Related papers: Group theoretic structures in the estimation of an…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…
Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not…
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
We determine all the multiplicity-free representations of the symmetric group. This project is motivated by a combinatorial problem involving systems of set-partitions with a specific pattern of intersection.
The article presents the results of experiments in computation of statistical values related to Young diagrams, including the estimates on maximum and average (by Plancherel distribution) dimension of irreducible representation of symmetric…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…
In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…
We present a method for estimating the maximal symmetry of a continuous regression function. Knowledge of such a symmetry can be used to significantly improve modelling by removing the modes of variation resulting from the symmetries.…
Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical…
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques.…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…