In this paper we define and study flexible links and flexible isotopy in projective space. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholms interpretation of Viros encomplexed writhe.
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48 results for “flexible links”
Flexible links have symplectic representatives in complex projective space.
problem Existence of symplectic representatives for flexible links.
method Construction of a symplectic surface invariant under complex conjugation.
result No obstructions to finding symplectic representatives beyond classical topology.
New tests for VaR and ES forecast encompassing using flexible link functions.
problem Testing forecast encompassing for Value at Risk and Expected Shortfall.
method Flexible link functions for testing convex forecast combinations and nonstandard asymptotic theory for boundary parameters.
result Tests based on new link functions outperform unrestricted linear link functions for one-step and multi-step forecasts.
Curves with constant curvature are flexible and can be deformed.
problem Understanding the flexibility of curves with constant curvature.
method Proving the parametric -dense relative -principle for curves of constant curvature.
result Two knots of constant curvature are isotopic and homotopic if their self-linking numbers are equal.
New method analyzes knots and links using multiscale Gauss link integral.
problem Lack of localization and quantization in knot theory applications.
method Integrates curve segmentation and multiscale analysis into the Gauss link integral.
result Significantly outperforms other methods in protein flexibility analysis.
From Partial Exchangeability to Predictive Probability: A Bayesian Perspective on Classificationstat.ME
Bayesian model improves classification performance with flexible uncertainty modeling.
problem Improving classification performance with flexible uncertainty modeling.
method Combines Gaussian process and Dirichlet process priors for latent function and link function, respectively.
result Outperforms standard logistic regression on simulated data.
We propose a link prediction algorithm that is based on spring-electrical models. The idea to study these models came from the fact that spring-electrical models have been successfully used for networks visualization. A good network visualization usually implies that nodes similar in terms of network topology, e.g., co…
Link prediction is a fundamental task in statistical network analysis. Recent advances have been made on learning flexible nonparametric Bayesian latent feature models for link prediction. In this paper, we present a max-margin learning method for such nonparametric latent feature relational models. Our approach attemp…
Researchers use estimated Kolmogorov complexity for better link prediction in graphs.
problem Improving link prediction accuracy in complex networks.
method Regularization based on an approximation of Kolmogorov complexity, which is differentiable and compatible with recent link prediction algorithms.
result The regularization method shows good performance on diverse real-world networks, but the success is likely due to an aggregation method rather than actual estimation of Kolmogorov complexity.
Chained Gaussian Processesstat.ML
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formal…
Relational data are usually highly incomplete in practice, which inspires us to leverage side information to improve the performance of community detection and link prediction. This paper presents a Bayesian probabilistic approach that incorporates various kinds of node attributes encoded in binary form in relational m…
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.
In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph b…
Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with …
The paper enhances representations to show left-orderability of certain 3-manifold groups.
problem Left-orderability of 3-manifold groups using enhanced representations.
method Recalibration of Calegari and Dunfield's flipping construction for $\mbox{Homeo}_+(S^1)$-representations.
result Branched covers of links are left-orderable, generalizing known results.
Improved flow matching using Gaussian processes for better sample quality.
problem Training continuous normalizing flows with reduced variance and flexibility.
method Extending conditional flow matching to streams modeled with Gaussian processes.
result Improved quality of generated samples with moderate computational cost.
In online social networks people often express attitudes towards others, which forms massive sentiment links among users. Predicting the sign of sentiment links is a fundamental task in many areas such as personal advertising and public opinion analysis. Previous works mainly focus on textual sentiment classification, …
Contact surgeries yield algebraically overtwisted manifolds.
problem Understanding algebraically overtwisted contact manifolds through surgeries.
method Contact -surgeries on Legendrian spheres in flexibly fillable contact manifolds.
result Yielding algebraically overtwisted manifolds when the Legendrian's homology class is not annihilated.
These introductory lectures show how to define finite type invariants of links and 3-manifolds by counting graph configurations in 3-manifolds, following ideas of Witten and Kontsevich. The linking number is the simplest finite type invariant for 2-component links. It is defined in many equivalent ways in the first sec…
Develops a flexible model for regime transitions in time series data.
problem Nonlinear and context-dependent regime transitions in time series data.
method Semi-parametric state-space model with learned transition functions.
result Improved recovery of nonlinear transition dynamics and earlier detection of regime changes.
Humans and animals show remarkable flexibility in adjusting their behaviour when their goals, or rewards in the environment change. While such flexibility is a hallmark of intelligent behaviour, these multi-task scenarios remain an important challenge for machine learning algorithms and neurobiological models alike. We…
Embedding-based Knowledge Base Completion models have so far mostly combined distributed representations of individual entities or relations to compute truth scores of missing links. Facts can however also be represented using pairwise embeddings, i.e. embeddings for pairs of entities and relations. In this paper we ex…
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogenity beyond what …
Persona2vec learns multiple node roles in graphs.
problem Graphs often have nodes with multiple overlapping roles.
method Persona2vec learns multiple node representations based on structural contexts.
result Persona2vec outperforms state-of-the-art models in link prediction.
Constrained clustering has been well-studied for algorithms such as -means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode many constraints is to use spectral clustering, which remains a developing area. I…
A novel GNN architecture improves link prediction by combining positive and negative samples.
problem Link prediction accuracy limited by node-wise methods and increased model complexity of edge-wise methods.
method Proposes a novel GNN architecture that uses both positive and negative samples to inform node embeddings.
result The method retains the inference speed of node-wise models while achieving competitive accuracy with edge-wise alternatives.
Flexible classifier using Mahalanobis distances for non-elliptical distributions.
problem Classifying non-elliptical and multimodal distributions.
method Semiparametric classifier based on Mahalanobis distances and generalized additive models.
result The proposed classifiers outperform traditional methods in high-dimensional, low-sample-size scenarios.
