We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid dense hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer energies are consistently lower than all previous projector Monte Carlo calculations for systems containing up to $128$ hydrogen atoms. In contrast to conventional methods, we introduce a universal trial wave function whose variational parameters are optimized simultaneously over a large set of proton configurations spanning a wide pressure-temperature spectrum and covering both molecular and atomic phases. This global optimization not only yields lower energies compared to benchmarks but also brings an enormous reduction in computational cost. By including nuclear quantum effects in the zero-temperature ground state, thus going beyond the Born-Oppenheimer approximation, our description overcomes major limitations of current wave functions, notably by avoiding any explicit symmetry assumption on the expected quantum crystal and sidestepping efficiency issues of imaginary time evolution with disparate mass scales. As a first application, we examine crystal formation in an extremely high-density region where pressure-induced melting is expected.

A major obstacle for quantum optimizers is the reformulation of constraints as a quadratic unconstrained binary optimization (QUBO). Current QUBO translators exaggerate the weight $M$ of the penalty terms. Classically known as the "Big-$M$" problem, the issue becomes even more daunting for quantum solvers, since it affects the physical energy scale. We take a systematic, encompassing look at the quantum big-$M$ problem, revealing NP-hardness in finding the optimal $M$ and establishing bounds on the Hamiltonian spectral gap $\Delta$, inversely related to the expected run-time of quantum solvers. We propose a practical translation algorithm, based on SDP relaxation, that outperforms previous methods in numerical benchmarks. Our algorithm gives values of $\Delta$ orders of magnitude greater, e.g. for portfolio optimization instances. Solving such instances with an adiabatic algorithm on 6-qubits of an IonQ device, we observe significant advantages in time to solution and average solution quality. Our findings are relevant to quantum and quantum-inspired solvers alike.

We provide an accurate comparison, against large cosmological $N$-body simulations, of different prescriptions for modelling nonlinear matter power spectra in the presence of massive neutrinos and dynamical dark energy. We test the current most widely used approaches: fitting functions (HALOFIT and HMcode), the halo-model reaction (ReACT) and emulators (baccoemu and EuclidEmulator2). Focussing on redshifts $z\leq2$ and scales $k\lesssim 1 \ h/$Mpc (where the simulation mass resolution provides $\sim 1\%$ accuracy), we find that HMcode and ReACT considerably improve over the HALOFIT prescriptions of Smith and Takahashi (both combined with the Bird correction), with an overall agreement of 2\% for all the cosmological scenarios considered. Concerning emulators, we find that, especially at low redshifts, EuclidEmulator2 remarkably agrees with the simulated spectra at $\lesssim 1\%$ level in scenarios with dynamical dark energy and massless neutrinos, reaching a maximum difference of $\sim 2\%$ at $z=2$. baccoemu has a similar behaviour as EuclidEmulator2, except for a couple of dark energy models. In cosmologies with massive neutrinos, at $z=0$ all the nonlinear prescriptions improve their agreement with respect to the massless neutrino case, except for the Bird and TakaBird models which, however, are not tailored to $w_0$--$w_a$ models. At $z>0$ we do not find a similar improvement when including massive neutrinos, probably due to the lower impact of neutrino free-streaming at higher redshifts; rather at $z=2$ EuclidEmulator2 exceeds $2\%$ agreement for some dark energy equation of state. When considering ratios between the matter power spectrum computed in a given cosmological model and its $\Lambda$CDM counterpart, all the tested prescriptions agree with simulated data, at sub-percent or percent level, depending on $z$. [ABRIDGED]

The Euclid mission of the European Space Agency will deliver weak gravitational lensing and galaxy clustering surveys that can be used to constrain the standard cosmological model and extensions thereof. We present forecasts from the combination of these surveys on the sensitivity to cosmological parameters including the summed neutrino mass $M_\nu$ and the effective number of relativistic species $N_{\rm eff}$ in the standard $\Lambda$CDM scenario and in a scenario with dynamical dark energy ($w_0 w_a$CDM). We compare the accuracy of different algorithms predicting the nonlinear matter power spectrum for such models. We then validate several pipelines for Fisher matrix and MCMC forecasts, using different theory codes, algorithms for numerical derivatives, and assumptions concerning the non-linear cut-off scale. The Euclid primary probes alone will reach a sensitivity of $\sigma(M_\nu)=$56meV in the $\Lambda$CDM+$M_\nu$ model, whereas the combination with CMB data from Planck is expected to achieve $\sigma(M_\nu)=$23meV and raise the evidence for a non-zero neutrino mass to at least the $2.6\sigma$ level. This can be pushed to a $4\sigma$ detection if future CMB data from LiteBIRD and CMB Stage-IV are included. In combination with Planck, Euclid will also deliver tight constraints on $\Delta N_{\rm eff}< 0.144$(95$\Lambda$CDM+$M_\nu$+$N_{\rm eff}$model, or$\Delta N_{\rm eff}< 0.063$when future CMB data are included. When floating$(w_0, w_a)$, we find that the sensitivity to$N_{\rm eff}$ remains stable, while that to $M_\nu$ degrades at most by a factor 2. This work illustrates the complementarity between the Euclid spectroscopic and imaging/photometric surveys and between Euclid and CMB constraints. Euclid will have a great potential for measuring the neutrino mass and excluding well-motivated scenarios with additional relativistic particles.

