Explains topological overlap in simple terms, with weighted vertices.
problem Understanding topological overlap in geometric contexts.
method Self-contained exposition based on Gromov's work and follow-ups.
result Deduction of a dual statement using von Neumann's minimax theorem.
We prove isoperimetric inequalities for quotients of n-dimensional Affine buildings. We use these inequalities to prove topological overlapping for the 2-dimensional skeletons of these buildings.
Improved retinal vessel segmentation with topology preservation trade-off.
problem Retinal vessel segmentation accuracy and topology preservation trade-off.
method Topology preserving term in the loss function and orientation score guided convolutional module.
result Model achieves higher topological accuracy at the expense of lower overlap metrics.
The paper proves a theorem about higher-dimensional expansion and its topological implications.
problem Higher-dimensional expansion properties and their topological consequences.
method Detailed proof of Gromov's Topological Overlap Theorem using cellular cochains and simplicial complexes.
result The theorem states that if a complex has strong higher-dimensional expansion properties, it has a topological overlap property.
Bayesian supertrees method uses variational Bayes for overlapping taxon subsets.
problem Inference of phylogenetic tree topologies for overlapping taxon sets.
method Variational Bayesian approach.
result Demonstrates effectiveness of variational Bayes for Bayesian supertrees.
New criterion proves high dimensional expansion in bounded degree complexes.
problem Proving high dimensional expansion in bounded degree complexes.
method Local to global criterion applied to Ramanujan complexes.
result Infinite families of bounded degree complexes with topological overlapping property.
The paper introduces vortex cycles and nerves, inspired by Thomson's vortex atoms.
problem Understanding vortex structures and their homology.
method Introducing and analyzing non-concentric, nesting vortex cycles and nerves.
result Whitehead CW topology and Leader uniform topology outcomes of vortex cycles.
3-manifolds with torsion homology expand in all dimensions.
problem Constructing 3-manifolds with good expansion properties.
method Constructing 3-manifolds with specific homological properties and demonstrating their expansion.
result 3-manifolds with torsion homology expand in all dimensions.
Graphs represent gene segment organization, revealing complex interrelationships in a scrambled genome.
problem Understanding gene segment organization and interrelationships in a scrambled genome.
method Directed graphs representing gene segments and their relationships, with graph properties mapped to higher-dimensional space for analysis.
result Emerging star-like structures indicate complex interrelationships, including segments from multiple genes interleaving or overlapping.
Pulli kolam is a ubiquitous art form in south India. It involves drawing a line looped around a collection of dots (pullis) place on a plane such that three mandatory rules are followed: all line orbits should be closed, all dots are encircled and no two lines can overlap over a finite length. The mathematical foundati…
Proposes a new framework for detecting overlapping and non-overlapping communities.
problem Lack of methods for both overlapping and non-overlapping community detection.
method Integrated framework based on primary node criteria of internal and external association degrees.
result Outperforms existing methods on evaluation criteria.
Study the topology of curve spaces on hyperbolic surfaces with curvature constraints.
problem Investigate the topology of curve spaces on hyperbolic surfaces with curvature constraints.
method Analyzes the space of curves on hyperbolic surfaces with constrained curvatures and computes their homotopy type.
result The space of curves falls into four qualitatively distinct classes based on curvature constraints.
This work introduces novel methods to identify and compare cycles across topological objects.
problem Identifying and comparing topological features, particularly cycles, across different topological objects.
method Two complementary approaches: dendrogram-based merge-tree algorithms and Stratified Gradient Sampling.
result Transformed cycle matching into hierarchical clustering and topological optimization framework.
Automated image segmentation distinguishes overlapping human chromosomes.
problem Distinguishing overlapping human chromosomes for medical diagnostics.
method Customized convolutional neural network for image segmentation.
result IOU scores of 94.7% for overlapping regions, 88-94% for non-overlapping regions.
Overlapping clustering problem is an important learning issue in which clusters are not mutually exclusive and each object may belongs simultaneously to several clusters. This paper presents a kernel based method that produces overlapping clusters on a high feature space using mercer kernel techniques to improve separa…
Constructs new topological theories in 2D not fitting standard axioms.
problem Developing new topological theories in 2D that don't conform to traditional axioms.
method Universal construction by Blanchet et al., Kronecker's characterization, field extension, Hankel matrices, Schur polynomials, and foam evaluation.
result Introduction of non-multiplicative theories and classification over finite-dimensional state spaces.
