Krzysztof Rzecki

We present the Julia package Manifolds.jl , providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in ManifoldsBase.jl , with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using Bézier splines, an optimization task on manifolds, and principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms all comparable packages for low-dimensional manifolds in speed; over Python and Matlab packages, the improvement is often several orders of magnitude, while over C/C++ packages, the improvement is two-fold. For high-dimensional manifolds, it outperforms all packages except for Tensorflow-Riemopt, which is specifically tailored for high-dimensional manifolds.

Successful application of external photon beam therapy in oncology requires that the dose delivered by a medical linear accelerator and distributed within the patient’s body is accurately calculated. Monte Carlo simulation is currently the most accurate method for this purpose but is computationally too extensive for routine clinical application. A very elaborate and time-consuming part of such Monte Carlo simulation is generation of the full set (phase space) of ionizing radiation components (mainly photons) to be subsequently used in simulating dose delivery to the patient. We propose a method of generating phase spaces in medical linear accelerators through learning, by artificial intelligence models, the joint multidimensional probability density distribution of the photon properties (their location in space, energy, and momentum). The models are conditioned with respect to the parameters of the primary electron beam (unique to each medical accelerator), which, through Bremsstrahlung, generates the therapeutical beam of ionizing radiation. Two variants of conditional generative adversarial networks are chosen, trained, and compared. We also present the second-best type of deep learning architecture that we studied: a variational autoencoder. Differences between dose distributions obtained in a water phantom, in a test phantom, and in real patients using generative-adversarial-network-based and Monte-Carlo-based phase spaces are very close to each other, as indicated by the values of standard quality assurance tools of radiotherapy. Particle generation with generative adversarial networks is three orders of magnitude faster than with Monte Carlo. The proposed GAN model, together with our earlier machine-learning-based method of tuning the primary electron beam of an MC simulator, delivers a complete solution to the problem of tuning a Monte Carlo simulator against a physical medical accelerator.

We present the Julia package Manifolds.jl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive definite matrices, or one of the models for hyperbolic spaces. We introduce a common interface, available in ManifoldsBase.jl, with which new manifolds, applications, and algorithms can be implemented. We demonstrate the utility of Manifolds.jl using B\'ezier splines, an optimization task on manifolds, and principal component analysis on nonlinear data. In a benchmark, Manifolds.jl outperforms all comparable packages for low-dimensional manifolds in speed; over Python and Matlab packages, the improvement is often several orders of magnitude, while over C/C++ packages, the improvement is two-fold. For high-dimensional manifolds, it outperforms all packages except for Tensorflow-Riemopt, which is specifically tailored for high-dimensional manifolds.

Both the lack of observation of ultra-high energy (UHE) photons and the limitations of the state-of-the-art methodology being applied for their identification motivate studies on alternative approaches to the relevant simulations and the related observational strategies. One of such new approaches is proposed in this report and it concerns new observables allowing indirect identification of UHE photons through cosmic ray phenomena composed of many spatially correlated extensive air showers or primary cosmic rays observed at one time. The study is based on simulations of interactions of UHE photons with the magnetic field of the Sun using the PRESHOWER program with some essential modifications. One of the expected results of such interactions is a generation of cosmic ray ensembles (CRE) in the form of very thin and very elongated cascades of secondary photons of energies spanning the whole cosmic ray energy spectrum. Upon entering the Earth's atmosphere, these cascades or their parts may generate uniquely characteristic walls of spatially correlated extensive air showers, and the effect is expected also in cases when primary UHE photons are not directed towards the Earth. Particle distributions in these multi-primary UHE photon footprints are expected to have thicknesses of the order of meters and elongations reaching even hundreds of millions kilometers, making them potentially observable with a global, multi-experiment approach, including re-exploring of the historical data, with the expected event rate exceeding the capabilities of even very large cosmic ray observatories. The methods described in this report allow for simulating potentially observable quantities related to CRE induced by UHE photons: densities, energy spectra and geographical orientations of particles at the top of the Earth's atmosphere.