The photophysics and photochemistry associated with irradiating UV light in liquid water is central to numerous physical, chemical and biological processes. One of the key events involved in this process is the generation of the hydrated electron. Despite long study from both experimental and theoretical fronts, a unified understanding of the underlying mechanisms associated with the generation of the solvated electron have remained elusive. Here, using excited-state molecular dynamics simulations of condensed phase photoexcited liquid water, we unravel the key sequence of chemical events leading to the creation of the hydrated electron on the excited state. The process begins through the excitation of electrons localized mostly on specific topological defects in water's hydrogen network which is subsequently followed by two main reaction pathways. The first, leads to the creation of a hydrogen atom culminating in non-radiative decay back to the ground-state within 100 femtoseconds. The second involves a proton coupled electron transfer, giving rise to the formation of the hydronium ion, hydroxyl radical and the hydrated excess electron on the excited-state. This process is facilitated by ultrafast coupled rotational and translational motions of water molecules leading to the formation of water mediated ion-radical pairs in the network. These species can survive on the picosecond timescale and ultimately modulate the emission of visible photons. All in all, our findings provide fresh perspectives into the interpretation of several independent time-dependent spectroscopies measured over the last decades, paving the way for new directions on both theoretical and experimental fronts.

Cosmological birefringence is a rotation of the polarization plane of photons coming from sources of astrophysical and cosmological origin. The rotation can also depend on the energy of the photons and not only on the distance of the source and on the cosmological evolution of the underlying theoretical model. In this work, we constrain few selected models for cosmological birefringence, combining CMB and astrophysical data at radio, optical, X and gamma wavelengths, taking into account the specific energy and distance dependences.

In this work I revisit the notion of gauge invariance in thermal transport and show, in the simplest and most general possibile terms, why heat conductivity is unaffected by the specific choice of energy density. I provide the minimal and general conditions under which any two energy densities, though differing locally, lead to the same heat conductivity within the Green-Kubo framework. The relevance of gauge invariance in heat-transport simulations performed with machine-trained neural-network potentials is also briefly highlighted.

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments.

In the context of maximum-likelihood parametric component separation for next-generation full-sky CMB polarization experiments, we study the impact of fitting different spectral parameters of Galactic foregrounds in distinct subsets of pixels on the sky, with the goal of optimizing the search for primordial B modes. Using both simulations and analytical arguments, we highlight how the post-component separation uncertainty and systematic foreground residuals in the cleaned CMB power spectrum depend on spatial variations in the spectral parameters. We show that allowing spectral parameters to vary across subsets of the sky pixels is essential to achieve competitive S/N on the reconstructed CMB after component separation while keeping residual foreground bias under control. Although several strategies exist to define pixel subsets for the spectral parameters, each with its advantages and limitations, we show using current foreground simulations in the context of next-generation space-borne missions that there are satisfactory configurations in which both statistical and systematic residuals become negligible. The exact magnitude of these residuals, however, depends on the mission's specific characteristics, especially its frequency coverage and sensitivity. We also show that the post-component separation statistical uncertainty is only weakly dependent on the properties of the foregrounds and propose a semi-analytical framework to estimate it. On the contrary, the systematic foreground residuals highly depend on both the properties of the foregrounds and the chosen spatial resolution of the spectral parameters.

