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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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
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48 results for “flexible topology”
Flexible approach for normal approximations in geometric and topological statistics.
problem Normal approximation for complex statistics not expressible as sums of score functions.
method Flexible add-one cost operator combined with strong stabilization theory.
result Established normal approximation results for geometric and topological statistics.
Study shows non-existence of certain contact structures on odd-dimensional manifolds.
problem Existence of contact structures with flexible pages on odd-dimensional manifolds.
method Proved a topological obstruction and used symplectic actions to show non-existence.
result Non-existence of contact open books with flexible pages for certain manifolds.
Refines a key lemma in symplectic topology, improving its applicability.
problem Improving the applicability of the holonomic approximation lemma in symplectic topology.
method Careful quantitative geometry and Gromov's convex integration method.
result Establishes several refinements of the holonomic approximation lemma.
The study examines the flexibility of entropies for negatively curved surfaces.
problem The study investigates the flexibility of topological and metric entropies for negatively curved surfaces.
method The authors compare different metrics on surfaces of negative curvature and analyze their topological and metric entropies.
result The study proves that the topological and metric entropies for metrics of negative curvature are flexible and only equal in the case of constant negative curvature.
Paper proves flexibility of specific relations using convex integration.
problem Holonomic approximation theorem in differential topology.
method Proves the holonomic approximation theorem for first order jets using convex integration.
result Relation is open and ample, leading to flexibility of the theorem.
Paper uses harmonic surfaces to model surfaces of any complexity.
problem Topological limitations of minimal surfaces restrict their use.
method Weierstrass representation for harmonic surfaces to construct arbitrary genus surfaces.
result Harmonic surfaces can be used to create surfaces of arbitrary genus.
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.
AutoShrink optimizes neural architectures by shrinking cell structures.
problem Resource constraints in deploying DNNs on mobile devices.
method Topology-aware node-based Neural Architecture Search (NAS).
result AutoShrink achieves up to 48% parameter reduction and 34% MACs savings.
Unified mathematical theory for analyzing biomolecular geometry and flexibility.
problem Lack of a unified mathematical theory for analyzing biomolecular geometry and flexibility.
method Introducing de Rham-Hodge theory, Helmholtz-Hodge decomposition, and discrete exterior calculus.
result Unified framework for predicting macromolecular flexibility and natural modes.
Flexible outlier detection using graph communities for robust performance.
problem Outlier detection in small sample size unbalanced problems.
method Local measure of label heterogeneity in a weighted graph topology.
result Overall outperforms local and global strategies in multi and single view settings.
This paper determines the flexible exponent for non-geometric 3-manifolds.
problem Bounding the mapping degree in terms of the Lipschitz constant for non-geometric 3-manifolds.
method Analyzing the infimum of α such that the inequality holds for any Lipschitz map.
result The flexible exponent for non-geometric 3-manifolds is determined.
Teichmüller geodesics can have flexible limit sets.
problem Teichmüller geodesics may not converge to a single point in the boundary.
method Analyzing the topology of the hierarchically hyperbolic space boundary.
result Limit sets of Teichmüller geodesics can be almost anything allowed by the topology.
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.
For power grid operations, a large body of research focuses on using generation redispatching, load shedding or demand side management flexibilities. However, a less costly and potentially more flexible option would be grid topology reconfiguration, as already partially exploited by Coreso (European RSC) and RTE (Frenc…
Neural ODEs extended to manifolds for flexible sampling.
problem Sampling from complex multimodal distributions on non-trivial topologies.
method Extending Neural ODEs to smooth manifolds using vector fields.
result A general methodology for building normalizing flows on manifolds.
The Allen-Cahn equation yields bounded solutions with any compact topology level sets.
problem Finding bounded solutions with specified compact topology level sets.
method Utilizing infinite-index solutions of the Allen-Cahn equation.
result Existence of bounded entire solutions with zero level sets of any compact topology.
