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In this paper, we address the issues of the explainability of reinforcement learning-based machine learning agents trained with Proximal Policy Optimization (PPO) that utilizes visual sensor data. We propose an algorithm that allows an effective and intuitive approximation of the PPO-trained neural network (NN). We conduct several experiments to confirm our method’s effectiveness. Our proposed method works well for scenarios where semantic clustering of the scene is possible. Our approach is based on the solid theoretical foundation of Gradient-weighted Class Activation Mapping (GradCAM) and Classification and Regression Tree with additional proxy geometry heuristics. It excels in the explanation process in a virtual simulation system based on a video system with relatively low resolution. Depending on the convolutional feature extractor of the PPO-trained neural network, our method obtains 0.945 to 0.968 accuracy of approximation of the black-box model. The proposed method has important application aspects. Through its use, it is possible to estimate the causes of specific decisions made by the neural network due to the current state of the observed environment. This estimation makes it possible to determine whether the network makes decisions as expected (decision-making is related to the model’s observation of objects belonging to different semantic classes in the environment) and to detect unexpected, seemingly chaotic behavior that might be, for example, the result of data bias, bad design of the reward function or insufficient generalization abilities of the model. We publish all source codes so our experiments can be reproduced.

Applying Machine Learning (ML) methods for the analysis of muon lateral distributions in Extensive Air Showers detected by citizen science projects, while taking into account the spatial distribution of detectors requires enormous training data sets. Therefore, generating these data sets with typical Monte Carlo (MC) generators like CORSIKA is computationally prohibitive. Here we present a method which by the application of special augmentation procedures produces the training dataset that is compatible in all essential aspects to the data produced with regular MC computations while avoiding their time overhead. We utilize the Nakamura-Kamata-Greisen (NKG) distribution which was proven to be an attractive alternative to full-fledged simulations. The simulation of $10^{4}$ muons at the ground level takes just a few seconds using our implementation of the NKG approach. For $10^{6}$ muons this figure is still around 1 minute. For comparison, CORSIKA based simulation performed on Prometheus supercomputer at CYFRONET computing center an ensemble of $\sim 100$ showers initiated by a particle of $10^{16} eV$ resulted in $\sim 10^{4}$ muons and $\sim 10^{5}$ electrons required computation time of the order of a few days.

In this paper we propose the method for detecting potential anomalous cosmic ray particle tracks in big data image dataset acquired by Complementary Metal-Oxide-Semiconductors (CMOS). Those sensors are part of scientific infrastructure of Cosmic Ray Extremely Distributed Observatory (CREDO). The use of Incremental PCA (Principal Components Analysis) allowed approximation of loadings which might be updated at runtime. Incremental PCA with Sequential Karhunen-Loeve Transform results with almost identical embedding as basic PCA. Depending on image preprocessing method the weighted distance between coordinate frame and its approximation was at the level from 0.01 to 0.02 radian for batches with size of 10,000 images. This significantly reduces the necessary calculations in terms of memory complexity so that our method can be used for big data. The use of intuitive parameters of the potential anomalies detection algorithm based on object density in embedding space makes our method intuitive to use. The sets of anomalies returned by our proposed algorithm do not contain any typical morphologies of particle tracks shapes. Thus, one can conclude that our proposed method effectively filter-off typical (in terms of analysis of variance) shapes of particle tracks by searching for those that can be treated as significantly different from the others in the dataset. We also proposed method that can be used to find similar objects, which gives it the potential, for example, to be used in minimal distance-based classification and CREDO image database querying. The proposed algorithm was tested on more than half a million (570,000+) images that contains various morphologies of cosmic particle tracks. To our knowledge, this is the first study of this kind based on data collected using a distributed network of CMOS sensors embedded in the cell phones of participants collaborating within the citizen science paradigm.

In this paper, we discuss a practice of potential cosmic ray detection using off-the-shelves CMOS cameras. We discuss and presents the limitations of up-to-date hardware and software approaches to this task. We also present a hardware solution that we made for long-term testing of algorithms for potential cosmic ray detection. We have also proposed, implemented and tested a novel algorithm that enables real-time processing of image frames acquired by CMOS cameras in order to detect tracks of potential particles. We have compared our results with already published results and obtained acceptable results overcoming some limitation of already existing algorithms. Both source codes and data are available to download.

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.

Reliable tools for artefact rejection and signal classification are a must for cosmic ray detection experiments based on CMOS technology. In this paper, we analyse the fitness of several feature-based statistical classifiers for the classification of particle candidate hits in four categories: spots, tracks, worms and artefacts. We use Zernike moments of the image function as feature carriers and propose a preprocessing and denoising scheme to make the feature extraction more efficient. As opposed to convolution neural network classifiers, the feature-based classifiers allow for establishing a connection between features and geometrical properties of candidate hits. Apart from basic classifiers we also consider their ensemble extensions and find these extensions generally better performing than basic versions, with an average recognition accuracy of 88%.

