The abstract discusses open problems in isoparametric theory.
problem Open problems in isoparametric theory.
method Survey and propose open problems.
result Discussion of open problems in isoparametric theory.
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We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …
Surveying entropies for negatively curved manifolds and their relations.
problem Understanding entropy in negatively curved manifolds.
method Exploring various entropy concepts and their interconnections.
result Relations between different entropy notions for negatively curved manifolds.
RSM improves relational learning efficiency and flexibility.
problem Efficiency and flexibility in relational learning for diverse tasks and data.
method Fast, flexible relational learning framework for supervised and semi-supervised learning.
result RSM outperforms existing methods in multi-class classification and sparse labeled graphs.
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.
Warm-start Bayesian optimization for related problems.
problem Optimizing stochastic simulators over multiple time periods or markets.
method Develops a joint statistical model and uses value of information to recommend evaluation points.
result Reduces solution time for sequences of related optimization problems.
Enhanced Transformer solves math problems better with explicit relation encoding.
problem Improving Transformer models for solving math word problems.
method Integrates Tensor-Product Representations and TP-Attention mechanism.
result Sets new state of the art on the Mathematics Dataset.
Solves empirical risk minimization for relational data using graph sampling.
problem Empirical risk minimization for relational data.
method Graph sampling theory, stochastic gradient descent, automatic differentiation.
result Automatic unbiased stochastic gradients for relational data.
A mass-type invariant for smooth metric measure spaces and its relation with the fractional Yamabe problem
problem Defining and analyzing a mass-type invariant for smooth metric measure spaces
method Defining a mass-type quantity and showing its geometric invariance properties
result The mass-type quantity has a close relation with the fractional Yamabe problem and the relevant Green's function
Discusses geometry problems for fun and learning.
problem Geometry problems and their solutions.
method Not original, but related to differential geometry course.
result Relation to differential geometry course.
Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.
problem Orlicz-Minkowski problem involving Gauss curvature and support function.
method Generalized Gauss curvature flow for convex hypersurfaces in Euclidean n-space.
result Long-time existence and convergence of the flow, leading to existence results for the Orlicz-Minkowski problem.
Wave relationsmath-ph
The wave equation (free boson) problem is studied from the viewpoint of the relations on the symplectic manifolds associated to the boundary induced by solutions. Unexpectedly there is still something to say on this simple, well-studied problem. In particular, boundaries which do not allow for a meaningful Hamiltonian …
New relation found in 4D symplectic mapping class group.
problem Relation between Dehn twists in symplectic 4-manifolds.
method Holomorphic curve techniques, symplectic isotopy problem solution.
result Relation between two products of Dehn twists.
Deep learning model extracts medical treatment-problem relationships.
problem Mining relationships between treatments and medical problems.
method Hybrid approach combining deep learning and rule-based systems.
result System achieved promising performance on medical relation extraction task.
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.
Characterizes embeddable relations in Euclidean space.
problem Embedding directed graphs into Euclidean space.
method Three types of embeddings, with characterizations and bounds.
result Characterizes which relations can be embedded and bounds on dimensionality.
Python library for boosting statistical relational models.
problem Expressing learning and inference problems in statistical relational models.
method Adapting scikit-learn interface for boosted statistical relational models.
result Provides examples for using srlearn.
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
problem Optimizing interval-valued functions on Riemannian manifolds under a total order relation.
method Generalized Hukuhara directional differentiability to derive KKT-type optimality conditions.
result Derives optimality conditions for interval-valued optimization problems on Riemannian manifolds.
We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional topological surgery conjecture. The A-B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surg…
We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be shown to relate to a risk-sensitive stochastic control problem for a sufficiently l…
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…
Maximum likelihood inference for high-dimensional problems with multiaffine variable relationsstat.ML
A novel AIRLS algorithm for multiaffine variable relations in high-dimensional problems.
problem Challenges in Maximum Likelihood Estimation in high-dimensional settings with complex variable relations.
method Proposes an Alternating and Iteratively-Reweighted Least Squares (AIRLS) algorithm for multiaffine variable relations.
result Proves convergence for problems with Generalized Normal Distributions and shows empirically super-linear convergence rate.