Both the lack of observation of ultra-high energy (UHE) photons and the limitations of the state-of-the-art methodology being applied for their identification motivate studies on alternative approaches to the relevant simulations and the related observational strategies. One such new approach is proposed in this report and it concerns new observables allowing indirect identification of UHE photons through cosmic ray phenomena composed of many spatially correlated extensive air showers or primary cosmic rays observed at one time. The study is based on simulations of interactions of UHE photons with the magnetic field of the Sun using the PRESHOWER program with some essential modifications. One of the expected results of such interactions is a generation of cosmic ray ensembles (CREs) in the form of very thin and very elongated cascades of secondary photons of energies spanning the whole cosmic ray energy spectrum. Upon entering the Earth’s atmosphere, these cascades or their parts may generate uniquely characteristic walls of spatially correlated extensive air showers, and the effect is expected also in cases when primary UHE photons are not directed towards the Earth. Particle distributions in these multi-primary UHE photon footprints are expected to have thicknesses of the order of meters and elongations reaching even hundreds of millions of kilometers, making them potentially observable with a global, multi-experiment approach, including re-exploring of the historical data, with the expected event rate exceeding the capabilities of even very large cosmic ray observatories. In this report, we introduce for the first time the methods allowing for simulating the isotropic flux of UHE photons in the Sun’s vicinity. Presented methods were verified and optimised in such a way that they would successfully model the cumulative spatial distribution of secondary photons at the top of the atmosphere. The preliminary results of simulations for the UHE photon flux of energy 100 EeV demonstrate the possibility of simulating potentially observable quantities related to CRE induced by UHE photons: densities, energy spectra and geographical orientations of secondary particles at the top of the Earth’s atmosphere. A measurement of at least one of these quantities would be equivalent to a confirmation of the existence of UHE photons, which would give an insight into fundamental physics processes at unprecedentedly high energies, far beyond the reach of man-made accelerators. On the other hand, a lack of such an observation would allow for further constraining of these fundamental processes with the physically new upper limits on UHE photon fluxes after careful analysis of the technical observation ability. The novel advantage of such an approach would lay in the purely electrodynamical character of the underlying simulations which are fully independent on extrapolations of hadronic interaction models by many orders of magnitude. Such extrapolations are necessary in the UHE photon identification methods based on the analyses of properties of individual extensive air showers presently used to determine the UHE photon upper limits.

One of the main objectives of the CREDO project is to register cosmic-ray cascades in many distributed detectors in the search for so-called Cosmic-Ray Ensembles (CRE). This requires precise knowledge of the probability of detection of individual Extensive Air Showers (EAS) in a very wide range of energies and an analysis of their correlations. The standard approach based on detailed and extensive simulations is not possible for many such systems; thus, a faster method is developed. Knowing the characteristics of EAS from more general simulations, any required probability is calculated. Such probability depends on particle density at a given point, which is a function of the distance from the centre of the cascade, the energy, mass and the zenith angle of the primary cosmic-ray particle. It is necessary to use proper distribution of the number of secondary particles reaching the ground and their fluctuations. Finally, to calculate the total probability of EAS detection, the primary cosmic-ray spectrum and abundance of various particles in it have to be taken into account. The effective probability can be used to estimate the expected number of EAS events measured by a set of small detectors. In this work, results from several versions of calculations, with different complexity levels, are presented and compared with the first measurement performed with a test detector system. These results confirm that the majority of events observed with this small detector array are caused by cosmic-ray particles with very high energies. Such analysis can be also useful for the design of more effective systems in the future. Slightly larger systems of simple detectors may be used to distinguish cascades initiated by photons from those started from other primary cosmic-ray particles.

The Cosmic Ray Extremely Distributed Observatory (CREDO) pursues a global research strategy dedicated to the search for correlated cosmic rays, so-called Cosmic Ray Ensembles (CRE). Its general approach to CRE detection does not involve any a priori considerations, and its search strategy encompasses both spatial and temporal correlations, on different scales. Here we search for time clustering of the cosmic ray events collected with a small sea-level extensive air shower array at the University of Adelaide. The array consists of seven one-square-metre scintillators enclosing an area of 10 m × 19 m. It has a threshold energy ~0.1 PeV, and records cosmic ray showers at a rate of ~6 mHz. We have examined event arrival times over a period of over 2.5 years in two equipment configurations (without and with GPS timing), recording ~300 k events and ~100 k events. We determined the event time spacing distributions between individual events and the distributions of time periods which contained specific numbers of multiple events. We find that the overall time distributions are as expected for random events. The distribution which was chosen a priori for particular study was for time periods covering five events (four spacings). Overall, these distributions fit closely with expectation, but there are two outliers of short burst periods in data for each configuration. One of these outliers contains eight events within 48 s. The physical characteristics of the array will be discussed together with the analysis procedure, including a comparison between the observed time distributions and expectation based on randomly arriving events.