Deep learning has potential to automate screening, monitoring and grading of disease in medical images. Pretraining with contrastive learning enables models to extract robust and generalisable features from natural image datasets, facilitating label-efficient downstream image analysis. However, the direct application of conventional contrastive methods to medical datasets introduces two domain-specific issues. Firstly, several image transformations which have been shown to be crucial for effective contrastive learning do not translate from the natural image to the medical image domain. Secondly, the assumption made by conventional methods, that any two images are dissimilar, is systematically misleading in medical datasets depicting the same anatomy and disease. This is exacerbated in longitudinal image datasets that repeatedly image the same patient cohort to monitor their disease progression over time. In this paper we tackle these issues by extending conventional contrastive frameworks with a novel metadata-enhanced strategy. Our approach employs widely available patient metadata to approximate the true set of inter-image contrastive relationships. To this end we employ records for patient identity, eye position (i.e. left or right) and time series information. In experiments using two large longitudinal datasets containing 170,427 retinal OCT images of 7,912 patients with age-related macular degeneration (AMD), we evaluate the utility of using metadata to incorporate the temporal dynamics of disease progression into pretraining. Our metadata-enhanced approach outperforms both standard contrastive methods and a retinal image foundation model in five out of six image-level downstream tasks related to AMD. Due to its modularity, our method can be quickly and cost-effectively tested to establish the potential benefits of including available metadata in contrastive pretraining.

Analyzing temporal developments is crucial for the accurate prognosis of many medical conditions. Temporal changes that occur over short time scales are key to assessing the health of physiological functions, such as the cardiac cycle. Moreover, tracking longer term developments that occur over months or years in evolving processes, such as age-related macular degeneration (AMD), is essential for accurate prognosis. Despite the importance of both short and long term analysis to clinical decision making, they remain understudied in medical deep learning. State of the art methods for spatiotemporal representation learning, developed for short natural videos, prioritize the detection of temporal constants rather than temporal developments. Moreover, they do not account for varying time intervals between acquisitions, which are essential for contextualizing observed changes. To address these issues, we propose two approaches. First, we combine clip-level contrastive learning with a novel temporal embedding to adapt to irregular time series. Second, we propose masking and predicting latent frame representations of the temporal sequence. Our two approaches outperform all prior methods on temporally-dependent tasks including cardiac output estimation and three prognostic AMD tasks. Overall, this enables the automated analysis of temporal patterns which are typically overlooked in applications of deep learning to medicine.

In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbolic, Euclidean and spherical geometry) within the realm of projective geometry. Klein's work was inspired by ideas of Cayley who derived the distance between two points and the angle between two planes in terms of an arbitrary fixed conic in projective space. We comment on these two papers of Klein and we make relations with other works.

We compare Evolutionary Algorithms with Minima Hopping for global optimization in the field of cluster structure prediction. We introduce a new {\em average offspring} recombination operator and compare it with previously used operators. Minima Hopping is improved with a {\em softening} method and a stronger feedback mechanism. Test systems are atomic clusters with Lennard-Jones interaction as well as silicon and gold clusters described by force fields. The improved Minima Hopping is found to be well-suited to all these homoatomic problems. The evolutionary algorithm is more efficient for systems with compact and symmetric ground states, including LJ$_{150}$, but it fails for systems with very complex energy landscapes and asymmetric ground states, such as LJ$_{75}$ and silicon clusters with more than 30 atoms. Both successes and failures of the evolutionary algorithm suggest ways for its improvement.

Oxygen to iron abundance ratios of metal-poor stars provide information on nucleosynthesis yields from massive stars which end in Type II supernova explosions. Using a standard model of chemical evolution of the Galaxy we have reproduced the solar neighborhood abundance data and estimated the oxygen and iron yields of genuine SN II origin. The estimated yields are compared with the theoretical yields to derive the relation between the lower and upper mass limits in each generation of stars and the IMF slope. Independently of this relation, we furthermore derive the relation between the lower mass limit and the IMF slope from the stellar mass to light ratio in the solar neighborhood. These independent relations unambiguously determine the upper mass limit of $m_u=50 \pm 10 M_sun$ and the IMF slope index of 1.3 - 1.6 above 1 M_sun. This upper mass limit corresponds to the mass beyond which stars end as black holes without ejecting processed matter into the interstellar medium. We also find that the IMF slope index below 0.5 M_sun cannot be much shallower than 0.8.

