful and flexible Bayesian factorization method for heterogeneous data. Our model can factorize any set of entities and relations that can be represented by a relational model, including tensors and also multiple relations for each entity. Macau can also incorporate side information, specificall…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches…