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The rapid growth of high-dimensional biological data has necessitated advanced data fusion techniques to integrate and interpret complex multi-omics and longitudinal datasets. Shared and unshared structure across such datasets can be identified in an unsupervised manner with Advanced Coupled Matrix and Tensor Factorization (ACMTF), but this cannot be related to an outcome. Conversely, N-way Partial Least Squares (NPLS) is supervised and captures outcome-associated variation but cannot identify shared and unshared structure. To bridge the gap between data exploration and prediction, we introduce ACMTF-Regression (ACMTF-R), an extension of ACMTF that incorporates a regression step, allowing for the simultaneous decomposition of multi-way data while explicitly capturing variation associated with a dependent variable. We present a detailed mathematical formulation of ACMTF-R, including its optimisation algorithm and implementation. Through extensive simulations, we systematically evaluate its ability to recover a small y - related component shared between multiple blocks, its robustness to noise, and the impact of the tuning parameter ( π ) which controls the balance between data exploration and outcome prediction. Our results demonstrate that ACMTF-R can robustly identify the y -related component, correctly identifying outcome-associated shared and distinct variation, distinguishing it from existing approaches such as NPLS and ACMTF. The development of ACMTF-R was motivated by a real-world dataset investigating how maternal pre-pregnancy BMI affects the human milk microbiome, human milk metabolome, and infant faecal microbiome. Emerging evidence suggests that inter-generational transfer of maternal obesity may affect multiple omics layers, highlighting the need to identify outcome-associated variation. The applicability of ACMTF-R is therefore validated by applying it to this multi-omics dataset. ACMTF-R successfully identifies novel mother-infant relationships associated with maternal pre-pregnancy BMI, underscoring its utility in multi-omics research. Our findings establish ACMTF-R as a versatile tool for multi-way data fusion, offering new insights into complex biological systems by integrating common, local, and distinct variation in the context of a dependent variable.

Magnetic fields are ubiquitous in the Universe. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations. However, experimental demonstration of the turbulent dynamo mechanism has remained elusive, since it requires plasma conditions that are extremely hard to re-create in terrestrial laboratories. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization. Exploring astrophysical turbulent effects in laboratory plasma is challenging due to high threshold values of relevant parameters, such as the magnetic Reynolds number. Here the authors demonstrate the turbulent dynamo effect at large magnetic Reynolds numbers in laser-generated magnetized plasma.

The properties of supersonic, compressible plasma turbulence determine the behavior of many terrestrial and astrophysical systems. In the interstellar medium and molecular clouds, compressible turbulence plays a vital role in star formation and the evolution of our galaxy. Observations of the density and velocity power spectra in the Orion B and Perseus molecular clouds show large deviations from those predicted for incompressible turbulence. Hydrodynamic simulations attribute this to the high Mach number in the interstellar medium (ISM), although the exact details of this dependence are not well understood. Here we investigate experimentally the statistical behavior of boundary-free supersonic turbulence created by the collision of two laser-driven high-velocity turbulent plasma jets. The Mach number dependence of the slopes of the density and velocity power spectra agree with astrophysical observations, and supports the notion that the turbulence transitions from being Kolmogorov-like at low Mach number to being more Burgers-like at higher Mach numbers. Supersonic turbulence is relevant to astrophysical plasmas with their study mostly limited to numerical simulations. Here the authors demonstrate supersonic turbulence in collisional high Mach number plasma jets generated in laboratory by using high power lasers.

Betatron radiation from laser wakefield accelerators is an ultrashort pulsed source of hard, synchrotron-like x-ray radiation. It emanates from a centimetre scale plasma accelerator producing GeV level electron beams. In recent years betatron radiation has been developed as a unique source capable of producing high resolution x-ray images in compact geometries. However, until now, the short pulse nature of this radiation has not been exploited. This report details the first experiment to utilize betatron radiation to image a rapidly evolving phenomenon by using it to radiograph a laser driven shock wave in a silicon target. The spatial resolution of the image is comparable to what has been achieved in similar experiments at conventional synchrotron light sources. The intrinsic temporal resolution of betatron radiation is below 100 fs, indicating that significantly faster processes could be probed in future without compromising spatial resolution. Quantitative measurements of the shock velocity and material density were made from the radiographs recorded during shock compression and were consistent with the established shock response of silicon, as determined with traditional velocimetry approaches. This suggests that future compact betatron imaging beamlines could be useful in the imaging and diagnosis of high-energy-density physics experiments.

The state and evolution of planets, brown dwarfs and neutron star crusts is determined by the properties of dense and compressed matter. Due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. Our results have profound consequences in the interpretation of transport coefficients in dense plasmas. Studying the properties of dense plasmas is challenging due to strong interactions between electrons and ions, and numerical methods overcome this difficulty using a static thermostat. Here the authors predict a strong diffusive ion mode at low energy by including dissipative processes in the model.

