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.
Flat fully augmented links with homeomorphic complements are equivalent.
problem Determining equivalence of flat fully augmented links based on their complements.
method Careful analysis of totally geodesic surfaces and cusps in link complements and their behavior under homeomorphism.
result Complete classification of flat fully augmented link complements with multiple reflection surfaces and symmetries.
The paper assesses dimensionality reduction for cryptocurrency link prediction.
problem Establishing a link between cryptocurrencies using dimensionality reduction techniques.
method Used canonical correlation analysis and principal component analysis on log returns and covariates of Bitcoin and Ethereum.
result Performance of dimensionality reduction techniques in forecasting Ethereum returns with Bitcoin features.
New algorithm detects network outliers with missing links.
problem Identifying outliers in networks with missing links.
method Proposes a new algorithm that detects outliers and predicts missing links.
result Proves the algorithm exactly detects outliers and achieves best error for missing link prediction.
Paper introduces a method to assess liquidity risk in meme tokens using entity-linked address analysis.
problem High market volatility and vulnerability to manipulation in meme tokens.
method Multi-dimensional approach integrating fund flow analysis, behavioral similarity, and anomalous transaction detection.
result Significant disparities between apparent and actual liquidity in meme token markets.
New heuristics for predicting links in multiplex networks.
problem Link prediction in networks with multiple types of connections.
method Proposed a general framework and three families of heuristics.
result Significantly outperformed baseline heuristics for ordinary networks.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
New proof found for Khovanov's assertion about Frobenius algebra twists.
problem Proving the isomorphism between chain complexes of twisted Frobenius algebras and link diagrams.
method Detailed analysis of configurations of circles in each state.
result A new proof of Khovanov's assertion with a detailed analysis of configurations.
Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface in…
Proposes a new model for high-dimensional data analysis with unknown link function.
problem Estimating link function, component functions, and variable interactions in high-dimensional data.
method Generalized Sparse Additive Model with Unknown Link Function (GSAMUL) using B-spline basis and MLP network for link estimation, with ℓ2,1-norm regularizer for variable selection. result Can realize both variable selection and hidden interaction.
New invariants for link analysis include biquandle power brackets.
problem Analyzing oriented links with new invariants.
method Introducing biquandle power brackets as an infinite family of link invariants.
result Biquandle power brackets encompass classical and previous invariants.
We study the space of "link maps": the space of maps of a disjoint union of compact, closed manifolds P_1, . . ., P_k into a manifold N whose images are pairwise disjoint. We apply the manifold calculus of functors developed by Goodwillie and Weiss to study the difference between it and its linear and quadratic approxi…
Study on factorizations of knot polynomials for up to 12 crossings.
problem Understanding factorizations of HOMFLY polynomials for knots and links.
method Computer analysis of knots up to 12 crossings; irreducibility criterion for 2-connected plane graphs.
result Found 17 non-trivial factorizations of knots with up to 12 crossings.
Algorithm simplifies Khovanov homology computations for 4-strand torus links.
problem Computing Khovanov homology of 4-strand torus links.
method Algorithmic Morse theoretic simplifications postponed until the end.
result Non-trivial Khovanov homology groups in all homological degrees for 4-strand torus links.
Study links in knitted textiles using knot theory.
problem Identify and classify links in knitted textiles.
method Correspondence between links in thickened torus and 2-periodic weft-knitted textiles, using link invariants and ribbon knots.
result New stitch patterns and links in knitted textiles identified.
In this paper, we show that any non-arithmetic hyperbolic 2-bridge link complement admits no hidden symmetries. As a corollary, we conclude that a hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic 3-manifold. By combining this corollary with the work of Boileau and Weidmann, we obtain a ch…
Proposes a method to enhance graph models by injecting unseen connections.
problem Enhancing graph models to utilize unseen connections.
method Parametric link injection layer to find and inject weak connections.
result Improves performance on node classification and link prediction tasks.
Proposes a novel tensor-based approach for multi-level link prediction.
problem Inferring potential links from observed networks.
method Tensor-based joint network embedding capturing pairwise and hyperlinks.
result Improves hyperlink and pairwise link prediction accuracy.
Witt algebra acts on Khovanov-Rozansky homology of links.
problem Understanding algebraic structures in knot theory.
method Construction of Witt algebra action on Khovanov-Rozansky homology.
result Induced maps between twists of the homology via link cobordisms.
We study configuration space integral formulas for Milnor's homotopy link invariants, showing that they are in correspondence with certain linear combinations of trivalent trees. Our proof is essentially a combinatorial analysis of a certain space of trivalent "homotopy link diagrams" which corresponds to all finite ty…
Delta-unlinking number measures how to unlink algebraically split links.
problem Measuring unlinking complexity of algebraically split links.
method Defining delta-unlinking number as minimum delta-moves to unlink, proving bounds and calculating specific values.
result Precise delta-unlinking numbers for algebraically split prime links up to 9 crossings, and 4-genus values for most.
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.
