arXiv research

Generic Hitchin representations generate dense subgroups.

The study finds conditions for certain groups to be dense in a specific mathematical space.

Example shows dense subgroup of SL5(Z) not finitely presented.

Method generates dense fields from sparse measurements without needing spatial statistics or examples.

We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of $\mathrm{Homeo}_{+}(I)$ admits a faithful discrete representation …

Generative model captures hubs and dense communities in social networks.

Generic metrics make geodesic nets dense.

Deforms surface groups to be Zariski dense in SL(n,R)

Sharp boundaries for detecting dense subhypergraphs established.

We begin by showing that commensurators of Zariski dense subgroups of isometry groups of symmetric spaces of non-compact type are discrete provided that the limit set on the Furstenberg boundary is not invariant under the action of a (virtual) simple factor. In particular for rank one or simple Lie groups, Zariski dens…

In this paper, we prove (1): for any closed contact three-manifold with a $C^\infty$-generic contact form, the union of periodic Reeb orbits is dense, (2): for any closed surface with a $C^\infty$-generic Riemannian metric, the union of closed geodesics is dense. The key observation is $C^\infty$-closing lemma for 3D R…

New lattices in higher dimensions have dense surface subgroups.

A dense amalgam connects boundaries of groups split by finite subgroups.

In this paper we show that certain generalizations of the $C^r$-Whitney topology, which include the Hölder-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the Baire property, to wit, the countable intersection of open and dense sets is dense.

Random 3-manifolds have no totally geodesic submanifolds.

The study finds dense orbits and absolute period leaves for complex flows.

New framework for dense weighted networks with community-specific patterns.

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…

Generative models can still learn from contaminated data, but with limitations.

The paper finds free semigroups in dense subgroups of Lie groups with critical exponents arbitrarily close to the subgroup's.

We consider dense 2-generator multiplicative subgroups in $\mathbb C$ and show that for each point $z\in \mathbb C$ the set of limit values for the arguments of the powers of each generator at the point $z$ is either finite or is $[-π,π]$

Polynomial-time test for detecting dense subgraphs in heterogeneous networks.

Study generalizes Lebesgue curves to new space-filling and fractal sets.

We show that any grafting ray in Teichmüller space determined by an arational lamination or a multi-curve is (strongly) asymptotic to a Teichmüller geodesic ray. As a consequence the projection of a generic grafting ray to moduli space is dense. We also show that the set of points in Teichmüller space obtained by integ…

We address feature interpretation and reproducibility issues in dense nets, proposing a modified loss function.

Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.

We introduce and study the operation, called dense amalgam, which to any tuple X_1,...,X_k of non-empty compact metric spaces associates some disconnected perfect compact metric space, denoted $\widetilde\sqcup(X_1,...,X_k)$, in which there are many appropriately distributed copies of the spaces X_1,...,X_k. We then sh…

We show that the topological groups $Diff_{+}^{1}(I)$ and $Diff_{+}^{1}(\mathbb{S}^1)$ of orientation-preserving $C^1$-diffeomorphisms of the interval and the circle, respectively, admit finitely generated dense subgroups. We also investigate the question of genericity (in the sense of Baire category) of such finite to…

New representations of hyperbolic 3-manifold groups into larger groups.

Complex projective manifolds without rational curves are quotients of Abelian varieties.

Detects dense subhypergraphs in heterogeneous random hypergraphs.

Dense neural networks can't approximate all functions.

The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by network architecture instead of learned from data. In this work, we propose the dense…

Generic geodesic nets are dense in high-dimensional manifolds.

Odd-dimensional SL(n,Q) contains dense surface subgroups.

Classifies manifolds with dense conjugacy classes in their mapping class groups.

The paper finds dense subgroups in certain Lie groups.

New examples of rigid Lie foliations with dense leaves found.

In an earlier paper of the authors it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can in an easy and natural manner incorporate singularities on arbitrary closed nowhere dense sets in Euclidean spaces, singularities which therefore can have arbitrar…

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations, and discuss what kind of regularization gives a favorable predictive accuracy. Our main target in this paper is dense type regularizations including \ellp-MKL. According to the recent numeri…

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

Paper tackles dense subgraph discovery with noisy feedback.

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…

Wave fronts on certain surfaces become dense.

We prove that every Bers slice of quasi-Fuchsian space is Zariski dense in the character variety.

The paper shows BNSR-invariants of McCool groups are either dense or empty.

RDL-Net improves speech enhancement with fewer parameters and better performance.

Study on detecting and recovering hidden dense cycles in random graphs.