High‐resolution inelastic X‐ray scattering is an established technique in the synchrotron community, used to investigate collective low‐frequency responses of materials. When fielded at hard X‐ray free‐electron lasers (XFELs) and combined with high‐intensity laser drivers, it becomes a promising technique for investigating matter at high temperatures and high pressures. This technique gives access to important thermodynamic properties of matter at extreme conditions, such as temperature, material sound speed, and viscosity. The successful realization of this method requires the acquisition of many identical laser‐pump/X‐ray‐probe shots, allowing the collection of a sufficient number of photons necessary to perform quantitative analyses. Here, a 2.5‐fold improvement in the energy resolution of the instrument relative to previous works at the Matter in Extreme Conditions (MEC) endstation, Linac Coherent Light Source (LCLS), and the High Energy Density (HED) instrument, European XFEL, is presented. Some aspects of the experimental design that are essential for improving the number of photons detected in each X‐ray shot, making such measurements feasible, are discussed. A careful choice of the energy resolution, the X‐ray beam mode provided by the XFEL, and the position of the analysers used in such experiments can provide a more than ten‐fold improvement in the photometrics. The discussion is supported by experimental data on 10 µm‐thick iron and 50 nm‐thick gold samples collected at the MEC endstation at the LCLS, and by complementary ray‐tracing simulations coupled with thermal diffuse scattering calculations. High‐resolution inelastic X‐ray scattering measurements at hard X‐ray free‐electron lasers coupled with energetic laser drivers have shown a 2.5‐fold improved energy resolution compared with previous experiments at similar XFEL instruments. Aspects of the experimental design that can be adjusted to improve the number of recorded photons on the detector are discussed.

Creating non-equilibrium states of matter with highly unequal electron and lattice temperatures ( T ele ≠ T ion ) allows unsurpassed insight into the dynamic coupling between electrons and ions through time-resolved energy relaxation measurements. Recent studies on low-temperature laser-heated graphite suggest a complex energy exchange when compared to other materials. To avoid problems related to surface preparation, crystal quality and poor understanding of the energy deposition and transport mechanisms, we apply a different energy deposition mechanism, via laser-accelerated protons, to isochorically and non-radiatively heat macroscopic graphite samples up to temperatures close to the melting threshold. Using time-resolved x ray diffraction, we show clear evidence of a very small electron-ion energy transfer, yielding approximately three times longer relaxation times than previously reported. This is indicative of the existence of an energy transfer bottleneck in non-equilibrium warm dense matter.

We present a method to determine the bulk temperature of a single crystal diamond sample at an X-Ray free electron laser using inelastic X-ray scattering. The experiment was performed at the high energy density instrument at the European XFEL GmbH, Germany. The technique, based on inelastic X-ray scattering and the principle of detailed balance, was demonstrated to give accurate temperature measurements, within 8 % for both room temperature diamond and heated diamond to 500 K. Here, the temperature was increased in a controlled way using a resistive heater to test theoretical predictions of the scaling of the signal with temperature. The method was tested by validating the energy of the phonon modes with previous measurements made at room temperature using inelastic X-ray scattering and neutron scattering techniques. This technique could be used to determine the bulk temperature in transient systems with a temporal resolution of 50 fs and for which accurate measurements of thermodynamic properties are vital to build accurate equation of state and transport models.

Recent laser-plasma experiments (Fox et al., Phys. Rev. Lett., vol. 111, 2013, 225002; Huntington et al., Nat. Phys., vol. 11(2), 2015, 173–176; Tzeferacos et al., Phys. Plasmas, vol. 24(4), 2017a, 041404; Tzeferacos et al., 2017b, arXiv:1702.03016 [physics.plasm-ph]) report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton-imaging diagnostic can be used to determine a range of relevant magnetic-field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This ‘Kugland image-flux relation’ was previously derived (Kugland et al., Rev. Sci. Instrum. vol. 83(10), 2012, 101301) under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as with regular electromagnetic fields, features of the beam’s final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter – the contrast parameter $\\unicode[STIX]{x1D707}\\equiv d_{s}/{\\mathcal{M}}l_{B}$ – which quantifies the relative size of the correlation length $l_{B}$ of the stochastic field, proton displacements $d_{s}$ due to magnetic deflections and the image magnification ${\\mathcal{M}}$ . For stochastic magnetic fields, we establish the existence of four contrast regimes, under which proton-flux images relate to their parent fields in a qualitatively distinct manner. These are linear, nonlinear injective, caustic and diffusive. The diffusive regime is newly identified and characterised. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the path-integrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magnetic-energy spectrum can be obtained under a further statistical assumption of isotropy. This is not the case in the caustic or diffusive regimes. We discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magnetic-field statistics. The results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of proton-flux images.