Study on embeddings of surfaces in 4-manifolds and their mapping classes.
problem Characterizing and understanding embeddings of surfaces in 4-manifolds and their mapping classes.
method Analyzing smooth proper embeddings and mapping classes induced by diffeomorphisms of 4-manifolds.
result Most surfaces do not admit flexible embeddings in 4-manifolds with specific homology types.
-Generalized Probit Regression and Scalable Maximum Likelihood Estimation via Sketching and Coresetscs.DS
New method for efficient maximum likelihood estimation of -generalized probit regression.
problem Efficient estimation of -generalized probit regression models.
method Combining sketching techniques with importance subsampling to obtain a coreset.
result Maximum likelihood estimator can be approximated efficiently up to a factor of on large data.
Graphs are general and powerful data representations which can model complex real-world phenomena, ranging from chemical compounds to social networks; however, effective feature extraction from graphs is not a trivial task, and much work has been done in the field of machine learning and data mining. The recent advance…
Many open problems and important theorems in low-dimensional topology have been formulated as statements about certain 2--complexes called gropes. This paper describes a precise correspondence between embedded gropes in 4--manifolds and the failure of the Whitney move in terms of iterated `towers' of Whitney disks. The…
Paper introduces a new edge exchangeable block model for complex networks.
problem Limitations of the stochastic block model in analyzing complex networks.
method Develops a Bayesian nonparametric edge exchangeable block model.
result The new model outperforms state-of-the-art SBMs for link prediction.
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links. Despite its flexibility and popularity, there has been a lack of principled statist…
In this self-contained book, following Edward Witten, Maxim Kontsevich, Greg Kuperberg and Dylan Thurston, we define an invariant Z of framed links in rational homology 3-spheres, and we study its properties. The invariant Z, which is often called the perturbative expansion of the Chern-Simons theory, is valued in a gr…
Bayesian graph learning improves graph representation accuracy.
problem Inaccurate graph construction from noisy data.
method Non-parametric Bayesian graph model for posterior inference of graph adjacency matrices.
result Model scales well to large graphs and improves node classification, link prediction, and recommendation tasks.
The use of drug combinations often leads to polypharmacy side effects (POSE). A recent method formulates POSE prediction as a link prediction problem on a graph of drugs and proteins, and solves it with Graph Convolutional Networks (GCNs). However, due to the complex relationships in POSE, this method has high computat…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a subset of the vertices. We characterize the possible partial configuration spaces of…
Proposes a Bayesian approach for integrating multiple linked matrices.
problem Integrating multiple linked matrices for diverse applications.
method Empirical Bayes Linked Matrix Decomposition (EB-LMD).
result Efficient estimation algorithm with no tuning parameters.
Stochastic Lipschitz bandit algorithms balance exploration and exploitation, and have been used for a variety of important task domains. In this paper, we present a framework for Lipschitz bandit methods that adaptively learns partitions of context- and arm-space. Due to this flexibility, the algorithm is able to effic…
Graph edges, along with their labels, can represent information of fundamental importance, such as links between web pages, friendship between users, the rating given by users to other users or items, and much more. We introduce LEAP, a trainable, general framework for predicting the presence and properties of edges on…
Eigen-GNN enhances GNNs by preserving graph structures.
problem Existing shallow GNNs fail to effectively preserve graph structures.
method Integrates eigenspace of graph structures into GNNs as a dimensionality reduction module.
result Eigen-GNN boosts GNNs' ability to preserve graph structures without increasing depth.
Paper formalizes Simon's satisficing through FFSD, proving its equivalence to expected utility theory.
problem Formalizing Herbert Simon's bounded rationality concept in economic decision-making.
method Developed FFSD framework using Lean 4 theorem prover, proving equivalence to expected utility theory.
result Equivalence theorem linking FFSD to expected utility maximization for approximate indicator functions.
The authors characterize flexibility in power and energy markets considering time, spatiality, resource, and risk.
problem Evaluating and maximizing flexibility in power systems and markets.
method Characterization of flexibility dimensions (time, spatiality, resource, risk) and their interrelations with flexibility assets, products, and services.
result Flexibility should be evaluated based on multiple dimensions for efficient power systems and markets.
Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of a knot i…
We exhibit a certain infinite family of three-stranded quasi-alternating pretzel knots which are counterexamples to Lobb's conjecture that the sl_3-knot concordance invariant s_3 (suitably normalised) should be equal to the Rasmussen invariant s_2. For this family, |s_3| < |s_2|. However, we also find other knots for w…
Constructs exotic proper 2-knots from open 2-handles.
problem Proving topological equivalence of exotic proper knotted surfaces.
method Flexible construction of exotic open 2-handles, distinguishing through genus functions and end Floer homology.
result Constructs infinite families of irreducible exotic proper knotted surfaces.
Smoothing graphons improve link prediction in Bayesian SBM without increasing computational complexity.
problem Accurate modeling of exchangeable relational data with flexible and computationally efficient graphons.
method Introducing smoothing procedures to piecewise-constant graphons to create smoothing graphons, which allow continuous intensity values for relations.
result Smoothing graphons improve AUC and precision for link prediction in real-world data sets.
Developed a flexible Bayesian g-formula for causal survival analysis with time-dependent confounding.
problem Estimating causal survival curves in longitudinal observational studies with time-varying treatments and confounding.
method Incorporated Bayesian Additive Regression Trees (BART) into the g-formula to model time-evolving generative components and mitigate bias due to model misspecification.
result Demonstrated improved empirical performance and practical utility of the proposed method through simulations and real-world data analysis.