We propose a method to represent bipartite networks using graph embeddings tailored to tackle the challenges of studying ecological networks, such as the ones linking plants and pollinators, where many covariates need to be accounted for, in particular to control for sampling bias. We adapt the variational graph auto-encoder approach to the bipartite case, which enables us to generate embeddings in a latent space where the two sets of nodes are positioned based on their probability of connection. We translate the fairness framework commonly considered in sociology in order to address sampling bias in ecology. By incorporating the Hilbert-Schmidt independence criterion (HSIC) as an additional penalty term in the loss we optimize, we ensure that the structure of the latent space is independent of continuous variables, which are related to the sampling process. Finally, we show how our approach can change our understanding of ecological networks when applied to the Spipoll data set, a citizen science monitoring program of plant-pollinator interactions to which many observers contribute, making it prone to sampling bias.

The interplay between electron correlation and nuclear quantum effects makes our understanding of elemental hydrogen a formidable challenge. Here, we present the phase diagram of hydrogen and deuterium at low temperatures and high-pressure ($P > 300$ GPa by accounting for highly accurate electronic and nuclear enthalpies. We evaluated internal electronic energies by diffusion quantum Monte Carlo, while nuclear quantum motion and anharmonicity have been included by the stochastic self-consistent harmonic approximation. Our results show that the long-sought atomic metallic hydrogen, predicted to host room-temperature superconductivity, forms at $577\pm 10$ GPa ($640\pm 14$ GPa in deuterium). Indeed, anharmonicity pushes the stability of this phase towards pressures much larger than previous theoretical estimates or attained experimental values. Before atomization, molecular hydrogen transforms from a conductive phase III to another metallic structure that is still molecular (phase VI) at $422\pm 40$ GPa ($442\pm30$ GPa in deuterium). We predict clear-cut signatures in optical spectroscopy and DC conductivity that can be used experimentally to distinguish between the two structural transitions. According to our findings, the experimental evidence of metallic hydrogen has so far been limited to molecular phases.

Climate projections have uncertainties related to components of the climate system and their interactions. A typical approach to quantifying these uncertainties is to use climate models to create ensembles of repeated simulations under different initial conditions. Due to the complexity of these simulations, generating such ensembles of projections is computationally expensive. In this work, we present ArchesClimate, a deep learning-based climate model emulator that aims to reduce this cost. ArchesClimate is trained on decadal hindcasts of the IPSL-CM6A-LR climate model at a spatial resolution of approximately 2.5x1.25 degrees. We train a flow matching model following ArchesWeatherGen, which we adapt to predict near-term climate. Once trained, the model generates states at a one-month lead time and can be used to auto-regressively emulate climate model simulations of any length. We show that for up to 10 years, these generations are stable and physically consistent. We also show that for several important climate variables, ArchesClimate generates simulations that are interchangeable with the IPSL model. This work suggests that climate model emulators could significantly reduce the cost of climate model simulations.

As a consequence of their spin-orbit entangled ground state, many $5d^{5}$ iridate materials display a peculiar double peak structure in optical transport quantities, such as absorption and conductivity. Their common interpretation is based on the presence of Hubbard subbands in the half-filled $j_{\mathrm{eff}}=1/2$ manifold. Herein, we challenge this picture, proposing a scenario based on the presence of spin-polaron (SP) quasiparticles, and assigning a dominant SP character to the first peak. We illustrate it by taking the materials Ba$_2$IrO$_4$ and Sr$_2$IrO$_4$ as paradigmatic examples, which we investigate within the dynamical mean-field theory and the self-consistent Born approximation. Both theories reproduce nontrivial features revealed by angle-resolved photoemission spectroscopy and optical transport measurements, supporting our interpretation. In the case of Sr$_2$IrO$_4$, we show how the SP scenario survives in the low-doped regime. Similar optical transport fingerprints are expected to be found in the wider class of $5d^5$ iridates and more generally in strongly correlated antiferromagnetic regimes, such as those found in cuprates.

