Related papers: F-method for symmetry breaking operators
Let G be a connected reductive linear algebraic group. We use geometric methods to investigate G-completely reducible subgroups of G, giving new criteria for G-complete reducibility. We show that a subgroup of G is G-completely reducible if…
In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry…
We study the breaking of rotational symmetry on the lattice for irreducible tensor operators and practical methods for suppressing this breaking. We illustrate the features of the general problem using an $\alpha$ cluster model for…
In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to get normal forms (or models) of the differential operators and…
Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
Group equivariant non-expansive operators have been recently proposed as basic components in topological data analysis and deep learning. In this paper we study some geometric properties of the spaces of group equivariant operators and show…
Identifying symmetries in data sets is generally difficult, but knowledge about them is crucial for efficient data handling. Here we present a method how neural networks can be used to identify symmetries. We make extensive use of the…
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of…
An algebraic method is devised to look for non-local symmetries of the pseudopotential type of nonlinear field equations. The method is based on the use of an infinite-dimensional subalgebra of the prolongation algebra $L$ associated with…
Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
The space of smooth sections of an equivariant line bundle over the real projective space $\mathbb{R}{\rm P}^n$ forms a natural representation of the group ${\rm GL}(n+1,\mathbb{R})$. We explicitly construct and classify all intertwining…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
For a pair $(G,G')=(O(n+1,1), O(n,1))$ of reductive groups, we investigate intertwining operators (symmetry breaking operators) between principal series representations $I_\delta(V,\lambda)$ of $G$, and $J_\epsilon(W,\nu)$ of the subgroup…
An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces. Necessary and…
In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…
For a pseudo-Riemannian manifold $X$ and a totally geodesic hypersurface $Y$, we consider the problem of constructing and classifying all linear differential operators $\mathcal{E}^i(X) \to \mathcal{E}^j(Y)$ between the spaces of…