Daniel Persson
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View article: Equivariant non-linear maps for neural networks on homogeneous spaces
Equivariant non-linear maps for neural networks on homogeneous spaces Open
This paper presents a novel framework for non-linear equivariant neural network layers on homogeneous spaces. The seminal work of Cohen et al. on equivariant $G$-CNNs on homogeneous spaces characterized the representation theory of such la…
View article: HEAL-SWIN: A Vision Transformer On The Sphere
HEAL-SWIN: A Vision Transformer On The Sphere Open
High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural networks or vision transformers on this data is problematic d…
View article: Massive Theta Lifts
Massive Theta Lifts Open
We use Poincare series for massive Maass-Jacobi forms to define a "massive theta lift", and apply it to the examples of the constant function and the modular invariant j-function, with the Siegel-Narain theta function as integration kernel…
View article: Equivariance versus Augmentation for Spherical Images
Equivariance versus Augmentation for Spherical Images Open
We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with…
View article: Emergent Sasaki-Einstein geometry and AdS/CFT
Emergent Sasaki-Einstein geometry and AdS/CFT Open
A central problem in any quantum theory of gravity is to explain the emergence of the classical spacetime geometry in some limit of a more fundamental, microscopic description of nature. The gauge/gravity-correspondence provides a framewor…
View article: BPS Algebras in 2D String Theory
BPS Algebras in 2D String Theory Open
We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form $V_1\otimes \bar V_2$, where $V_1, V_2$ are self-dual (super) vertex oper…
View article: Eulerianity of Fourier coefficients of automorphic forms
Eulerianity of Fourier coefficients of automorphic forms Open
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficien…
View article: Geometric Deep Learning and Equivariant Neural Networks
Geometric Deep Learning and Equivariant Neural Networks Open
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using p…
View article: Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups
Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups Open
In this paper, we analyze Fourier coefficients of automorphic forms on a finite cover G of an adelic split simply-laced group. Let $\pi $ be a minimal or next-to-minimal automorphic representation of G . We prove that any $\eta \in \pi $ i…
View article: Efficient Calculations of Two-Dimensional Radar Cross-Section Using DGFEM
Efficient Calculations of Two-Dimensional Radar Cross-Section Using DGFEM Open
A two-dimensional discontinuous Galerkin finite element method algorithm in the time domain was developed for calculation of the radar cross-section of an arbitrary object. The algorithm was formed using local nodal basis functions in each…
View article: Probabilistic H-norm estimation via Gaussian process system identification
Probabilistic H-norm estimation via Gaussian process system identification Open
We present a method for data-based estimation of the H2-norm of a linear time-invariant system from input-output data in a probabilistic setting by employing the recent advances in Gaussian process system identification using stable-spline…
View article: Fourier coefficients of minimal and next-to-minimal automorphic\n representations of simply-laced groups
Fourier coefficients of minimal and next-to-minimal automorphic\n representations of simply-laced groups Open
In this paper we analyze Fourier coefficients of automorphic forms on a\nfinite cover $G$ of an adelic split simply-laced group. Let $\\pi$ be a minimal\nor next-to-minimal automorphic representation of $G$. We prove that any\n$\\eta\\in \…
View article: Fourier coefficients and small automorphic representations
Fourier coefficients and small automorphic representations Open
In this paper we analyze Fourier coefficients of automorphic forms on adelic reductive groups $G(\mathbb{A})$. Let $\pi$ be an automorphic representation of $G(\mathbb{A})$. It is well-known that Fourier coefficients of automorphic forms c…
View article: Optimal MIMO Precoding Under a Constraint on the Amplifier Power Consumption
Optimal MIMO Precoding Under a Constraint on the Amplifier Power Consumption Open
The capacity of the MIMO channel taking into account both a limitation on total consumed power, and per-antenna radiated power constraints is considered. The total consumed power takes into account the traditionally used sum radiated power…
View article: Eisenstein Series and Automorphic Representations
Eisenstein Series and Automorphic Representations Open
This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the L…
View article: Fourier coefficients attached to small automorphic representations of\n ${\\mathrm{SL}}_n(\\mathbb{A})$
Fourier coefficients attached to small automorphic representations of\n ${\\mathrm{SL}}_n(\\mathbb{A})$ Open
We show that Fourier coefficients of automorphic forms attached to minimal or\nnext-to-minimal automorphic representations of ${\\mathrm{SL}}_n(\\mathbb{A})$\nare completely determined by certain highly degenerate Whittaker coefficients.\n…
View article: Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ Open
We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We gi…
View article: Real-time image processing on handheld devices and UAV
Real-time image processing on handheld devices and UAV Open
The forest industry needs an up-to-date overview of certain areas of a forest, to either estimate damages after a storm or assess its overall health. Today, the use of unmanned aerial vehicles (UAV) have exploded. Almost anyone can own one…
View article: Monstrous BPS-algebras and the superstring origin of moonshine
Monstrous BPS-algebras and the superstring origin of moonshine Open
We provide a physics derivation of Monstrous moonshine. We show that the McKay-Thompson series $T_g$, $g\in \mathbb{M}$, can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models. The inv…