In this paper, a new phase-retrieval algorithm from an X-ray schlieren image is proposed. The schlieren method allows phase-contrast imaging with an objective lens and a knife-edge filter placed at the back focal plane of the objective. This method finds a wide range of applications in the visible-light region for transparent specimen visualization. The schlieren contrast does not directly correspond to the phase shift. However, the phase map can be reconstructed from a single-shot schlieren image of a transparent and weak-phase object using the filtered Fourier transform method. A proof-of-principle experiment was performed in the hard-X-ray region at the AR-NE1A beamline of the Photon Factory facility at the High Energy Accelerator Research Organization (KEK).

The classical Maximum-Entropy Principle (MEP) based on Shannon entropy is widely used to construct least-biased probability distributions from partial information. However, the Shore-Johnson axioms that single out the Shannon functional hinge on strong system independence, an assumption often violated in real-world, strongly correlated systems. We provide a self-contained guide to when and why practitioners should abandon the Shannon form in favour of the one-parameter Uffink-Jizba-Korbel (UJK) family of generalized entropies. After reviewing the Shore and Johnson axioms from an applied perspective, we recall the most commonly used entropy functionals and locate them within the UJK family. The need for generalized entropies is made clear with two applications, one rooted in economics and the other in ecology. A simple mathematical model worked out in detail shows the power of generalized maximum entropy approaches in dealing with cases where strong system independence does not hold. We conclude with practical guidelines for choosing an entropy measure and reporting results so that analyses remain transparent and reproducible.

Precise modeling of detector energy response is crucial for next-generation neutrino experiments which present computational challenges due to lack of analytical likelihoods. We propose a solution using neural likelihood estimation within the simulation-based inference framework. We develop two complementary neural density estimators that model likelihoods of calibration data: conditional normalizing flows and a transformer-based regressor. We adopt JUNO - a large neutrino experiment - as a case study. The energy response of JUNO depends on several parameters, all of which should be tuned, given their non-linear behavior and strong correlations in the calibration data. To this end, we integrate the modeled likelihoods with Bayesian nested sampling for parameter inference, achieving uncertainties limited only by statistics with near-zero systematic biases. The normalizing flows model enables unbinned likelihood analysis, while the transformer provides an efficient binned alternative. By providing both options, our framework offers flexibility to choose the most appropriate method for specific needs. Finally, our approach establishes a template for similar applications across experimental neutrino and broader particle physics.

The field of high energy physics (HEP) has seen a marked increase in the use of machine learning (ML) techniques in recent years. The proliferation of applications has revolutionised many aspects of the data processing pipeline at collider experiments including the Large Hadron Collider (LHC). In this whitepaper, we discuss the increasingly crucial role that ML plays in real-time analysis (RTA) at the LHC, namely in the context of the unique challenges posed by the trigger systems of the large LHC experiments. We describe a small selection of the ML applications in use at the large LHC experiments to demonstrate the breadth of use-cases. We continue by emphasising the importance of collaboration and engagement between the HEP community and industry, highlighting commonalities and synergies between the two. The mutual benefits are showcased in several interdisciplinary examples of RTA from industrial contexts. This whitepaper, compiled by the SMARTHEP network, does not provide an exhaustive review of ML at the LHC but rather offers a high-level overview of specific real-time use cases.

We present UniFoil, a large publicly available universal airfoil dataset based on Reynolds-averaged Navier-Stokes (RANS) simulations. It contains over 500,000 samples spanning a wide range of Reynolds and Mach numbers, capturing both transitional and fully turbulent flows across incompressible to compressible regimes. UniFoil is designed to support machine learning research in fluid dynamics, particularly for modeling complex aerodynamic phenomena. Most existing datasets are limited to incompressible, fully turbulent flows with smooth field characteristics, overlooking the critical physics of laminar\-turbulent transition and shock\-wave interactions\-features that exhibit strong nonlinearity and sharp gradients. UniFoil addresses this limitation by offering a broad spectrum of realistic flow conditions. Turbulent simulations utilize the Spalart\-Allmaras (SA) model, while transitional flows are modeled using an e^N\-based transition prediction method coupled with the SA model. The dataset includes a comprehensive geometry set comprising over 4,800 natural laminar flow (NLF) airfoils and 30,000 fully turbulent (FT) airfoils, covering a diverse range of airfoil designs relevant to aerospace, wind energy, and marine applications. This dataset is also valuable for scientific machine learning, enabling the development of data-driven models that more accurately capture the transport processes associated with laminar-turbulent transition. UniFoil is freely available under a permissive CC\-BY\-SA license.