Deconfounding scores improve causal effect estimation with weak overlap.
problem Challenges in causal treatment effect estimation due to weak overlap in high-dimensional data.
method Propose deconfounding scores to preserve identification and target estimation while improving overlap.
result Prognostic scores are overlap-optimal under a broad family of generalized linear models with Gaussian features.
A new method speeds up overlapping group lasso computations.
problem Time-consuming optimization of overlapping group lasso on large-scale problems.
method Non-overlapping statistical approximation to overlapping group lasso.
result The proposed penalty is statistically equivalent to overlapping group lasso.
New method improves CATE estimation in low overlap regions.
problem Low overlap in CATE estimation leads to poor performance of meta-learners.
method Overlap-Adaptive Regularization (OAR) that regularizes models proportionally to overlap weights.
result OAR significantly improves CATE estimation in low-overlap settings.
Proposes a sensitivity framework to handle limited overlap in causal inference.
problem Limited overlap between treated and control groups in observational studies.
method Sensitivity framework based on worst-case confidence bounds on bias introduced by trimming.
result Protects against spurious findings by quantifying uncertainty in regions with limited overlap.
Producing overlapping schemes is a major issue in clustering. Recent proposed overlapping methods relies on the search of an optimal covering and are based on different metrics, such as Euclidean distance and I-Divergence, used to measure closeness between observations. In this paper, we propose the use of another meas…
The study simplifies assessing overlap in logistic regression models using empirical likelihood.
problem Assessing overlap in multidimensional logistic regression models.
method Translation of Silvapulle's condition to empirical likelihood maximization, mechanized with R code.
result Minimal overlapping structures are cataloged in dimensions less than four, providing rules for higher dimensions.
Estimates overlap in observational studies for causal effect estimation.
problem Overlap between treatment groups is crucial for causal effect estimation.
method Formalizes overlap estimation as a binary classification problem with Boolean rule classifiers.
result Rules provide interpretable explanations for causal conclusions.
New algorithm finds overlapping groups in network data.
problem Identifying overlapping communities in network data.
method Spectral algorithm with additive clustering based on SBMO model.
result Adaptive algorithm consistent under SBMO for logarithmic degrees.
Study on geodesic surfaces in hyperbolic 3-orbifolds, proving overlaps in area sets.
problem Understanding overlaps in geometric genus spectra of non-commensurable hyperbolic 3-orbifolds.
method Defined geometric genus spectrum and totally geodesic area set, proving results on overlaps.
result Arithmetic hyperbolic 3-orbifolds can have large overlaps in their totally geodesic area sets.
Recently, to solve large-scale lasso and group lasso problems, screening rules have been developed, the goal of which is to reduce the problem size by efficiently discarding zero coefficients using simple rules independently of the others. However, screening for overlapping group lasso remains an open challenge because…
RISA improves VFL by using imputed samples with low uncertainty.
problem Limited overlapping samples constrain VFL performance.
method Imputing non-overlapping samples and using evidence theory to select reliable imputed samples.
result Significant performance gains achieved, especially with limited overlapping samples.
Community detection is a fundamental problem in network analysis which is made more challenging by overlaps between communities which often occur in practice. Here we propose a general, flexible, and interpretable generative model for overlapping communities, which can be thought of as a generalization of the degree-co…
As research into community finding in social networks progresses, there is a need for algorithms capable of detecting overlapping community structure. Many algorithms have been proposed in recent years that are capable of assigning each node to more than a single community. The performance of these algorithms tends to …
We present a principled approach for detecting overlapping temporal community structure in dynamic networks. Our method is based on the following framework: find the overlapping temporal community structure that maximizes a quality function associated with each snapshot of the network subject to a temporal smoothness c…
New mechanism detects overlap density for weak-to-strong generalization.
problem Understanding what aspects of data enable weak-to-strong generalization.
method Data-centric mechanism and overlap detection algorithm.
result Overlap density is a key factor in weak-to-strong generalization.
