Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.
problem Characterize dilation surfaces with dense hyperbolic geodesics.
method Analyzing saddle connections and directional flow properties.
result Dilation surfaces with horizon saddle connections have dense hyperbolic geodesics.
The paper proves that on translation surfaces, regular points are part of infinitely many geodesics with dense directions.
problem Existence and density of geodesics through regular points on translation surfaces.
method Apisa's classifications of periodic points and orbit closures, recent Eskin-Filip-Wright result.
result Regular points on translation surfaces are part of infinitely many geodesics with dense directions.
Closed geodesics densely cover a circle in dilation surfaces.
problem Density of closed geodesics in dilation surfaces.
method Study of Teichmüller flow and Delaunay triangulation.
result Directions of closed geodesics are dense in the circle.
Research examines coamenable subgroups in higher rank groups.
problem Investigates coamenable normal subgroups in higher rank groups.
method Analyzes three complementary phenomena in higher rank groups.
result Growth indicators of coamenable subgroups are not preserved but the Riemannian critical exponent remains rigid.
DenseHMM improves HMMs by learning dense representations that enable gradient-based optimization.
problem Learning dense representations for hidden states and observables in HMMs.
method DenseHMM uses kernelized transition probabilities and two optimization schemes.
result DenseHMM achieves superior performance and expressiveness compared to standard HMMs.
The study constructs a dense orbit in the universal commensurability augmented Teichmüller space.
problem Understanding the dense orbit in the universal commensurability augmented Teichmüller space.
method Using isometric embeddings and directed limits of augmented Teichmüller and moduli spaces.
result The action of the universal commensurability modular group on the universal commensurability augmented Teichmüller space produces a dense orbit.
Finding "densely connected clusters" in a graph is in general an important and well studied problem in the literature \cite{Schaeffer}. It has various applications in pattern recognition, social networking and data mining \cite{Duda,Mishra}. Recently, Ames and Vavasis have suggested a novel method for finding cliques i…
Study shows mixing of flows on specific geometric spaces.
problem Mixing of one-parameter diagonal flows on Anosov homogeneous spaces.
method Proves local mixing for flows on $Γackslash G$ with deviations in transverse subspaces.
result Local mixing of flows on $Γackslash G$ for various directions.
A new method identifies causal direction using dense functional classes.
problem Determining causal direction between two univariate, continuous-valued variables.
method Minimum Description Length (MDL) principle applied to cubic regression splines.
result LCUBE method achieves superior precision in identifying causal direction.
Delaunay triangulation fails on dense point sets in Riemannian manifolds.
problem Obtaining a Delaunay triangulation for dense point sets on Riemannian manifolds.
method Analysis of Delaunay complexes on Riemannian manifolds, focusing on sample density.
result Sample density alone is not sufficient to ensure Delaunay triangulation in manifolds of dimension > 2.
We analyze the sample complexity of learning graphical games from purely behavioral data. We assume that we can only observe the players' joint actions and not their payoffs. We analyze the sufficient and necessary number of samples for the correct recovery of the set of pure-strategy Nash equilibria (PSNE) of the true…
DenseNets improve accuracy and efficiency in convolutional networks.
problem Improving accuracy and efficiency in deep convolutional networks.
method Introducing Dense Convolutional Networks (DenseNet) with direct connections between all layers.
result DenseNets achieve significant improvements over state-of-the-art networks on object recognition benchmarks.
This paper improves neural network learning by escaping the NTK regime and efficiently learning sparse polynomials.
problem Learning sparse polynomials efficiently using neural networks.
method Spectral analysis of NTK, identifying 'good' directions, and constructing a regularizer.
result Gradient descent on a two-layer neural network can learn sparse polynomials efficiently, improving over the NTK and QuadNTK.
The study bounds the complexity of meromorphic differentials' directions.
problem Understanding the descriptive complexity of meromorphic differentials.
method Geometric lemma and topological analysis of saddle connections.
result Sharp upper bound on the Cantor-Bendixson rank of meromorphic differentials.
Study critical exponents in normal subgroups of higher rank Lie groups.
problem Understanding critical exponents in normal subgroups of higher rank Lie groups.
method Analyzing subgroups and their critical exponents in a higher rank semi-simple Lie group.
result Critical exponents of normal subgroups coincide under certain conditions.