The Laser Interferometer Space Antenna (LISA) will observe gravitational waves in the millihertz frequency band, detecting signals from a vast number of astrophysical sources embedded in instrumental noise. Extracting individual signals from these overlapping contributions is a fundamental challenge in LISA data analysis and is traditionally addressed using computationally expensive stochastic Bayesian techniques. In this work, we present a deep learning-based framework for blind source separation in LISA data, employing an encoder-decoder architecture commonly used in digital audio processing to isolate individual signals within complex mixtures. Our approach enables signals from massive black-hole binaries, Galactic binaries, and instrumental glitches to be disentangled directly in a single step, circumventing the need for sequential source identification and subtraction. By learning clustered latent space representations, the framework provides a scalable alternative to conventional methods, with applications in both low-latency event detection and full-scale global-fit analyses. As a proof of concept, we assess the model's performance using simulated LISA data in a controlled setting with a limited number of overlapping sources. The results highlight deep source separation as a promising tool for LISA, paving the way for future extensions to more complex datasets.

We consider a generalization of the so-called elephant random walk by introducing multiple elephants moving along the integer line, $\mathbb{Z}$. When taking a new step, each elephant considers not only its own previous steps but also the past steps of other elephants. The dynamics of "who follows whom" are governed by a directed graph, where each vertex represents an elephant, and the edges indicate that an elephant will consider the past steps of its in-neighbour elephants when deciding its next move. In other words, this model involves a collection of reinforced random walks evolving through graph-based interactions. We briefly investigate the first- and second-order asymptotic behaviour of the joint walks and establish connections with other network-based reinforced stochastic processes studied in the literature. We show that the joint walk can be expressed as a stochastic approximation scheme. In certain regimes, we employ tools from stochastic approximation theory to derive the asymptotic properties of the joint walks. Additionally, in a specific regime, we use better techniques to establish a strong invariance principle and a central limit theorem with improved rates compared to existing results in the stochastic approximation literature. These techniques can also be used to strengthen equivalent results in stochastic approximation theory. As a byproduct, we establish a strong invariance principle for the simple elephant random walk with significantly improved rates.

Incorporating novelties into deep learning systems remains a challenging problem. Introducing new information to a machine learning system can interfere with previously stored data and potentially alter the global model paradigm, especially when dealing with non-stationary sources. In such cases, traditional approaches based on validation error minimization offer limited advantages. To address this, we propose a training algorithm inspired by Stuart Kauffman's notion of the Adjacent Possible. This novel training methodology explores new data spaces during the learning phase. It predisposes the neural network to smoothly accept and integrate data sequences with different statistical characteristics than expected. The maximum distance compatible with such inclusion depends on a specific parameter: the sampling temperature used in the explorative phase of the present method. This algorithm, called Dreaming Learning, anticipates potential regime shifts over time, enhancing the neural network's responsiveness to non-stationary events that alter statistical properties. To assess the advantages of this approach, we apply this methodology to unexpected statistical changes in Markov chains and non-stationary dynamics in textual sequences. We demonstrated its ability to improve the auto-correlation of generated textual sequences by $\sim 29\%$ and enhance the velocity of loss convergence by $\sim 100\%$ in the case of a paradigm shift in Markov chains.

Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during training to enforce each PDE and initial/boundary conditions, and experimental points which are usually costly to obtain via experiments or simulations. Training PINNs using this loss function is challenging as it typically requires selecting large numbers of points of different types, each with different training dynamics. Unlike past works that focused on the selection of either collocation or experimental points, this work introduces PINN Adaptive ColLocation and Experimental points selection (PINNACLE), the first algorithm that jointly optimizes the selection of all training point types, while automatically adjusting the proportion of collocation point types as training progresses. PINNACLE uses information on the interaction among training point types, which had not been considered before, based on an analysis of PINN training dynamics via the Neural Tangent Kernel (NTK). We theoretically show that the criterion used by PINNACLE is related to the PINN generalization error, and empirically demonstrate that PINNACLE is able to outperform existing point selection methods for forward, inverse, and transfer learning problems.

Atmospheric interaction with light has been an area of fascination for many researchers over the last century. Environmental conditions, such as temperature and wind speed, heavily influence the complex and rapidly varying optical distortions propagating optical fields experience. The continuous random phase fluctuations commonly make deciphering the exact origins of specific optical aberrations challenging. The generation of eddies is a major contributor to atmospheric turbulence, similar in geometric structure to optical vortices that sit at the centre of OAM beams. Decomposing the received optical fields into OAM provides a unique spatial similarity that can be used to analyse turbulent channels. In this work, we present a novel mode decomposition assisted machine learning approach that reveals trainable features in the distortions of vortex beams that allow for effective environmental monitoring. This novel technique can be used reliably with Support Vector Machine regression models to measure temperature variations of 0.49C and wind speed variations of 0.029 m/s over a 36m experimental turbulent free-space channels with controllable and verifiable temperature and wind speed with short 3s measurement. The predictable nature of these findings could indicate the presence of an underlying physical relationship between environmental conditions that lead to specific eddy formation and the OAM spiral spectra.