Non structural protein 3 (NS3) helicase from hepatitis C virus is an enzyme that unwinds and translocates along nucleic acids with an ATP-dependent mechanism and has a key role in the replication of the viral RNA. An inchworm-like mechanism for translocation has been proposed based on crystal structures and single molecule experiments. We here perform atomistic molecular dynamics in explicit solvent on the microsecond time scale of the available experimental structures. We also construct and simulate putative intermediates for the translocation process, and we perform non-equilibrium targeted simulations to estimate their relative stability. For each of the simulated structures we carefully characterize the available conformational space, the ligand binding pocket, and the RNA binding cleft. The analysis of the hydrogen bond network and of the non-equilibrium trajectories indicates an ATP-dependent stabilization of one of the protein conformers. Additionally, enthalpy calculations suggest that entropic effects might be crucial for the stabilization of the experimentally observed structures.

Active systems, or active matter, are self-driven systems which live, or function, far from equilibrium - a paradigmatic example which we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The nonequilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one which has recently been the subject of intense interest among biological and soft matter physicists is that of the so-called "motility-induced phase separation", whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions - we will briefly discuss at the end their role, which is not currently fully understood in this context.

These notes aim at providing a complete and systematic account of some foundational aspects of algebraic supergeometry, namely, the extension to the geometry of superschemes of many classical notions, techniques and results that make up the general backbone of algebraic geometry, most of them originating from Grothendieck's work. In particular, we extend to algebraic supergeometry such notions as projective and proper morphisms, finiteness of the cohomology, vector and projective bundles, cohomology base change, semicontinuity theorems, relative duality, Castelnuovo-Mumford regularity, flattening, Hilbert and Quot schemes, faithfully flat descent, quotient \'etale relations (notably, Picard schemes), among others. Some results may be found elsewhere, and, in particular, there is some overlap with a recent preprint by Moosavian and Zhou. However, many techniques and constructions are presented here for the first time, notably, a first development of Grothendieck relative duality for proper morphisms of superschemes, the construction of the Hilbert superscheme in a more general situation than the one already known (which in particular allows one to treat the case of sub-superschemes of supergrassmannians), and a rigorous construction of the Picard superscheme for a locally superprojective morphism of noetherian superschemes with geometrically integral fibres. Moreover, some of the proofs given here are new as well, even when restricted to ordinary schemes. In a final section we construct a period map from an open substack of the moduli of proper and smooth supercurves to the moduli stack of principally polarized abelian superchemes.

We study the thermal structure of the intra-cluster medium (ICM) in a set of cosmological hydrodynamical cluster simulations performed with an SPH numerical scheme employing an artificial conductivity (AC) term. We explore the effects of this term on the ICM temperature and entropy profiles, thermal distribution, velocity field and expected X-ray emission. We find that in adiabatic runs the artificial conductivity favours (i) the formation of an entropy core, raising and flattening the central entropy profiles, in better agreement with findings from Eulerian codes; and (ii) a systematic reduction of the cold gas component. In fact, the cluster large-scale structure and dynamical state are preserved across different runs, but the improved gas mixing enabled by the AC term strongly increases the stripping rate of gas from the cold clumps moving through the ICM. This in turn reduces the production of turbulence generated by the instabilities which develop because of the interaction between clumps and ambient ICM. We then find that turbulent motions, enhanced by the time-dependent artificial viscosity scheme we use, are rather damped by the AC term. The ICM synthetic X-ray emission substantially mirrors the changes in its thermo-dynamical structure, stressing the robustness of the AC impact. All these effects are softened by the introduction of radiative cooling but still present, especially a partial suppression of cold gas. Therefore, not only the physics accounted for, but also the numerical approach itself can have an impact in shaping the ICM thermo-dynamical structure and ultimately in the use of SPH cluster simulations for cosmological studies.

This paper gives a short overview of the calculation of thermal properties of materials from first principles, using the Quasi-Harmonic Approximation (QHA). We first introduce some of the thermal properties of interest and describe how they can be calculated in the framework of the QHA; then we briefly recall Density-Functional Perturbation Theory as a tool for calculating phonons from first principles, and present some codes that implement it; finally we review recent applications of first-principle QHA.

Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -- the first in a series aimed at illustrating the power of these methods in astronomical applications -- we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity $\approx 1.3 \times 10^{-4} Z_{\bigodot}$, an increase of$1.2 \times 10^{-2}$ in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.

We present a new release of the turboTDDFT code featuring an implementation of hybrid functionals, a recently introduced pseudo-Hermitian variant of the Liouville-Lanczos approach to time-dependent density-functional perturbation theory, and a newly developed Davidson-like algorithm to compute selected interior eigenvalues/vectors of the Liouvillian super-operator. Our implementation is thoroughly validated against benchmark calculations performed on the cyanin (C$_{21}$O$_{11}$H$_{21}$) molecule using the Gaussian09 and turboTDDFT 1.0 codes.