The dynamics of the El Niño Southern Oscillation (ENSO) are succinctly captured by the Recharge Oscillator (RO) framework. However, to simulate ENSO realistically, careful choices must be made regarding the RO's key parameters. In particular, nonlinear parameters govern how well the model reproduces key ENSO asymmetries-El Niño events tend to be stronger but shorter-lived, often transitioning into La Niña, whereas La Niña events are typically weaker but more persistent, sometimes lasting into a second year or beyond. While amplitude asymmetry has been widely studied within the RO framework, duration and transition asymmetries have received little attention, and their underlying causes remain debated. In this study, by systematically exploring the RO parameter space-rather than relying on commonly used fitting methods-we identify optimal parameter values that successfully capture key linear and nonlinear ENSO characteristics. An analytical expression for the temperature-heat content anomaly slope shows that the choice of heat content variable inherently reflects the sign of the Bjerknes feedback and the ocean adjustment timescale. We further show that self-sustained oscillations fail to reproduce the observed Nino 3 and 3.4 kurtosis. Finally, we demonstrate that incorporating red noise forcing distorts the RO simulated power spectrum and add unnecessary complexity. The most realistic yet simplest RO configuration is a strongly damped oscillator, with a decay timescale shorter than the dominant period, forced by multiplicative white noise and influenced by relatively weak deterministic nonlinearities. Identifying these minimal components preserves the conceptual clarity of the RO framework and isolates the core physical processes underlying ENSO behavior.

1 - Spatial confounding is a phenomenon that has been studied extensively in recent years in the statistical literature to describe and mitigate apparent inconsistencies between the results obtained by regression models with and without random spatial effects. While the most common solutions target almost exclusively areal data or geostatistical data modelling by splines, we aim to extend some resolution methods in the context of geostatistical data modelling by Gaussian Markov Random Fields (GMRF) using R-INLA methodology. 2 - First, we present three approaches for alleviating spatial confounding: Restricted Spatial Regression (RSR), Spatial+, and its recent simplified version, called here Spatial+ 2.0. We show how each can be implemented from geostatistical data in a GMRF framework using R-inlabru. 3 - Next, a simulation study that reproduces a spatial confounding phenomenon is carried out to assess the coherence of the extensions with the expectations of these methods. Finally, we apply the expanded methods to a case study, linking cadmium (Cd) concentration in terrestrial mosses to Cd concentration in air. 4 - Our findings support the feasibility of our extended approach of spatial confounding resolution methods to geostatistical data using R-INLA in keeping with the previous contexts, although certain precautions and limitations must be considered.

TurboRVB is a computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC), and Diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions. The electronic wave function (WF) is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal product with spin-singlet pairing, or as a Pfaffian, including both singlet and triplet correlations. This wave function can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) ansatz, first proposed by L. Pauling and P. W. Anderson in quantum chemistry and condensed matter physics, respectively. The RVB ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization is made possible thanks to state-of-the-art stochastic algorithms for energy minimization. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, that is also an ideal environment for exploiting the computational power of modern GPU accelerators.

The anisotropic potential energy surface of the (H$_2$)$_2$ dimer represents a challenging problem for many-body methods. Here, we determine the potential energy curves of five different dimer configurations (T, Z, X, H, L) using the lattice regularized diffusion Monte Carlo (LRDMC) method and a number of approximate functionals within density functional theory (DFT), including advanced orbital-dependent functionals based on the random phase approximation (RPA). We assess their performance in describing the potential wells, bond distances and relative energies. The repulsive potential wall is studied by looking at the relative stability of the different dimer configurations as a function of an applied force acting along the intermolecular axis. It is shown that most functionals within DFT break down at finite compression, even those that give an accurate description around the potential well minima. Only by including exchange within RPA a qualitatively correct description along the entire potential energy curve is obtained. Finally, we discuss these results in the context of solid molecular hydrogen at finite pressures.

