arXiv research

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

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…

Dense neural networks can't approximate all functions.

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

Horizon saddle connections imply dense hyperbolic geodesics on dilation surfaces.

Sparse Transformers can approximate dense Transformers with only O(n) connections.

We show that for every sequence $(n_i)$, where each $n_i$ is either an integer greater than 1 or is $\infty$, there exists a simply connected open 3-manifold $M$ with a countable dense set of ends $\{e_i\}$ so that, for every $i$, the genus of end $e_i$ is equal to $n_i$. In addition, the genus of the ends not in the d…

Social media sites are becoming a key factor in politics. These platforms are easy to manipulate for the purpose of distorting information space to confuse and distract voters. Past works to identify disruptive patterns are mostly focused on analyzing the content of tweets. In this study, we jointly embed the informati…

Currents on cusped hyperbolic surfaces have a denseness property similar to compact surfaces.

As an important part of the power system, power load forecasting directly affects the national economy. The data shows that improving the load forecasting accuracy by 0.01% can save millions of dollars for the power industry. Therefore, improving the accuracy of power load forecasting has always been the pursuing goals…

DenseNets improve accuracy and efficiency in convolutional networks.

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…

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

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

Compact Lie groups can be realized as automorphism groups of Riemannian manifolds.

Narasimhan and Ramadas showed that the restricted holonomy group of the Coulomb connection is dense in the connected component of the identity of the gauge group when one considers the product principal bundle $S^3 \times SU(2)\to S^3$. Instead of a base manifold S^3, we consider here a base manifold of dimension $n\ge…

The recent application of deep learning in various areas of medical image analysis has brought excellent performance gains. In particular, technologies based on deep learning in medical image registration can outperform traditional optimisation-based registration algorithms both in registration time and accuracy. Howev…

DVNet efficiently segments large neurovascular datasets using skip connections.

While sparse inverse covariance matrices are very popular for modeling network connectivity, the value of the dense solution is often overlooked. In fact the L2-regularized solution has deep connections to a number of important applications to spectral graph theory, dimensionality reduction, and uncertainty quantificat…

New tests detect communities in dense bipartite graphs with high accuracy.

Let $G$ be a simply connected, solvable Lie group and $Γ$ a lattice in $G$. The deformation space $\mathcal{D}(Γ,G)$ is the orbit space associated to the action of $\Aut(G)$ on the space $\mathcal{X}(Γ,G)$ of all lattice embeddings of $Γ$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev…

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

Narasimhan and Ramadas showed that the Gribov ambiguity was maximal for the product SU(2) bundle over S^3. Specifically they showed that the holonomy group of the Coulomb connection is dense in the connected component of the identity of the gauge group. Instead of base manifold S^3, we consider here a base manifold wit…

This paper presents a new artificial neuron model capable of learning its receptive field in the topological domain of inputs. The model provides adaptive and differentiable local connectivity (plasticity) applicable to any domain. It requires no other tool than the backpropagation algorithm to learn its parameters whi…

We present two related methods for deriving connectivity-based brain atlases from individual connectomes. The proposed methods exploit a previously proposed dense connectivity representation, termed continuous connectivity, by first performing graph-based hierarchical clustering of individual brains, and subsequently a…

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

In high dimensions, find paths connecting points with intermediate steps in a dense set.

The paper bounds crossing numbers of dense graphs on surfaces.

In this paper we construct a complete injective holomorphic immersion $\mathbb{C}\to\mathbb{C}^2$ whose image is dense in $\mathbb{C}^2$. The analogous result is obtained for any closed complex submanifold $X\subset \mathbb{C}^n$ for $n>1$ in place of $\mathbb{C}\subset\mathbb{C}^2$. We also show that, if $X$ intersect…

The paper explores the twisted Rokhlin property in mapping class groups of surfaces.

Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networ…

Improvements in the performance of deep neural networks have often come through the design of larger and more complex networks. As a result, fast memory is a significant limiting factor in our ability to improve network performance. One approach to overcoming this limit is the design of sparse neural networks, which ca…

Nontrivial connectivity has allowed the training of very deep networks by addressing the problem of vanishing gradients and offering a more efficient method of reusing parameters. In this paper we make a comparison between residual networks, densely-connected networks and highway networks on an image classification tas…

Model pruning seeks to induce sparsity in a deep neural network's various connection matrices, thereby reducing the number of nonzero-valued parameters in the model. Recent reports (Han et al., 2015; Narang et al., 2017) prune deep networks at the cost of only a marginal loss in accuracy and achieve a sizable reduction…

New algorithms reduce communication in GNN training.

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…

The study proposes a conjecture about the monodromy group of singular hyperbolic metrics and provides evidence and confirmations.

We give examples of rank one compact surfaces on which there exist recurrent geodesics that cannot be shadowed by periodic geodesics. We build rank one compact surfaces such that ergodic measures on the unit tangent bundle of the surface are not dense in the set of probability measures invariant by the geodesic flow. F…

Topologically and geometrically engaging actions have proved to be useful to obtain rigidity results for semisimple Lie group actions. We show that the action of a simple noncompact Lie group on a compact manifold preserving a unimodular rigid geometric structure of algebraic type (e.g. a connection together with a vol…

A transitive compact foliated space is shown to be a Riemannian foliation if and only if it is locally connected, finite dimensional, strongly equicontinuous and quasi-analytic, and the closure of its holonomy pseudogroup is quasi-analytic.

Sparse sampling method for tensor factorization and completion of high rank tensors.

We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz …

A new algorithm reduces graph complexity for better dense subgraph analysis.

Modern audio source separation techniques rely on optimizing sequence model architectures such as, 1D-CNNs, on mixture recordings to generalize well to unseen mixtures. Specifically, recent focus is on time-domain based architectures such as Wave-U-Net which exploit temporal context by extracting multi-scale features. …

Study parametrized Kähler class for cocycles on Hermitian symmetric spaces.

Study differential operators on non-compact harmonic manifolds, finding conditions for radial fundamental solutions and dense heat-semigroups.

Study on horospheres in higher rank homogeneous spaces, proving density properties.