Related papers: Characterizing co-NL by a group action
Many systems exhibit complex interactions between their components: some features or actions amplify each other's effects, others provide redundant information, and some contribute independently. We present a simple geometric method for…
We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal…
For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…
Consider pairs of the form (G, N), with G a group and N \normal G, as objects of a category \PG. A morphism (G_1, N_1) \To (G_2, N_2) will be a group homomorphism f : G_1 \To G_2 such that f(N_1) \subset N_2. We introduce a functor Q : \PG…
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show…
Complex real-world networks commonly reveal characteristic groups of nodes like communities and modules. These are of value in various applications, especially in the case of large social and information networks. However, while numerous…
We present a novel method to perform multi-class pattern classification with neural networks and test it on a challenging 3D hand gesture recognition problem. Our method consists of a standard one-against-all (OAA) classification, followed…
In comparison to graphs, combinatorial methods for the isomorphism problem of finite groups are less developed than algebraic ones. To be able to investigate the descriptive complexity of finite groups and the group isomorphism problem, we…
In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in…
We combine the theory of traces in homotopical algebra with sheaf theory in derived algebraic geometry to deduce general fixed point and character formulas. The formalism of dimension (or Hochschild homology) of a dualizable object in the…
Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…
In this paper, we propose a novel method named GP-Aligner to deal with the problem of non-rigid groupwise point set registration. Compared to previous non-learning approaches, our proposed method gains competitive advantages by leveraging…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
Recently an algorithm, was discovered, which separates points in n-dimension by planes in such a manner that no two points are left un-separated by at least one plane{[}1-3{]}. By using this new algorithm we show that there are two ways of…
We introduce Clifford Group Equivariant Neural Networks: a novel approach for constructing $\mathrm{O}(n)$- and $\mathrm{E}(n)$-equivariant models. We identify and study the $\textit{Clifford group}$, a subgroup inside the Clifford algebra…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…