Hydrodynamical instabilities and shocks are ubiquitous in astrophysical scenarios. Therefore, an accurate numerical simulation of these phenomena is mandatory to correctly model and understand many astrophysical events, such as Supernovas, stellar collisions, or planetary formation. In this work, we attempt to address many of the problems that the smoothed particle hydrodynamics (SPH) technique has when dealing with subsonic hydrodynamical instabilities or shocks. To that aim we built a new SPH code named SPHYNX, that includes many of the recent advances in the SPH technique and some other new ones, which we present here. SPHYNX is of Newtonian type and grounded in the Euler-Lagrange formulation of the SPH technique. Its distinctive features are: the use of an integral approach to estimating the gradients; the use of a flexible family of interpolators called sinc kernels, which suppress pairing instability; and the incorporation of a new type of volume element which provides a better partition of the unity. Unlike other modern formulations, which consider volume elements linked to pressure, our volume element choice relies on density. SPHYNX conserves mass, linear and angular momentum, energy, entropy, and preserves kernel normalization even in strong shocks. The coupling between the integral approach to calculate gradients and the new family of volume elements reduces the so-called tensile instability. Both features help to suppress the damp which often prevents the growth of hydrodynamic instabilities in regular SPH codes. On the whole, SPHYNX has passed the verification tests described below. For identical particle setting and initial conditions the results were similar (or better in some particular cases) than those obtained with other SPH schemes such as GADGET-2, PSPH or with the recent density-independent formulation (DISPH) and conservative reproducing kernel (CRKSPH) techniques.

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of DFT calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the contracted basis functions for closely related environments, e.g. in geometry optimizations or combined calculations of neutral and charged systems.

We demonstrate a quantum key distribution (QKD) testbed for room temperature single photon sources based on defect centres in diamond. A BB84 protocol over a short free-space transmission line is implemented. The performance of nitrogen-vacancy (NV) as well as silicon-vacancy defect (SiV) centres is evaluated and an extrapolation for next-generation sources with enhanced efficiency is discussed.

Intrinsic ripples in freestanding graphene have been exceedingly difficult to study. Individual ripple geometry was recently imaged using scanning tunneling microscopy, but these measurements are limited to static configurations. Thermally-activated flexural phonon modes should generate dynamic changes in curvature. Here we show how to track the vertical movement of a one-square-angstrom region of freestanding graphene using scanning tunneling microscopy, thereby allowing measurement of the out-of-plane time trajectory and fluctuations over long time periods. We also present a model from elasticity theory to explain the very-low-frequency oscillations. Unexpectedly, we sometimes detect a sudden colossal jump, which we interpret as due to mirror buckling. This innovative technique provides a much needed atomic-scale probe for the time-dependent behavior of intrinsic ripples. The discovery of this novel progenitor represents a fundamental advance in the use of scanning tunneling microscopy, which together with the application of a thermal load provides a low-frequency nano-resonator.

We demonstrate the controlled preparation of heteroepitaxial diamond nano- and microstructures on silicon wafer based iridium films as hosts for single color centers. Our approach uses electron beam lithography followed by reactive ion etching to pattern the carbon layer formed by bias enhanced nucleation on the iridium surface. In the subsequent chemical vapor deposition process, the patterned areas evolve into regular arrays of (001) oriented diamond nano-islands with diameters of <500nm and a height of approx. 60 nm. In the islands, we identify single SiV color centers with narrow zero phonon lines down to 1 nm at room temperature.

Based on an analysis of the short range chemical environment of each atom in a system, standard machine learning based approaches to the construction of interatomic potentials aim at determining directly the central quantity which is the total energy. This prevents for instance an accurate description of the energetics of systems where long range charge transfer is important as well as of ionized systems. We propose therefore not to target directly with machine learning methods the total energy but an intermediate physical quantity namely the charge density, which then in turn allows to determine the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chemical accuracy, i.e. errors of less than a milli Hartree per atom compared to the reference density functional results. The introduction of physically motivated quantities which are determined by the short range atomic environment via a neural network leads also to an increased stability of the machine learning process and transferability of the potential.

Let $m\ge 2$ be an integer. For any open domain $\Omega\subset\mathbb{R}^{2m}$, non-positive function $\varphi\in C^\infty(\Omega)$such that$\Delta^m \varphi\equiv 0$, and bounded sequence $(V_k)\subset L^\infty(\Omega)$ we prove the existence of a sequence of functions $(u_k)\subset C^{2m-1}(\Omega)$ solving the Liouville equation of order $2m$ $$(-\Delta)^m u_k = V_ke^{2mu_k}\quad \text{in }\Omega, \quad \limsup_{k\to\infty} \int_\Omega e^{2mu_k}dx<\infty,$$ and blowing up exactly on the set $S_{\varphi}:=\{x\in \Omega:\varphi(x)=0\}$, i.e. $$\lim_{k\to\infty} u_k(x)=+\infty \text{ for }x\in S_{\varphi} \text{ and }\lim_{k\to\infty} u_k(x)=-\infty \text{ for }x\in \Omega\setminus S_{\varphi},$$ thus showing that a result of Adimurthi, Robert and Struwe is sharp. We extend this result to the boundary of $\Omega$ and to the case $\Omega=\mathbb{R}^{2m}$. Several related problems remain open.

We review the recent results [45, 46] concerning the semiclassical limit from the Hartree dynamics to the Vlasov equation with singular potentials and extend them to the case of more general radial interactions. We prove that, at positive temperature, the Hartree dynamics converges in trace norm to the Vlasov one, for a particular class of initial states.

