Related papers: Normalized Indexing for Ramification Subgroups
In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous…
This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary…
We review the appearance of Hopf algebras in the renormalization of quantum field theories and in the study of diffeomorphisms of the frame bundle important for index computations in noncommutative geometry.
Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding…
A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…
We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal…
We give a normalizer decomposition for a p-local compact group (S, F, L) that describes |L| as a homotopy colimit indexed over a finite poset. Our work generalizes the normalizer decompositions for finite groups due to Dwyer, for p-local…
In this paper we develop a new renormalization group method, which is based on conditional expectations and harmonic extensions, to study functional integrals related with small perturbations of Gaussian fields. In this new method one…
This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local…
We propose Regularized Learning under Label shifts (RLLS), a principled and a practical domain-adaptation algorithm to correct for shifts in the label distribution between a source and a target domain. We first estimate importance weights…
We propose the notion of normalized Laplacian matrix $\mathcal{L}(\Phi)$ for a gain graphs and study its properties in detail, providing insights and counterexamples along the way. We establish bounds for the eigenvalues of…
Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…
In many applications, finding adequate labeled data to train predictive models is a major challenge. In this work, we propose methods to use group-level binary labels as weak supervision to train instance-level binary classification models.…
Semi-supervised Laplacian regularization, a standard graph-based approach for learning from both labelled and unlabelled data, was recently demonstrated to have an insignificant high dimensional learning efficiency with respect to…
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
Graph Neural Networks (GNNs) have received a lot of interest in the recent times. From the early spectral architectures that could only operate on undirected graphs per a transductive learning paradigm to the current state of the art…
In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with…
Many real-world networks have associated metadata that assigns categorical labels to nodes. Analysis of these annotations can complement the topological analysis of complex networks. Annotated networks have typically been used to evaluate…
We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…