Gamification is known to enhance users’ participation in education and research projects that follow the citizen science paradigm. The Cosmic Ray Extremely Distributed Observatory (CREDO) experiment is designed for the large-scale study of various radiation forms that continuously reach the Earth from space, collectively known as cosmic rays. The CREDO Detector app relies on a network of involved users and is now working worldwide across phones and other CMOS sensor-equipped devices. To broaden the user base and activate current users, CREDO extensively uses the gamification solutions like the periodical Particle Hunters Competition. However, the adverse effect of gamification is that the number of artefacts, i.e., signals unrelated to cosmic ray detection or openly related to cheating, substantially increases. To tag the artefacts appearing in the CREDO database we propose the method based on machine learning. The approach involves training the Convolutional Neural Network (CNN) to recognise the morphological difference between signals and artefacts. As a result we obtain the CNN-based trigger which is able to mimic the signal vs. artefact assignments of human annotators as closely as possible. To enhance the method, the input image signal is adaptively thresholded and then transformed using Daubechies wavelets. In this exploratory study, we use wavelet transforms to amplify distinctive image features. As a result, we obtain a very good recognition ratio of almost 99% for both signal and artefacts. The proposed solution allows eliminating the manual supervision of the competition process.

In this paper, we describe the convolutional neural network (CNN)-based approach to the problems of categorization and artefact reduction of cosmic ray images obtained from CMOS sensors used in mobile phones. As artefacts, we understand all images that cannot be attributed to particles’ passage through sensor but rather result from the deficiencies of the registration procedure. The proposed deep neural network is composed of a pretrained CNN and neural-network-based approximator, which models the uncertainty of image class assignment. The network was trained using a transfer learning approach with a mean squared error loss function. We evaluated our approach on a data set containing 2350 images labelled by five judges. The most accurate results were obtained using the VGG16 CNN architecture; the recognition rate (RR) was 85.79% ± 2.24% with a mean squared error (MSE) of 0.03 ± 0.00. After applying the proposed threshold scheme to eliminate less probable class assignments, we obtained a RR of 96.95% ± 1.38% for a threshold of 0.9, which left about 62.60% ± 2.88% of the overall data. Importantly, the research and results presented in this paper are part of the pioneering field of the application of citizen science in the recognition of cosmic rays and, to the best of our knowledge, this analysis is performed on the largest freely available cosmic ray hit dataset.

The teaching of motion activities in rehabilitation, sports, and professional work has great social significance. However, the automatic teaching of these activities, particularly those involving fast motions, requires the use of an adaptive system that can adequately react to the changing stages and conditions of the teaching process. This paper describes a prototype of an automatic system that utilizes the online classification of motion signals to select the proper teaching algorithm. The knowledge necessary to perform the classification process is acquired from experts by the use of the machine learning methodology. The system utilizes multidimensional motion signals that are captured using MEMS (Micro-Electro-Mechanical Systems) sensors. Moreover, an array of vibrotactile actuators is used to provide feedback to the learner. The main goal of the presented article is to prove that the effectiveness of the described teaching system is higher than the system that controls the learning process without the use of signal classification. Statistical tests carried out by the use of a prototype system confirmed that thesis. This is the main outcome of the presented study. An important contribution is also a proposal to standardize the system structure. The standardization facilitates the system configuration and implementation of individual, specialized teaching algorithms.

In this paper, we propose using the radial basis functions (RBF) to determine the upper bound of absolute dynamic error (UAE) at the output of a voltage-mode accelerometer. Such functions can be obtained as a result of approximating the error values determined for the assumed-in-advance parameter variability associated with the mathematical model of an accelerometer. This approximation was carried out using the radial basis function neural network (RBF-NN) procedure for a given number of the radial neurons. The Monte Carlo (MC) method was also applied to determine the related error when considering the uncertainties associated with the parameters of an accelerometer mathematical model. The upper bound of absolute dynamic error can be a quality ratio for comparing the errors produced by different types of voltage-mode accelerometers that have the same operational frequency bandwidth. Determination of the RBFs was performed by applying the Python-related scientific packages, while the calculations related both to the UAE and the MC method were carried out using the MathCad program. Application of the RBFs represent a new approach for determining the UAE. These functions allow for the easy and quick determination of the value of such errors.

The aim of this paper is to propose and evaluate the novel method of template generation, matching, comparing and visualization applied to motion capture (kinematic) analysis. To evaluate our approach, we have used motion capture recordings (MoCap) of two highly-skilled black belt karate athletes consisting of 560 recordings of various karate techniques acquired with wearable sensors. We have evaluated the quality of generated templates; we have validated the matching algorithm that calculates similarities and differences between various MoCap data; and we have examined visualizations of important differences and similarities between MoCap data. We have concluded that our algorithms works the best when we are dealing with relatively short (2–4 s) actions that might be averaged and aligned with the dynamic time warping framework. In practice, the methodology is designed to optimize the performance of some full body techniques performed in various sport disciplines, for example combat sports and martial arts. We can also use this approach to generate templates or to compare the correct performance of techniques between various top sportsmen in order to generate a knowledge base of reference MoCap videos. The motion template generated by our method can be used for action recognition purposes. We have used the DTW classifier with angle-based features to classify various karate kicks. We have performed leave-one-out action recognition for the Shorin-ryu and Oyama karate master separately. In this case, 100 % actions were correctly classified. In another experiment, we used templates generated from Oyama master recordings to classify Shorin-ryu master recordings and vice versa. In this experiment, the overall recognition rate was 94.2 % , which is a very good result for this type of complex action.