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Showing 1 to 6 of 6 for “"group-invariant"”.
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Group-invariant random processes
First we consider some isometry-invariant point process on Rd and examine what types of graphs can be defined on the points of the process in such a way that the point process and the graph have an equivariant distribution. We show that 1-ended trees and Zn can be achieved for invariant point …
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Group-invariant CR mappings
We consider group-invariant CR mappings from spheres to hyperquadrics. Given a finite subgroup $\Gamma \subset U(n)$, a construction of D'Angelo and Lichtblau yields a target hyperquadric $Q(\Gamma)$ and a canonical non-constant CR map $h_{\Gamma} : S^{2n-1}/\Gamma \to Q(\Gamma)$. For every $\Gamma …
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Lie group invariant finite-difference schemes for the neutron diffusion equation
… difference equations. Using the concept of an invariant difference operator, the invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant …
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Mathematical Connections between Convolutional Neural Networks and the Scattering Transformation
… architecture. Stéphane Mallat, in his paper “Group Invariant Scattering,” provides one of the earliest attempts by creating the scattering transformation and its finite approximation, the windowed scattering. Importantly, it is invariant to diffeomorphic translation. We review and rederive …
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Application of Lie symmetries to Solving Partial Differential Equations associated with the Mathematics of Finance
… that we then use to deduce their exact group-invariant solutions. In particular, we analyse a zero-coupon bond pricing PDE model and obtain its various reductions that we then use to solve and produce the pricing models for the aforementioned contingent claim. A systematic reductions on …
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Invariant polynomials and machine learning
… the necessary tools from commutative algebra and invariant theory, we construct systematic methods to obtain sets of invariant variables that describe two such systems: particle physics and physical chemistry. In both cases, our systems are described by a collection of vectors. In the former, …