# Gaussian Whittle-Matérn fields on metric graphs

no code yet • 12 May 2022

The model class in particular contains differentiable Gaussian processes.

Statistics Theory Probability Statistics Theory 60G60 (Primary) 62M99, 62M30 (Secondary)

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# All Melodies are Lost -- Recognizability for weak and strong $α$-ITRMs

no code yet • 10 May 2022

For exponentially closed ordinals $\alpha$, we consider recognizability of constructible subsets of $\alpha$ for $\alpha$-(w)ITRMs and their distribution in the constructible hierarchy.

Logic

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# Optimizing a DIscrete Loss (ODIL) to solve forward and inverse problems for partial differential equations using machine learning tools

10 May 2022

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools.

Numerical Analysis Numerical Analysis Computational Physics

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# Bridging the gap: symplecticity and low regularity on the example of the KdV equation

no code yet • 10 May 2022

We introduce a novel symplectic (in the Hamiltonian picture) resonance-based method on the example of the KdV equation that allows for low-regularity approximations to the solution while preserving the underlying geometric structure of the continuous problem on the discrete level.

Numerical Analysis Numerical Analysis 65M12, 65M70, 35Q53

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# Towards a Geometric Understanding of the 4-Dimensional Point Groups

10 May 2022

We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes.

Metric Geometry

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# Generalizations of Bilinear Maps -- Technical Report

no code yet • 11 May 2022

Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory.

Category Theory

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# The quantum metric structure of quantum SU(2)

no code yet • 12 May 2022

We introduce a two parameter family of Dirac operators on quantum SU(2) and analyse their properties from the point of view of non-commutative metric geometry.

Operator Algebras Functional Analysis Metric Geometry 58B32, 58B34, 46L89, 46L30, 81R60

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# Characteristics of the switch process and geometric divisibility

no code yet • 12 May 2022

Moreover, an explicit relation between the switching time distribution and the autocovariance function of the switch process stationary counterpart is obtained, which allows parallel results for the stationary switch process and its covariance function.

Probability 60K05 (Primary) 60G55, 60E07, 60G10 (Secondary)

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# Standard position for surfaces in link complements in arbitrary 3-manifolds

no code yet • 12 May 2022

Since the 1980s, it has been known that essential surfaces in alternating link complements can be isotoped into a form that satisfies certain combinatorial restrictions, interacting with the link diagram.

Geometric Topology 57K12, 57K10, 57K30

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