We calculate eigenvector overlaps between intersecting time periods of covariance matrices.
problem Analyzing overlapping time periods in covariance matrices.
method Girko linearisation and extended local laws.
result Computed eigenvector overlaps for intersecting time intervals.
Overlap-Local-SGD improves distributed SGD by overlapping communication and computation.
problem High communication delay and node slowdown in distributed SGD.
method Adding an anchor model to synchronize local updates and pull them towards the anchor model.
result Overlap-Local-SGD speeds up distributed training and mitigates straggler effects.
Unified approach for fair classification with overlapping groups.
problem Ensuring fairness across multiple overlapping groups in prediction problems.
method Probabilistic population analysis leading to Bayes-optimal classifier, unifying existing methods.
result Outperforms baselines in fairness-performance tradeoff on real datasets.
New LT-O-learners improve HLTE estimation with low overlap.
problem Challenges in estimating heterogeneous long-term treatment effects due to limited overlap.
method Introduces LT-O-learners that use custom overlap weights to downweight low-overlap samples.
result LT-O-learners provide robust HLTE estimates with lower variance in low-overlap regimes.
ION-C solves overlapping network integration problems efficiently.
problem Integrating overlapping networks with different datasets.
method Formulated as an ASP problem and solved with clingo.
result Significantly improved efficiency in runtime and solution graphs.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Study on Langevin dynamics for recovering planted signals in spiked matrix models.
problem Recovering a planted signal in spiked matrix models.
method Path-wise characterization of overlap using integro-differential equations and explicit formula derivation.
result Sharp phase transition in limiting overlap: positive in one regime, zero in another due to injected noise.
Mapper-GIN simplifies 3D point cloud classification with lightweight structure.
problem Robust 3D point cloud classification under corruption.
method Mapper algorithm for structural decomposition, GIN for graph classification.
result Mapper-GIN achieves competitive accuracy with minimal parameters.
Subject Cross Validation improves Human Activity Recognition performance by up to 16%.
problem Overestimation of Human Activity Recognition performance using k-fold cross validation.
method Investigated Subject Cross Validation vs. k-fold cross validation for Human Activity Recognition.
result Subject Cross Validation increases performance by up to 16%.
New method removes lexical treatment signals to avoid overlap violations in causal inference from text.
problem Overlap violations in estimating causal effects from text due to treatment encoding.
method Masking-based adjustment representations to remove lexical treatment signals.
result Masking improves overlap diagnostics and reduces bias in treatment effect estimates.
Model for sparse networks with overlapping communities.
problem Sparse and modular graph structures with overlapping communities.
method Exchangeable point process and completely random measures.
result Can recover interpretable structure from real-world networks.
New method detects overlapping communities in weighted graphs without pure nodes assumption.
problem Detect overlapping communities in weighted graphs without making pure nodes assumption.
method Convex optimization-based approach for weighted graphs.
result Success on artificial and real-world datasets.
Improved SIR algorithm identifies effective factors more accurately.
problem Identifying significant factors with lower intrinsic dimensionality.
method Overlapping Sliced Inverse Regression (OSIR) algorithm.
result OSIR algorithm estimates effective dimension reduction space and number of effective factors more accurately.
We construct a C-space associated with every closed 3-form on a spacetime M and show that it depends on the class of the form in H3(M,Z). We also demonstrate that C-spaces have a relation to generalized geometry and to gerbes. C-spaces are constructed after introducing additional coordinates at the open sets and …
Study on overlaps of singular vectors in Gaussian matrix submatrices.
problem Analyzing overlaps of singular vectors in submatrices of Gaussian matrices.
method Utilizes dynamics of singular vectors and specific resolvents for Brownian trajectories.
result Explicit forms for limiting rescaled mean squared overlaps in the bulk of spectra.
Deconfounding scores improve causal effect estimation with weak overlap.
problem Poor overlap in treatment and control groups makes causal effect estimators brittle.
method Introduces feature representations that improve overlap without introducing bias.
result Deconfounding scores satisfy a zero-covariance condition that is identifiable in observed data.
DVAE++ uses overlapping distributions to train discrete latent variables.
problem Training discrete latent variable models with gradient information.
method Proposes a new class of smoothing transformations based on a mixture of two overlapping distributions.
result Overlapping transformations outperform other recent methods in training discrete latent variables.