Riboswitches are structured mRNA elements that modulate gene expression. They undergo conformational changes triggered by highly specific interactions with sensed metabolites. Among the structural rearrangements engaged by riboswitches, the forming and melting of the aptamer terminal helix, the so-called P1 stem, is essential for genetic control. The structural mechanisms by which this conformational change is modulated upon ligand binding mostly remain to be elucidated. Here, we used pulling molecular dynamics simulations to study the thermodynamics of the P1 stem in the add adenine riboswitch. The P1 ligand-dependent stabilization was quantified in terms of free energy and compared with thermodynamic data. This comparison suggests a model for the aptamer folding in which direct P1-ligand interactions play a minor role on the conformational switch when compared with those related to the ligand-induced aptamer preorganization.

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several configurations, i.e. for several properly chosen values of the physical/geometrical parameters characterizing the problem. In this contribution, we propose an efficient non-intrusive data-driven framework involving ROM techniques in computational fluid dynamics (CFD) for hemodynamics applications. By starting from a database of high-fidelity solutions related to a certain values of the parameters, we apply the proper orthogonal decomposition with interpolation (PODI) and then reconstruct the variables of interest for new values of the parameters, i.e. different values from the ones included in the database. Furthermore, we present a preliminary web application through which one can run the ROM with a very user-friendly approach, without the need of having expertise in the numerical analysis and scientific computing field. The case study we have chosen to test the efficiency of our algorithm is represented by the aortic blood flow pattern in presence of a Left Ventricular Assist Device (LVAD) when varying the pump flow rate.

It is known that the spectrum of quasi-normal modes of potential barriers is related to the spectrum of bound states of the corresponding potential wells. This property has been widely used to compute black hole quasi-normal modes, but it is limited to a few "approximate" potentials with certain transformation properties for which the spectrum of bound states must be known analytically. In this work we circumvent this limitation by proposing an approach that allows one to make use of potentials with similar transformation properties, but where the spectrum of bound states can also be computed numerically. Because the numerical calculation of bound states is usually more stable than the direct computation of the corresponding quasi-normal modes, the new approach is also interesting from a technical point of view. We apply the method to different potentials, including the P\"oschl-Teller potential for which all steps can be understood analytically, as well as potentials for which we are not aware of analytic results but provide independent numerical results for comparison. As a canonical test, all potentials are chosen to match the Regge-Wheeler potential of axial perturbations of the Schwarzschild black hole. We find that the new approximate potentials are more suitable to approximate the exact quasi-normal modes than the P\"oschl-Teller potential, particularly for the first overtone. We hope this work opens new perspectives to the computation of quasi-normal modes and finds further improvements and generalizations in the future.

We present a UV spectroscopic study of ionized outflows in 21 active galactic nuclei (AGN), observed with the HST. The targets of the SUBWAYS sample were selected with the aim to probe the parameter space of the underexplored AGN between the local Seyfert galaxies and the luminous quasars at high redshifts. Our targets, spanning redshifts of 0.1-0.4 and bolometric luminosities (L_bol) of 10^45-10^46 erg/s, have been observed with a large multi-wavelength campaign. Here, we model the UV spectra and look for different types of AGN outflows. We find that 60% of our targets show a presence of outflowing H I absorption, while 40% exhibit ionized outflows seen as absorption by either C IV, N V, or O VI. This is comparable to the occurrence of ionized outflows seen in the local Seyfert galaxies. All UV absorption lines in the sample are relatively narrow, with outflow velocities reaching up to -3300 km/s. We did not detect any UV counterparts to the X-ray ultra-fast outflows (UFOs), most likely due to their being too highly ionized. However, all SUBWAYS targets with an X-ray UFO demonstrate the presence of UV outflows at lower velocities. We find significant correlations between the column density (N) of the UV ions and L_bol of the AGN, with N of H I decreasing with L_bol, while N of O VI is increasing with L_bol. This is likely to be a photoionization effect, where toward higher AGN luminosities, the wind becomes more ionized, resulting in less absorption by neutral or low-ionization ions and more absorption by high-ionization ions. In addition, we find that N of the UV ions decreases as their outflow velocity increases. This may be explained by a mechanical power that is evacuating the UV-absorbing medium. Our observed relations are consistent with multiphase AGN feeding and feedback simulations indicating that a combination of both radiative and mechanical processes are in play.