In this monograph, we review and develop variable projection Gauss-Newton, Levenberg-Marquardt and Newton methods for the Weighted Low-Rank Approximation (WLRA) problem, which has now an increasing number of applications in many scientific fields. Particular attention is drawn at the robustness, efficiency and scalability of these variable projection second-order algorithms such that they can be used also on larger datasets now commonly found in many practical problems for which only first-order algorithms based on sequential repetitions of local optimization (e.g., majorization, Expectation-Maximization or alternating least-squares methods) or variations of gradient descent (e.g., conjugate, proximal or stochastic gradient descent methods), or hybrid algorithms from these two classes of methods, were only feasible due to their lower cost and memory requirement per iteration. In parallel with this review of variable projection algorithms, we develop new formulae for the Jacobian and Hessian matrices involved in these variable projection methods and demonstrate their very specific properties such as the uniform rank deficiency of the Jacobian matrix or the rank deficiency of the Hessian matrix at the (local) minimizers of the cost function associated with the WLRA problem. These systematic deficiencies must be taken into account in any practical implementations of the algorithms. These different properties and the very particular geometry of the WLRA problem have not been well appreciated in the past and have been the main obstacles in the development of robust variable projection second-order algorithms for solving the WLRA problem. In addition, we demonstrate that the variable projection framework gives original insights on the solvability, the landscape and the non-smoothness of the WLRA problem. It also helps to describe the tight links between previously unrelated methods, which have been proposed to solve it. Specifically, we illustrate the closed links between the variable projection framework and Riemannian optimization on the Grassmann manifold for the WLRA problem. We expect that software's developers and practitioners in different fields such as computer vision, signal processing, recommender systems, machine learning, multivariate statistics and geophysical sciences will benefit from the results in this monograph in order to devise more robust and accurate algorithms to solve the WLRA problem.

TurboRVB is a computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC), and Diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions. The electronic wave function (WF) is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal product with spin-singlet pairing, or as a Pfaffian, including both singlet and triplet correlations. This wave function can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) ansatz, first proposed by L. Pauling and P. W. Anderson in quantum chemistry and condensed matter physics, respectively. The RVB ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization is made possible thanks to state-of-the-art stochastic algorithms for energy minimization. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, that is also an ideal environment for exploiting the computational power of modern GPU accelerators.

We study two related universal anomalies of the spectral function of cuprates, so called waterfall and high-energy kink features, by a combined cellular dynamical mean-field theory and angle-resolved photoemission study for the oxychloride Na$_x$Ca$_{2-x}$CuO$_2$Cl$_2$ (Na-CCOC). Tracing their origin back to an interplay of spin-polaron and local correlation effects both in undoped and hole-doped (Na-)CCOC, we establish them as a universal crossover between regions differing in the momentum dependence of the coupling and not necessarily in the related quasiparticles' energies. The proposed scenario extends to doping levels coinciding with the cuprate's superconducting dome and motivates further investigations of the fate of spin-polarons in the superconducting phase.

The high-pressure II-III phase transition in solid hydrogen is investigated using the random phase approximation and diffusion Monte Carlo. Good agreement between the methods is found confirming that an accurate treatment of exchange and correlation increases the transition pressure by more than 100 GPa with respect to semilocal density functional approximations. Using an optimized hybrid functional, we then reveal a low-symmetry structure for phase II generated by an out-of-plane librational instability of the C2/c phase III structure. This instability weakens the in-plane polarization of C2/c leading to the well-known experimental signatures of the II-III phase transition such as a sharp shift in vibron frequency, infrared activity and $c/a$ lattice parameter ratio. Finally, we discuss the zero-point vibrational energy that plays an important role in stabilizing phase III at lower pressures.

The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of data, and (iii) the unstable nature of the dynamics. To achieve such inference from the observations over long time series, it has been suggested to combine data assimilation and machine learning in several ways. We show how to unify these approaches from a Bayesian perspective using expectation-maximization and coordinate descents. In doing so, the model, the state trajectory and model error statistics are estimated all together. Implementations and approximations of these methods are discussed. Finally, we numerically and successfully test the approach on two relevant low-order chaotic models with distinct identifiability.