An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected size is a time-dependent quantity and so enables the identification of nodes who are the most influential early or late in the spreading process. The measure is accurate for both critical and subcritical dynamic regimes and so generalises the nonbacktracking centrality that was previously shown to successfully identify the most influential single spreaders in a model of critical epidemics on networks.

The Symmetric Information Bottleneck (SIB), an extension of the more familiar Information Bottleneck, is a dimensionality reduction technique that simultaneously compresses two random variables to preserve information between their compressed versions. We introduce the Generalized Symmetric Information Bottleneck (GSIB), which explores different functional forms of the cost of such simultaneous reduction. We then explore the dataset size requirements of such simultaneous compression. We do this by deriving bounds and root-mean-squared estimates of statistical fluctuations of the involved loss functions. We show that, in typical situations, the simultaneous GSIB compression requires qualitatively less data to achieve the same errors compared to compressing variables one at a time. We suggest that this is an example of a more general principle that simultaneous compression is more data efficient than independent compression of each of the input variables.

We have integrated Easy JavaScript Simulation (EJSS) Data Analytics into the national Learning Management System for Singapore schools, known as the Singapore Student Learning Space (SLS). EJSS Data Analytics enhances the teaching and learning experience for educators and students by enabling educators to monitor and evaluate students interactions with interactive computer simulations. The data analytics and visualisation capabilities are delivered using the Moodle platform and version 1.3 of the specifications for Learning Tools Interoperability (LTI). In this paper, we showcase the potential for EJSS Data Analytics to identify students learning difficulties and misconceptions. Four examples of EJSS Data Analytics applications are provided to illustrate insights on aspects that include understanding a students sequential actions leading to specific task outcomes, the frequency of task attempts by each student, and the ratio of students achieving correct versus incorrect task completions. We identify five key considerations for designing the EJSS teacher dashboard. These considerations relate to Student Thought Process, Student Behaviour, Student Engagement, Student Choice, and Teacher Feedback. These five facets provide a framework for aligning our design efforts with the needs of students and teachers, also drawing upon research in data analytics for education.

In this paper, we propose a novel inverse parameter estimation approach called Bayesian optimized physics-informed neural network (BOPINN). In this study, a PINN solves the partial differential equation (PDE), whereas Bayesian optimization (BO) estimates its parameter. The proposed BOPINN estimates wave velocity associated with wave propagation PDE using a single snapshot observation. An objective function for BO is defined as the mean squared error (MSE) between the surrogate displacement field and snapshot observation. The inverse estimation capability of the proposed approach is tested in three different isotropic media with different wave velocities. From the obtained results, we have observed that BOPINN can accurately estimate wave velocities with lower MSE, even in the presence of noisy conditions. The proposed algorithm shows robust predictions in limited iterations across different runs.

This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and transaction number, sampled every 10 seconds, were divided into intraday and intraweek periods and then further decomposed into recurring and noise components via correlation matrix formalism. The key findings include the distinctive market behavior from traditional stock markets due to the nonexistence of trade opening and closing. This was manifest in three enhanced-activity phases aligning with Asian, European, and U.S. trading sessions. An intriguing pattern of activity surge in 15-minute intervals, particularly at full hours, was also noticed, implying the potential role of algorithmic trading. Most notably, recurring bursts of activity in bitcoin and ether were identified to coincide with the release times of significant U.S. macroeconomic reports such as Nonfarm payrolls, Consumer Price Index data, and Federal Reserve statements. The most correlated daily patterns of activity occurred in 2022, possibly reflecting the documented correlations with U.S. stock indices in the same period. Factors that are external to the inner market dynamics are found to be responsible for the repeatable components of the market dynamics, while the internal factors appear to be substantially random, which manifests itself in a good agreement between the empirical eigenvalue distributions in their bulk and the random matrix theory predictions expressed by the Marchenko-Pastur distribution. The findings reported support the growing integration of cryptocurrencies into the global financial markets.

We introduce a new information-geometric structure associated with the dynamics on discrete objects such as graphs and hypergraphs. The presented setup consists of two dually flat structures built on the vertex and edge spaces, respectively. The former is the conventional duality between density and potential, e.g., the probability density and its logarithmic form induced by a convex thermodynamic function. The latter is the duality between flux and force induced by a convex and symmetric dissipation function, which drives the dynamics of the density. These two are connected topologically by the homological algebraic relation induced by the underlying discrete objects. The generalized gradient flow in this doubly dual flat structure is an extension of the gradient flows on Riemannian manifolds, which include Markov jump processes and nonlinear chemical reaction dynamics as well as the natural gradient and mirror descent. The information-geometric projections on this doubly dual flat structure lead to information-geometric extensions of the Helmholtz-Hodge decomposition and the Otto structure in $L^{2}$ Wasserstein geometry. The structure can be extended to non-gradient nonequilibrium flows, from which we also obtain the induced dually flat structure on cycle spaces. This abstract but general framework can extend the applicability of information geometry to various problems of linear and nonlinear dynamics.