Solved A-B slice problem using link-homotopy+.
problem 4D topological surgery conjecture for free groups.
method Geometric applications of 2-Engel relation.
result Solved A-B slice problem.
Mathematical framework for minimum enclosing ball problem.
problem Determining the smallest sphere enclosing a set in d-dimensional space.
method Theoretical framework based on enclosing and partitioning theorems.
result Bounds and relations between circumradius, inradius, diameter, and width.
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.
We study the isoperimetric problem in Euclidean space endowed with a density. We first consider piecewise constant densities and examine particular cases related to the characteristic functions of half-planes, strips and balls. We also consider continuous modification of Gauss density in . Finally, we give a list…
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.
Enhances relational reasoning with multi-layer architecture.
problem Limited relational reasoning with shallow architectures.
method Multi-layer relation network architecture.
result Solved all 20 tasks in bAbI 20 QA dataset.
Proposes a new method to learn data representations by modeling sample relations.
problem Lack of rich latent structural information in DAEs.
method Explicitly models and leverages sample relations as supervision for representation learning.
result Significantly improves clustering performance on benchmark datasets.
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.
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.
A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth of the problem to maximize the expected -utility of the terminal wealth generated by admissible portfolios $\varp…
We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if they have the same geodesics as point sets. This is closely related to Hilbert'…
Compact method proves Brown-York mass positivity and connects to major conjectures.
problem Proving positivity of Brown-York's mass and its connections to conjectures.
method Compact approach to proving mass positivity and exploring connections.
result Proved the positivity of Brown-York's mass and its relation to conjectures.
We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual problem. We give two versions of this theorem. The first theorem relates a numéra…
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.
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.
Survey of Weber's class number problem and related topics.
problem Weber's class number problem and its variants.
method Arithmetic topology, units, generalized Pell's equation, -adic limits of class numbers.
result Numerical investigation of class numbers in -adic towers for knots and elliptic curves.
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.
We present and discuss some open problems formulated by participants of the International Workshop "Knots, Braids, and Auto\-mor\-phism Groups" held in Novosibirsk, 2014. Problems are related to palindromic and commutator widths of groups; properties of Brunnian braids and two-colored braids, corresponding to an amalga…
Bayesian approach improves network lasso for multi-task learning.
problem Improving the determination of relational coefficients in network lasso.
method Proposes a Bayesian approach to solve multi-task learning problems using network lasso.
result Objective determination of relational coefficients through Bayesian estimation.
New method uses spectral geometry to improve matrix completion with geometric relations.
problem Matrix completion problems with underlying geometric or topological relations.
method Interprets DMF through spectral geometry to incorporate explicit regularization.
result DMF models can exploit geometric relations, improving performance on real benchmarks.
27 problems identified in automating movie/TV subtitle translation.
problem Challenges in translating movie/TV subtitles.
method Categorized problems into three categories and evaluated translation quality.
result Frontier NLP systems struggle with subtitles and require post-processing.
Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metro…
In this paper we introduce in study the projectively related complex Finsler metrics. We prove the complex versions of the Rapcsák's theorem and characterize the weakly Kähler and generalized Berwald projectively related complex Finsler metrics. The complex version of Hilbert's Fourth Problem is also pointed out. As an…
GMNN combines conditional random fields and graph neural networks for relational data.
problem Semi-supervised object classification in relational data.
method Combines conditional random fields and graph neural networks. Uses variational EM algorithm for training.
result GMNN achieves state-of-the-art results on object classification, link classification, and unsupervised node representation learning.
In this paper we consider an interval portfolio selection problem with uncertain returns and introduce an inclusive concept of satisfaction index for interval inequality relation. Based on the satisfaction index, we propose an approach to reduce the interval programming problem with uncertain objective and constraints …