The study classifies compact Cauchy horizons in vacuum spacetimes.
problem Classifying compact Cauchy horizons in vacuum spacetimes.
method Complete classification theorem based on topology and null generators.
result Different cases of compact Cauchy horizons with specific manifolds and spacetime properties.
The asymptotic behavior of open plane sections of triply periodic surfaces is dictated, for an open dense set of plane directions, by an integer second homology class of the three-torus. The dependence of this homology class on the direction can have a rather rich structure, leading in special cases to a fractal. In th…
Gradient-free method solves infinite-dimensional optimization problems.
problem Optimizing functions in infinite-dimensional spaces.
method Uses directional derivatives and a pre-basis for Hilbert space.
result Proves convergence for solving PDEs using PINNs.
Generic Hitchin representations generate dense subgroups.
problem Understanding dense subgroups in SL_n(R) representations.
method Using a theorem by Rapinchuk, Benyash-Krivetz, and Chernousov.
result Generic Hitchin representations are strongly dense.
Maximal representations in infinite dimensional Hermitian spaces are studied with boundary maps.
problem Characterizing maximal representations in infinite dimensional Hermitian symmetric spaces.
method Definition of Toledo number, study of boundary maps, geometric constructions.
result Existence and non-existence conditions for maximal representations.
New lattices in higher dimensions have dense surface subgroups.
problem Finding dense subgroups in higher-dimensional arithmetic lattices.
method Exhibited nonuniform arithmetic lattices in SO(n,1).
result Contain Zariski-dense surface subgroups.
Directly learns sparse changes in Markov networks without modeling individual structures.
problem Learning sparse structural changes in Markov networks.
method Directly learns sparse changes without modeling individual dense networks.
result Direct learning method provides insights into system changes.
Effective estimates for lattice orbits in homogeneous spaces.
problem Distribution of lattice orbits in homogeneous spaces.
method Refined techniques on equidistribution of regions under flows.
result Effective convergence of orbit distribution to a limiting density.
New method for community detection in sparse directed SBMs with exact recovery guarantees.
problem Exact recovery in sparse directed SBMs, especially with growing communities.
method Two-stage procedure: neighborhood-smoothing followed by K-means clustering. result Exact recovery of all community labels with probability tending to one under mild sparsity and separation conditions.
We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…
In this paper, we investigate the closure of a large class of Teichmüller discs in the stratum Q(1,1,1,1) or equivalently, in a GL^+_2(R)-invariant locus L of translation surfaces of genus three. We describe a systematic way to prove that the GL^+_2(R)-orbit closure of a translation surface in L is the whole of L. The …
Study on mapping class groups of non-orientable surfaces, proving some conjectures and refuting others.
problem Analogies between Fuchsian groups and mapping class groups of non-orientable surfaces.
method Analyzing limit sets, foliations, and geometric properties.
result Established parts of a conjecture about the limit set and provided evidence for and against the analogy.
Proposes dense transformer networks for better pixel-wise predictions.
problem Current deep learning methods for dense prediction are limited by fixed patch sizes.
method Introduces dense transformer networks with learnable patch sizes and shapes.
result Superior performance in natural and biological image segmentation tasks.
Sparse neural networks can match dense models on Lipschitz functions.
problem Sparse networks are more efficient but lack theoretical guarantees.
method Formal model of sparse networks, LSH-based routing function, Lipschitz function approximation.
result Sparse networks can approximate dense networks on Lipschitz functions.
Method converts sparse systems to dense ones for statistical mechanics problems.
problem Statistical mechanics on sparse graphs
method Extracts a Feedback Vertex Set, learns variational distribution, estimates free energy.
result More accurate and faster than existing methods for sparse systems.
Enhances GCNs using VAT for better node classification.
problem Limited use of unlabeled data in GCNs.
method Virtual Adversarial Training (VAT) on GCN supervised loss.
result Improves GCN generalization performance.
Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.
problem Characterizing dense subgroups of algebraic groups.
method Bi-Lipschitz rigidity theorem for Zariski dense discrete subgroups.
result No C1-smooth slim limit set for higher rank semisimple algebraic groups. The study finds conditions for certain groups to be dense in a specific mathematical space.
problem Conditions for linear reflection groups to be dense in a projective space.
method Analyzes necessary and sufficient conditions for Zariski-density, applies to Coxeter groups and surface subgroups.
result Establishes conditions for Zariski-dense subgroups in SLn(Z) for various n. Study geodesic trees and exceptional directions in FPP on hyperbolic groups.
problem Understanding the geometry and uniqueness of geodesics in FPP on hyperbolic groups.
method Analyzing random geodesic trees and exceptional directions in the context of FPP on hyperbolic groups.
result The set of exceptional directions has strictly smaller Hausdorff dimension than the boundary, and hence has measure zero.
New representations of hyperbolic 3-manifold groups into larger groups.
problem Finding representations of hyperbolic 3-manifold groups into larger matrix groups.
method Holonomy representations from projective deformations of hyperbolic structures.
result First examples of strongly dense representations into SL(4,R) and SU(3,1). 3BASiL-TM decomposes LLMs into sparse and low-rank matrices for efficient compression.
problem Efficiently compressing large language models without significant performance loss.
method 3-Block ADMM method and transformer-matching refinement step for sparse plus low-rank decomposition.
result 3BASiL-TM reduces perplexity gap by over 30% and speeds up compression by 2.5x.
A new metric based on hitting probabilities for directed graphs and Markov chains.
problem Lack of metrics specifically adapted to asymmetric structure of directed graphs and Markov chains.
method Metric based on hitting probabilities, insensitive to shortest and average walk distances.
result New structural theory of directed graphs and utility for various applications.
Detects dense subhypergraphs in heterogeneous random hypergraphs.
problem Testing for the existence of a dense subhypergraph in heterogeneous random hypergraphs.
method Established detection boundaries and constructed asymptotically powerful and adaptive tests.
result Developed tests for distinguishing between null and alternative hypotheses.
Dense neural networks can't approximate all functions.
problem Approximation capabilities of dense neural networks.
method Model compression approach combining weak regularity lemma and graph neural networks.
result Existence of Lipschitz continuous functions not approximable by dense neural networks.
Odd-dimensional SL(n,Q) contains dense surface subgroups.
problem Finding dense subgroups in SL(n,Q) for odd n.
method Constructing a continuous path of representations.
result Existence of dense surface subgroups in SL(n,Q) for odd n.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
The paper finds dense subgroups in certain Lie groups.
problem Finding dense subgroups in Lie groups.
method Constructing dense surface subgroups in specific Lie groups.
result Uniform lattices contain infinitely many dense Hitchin representations.
New examples of rigid Lie foliations with dense leaves found.
problem Infinitesimal rigidity of Lie foliations with dense leaves.
method Construction of specific Lie foliations.
result First examples of infinitesimally rigid Riemannian foliations with dense leaves.
Sharp criteria found for dense eigenvalues in Riemannian manifolds.
problem Finding conditions for dense eigenvalues in Riemannian manifolds.
method Sharp criteria on radial curvature for existence of asymptotically flat or hyperbolic manifolds.
result Construction of manifolds with dense embedded point spectrum and sharp curvature bounds.
The paper proposes using low rank assumption to improve causal structure learning in DAGs.
problem Challenges in learning causal structures in high-dimensional, non-sparse DAGs.
method Exploits low rank assumption of DAG adjacency matrix to adapt causal structure learning methods.
result Maximum rank is highly related to hubs, suggesting low rank for scale-free networks.
Filters on order flow improve short-term market directionality.
problem Improving directional signals from order flow in financial markets.
method Structural filters on order lifetime, modification count, and timing applied to BankNifty index futures.
result Filters on parent orders of executed trades show stronger directional association with returns.
Paper hypothesizes MLP layers in LLMs can be approximated by sparse Mixture of Experts.
problem Understanding dense MLP layers in LLMs.
method Theoretical connection between MoE models and SAE structure in activation space.
result MLP layers in LLMs can be well approximated by sparse Mixture of Experts.
Sharp boundaries for detecting dense subhypergraphs established.
problem Detecting dense subhypergraphs in random hypergraphs.
method Established sharp detection boundaries for known and unknown edge probabilities.
result Sharp detectable regions differ significantly from graph counterparts.