Three types of branched covers are identified.
problem Identifying the number of distinct branched covers for a given branch datum.
method Analyzing the compatibility conditions and using Grothendieck's dessins d'enfant.
result There are exactly three distinct types of branched covers.
We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the base of any sheaf on a family of admissible G-covers. This formula can be interp…
Paper solves the Hurwitz existence problem using fiber products.
problem Determining when a combinatorial map datum corresponds to a holomorphic map.
method Using fiber products of holomorphic maps between Riemann surfaces.
result Proves non-realizability of many branch data and constructs new data.
Given two closed orientable surfaces, the Hurwitz existence problem asks whether there exists a branched cover between them having prescribed global degree and local degrees over the branching points. The Riemann-Hurwitz formula gives a necessary condition, which was shown to be also sufficient when the base surface ha…
We give an asymptotic probabilistic real Riemann-Hurwitz formula computing the expected real ramification index of a random covering over the Riemann sphere. More generally, we study the asymptotic expected number and distribution of critical points of a random real Lefschetz pencil over a smooth real algebraic variety…
The paper explores rational functions with 3 branching points on the Riemann sphere.
problem Existence of rational functions with specific branching points.
method Utilizes complex analysis to establish properties of rational functions.
result Identifies new types of exceptional branching data.
The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g > 1 the order of this group is naturally bounded in terms of g due to a Riemann-Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maxima…
For a given branched covering between closed connected surfaces, there are several easy relations one can establish between the Euler characteristics of the surfaces, their orientability, the total degree, and the local degrees at the branching points, including the classical Riemann-Hurwitz formula. These necessary re…
To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate su…
The study examines surface branch data on spheres with specific properties and computes the number of realizations.
problem Examining surface branch data on spheres with specific properties and computing the number of realizations.
method Analyzing surface branch data on spheres with three branching points and two partitions of degree d, computing the number of realizations based on arithmetic properties of the entries of the third partition.
result In the only case where n is 0, the entries have a common divisor, supporting conjectures by Edmonds-Kulkarny-Stong and Zieve.
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
For a branched cover between two closed orientable surfaces, the Riemann-Hurwitz formula relates the Euler characteristics of the surfaces, the total degree of the cover, and the total length of the partitions of the degree given by the local degrees at the preimages of the branching points. A very old problem asks whe…
Let M be an orientable compact flat Riemannian manifold endowed with a spin structure. In this paper we determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles of M, and we derive a formula for the corresponding eta series. In the case of manifolds with holonomy group Z2k,…
Rational maps structure theorem with geometric decomposition and realizability proof.
problem Realizability of rational maps branch data.
method Geometric decomposition of pullback metric into footballs and application to realizability.
result Realizability of branch data for rational maps when k>l+1. 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.
A new model improves relation extraction accuracy through relation-gated adversarial learning.
problem Relation extraction from sentences is challenging due to expensive human annotation and noisy distant supervision.
method Proposes relation-gated adversarial learning for relation extraction, extending domain adaptation methods.
result The model outperforms previous domain adaptation methods and improves accuracy of distance supervised relation extraction.
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.
Paper uses knowledge bases to discover new relations from text.
problem Discover new relations from text without annotated data.
method Construct constraints based on knowledge base embeddings and incorporate into variational auto-encoder for relation discovery.
result Improves relation discovery performance significantly.
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.
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.
Paper uses AC-GAN to generate high-quality relational sentences for relation extraction.
problem Limited training data for relation extraction models.
method Auxiliary Classifier Generative Adversarial Networks (AC-GANs).
result Significantly improved performance of relation extraction.
R-SQAIR adds relational bias to sequential object attention models for better object interactions.
problem Traditional sequential multi-object attention models struggle with relational inferences.
method Proposes R-SQAIR, a relational extension of SQAIR with a parallel pairwise interaction module.
result Demonstrates gains in object relations and combinatorial generalization over sequential mechanisms.
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…
New model improves graph attention for relational data.
problem Improving graph attention models for relational data.
method Relational Graph Attention Networks (R-GAT) extending non-relational graph attention to relational data.
result R-GAT performs worse than expected, but some configurations marginally improve molecular property modeling.
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…
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.
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…
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.
Proposes RT decomposition for better multi-relational link prediction.
problem Improving multi-relational link prediction in knowledge graphs.
method Relational Tucker3 (RT) decomposition, decouples entity and relation embeddings, allows parameter sharing, and learns sparsity patterns.
result RT decomposition can outperform existing sparse models in multi-relational link prediction.
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 $\Gr_{r|1}(n|1)$.
Attention-based embeddings improve relation prediction in incomplete KGs.
problem Incomplete or missing relations in knowledge graphs.
method Attention-based feature embedding that captures entity and relation features in local neighborhoods.
result Marked performance gains on all datasets compared to state-of-the-art methods.
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.
CompGCN embeds nodes and relations in multi-relational graphs.
problem Handling multi-relational graphs with direction and labels.
method CompGCN uses entity-relation composition operations from KG embedding.
result CompGCN achieves superior results on node classification, link prediction, and graph classification.