Related papers: Equiangular tight frames from group divisible desi…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…
We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor…
$t$-spanners are used to approximate the pairwise distances between a set of points in a metric space. They have only a few edges compared to the total number of pairs and they provide a $t$-approximation on the distance of any two…
In this paper we study a new product of graphs called {\em tight product}. A graph $H$ is said to be a tight product of two (undirected multi) graphs $G_1$ and $G_2$, if $V(H)=V(G_1)\times V(G_2)$ and both projection maps $V(H)\to V(G_1)$…
The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to…
A class of topological spaces is topologically rigid if any two spaces with the same fundamental group are also homeomorphic. Topological rigidity, in addition to its intrinsic interest, has been useful for solving abstract commensurability…
It is known that invariance and equivariance properties for systems on Lie groups can be exploited in the design of high performance and robust observers and filters for real-world robotic systems. This paper proposes an analysis framework…
A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are…
Differential geometric approaches to the analysis and processing of data in the form of symmetric positive definite (SPD) matrices have had notable successful applications to numerous fields including computer vision, medical imaging, and…
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…
Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…
Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
We consider inference for high-dimensional separately and jointly exchangeable arrays where the dimensions may be much larger than the sample sizes. For both exchangeable arrays, we first derive high-dimensional central limit theorems over…
Constructing model-agnostic group equivariant networks, such as equitune (Basu et al., 2023b) and its generalizations (Kim et al., 2023), can be computationally expensive for large product groups. We address this problem by providing…
Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…
Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order…
A framework is a graph and a map from its vertices to R^d. A framework is called universally rigid if there is no other framework with the same graph and edge lengths in R^d' for any d'. A framework attachment is a framework constructed by…
There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…