arXiv subjects

Gordian Edenhofer

Publications and source records attributed to Gordian Edenhofer.

22 records · Page 2Linked to original sources

arXiv2023

Reconstructing Galactic magnetic fields from local measurements for backtracking ultra-high-energy cosmic rays

(abridged) Ultra-high energy cosmic rays (UHECRs) are highly energetic charged particles with energies exceeding $10^{18}$ eV. Identifying their sources and production mechanism can provide insight into many open questions in astrophysics and high energy physics. However, the Galactic magnetic field (GMF) deflects UHECRs, and the high uncertainties in our current understanding of the $3$-dimensional structure of the GMF does not permit us to accurately determine their true arrival direction on the plane of the sky (PoS). This difficulty arises from the fact that currently all GMF observations are integrated along the line-of-sight (LoS). Upcoming stellar optopolarimetric surveys as well as Gaia data on stellar parallaxes, are expected to provide local measurements of the GMF in the near future. In this paper, we evaluate the reconstruction of the GMF in a limited region of the Galaxy given sparse and local GMF measurements within that region, through Bayesian inference using principles of Information Field Theory. We backtrack UHECRs through GMF configurations drawn from the posterior to improve our knowledge of their true arrival directions. We show that, for a weakly turbulent GMF, it is possible to correct for its effect on the observed arrival direction of UHECRs to within $\sim 3^\circ$. For completely turbulent fields, we show that our procedure can still be used to significantly improve our knowledge on the true arrival direction of UHECRs.

astro-ph.HE↗

arXiv2022

Causal, Bayesian, & Non-parametric Modeling of the SARS-CoV-2 Viral Load Distribution vs. Patient's Age

The viral load of patients infected with SARS-CoV-2 varies on logarithmic scales and possibly with age. Controversial claims have been made in the literature regarding whether the viral load distribution actually depends on the age of the patients. Such a dependence would have implications for the COVID-19 spreading mechanism, the age-dependent immune system reaction, and thus for policymaking. We hereby develop a method to analyze viral-load distribution data as a function of the patients' age within a flexible, non-parametric, hierarchical, Bayesian, and causal model. The causal nature of the developed reconstruction additionally allows to test for bias in the data. This could be due to, e.g., bias in patient-testing and data collection or systematic errors in the measurement of the viral load. We perform these tests by calculating the Bayesian evidence for each implied possible causal direction. The possibility of testing for bias in data collection and identifying causal directions can be very useful in other contexts as well. For this reason we make our model freely available. When applied to publicly available age and SARS-CoV-2 viral load data, we find a statistically significant increase in the viral load with age, but only for one of the two analyzed datasets. If we consider this dataset, and based on the current understanding of viral load's impact on patients' infectivity, we expect a non-negligible difference in the infectivity of different age groups. This difference is nonetheless too small to justify considering any age group as noninfectious.

stat.AP↗

arXiv2022

Sparse Kernel Gaussian Processes through Iterative Charted Refinement (ICR)

Gaussian Processes (GPs) are highly expressive, probabilistic models. A major limitation is their computational complexity. Naively, exact GP inference requires $\mathcal{O}(N^3)$ computations with $N$ denoting the number of modeled points. Current approaches to overcome this limitation either rely on sparse, structured or stochastic representations of data or kernel respectively and usually involve nested optimizations to evaluate a GP. We present a new, generative method named Iterative Charted Refinement (ICR) to model GPs on nearly arbitrarily spaced points in $\mathcal{O}(N)$ time for decaying kernels without nested optimizations. ICR represents long- as well as short-range correlations by combining views of the modeled locations at varying resolutions with a user-provided coordinate chart. In our experiment with points whose spacings vary over two orders of magnitude, ICR's accuracy is comparable to state-of-the-art GP methods. ICR outperforms existing methods in terms of computational speed by one order of magnitude on the CPU and GPU and has already been successfully applied to model a GP with $122$ billion parameters.

cs.LG↗

arXiv2021

On the Three-Dimensional Structure of Local Molecular Clouds

We leverage the 1 pc spatial resolution of the Leike et al. 2020 3D dust map to characterize the three-dimensional structure of nearby molecular clouds ($d \lesssim 400$ pc). We start by "skeletonizing" the clouds in 3D volume density space to determine their "spines," which we project on the sky to constrain cloud distances with $\approx 1\%$ uncertainty. For each cloud, we determine an average radial volume density profile around its 3D spine and fit the profiles using Gaussian and Plummer functions. The radial volume density profiles are well-described by a two-component Gaussian function, consistent with clouds having broad, lower-density outer envelopes and narrow, higher-density inner layers. The ratio of the outer to inner envelope widths is $\approx 3:1$. We hypothesize that these two components may be tracing a transition between atomic and diffuse molecular gas or between the unstable and cold neutral medium. Plummer-like models can also provide a good fit, with molecular clouds exhibiting shallow power-law wings with density, $n$, falling off like $n^{-2}$ at large radii. Using Bayesian model selection, we find that parameterizing the clouds' profiles using a single Gaussian is disfavored. We compare our results with 2D dust extinction maps, finding that the 3D dust recovers the total cloud mass from integrated approaches with fidelity, deviating only at higher levels of extinction ($A_V \gtrsim 2 - 3$ mag). The 3D cloud structure described here will enable comparisons with synthetic clouds generated in simulations, offering unprecedented insight into the origins and fates of molecular clouds in the interstellar medium.

astro-ph.GA↗