arXiv subjects

Johannes Schulz

Publications and source records attributed to Johannes Schulz.

5 recordsLinked to original sources

arXiv2022

Modeling Node Exposure for Community Detection in Networks

In community detection, datasets often suffer a sampling bias for which nodes which would normally have a high affinity appear to have zero affinity. This happens for example when two affine users of a social network were not exposed to one another. Community detection on this kind of data suffers then from considering affine nodes as not affine. To solve this problem, we explicitly model the (non-)exposure mechanism in a Bayesian community detection framework, by introducing a set of additional hidden variables. Compared to approaches which do not model exposure, our method is able to better reconstruct the input graph, while maintaining a similar performance in recovering communities. Importantly, it allows to estimate the probability that two nodes have been exposed, a possibility not available with standard models.

cs.SI↗

arXiv2016

Simulation of the Radiation Energy Release in Air Showers

A simulation study of the energy released by extensive air showers in the form of MHz radiation is performed using the CoREAS simulation code. We develop an efficient method to extract this radiation energy from air-shower simulations. We determine the longitudinal profile of the radiation energy release and compare it to the longitudinal profile of the energy deposit by the electromagnetic component of the air shower. We find that the radiation energy corrected for the geometric dependence of the geomagnetic emission scales quadratically with the energy in the electromagnetic component of the air shower with a second order dependency on the atmospheric density at the position of the maximum of the shower development $X_\mathrm{max}$. In a measurement where $X_\mathrm{max}$ is not accessible, this second order dependence can be approximated using the zenith angle of the incoming direction of the air shower with only a minor deterioration in accuracy. This method results in an intrinsic uncertainty of 4% with respect to the electromagnetic shower energy which is well below current experimental uncertainties.

astro-ph.HE↗

arXiv2016

Simulation of Radiation Energy Release in Air Showers

A simulation study of the energy released by extensive air showers in the form of MHz radiation is performed using the CoREAS simulation code. We develop an efficient method to extract this radiation energy from air-shower simulations. We determine the longitudinal profile of the radiation energy release and compare it to the longitudinal profile of the energy deposit by the electromagnetic component of the air shower. We find that the radiation energy corrected for the geometric dependence of the geomagnetic emission scales quadratically with the energy in the electromagnetic component of the air shower with a second-order dependence on the atmospheric density at the position of the maximum shower development $X_\mathrm{max}$. In a measurement where $X_\mathrm{max}$ is not accessible, this second order dependence can be approximated using the zenith angle of the incoming direction of the air shower with only a minor loss in accuracy. Our method results in an intrinsic uncertainty of 4% in the determination of the energy in the electromagnetic air-shower component, which is well below current experimental uncertainties.

astro-ph.HE↗

arXiv2013

Transient ageing in fractional Brownian and Langevin equation motion

Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion and fractional Langevin equation motion under external confinement are transiently non-ergodic---time and ensemble averages behave differently---from the moment when the particle starts to sense the confinement. Here we show that these processes also exhibit transient ageing, that is, physical observables such as the time averaged mean squared displacement depend on the time lag between the initiation of the system at time $t=0$ and the start of the measurement at the ageing time $t_a$. In particular, it turns out that for fractional Langevin equation motion the ageing dependence on $t_a$ is different between the cases of free and confined motion. We obtain explicit analytical expressions for the aged moments of the particle position as well as the time averaged mean squared displacement and present a numerical analysis of this transient ageing phenomenon.

cond-mat.stat-mech↗

arXiv2012

Ageing effects in single particle trajectory averages

We study time averages of single particle trajectories in scale free anomalous diffusion processes, in which the measurement starts at some time t_a>0 after initiation of the process at the time origin, t=0. Using ageing renewal theory we show that for such non-stationary processes a large class of observables are affected by a unique ageing function, which is independent of boundary conditions or the external forces. We quantify the weakly non-ergodic nature of this process in terms of the distribution of time averages and the ergodicity breaking parameter which both explicitly depend on the ageing time t_a. Consequences for the interpretation of single particle tracking data are discussed.

cond-mat.stat-mech↗