New method simplifies classifier structure via topological complexity.
problem Global regularization in classifiers is structure agnostic.
method Topological regularization using persistent homology.
result Demonstrated effectiveness on various datasets.
ARTree uses deep learning to infer tree topologies efficiently.
problem Efficient phylogenetic inference from tree topologies.
method Deep autoregressive model based on graph neural networks (GNNs).
result ARTree provides a flexible family of distributions over tree topologies.
Neural network learns its size and structure during training.
problem Adapting neural network architecture to specific datasets.
method Flexible setup allowing neural network to learn size and topology during training.
result Trained networks achieve virtually identical performance and have learned optimal structure.
Paper speeds up topological signal identification and cycle matching.
problem Efficiently identifying and matching topological signals across datasets.
method Cohomological approach to persistent homology computation.
result Significantly faster performance on large-scale datasets.
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.
The study translates Weinstein structures to Legendrian handlebodies for symplectic topology.
problem Detecting flexibility and rigidity in Weinstein manifolds.
method Systematic recipe for translating Weinstein Lefschetz fibrations to Legendrian handlebodies.
result Verification of Stein deformation equivalence and existence of closed exact Lagrangian submanifolds.
A neural network visualizes data structure and concepts.
problem Data visualization and concept understanding.
method Mixing autoencoder and classifier for multi-perspective visualization.
result The network produces different topological maps based on training as autoencoder or classifier.
New clustering algorithm uses persistent homology for space-time data.
problem Clustering space-time data without labeled examples.
method Persistent homology for topological data analysis, analyzing data at multiple resolutions.
result The algorithm distinguishes true features from noise based on persistence.
IVFS simplifies feature selection for high-dimensional data preservation.
problem Maintaining structure and pairwise distances in high-dimensional data.
method IVFS framework based on persistent diagrams from computational topology.
result IVFS well preserves pairwise distances and topological patterns of full data.
A new method for graph-structured data improves transformer performance by incorporating topology.
problem Improving transformer performance on graph-structured data.
method Parameterizing topological masks as a learnable function of a weighted adjacency matrix, approximated with graph random features.
result Efficient masking algorithms provide strong performance gains for tasks on image and point cloud data.
Bayesian topological learning improves EEG signal analysis for brain state classification.
problem Challenges in classifying and analyzing noisy, nonlinear, nonstationary EEG signals.
method Persistent homology with Bayesian framework to track topological features and incorporate prior knowledge.
result Bayesian topological learning outperforms existing methods for noisy EEG classification.
Study on flexibility of metric entropy and geodesic flow constraints on surfaces.
problem Flexibility and constraints of metrics and flows on surfaces.
method Analysis of geodesic flow, entropy, and metrics in a fixed conformal class.
result Additional restrictions on topological entropy and new geometric properties.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
Quotient manifolds of flowsmath.DS
This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of countably presented groups is induced by the quotient map of some flow, and that higher…
Bayesian method classifies actin cytoskeleton networks using topological data.
problem Classifying the structure of biological networks, especially actin cytoskeleton networks.
method Transform actin cytoskeleton networks into persistence diagrams, quantify variability with Bayesian framework, estimate posterior distributions.
result Bayesian framework successfully classifies actin filament networks, outperforming state-of-the-art methods.
A new model learns graph structures from data.
problem Learning graph topologies from data.
method Proposes a learning to optimise (L2O) approach to learn graph structures from node data.
result The proposed model learns graph structures more efficiently than classic iterative algorithms.
Study shows flexibility of homology groups of Reeb spaces of fold maps through surgery operations.
problem Understanding changes in homology groups of Reeb spaces of fold maps.
method Introduced surgery operations (bubbling operations) to fold maps and used elementary theory of sequences and continuous functions.
result Homology groups of Reeb spaces of fold maps constructed by iterations of these operations are flexible and can be represented as direct sums of original homology groups and finitely generated commutative groups.
