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In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler equations of gas dynamics which we focus on in this paper. To take stochastic effects into account, we incorporate a stochastic forcing term in the momentum equation of the Euler system. To solve the extended system, we apply an entropy dissipative discontinuous Galerkin spectral element method including the Finite Volume setting, adjust it to the stochastic Euler equations and analyze its convergence properties. Our analysis is grounded in the concept of dissipative martingale solutions, as recently introduced by Moyo (J. Diff. Equ. 365, 408-464, 2023). Assuming no vacuum formation and bounded total energy, we proof that our scheme converges in law to a dissipative martingale solution. During the lifespan of a pathwise strong solution, we achieve convergence of at least order 1/2, measured by the expected $L^1$ norm of the relative energy. The results built a counterpart of corresponding results in the deterministic case. In numerical simulations, we show the robustness of our scheme, visualise different stochastic realizations and analyze our theoretical findings., Comment: 29 pages, 2 Figures

We present a novel method for learning hierarchical abstractions that prioritize competing objectives, leading to improved global expected rewards. Our approach employs a secondary rewarding agent with multiple scalar outputs, each associated with a distinct level of abstraction. The traditional agent then learns to maximize these outputs in a hierarchical manner, conditioning each level on the maximization of the preceding level. We derive an equation that orders these scalar values and the global reward by priority, inducing a hierarchy of needs that informs goal formation. Experimental results on the Pendulum v1 environment demonstrate superior performance compared to a baseline implementation.We achieved state of the art results., Comment: 5 pages

In positron emission tomography acquisition (PET), sensitivity along a line of response can vary due to crystal geometrical arrangements in the scanner and/or detector inefficiencies, leading to severe artefacts in the reconstructed image. To mitigate these effects, data must be corrected by a set of normalization coefficients applied to each line of response. The J-PET Modular scanner is a PET device made of 50 cm long plastic strips arranged axially, currently in operation at the Jagiellonian University in Krak\'ow (Poland). We have implemented a normalization method for the large field-of-view plastic-based J-PET Modular scanner using the component-based approach. We estimated the geometric normalization factors for the J-PET Modular scanner using Monte Carlo simulations. We also analysed the effects of variations in detection efficiency. A dedicated cylindrical phantom was simulated to investigate the impact of various factors on image quality. The image quality was quantified in terms of radial and axial uniformity metrics, and the standard deviation to mean intensity ratio, determined for a set of image slices. Without normalization, reconstructions of a uniform cylinder exhibit artefacts. These artefacts were satisfactorily compensated using the normalization factors. Applying geometrical corrections lowers the non-uniformity of the image expressed as a standard deviation-to-mean ratio to a range between 5.5 % to 8.5 %. Computationally, the technique is straightforward to parallelize, making it time-efficient. Preliminary estimates suggest that the method is appropriate for use with long axial field-of-view scanners, such as the total-body J-PET, currently under development at the Jagiellonian University., Comment: 36 pages, 16 figures, 4 tables

In this paper, we explore the intriguing similarities between the structure of a discrete neural network, such as a spiking network, and the composition of a piano piece. While both involve nodes or notes that are activated sequentially or in parallel, the latter benefits from the rich body of music theory to guide meaningful combinations. We propose a novel approach that leverages musical grammar to regulate activations in a spiking neural network, allowing for the representation of symbols as attractors. By applying rules for chord progressions from music theory, we demonstrate how certain activations naturally follow others, akin to the concept of attraction. Furthermore, we introduce the concept of modulating keys to navigate different basins of attraction within the network. Ultimately, we show that the map of concepts in our model is structured by the musical circle of fifths, highlighting the potential for leveraging music theory principles in deep learning algorithms., Comment: 3 pages

Discrete symmetries play an important role in particle physics with violation of CP connected to the matter-antimatter imbalance in the Universe. We report the most precise test of P, T and CP invariance in decays of ortho-positronium, performed with methodology involving polarization of photons from these decays. Positronium, the simplest bound state of an electron and positron, is of recent interest with discrepancies reported between measured hyperfine energy structure and theory at the level of $10^{-4}$ signaling a need for better understanding of the positronium system at this level. We test discrete symmetries using photon polarizations determined via Compton scattering in the dedicated J-PET tomograph on an event-by-event basis and without the need to control the spin of the positronium with an external magnetic field, in contrast to previous experiments. Our result is consistent with QED expectations at the level of 0.0007 and one standard deviation., Comment: 17 pages, 10 figures

We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the literature but only analysed in simplified cases. We investigate the full model with transport noise, where (a part of) the boundary of the fluid domain is randomly moving in time. We prove the existence of a weak martingale solution to the underlying system., Comment: 44 pages. To appear in Journal of Nonlinear Science

Studies based on imaging the annihilation of the electron (e$^{-}$) and its antiparticle positron (e$^{+}$) open up several interesting applications in nuclear medicine and fundamental research. The annihilation process involves both the direct conversion of e$^{+}$e$^{-}$ into photons and the formation of their atomically bound state, the positronium atom (Ps), which can be used as a probe for fundamental studies. With the ability to produce large quantities of Ps, manipulate them in long-lived Ps states, and image their annihilations after a free fall or after passing through atomic interferometers, this purely leptonic antimatter system can be used to perform inertial sensing studies in view of a direct test of Einstein equivalence principle. It is envisioned that modular multistrip detectors can be exploited as potential detection units for this kind of studies. In this work, we report the results of the first feasibility study performed on a e$^{+}$ beamline using two detection modules to evaluate their reconstruction performance and spatial resolution for imaging e$^{+}$e$^{-}$ annihilations and thus their applicability for gravitational studies of Ps.

Examinations are a crucial part of the learning process, and academic institutions invest significant resources into maintaining their integrity by preventing cheating from students or facilitators. However, cheating has become rampant in examination setups, compromising their integrity. The traditional method of relying on invigilators to monitor every student is impractical and ineffective. To address this issue, there is a need to continuously record exam sessions to monitor students for suspicious activities. However, these recordings are often too lengthy for invigilators to analyze effectively, and fatigue may cause them to miss significant details. To widen the coverage, invigilators could use fixed overhead or wearable cameras. This paper introduces a framework that uses automation to analyze videos and detect suspicious activities during examinations efficiently and effectively. We utilized the OpenPose framework and Convolutional Neural Network (CNN) to identify students exchanging objects during exams. This detection system is vital in preventing cheating and promoting academic integrity, fairness, and quality education for institutions.

We study the 2D Navier-Stokes equation with transport noise subject to periodic boundary conditions. Our main result is an error estimate for the time-discretisation showing a convergence rate of order (up to) 1/2. It holds with respect to mean square error convergence, whereas previously such a rate for the stochastic Navier-Stokes equations was only known with respect to convergence in probability. Our result is based on uniform-in-probability estimates for the continuous as well as the time-discrete solution exploiting the particular structure of the noise. Eventually, we perform numerical simulations for the corresponding problem on bounded domains with no-slip boundary conditions. They suggest the same convergence rate as proved for the periodic problem hinging sensitively on the compatibility of the data. We also compare the energy profiles with those for corresponding problems with additive or multiplicative It\^o-type noise., Comment: We added extensive numerical simulations. They underline the sharpness of our theoretical results and hinge sensitively on the compatibility of the data