We show that strongly interacting multicomponent gases in one dimension realize an effective spin chain, offering an alternative simple scenario for the study of one-dimensional quantum magnetism in cold gases in the absence of an optical lattice. The spin-chain model allows for an intuitive understanding of recent experiments and for a simple calculation of relevant observables. We analyze the adiabatic preparation of antiferromagnetic and ferromagnetic ground states, and show that many-body spin states may be efficiently probed in tunneling experiments. The spin-chain model is valid for more than two components, opening the possibility of realizing SU(N) quantum magnetism in strongly interacting one-dimensional alkaline-earth-metal or ytterbium Fermi gases.

We study the world data on elastic electron-proton scattering in order to determine the proton charge rms-radius. After accounting for the Coulomb distortion and using a parameterization that allows to deal properly with the higher moments we find a radius of 0.895+-0.018 fm, which is significantly larger than the radii used in the past.

We study the formation of molecular precursors to dust in the ejecta of Population III supernovae using a chemical kinetic approach. Our work focuses on zero-metallicity 20 Msun and 170 Msun progenitors, and we consider fully-macroscopically mixed and unmixed ejecta. The nucleation stage for small silica, metal oxides and sulphides, pure metal, and carbon clusters is described with a new chemical reaction network. We consider the effect of the pressure dependence of critical nucleation rates, and test the impact of microscopically-mixed He+ on carbon dust formation. The unmixed ejecta of a 170 Msun progenitor supernova synthesizes ~ 5.6 Msun of small clusters, while its 20 Msun counterpart produces ~ 0.103 Msun. Our results point to smaller amounts of dust formed in the ejecta of Pop. III supernovae by a factor ~ 5 compared to values derived by previous studies, and to different dust chemical composition. Such deviations result from some erroneous assumptions made, the inappropriate use of classical nucleation theory to model dust formation, and the omission of the synthethis of molecules in supernova ejecta. Unmixed ejecta of massive Pop. III supernovae chiefly form silica and/or silicates, and pure silicon grains whereas their lower mass counterparts form a dust mixture dominated by silica and/or silicates, pure silicon and iron sulphides. Amorphous carbon can only condense in ejecta where the carbon-rich zone is deprived of He+. The first dust enrichment to the primordial gas in the early universe from Pop. III massive supernova comprises primarily pure silicon, silica and silicates. If carbon dust is present at redshift z> 6, alternative dust sources must be considered.

Recent experiments on mesoscopic normal-metal--superconductor heterostructures resolve properties on length scales and at low temperatures such that the temperature is below the Thouless energy $k_B T \le E_{Th}$. We describe the properties of these systems within the framework of quasiclassical many-body techniques. Diffusive and ballistic systems are covered, both in equilibrium and nonequilibrium situations. Thereby we demonstrate the common physical basis of various subtopics.

This review concentrates on the two principle methods used to evolve nuclear abundances within astrophysical simulations, evolution via rate equations and via equilibria. Because in general the rate equations in nucleosynthetic applications form an extraordinarily stiff system, implicit methods have proven mandatory, leading to the need to solve moderately sized matrix equations. Efforts to improve the performance of such rate equation methods are focused on efficient solution of these matrix equations, by making best use of the sparseness of these matrices. Recent work to produce hybrid schemes which use local equilibria to reduce the computational cost of the rate equations is also discussed. Such schemes offer significant improvements in the speed of reaction networks and are accurate under circumstances where calculations with complete equilibrium fail.

The astrophysical nature of r-process sites is a long standing mystery and many probable sources have been suggested in the past, among them lower-mass core-collapse supernovae (in the range 8 - 10 Msol), higher-mass core-collapse supernovae (with masses > 20 Msol) and neutron star mergers. In this work, we present a detailed inhomogeneous chemical evolution study that considers for the first time neutron star mergers as major r-process sources, and compare this scenario to the ones in which core-collapse supernovae act as dominant r-process sites. We conclude that, due to the lack of reliable iron and r-process yields as function of progenitor mass, it is not possible at present to distinguish between the lower-mass and higher-mass supernovae scenarios within the framework of inhomogeneous chemical evolution. However, neutron-star mergers seem to be ruled out as the dominant r-process source, since their low rates of occurrence would lead to r-process enrichment that is not consistent with observations at very low metallicities. Additionally, the considerable injection of r-process material by a single neutron-star merger leads to a scatter in [r-process/Fe] ratios at later times which is much too large compared to observations.

We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the widely used EOS of H. Shen et al. and Lattimer & Swesty. The systematic comparison shows that the model description of inhomogeneous nuclear matter is as important as the parameterization of the nuclear interactions for the supernova dynamics and the neutrino signal. Furthermore, several new aspects of nuclear physics are investigated: the HS EOS contains distributions of nuclei, including nuclear shell effects. The appearance of light nuclei, e.g., deuterium and tritium is also explored, which can become as abundant as alphas and free protons. In addition, we investigate the black hole formation in failed core-collapse supernovae, which is mainly determined by the high-density EOS. We find that temperature effects lead to a systematically faster collapse for the non-relativistic LS EOS in comparison to the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows to determine the maximum mass of proto-neutron stars, if the neutrino signal from such a failed supernova would be measured in the future. This would give a constraint for the nuclear EOS at finite entropy, complementary to observations of cold neutron stars.