This paper explores rigid properties of Alexandrov spaces with maximal radius.
problem Rigidity of Alexandrov spaces with maximal radius and specific curvature conditions.
method Analyzes Alexandrov spaces with \curv\geq1, nonempty boundary, and maximal radius \fracπ{2}. Uses rigidity theorems and geometric/topological constraints.
result Shows flexibility and rigidity in Alexandrov spaces with maximal radius under different conditions.
Proposes a method to infer complex network topologies from multiple graphs.
problem Learning multiple graph Laplacian matrices from heterogeneous graph signals with intricate topological patterns.
method Structured fusion regularization and ADMM algorithm for efficient computation.
result Establishes a non-asymptotic bound of the estimation error and reflects the effect of key factors on convergence rate.
New topological methods for hypergraph data improve community detection and pattern recognition.
problem Community detection and pattern recognition in hypergraph data.
method Introducing a new topological space structure of hypergraph data, proposing modified nearest neighbors methods.
result Improved methods for community detection and pattern recognition in hypergraph data.
This paper formalizes the h-principle and sphere eversion in differential topology.
problem Formalizing the h-principle and sphere eversion in differential topology.
method Lean formalization of the local h-principle for first-order partial differential relations, using convex integration.
result Reproves Smale's sphere eversion theorem and formalizes advanced mathematics.
Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layersstat.ML
Paper learns DAGs with quadratic variance functions efficiently.
problem Learning DAGs with quadratic variance functions.
method Introduces topological layers to reconstruct DAGs hierarchically.
result Efficient algorithm reduces computational cost.
The paper introduces pseudo-quotients for algebraic actions and applies them to character varieties.
problem Characterizing algebraic actions and their quotients.
method Introducing pseudo-quotients as a weak version of quotients for algebraic actions, focusing on purely topological properties.
result Pseudo-quotients are unique up to virtual class in characteristic zero and can be used to compute character varieties.
Spring-electrical models predict network links based on node proximity.
problem Predicting links in networks.
method Spring-electrical models applied to network layouts.
result The Euclidean distance in network layouts correlates with link probabilities.
A new model learns networked data with topology and features.
problem Learning from networked data with topology and features.
method Networked exponential families and network Lasso for efficient learning.
result Efficiently learns networked data with topology and features.
New bounds on mapping degrees for geometric 3-manifolds.
problem Bounding the mapping degree in terms of Lipschitz constant for geometric 3-manifolds.
method Constructing Legendrian maps to prove bounds on flexible exponent.
result Complete result for flexible exponent of geometric 3-manifolds.
CycleMorph improves image registration by preserving topology with cycle consistency.
problem Preserving original topology during deformation in image registration.
method Cycle-consistent deformable image registration approach.
result Effective and accurate registration on diverse image pairs within seconds.
CIFs improve VI by providing flexible posteriors for complex topologies.
problem Complex posterior distributions in VI problems.
method Using CIFs as part of an auxiliary VI scheme, exploiting conditional independence.
result CIFs yield low-variance estimators of model evidence and improve VI results.
A novel framework for adaptive multi-agent communication in reinforcement learning.
problem Manual specification of communication structures in multi-agent reinforcement learning.
method Learning Structured Communication (LSC) framework using hierarchical graph neural networks.
result Adaptive hierarchical formations and efficient message propagation among agents.
This work develops algorithms to infer network structure and dynamics from partial nodal observations.
problem Inferring network structure and dynamics from limited nodal observations.
method Develops algorithms for joint inference of network topology and processes using structural equation models and structural vector autoregressive models.
result Effective algorithms for joint inference of network topology and processes from partial nodal observations, even in time-evolving networks.
New examples challenge Geroch conjecture stability.
problem Stability of the Geroch conjecture in warped products.
method Constructing warped-product manifolds with specific curvature properties.
result First counterexample to Sormani's conjecture on stability.