Pollinators play a crucial role for plant reproduction, either in natural ecosystem or in human-modified landscape. Global change drivers,including climate change or land use modifications, can alter the plant-pollinator interactions. To assess the potential influence of global change drivers on pollination, large-scale interactions, climate and land use data are required. While recent machine learning methods, such as graph neural networks (GNNs), allow the analysis of such datasets, interpreting their results can be challenging. We explore existing methods for interpreting GNNs in order to highlight the effects of various environmental covariates on pollination network connectivity. A large simulation study is performed to confirm whether these methods can detect the interactive effect between a covariate and a genus of plant on connectivity, and whether the application of debiasing techniques influences the estimation of these effects. An application on the Spipoll dataset, with and without accounting for sampling effects, highlights the potential impact of land use on network connectivity and shows that accounting for sampling effects partially alters the estimation of these effects.

We report here the first equation of state measurements of Fe$_2$O$_3$ obtained with laser-driven shock compression. The data are in excellent agreement with previous dynamic and static compression measurements at low pressure, and extend the known Hugoniot up to 700 GPa. We observe a large volume drop of $\sim$10% at 86 GPa, which could be associated, according to static compression observations, with the iron spin transition. Our measurements also suggest a change of the Hugoniot curve between 150 and 250 GPa. Above 250 GPa and within our error bars, we do not observe significant modifications up to the maximum pressure of 700 GPa reached in our experiment.

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at this http URL .

An efficient first principles approach to calculate X-ray magnetic circular dichroism (XMCD) and X-ray natural circular dichroism (XNCD) is developed and applied in the near edge region at the K-and L1-edges in solids. Computation of circular dichroism requires precise calculations of X-ray absorption spectra (XAS) for circularly polarized light. For the derivation of the XAS cross section, we used a relativistic description of the photon-electron interaction that results in an additional term in the cross-section that couples the electric dipole operator with an operator $\mathbf{\sigma}\cdot (\mathbf{\epsilon} \times \mathbf{r})$ that we name spin-position. The numerical method relies on pseudopotentials, on the gauge including projected augmented wave method and on a collinear spin relativistic description of the electronic structure. We apply the method to the calculations of K-edge XMCD spectra of ferromagnetic iron, cobalt and nickel and of I L1-edge XNCD spectra of $\alpha$-LiIO3, a compound with broken inversion symmetry. For XMCD spectra we find that, even if the electric dipole term is the dominant one, the electric quadrupole term is not negligible (8% in amplitude in the case of iron). The term coupling the electric dipole operator with the spin-position operator is significant (28% in amplitude in the case of iron). We obtain a sum-rule relating this new term to the spin magnetic moment of the p-states. In $\alpha$-LiIO3 we recover the expected angular dependence of the XNCD spectra.

We report the first successful application of the {\it ab initio} quantum Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon dispersion of diamond is successfully calculated at the variational Monte Carlo (VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is in good agreement with the experimental results, giving renormalized harmonic optical frequencies very close to the experimental values, by significantly improving upon density functional theory (DFT) in the generalized gradient approximation. Key to success for the QMC approach is the statistical error reduction in atomic force evaluation. We show that this can be achieved by using well conditioned atomic basis sets, by explicitly removing the basis-set redundancy, which reduces the statistical error of forces by up to two orders of magnitude. This leads to affordable and accurate QMC-phonons calculations, up to $10^{4}$ times more efficient than previous attempts, and paves the way to new applications, particularly in correlated materials, where phonons have been poorly reproduced so far.

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled by an unknown time-varying differential equation, and the evolution term is estimated from the data, using a neural network. Any future state can then be computed by placing the associated differential equation in an ODE solver. We first evaluate our approach on shallow water and Euler simulations. We find that our method not only demonstrates high quality long-term forecasts, but also learns to produce hidden states closely resembling the true states of the system, without direct supervision on the latter. Additional experiments conducted on challenging, state of the art ocean simulations further validate our findings, while exhibiting notable improvements over classical baselines.

NbO2 is a potential material for nanometric memristor devices, both in the amorphous and the crystalline form. We fabricated NbO2 thin films using RF-magnetron sputtering from a stoichiometric target. The as-deposited films were amorphous regardless of the sputtering parameters. Post deposition vacuum annealing of the films was necessary to achieve crystallinity. A high degree of crystallinity was obtained by optimizing annealing duration and temperature. The resistivity of the material increases as it undergoes a structural transition from amorphous to crystalline with the crystalline films being one order of magnitude more resistive.