arXiv subjects

Viktor Andersson

Publications and source records attributed to Viktor Andersson.

7 recordsLinked to original sources

arXiv2026

The Littlewood-Paley formula and mean counting function for vertical limits of Dirichlet series

We prove a Littlewood-Paley formula for the Hardy space of Dirichlet series $\mathscr{H}^p$ with $1\leq p<\infty$ in terms of almost every vertical limit function. This significantly strengthens previous results, which hold either only as an average over the vertical limit functions or under additional assumptions of uniform convergence. As part of our approach, we obtain a Hardy-Stein identity for the derivative of the $p$-mean of almost every vertical limit. We further show that the mean counting function exists for any $f$ in $\mathscr{H}^p$ in terms of almost all of its vertical limit functions. This is done by establishing a version of Jensen's formula in this setting. In the process, we also deduce ergodic versions of Fatou's lemma and the monotone and dominated convergence theorems for the Kronecker flow.

math.CA↗

arXiv2026

Harald Bohr's splitting theorem

We present a new elementary proof of a theorem due to Harald Bohr, which states that an unbounded, analytic, and almost periodic function in a half-plane can be written as the sum of two analytic functions: the first is unbounded and periodic, while the second is bounded and almost periodic. The proof is based on a well-known arithmetical property of translation numbers of almost periodic functions.

math.CA↗

arXiv2025

Montel's theorem and composition operators for analytic almost periodic functions

We consider the Banach space $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ of bounded analytic functions on the open right half-plane $\mathbb{C}_0$ that are almost periodic on some smaller half-plane, as well as the subspace $A_{\mathrm{ap}}(\mathbb{C}_0)$ of those functions in $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ that are uniformly continuous on $\mathbb{C}_0$. We prove a strong version of Montel's theorem for $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and characterize the bounded composition operators on $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and $A_{\mathrm{ap}}(\mathbb{C}_0)$, as well as the compact composition operators on $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ and certain subspaces of it.

math.FA↗

arXiv2023

Controlled Descent Training

In this work, a novel and model-based artificial neural network (ANN) training method is developed supported by optimal control theory. The method augments training labels in order to robustly guarantee training loss convergence and improve training convergence rate. Dynamic label augmentation is proposed within the framework of gradient descent training where the convergence of training loss is controlled. First, we capture the training behavior with the help of empirical Neural Tangent Kernels (NTK) and borrow tools from systems and control theory to analyze both the local and global training dynamics (e.g. stability, reachability). Second, we propose to dynamically alter the gradient descent training mechanism via fictitious labels as control inputs and an optimal state feedback policy. In this way, we enforce locally $\mathcal{H}_2$ optimal and convergent training behavior. The novel algorithm, \textit{Controlled Descent Training} (CDT), guarantees local convergence. CDT unleashes new potentials in the analysis, interpretation, and design of ANN architectures. The applicability of the method is demonstrated on standard regression and classification problems.

math.OC↗

arXiv2022

On the Interpretability of Regularisation for Neural Networks Through Model Gradient Similarity

Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit regularisation when trained with gradient descent, often require the aid of explicit regularisers. We introduce a new framework, Model Gradient Similarity (MGS), that (1) serves as a metric of regularisation, which can be used to monitor neural network training, (2) adds insight into how explicit regularisers, while derived from widely different principles, operate via the same mechanism underneath by increasing MGS, and (3) provides the basis for a new regularisation scheme which exhibits excellent performance, especially in challenging settings such as high levels of label noise or limited sample sizes.

stat.ML↗

arXiv2014

The PAC2MAN mission: a new tool to understand and predict solar energetic events

An accurate forecast of flare and CME initiation requires precise measurements of the magnetic energy build up and release in the active regions of the solar atmosphere. We designed a new space weather mission that performs such measurements using new optical instruments based on the Hanle and Zeeman effects. The mission consists of two satellites, one orbiting the L1 Lagrangian point (Spacecraft Earth, SCE) and the second in heliocentric orbit at 1AU trailing the Earth by 80$^\circ$ (Spacecraft 80, SC80). Optical instruments measure the vector magnetic field in multiple layers of the solar atmosphere. The orbits of the spacecraft allow for a continuous imaging of nearly 73\% of the total solar surface. In-situ plasma instruments detect solar wind conditions at 1AU and ahead of our planet. Earth directed CMEs can be tracked using the stereoscopic view of the spacecraft and the strategic placement of the SC80 satellite. Forecasting of geoeffective space weather events is possible thanks to an accurate surveillance of the magnetic energy build up in the Sun, an optical tracking through the interplanetary space, and in-situ measurements of the near-Earth environment.

astro-ph.IM↗

arXiv2008

PoGOLite - A High Sensitivity Balloon-Borne Soft Gamma-ray Polarimeter

We describe a new balloon-borne instrument (PoGOLite) capable of detecting 10% polarisation from 200mCrab point-like sources between 25 and 80keV in one 6 hour flight. Polarisation measurements in the soft gamma-ray band are expected to provide a powerful probe into high-energy emission mechanisms as well as the distribution of magnetic fields, radiation fields and interstellar matter. At present, only exploratory polarisation measurements have been carried out in the soft gamma-ray band. Reduction of the large background produced by cosmic-ray particles has been the biggest challenge. PoGOLite uses Compton scattering and photo-absorption in an array of 217 well-type phoswich detector cells made of plastic and BGO scintillators surrounded by a BGO anticoincidence shield and a thick polyethylene neutron shield. The narrow FOV (1.25msr) obtained with well-type phoswich detector technology and the use of thick background shields enhance the detected S/N ratio. Event selections based on recorded phototube waveforms and Compton kinematics reduce the background to that expected for a 40-100mCrab source between 25 and 50keV. A 6 hour observation on the Crab will differentiate between the Polar Cap/Slot Gap, Outer Gap, and Caustic models with greater than 5 sigma; and also cleanly identify the Compton reflection component in the Cygnus X-1 hard state. The first flight is planned for 2010 and long-duration flights from Sweden to Northern Canada are foreseen thereafter.

astro-ph↗