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
This paper examines number theoretic and topological properties of fully augmented pretzel link complements. In particular, we determine exactly when these link complements are arithmetic and exactly which are commensurable with one another. We show these link complements realize infinitely many CM-fields as invariant …
Develops persistent Khovanov homology for tangles.
problem Lack of local topological features in evolutionary Khovanov homology for knots and links.
method Introduces a new mathematical framework using persistent Khovanov homology of tangles, employing functor and planar algebra.
result Provides a new method to characterize local features in curve-type data.
This study compares 16 embedding-based link prediction methods for knowledge graphs.
problem KG incompleteness and missing facts prediction.
method Embedding-based link prediction methods compared.
result Effective and efficient comparison of 16 embedding-based LP methods.
BIDIFAC+ factorizes linked matrices for cancer studies.
problem Integrating multiple omics platforms across various cancer types.
method Flexible approach to simultaneous factorization and decomposition of linked matrices using BIDIFAC+.
result Identifies shared and specific modes of variability across multiple omics platforms and cancer types.
PHLP uses persistent homology to interpret graph link prediction.
problem Interpreting why graph neural network models perform well in link prediction.
method Employing persistent homology to analyze graph topology and extract features.
result PHLP outperforms state-of-the-art models on most benchmark datasets.
We highlight a very simple statistical tool for the analysis of financial bubbles, which has already been studied in [1]. We provide extensive empirical tests of this statistical tool and investigate analytically its link with stocks correlation structure.
We derive a new radial link for binary classification under shared elliptical distributions.
problem Binary classification under shared-generator elliptical class-conditional distributions.
method We derive the Bayes radial-link family from the within-class radius law and estimate it by a finite fractional-power stochastic-polynomial projection.
result The derived link is asymptotically Bayes-optimal and significantly better than QDA on various benchmarks.
The data in many disciplines such as social networks, web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this paper, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T+1? If our da…
Complex analysis techniques link Gaussian RBF kernels to quantum mechanics.
problem Understanding the Gaussian RBF kernel in machine learning and SVMs.
method Using Fock space and Segal-Bargmann theories in complex analysis.
result Proves connections between Gaussian RBF kernels and quantum mechanics operators.
In this work, we consider the problem of combining link, content and temporal analysis for community detection and prediction in evolving networks. Such temporal and content-rich networks occur in many real-life settings, such as bibliographic networks and question answering forums. Most of the work in the literature (…
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main …
Corrected a false lemma in Cimasoni's work on linking theory.
problem A false lemma in Cimasoni's geometric construction of the Conway potential function.
method Presented counterexamples and a detailed proof of the corrected lemma.
result The lemma is false and its correction has significant consequences for subsequent works.
The paper uses neural networks to price complex life insurance contracts with multiple risk factors.
problem Pricing equity-linked life insurance contracts with various stochastic risk factors.
method Assuming hedging to reduce local variance, the price is expressed as a system of non-linear PDEs. Reformulated as a backward SDE with jumps, solved numerically using neural networks.
result Neural networks provide an efficient numerical solution for pricing these complex contracts.
In this paper, we study a geometric/topological measure of knots and links called the nullification number. The nullification of knots/links is believed to be biologically relevant. For example, in DNA topology, one can intuitively regard it as a way to measure how easily a knotted circular DNA can unknot itself throug…
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.
Knots and links have been considered to be useful models for structural analysis of molecular chains such as DNA and proteins. One quantity that we are interested on molecular links is the minimum number of monomers necessary to realize them. In this paper we consider every link in the cubic lattice. Lattice stick numb…
Proves existence of Yamabe metrics on conical manifolds with conical points and links.
problem Existence of Yamabe metrics on singular manifolds with conical points and links.
method Derives a counterpart of Aubin's result, uses conical links and Fourier analysis, adds lower-order correction to standard bubbles.
result Derives asymptotic expansions on the Yamabe quotient for generic type metrics.
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…
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…
The Whitehead link exterior lacks most Euler class taut foliations.
problem Existence of co-orientable taut foliations with specific Euler classes.
method Combining foliation theory techniques and topological obstructions.
result Most lattice points in the dual Thurston ball cannot be Euler classes of co-orientable taut foliations.
Combines topological and geometric approaches to data analysis.
problem Understanding when and how geometric objects intersect.
method Connects topological and geometric concepts of curvature.
result Reconceptualizes curvature and links it to hyperconvexity.
It has often been taken as a working assumption that directed links in information networks are frequently formed by "short-cutting" a two-step path between the source and the destination -- a kind of implicit "link copying" analogous to the process of triadic closure in social networks. Despite the role of this assump…
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t−1) as the shape parameters of those at time t, which are linked …
Study on scalar curvature decay on non-compact manifolds linked at infinity.
problem Understanding scalar curvature decay on non-compact manifolds with topological linking at infinity.
method Analyzing polynomial decay, developing obstruction theory, using μ--bubble exhaustions, and index theory. result Topological linking at infinity forces polynomial decay of scalar curvature on manifolds of weakly bounded geometry.
Study finds strong link between crypto narratives and prices.
problem Understanding the impact of crypto narratives on prices.
method Topic modeling of Twitter data combined with sentiment analysis.
result Strong correlation between narratives and crypto prices.