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We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by parts identities, (relative) twisted cohomology and the method of differential equations. We explicitly express the internally massive, externally conformally coupled correlator as a power series with respect to a small mass parameter, where the various terms in the series are given by multiple polylogarithms., Comment: 43 pages, 6 figures, 4 ancillary files

Ultra-light bosons, naturally appearing in well-motivated extensions to the Standard Model, can constitute all the dark matter. Models with particle mass close to the smallest phenomenologically allowed exhibit coherent field configurations at (sub)galactic scales, oscillating at a frequency corresponding to the fundamental mass of the dark matter particle. The gravitational field of these structures inherits the dark matter field's coherent oscillations, leaving an imprint on gravitational (and electromagnetic) waves sourced close to (or in) such overdensities. This happens via a heterodyning frequency modulation, which can later be decoded in a gravitational-wave detector. An analogous effect occurs in models with universal (conformal) couplings of ultra-light bosons with ordinary matter, generated by the direct interaction with the oscillating field. In this work, we explore this phenomenon in detail and assess the capability of near-future interferometers to probe ultra-light dark matter and its potential conformal couplings to matter. Using astrophysical population models, together with results from cosmological simulations, we find that the observation of gravitational waves from spinning neutron stars at the Galactic Centre with the Einstein Telescope/Cosmic Explorer would be particularly effective in constraining ultra-light dark matter., Comment: 23 pages, 10 figures

We compute the electron self-energy in Quantum Electrodynamics to three loops in terms of iterated integrals over kernels of elliptic type. We make use of the differential equations method, augmented by an $\epsilon$-factorized basis, which allows us to gain full control over the differential forms appearing in the iterated integrals to all orders in the dimensional regulator. We obtain compact analytic expressions, for which we provide generalized series expansion representations that allow us to evaluate the result numerically for all values of the electron momentum squared. As a by product, we also obtain $\epsilon$-resummed results for the self-energy in the on-shell limit $p^2 = m^2$, which we use to recompute the known three-loop renormalization constants in the on-shell scheme., Comment: 41 pages, 4 tables, 7 figures v2: typos corrected, references updated

Gravitational wave (GW) astronomy has revolutionized our capacity to explore nature. The next generation of observatories, among which the space-borne detector Laser Interferometer Space Antenna LISA, is expected to yield orders of magnitude of signal-to-noise ratio improvement, and reach fainter and novel features of General Relativity. Among them, an exciting possibility is the detection of GW memory. Interpreted as a permanent deformation of the background spacetime after a GW perturbation has passed through the detector, GW memory offers a novel avenue to proof-test General Relativity, access the non-linear nature of gravity, and provide complementary information to better characterize the GW source. Previous studies have shown that GW memory detection from individual mergers of massive black hole binaries is expected with LISA. However, these works have not simulated the proper time domain response of the detector to the GW memory. This work is filling this gap and presents the detection prospects of LISA regarding GW memory and the expected signature of GW memory on the data-streams using the most up-to-date LISA consortium simulations of the response. We focus on the GW memory of massive black hole binary mergers and use state-of-the-art population models to assess the likelihood of detecting the GW memory within the LISA lifetime. We conclude that GW memory will be a key feature of several events detected by LISA, and will help to exploit the scientific potential of the mission fully., Comment: 19 pages, 15 figures. v2 structure of document and modeling of memory signal revised, with extra clarifications. Main results and conclusions unchanged

The evidence for a non-vanishing isotropic cosmic birefringence in recent analyses of the CMB data provides a tantalizing hint for new physics. Domain wall (DW) networks have recently been shown to generate an isotropic birefringence signal in the ballpark of the measured value when coupled to photons. In this work, we explore the axionic defects hypothesis in more detail and extending previous results to annihilating and late-forming networks, and by pointing out other smoking-gun signatures of the network in the CMB spectrum such as the anisotropic birefringent spectrum and B-modes. We also argue that the presence of cosmic strings in the network does not hinder a large isotropic birefringence signal because of an intrinsic environmental contribution coming from low redshifts thus leaving open the possibility that axionic defects can explain the signal. Regarding the remaining CMB signatures, with the help of dedicated 3D numerical simulations of DW networks, that we took as a proxy for the axionic defects, we show how the anisotropic birefringence spectrum combined with a tomographic approach can be used to infer the formation and annihilation time of the network. From the numerical simulations, we also computed the spectrum of gravitational waves (GWs) generated by the network in the post-recombination epoch and use previous searches for stochastic GW backgrounds in the CMB to derive for the first time a bound on the tension and abundance of networks with DWs that annihilate after recombination. Our bounds extend to the case where the network survives until the present time and improve over previous bounds by roughly one order of magnitude. Finally, we show the interesting prospects for detecting B-modes of DW origin with future CMB experiments., Comment: 30 pages, 13 figures

We propose HydraScreen, a deep-learning approach that aims to provide a framework for more robust machine-learning-accelerated drug discovery. HydraScreen utilizes a state-of-the-art 3D convolutional neural network, designed for the effective representation of molecular structures and interactions in protein-ligand binding. We design an end-to-end pipeline for high-throughput screening and lead optimization, targeting applications in structure-based drug design. We assess our approach using established public benchmarks based on the CASF 2016 core set, achieving top-tier results in affinity and pose prediction (Pearson's r = 0.86, RMSE = 1.15, Top-1 = 0.95). Furthermore, we utilize a novel interaction profiling approach to identify potential biases in the model and dataset to boost interpretability and support the unbiased nature of our method. Finally, we showcase HydraScreen's capacity to generalize across unseen proteins and ligands, offering directions for future development of robust machine learning scoring functions. HydraScreen (accessible at https://hydrascreen.ro5.ai) provides a user-friendly GUI and a public API, facilitating easy assessment of individual protein-ligand complexes.

We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts identities (supplemented with symmetry relations) and the method of differential equations, cast in the framework of twisted co-homology. We report on calculations of correlation functions for a scalar $\lambda \phi^4$ theory and lattices of small size, both in Euclidean and Minkowskian signature., Comment: 10 pages, talk given at RADCOR 2023

We present the analytic evaluation of the second-order corrections to the massive form factors, due to two-loop vertex diagrams with a vacuum polarization insertion, with exact dependence on the external and internal fermion masses, and on the squared momentum transfer. We consider vector, axial-vector, scalar and pseudoscalar interactions between the external fermion and the external field. After renormalization, the finite expressions of the form factors are expressed in terms of polylogarithms up to weight three., Comment: 20 pages, 3 figures, 2 ancillary files. v2: results.m ancillary file updated (constants in the expression "canonicalMasters" simplified, residual logarithms in the renormalisedFormFactorsGPLS converted to GPLS), final version

We revisit the evidence for CMB birefringence in the context of a rich Axiverse. Using probability density functions (PDFs) for various axion parameters, such as the mass and axion decay constant, we construct the PDF for the cosmic birefringence angle and investigate its properties. By relating the observed value of the birefringence angle to the mean or standard deviation of the constructed PDF, we constrain the shape of the input PDFs, providing insights into the statistical distribution of the Axiverse. We focus on three different types of axion potentials: cosine, quadratic, and asymptotically linear axion monodromy. Our analysis showcases the potential of cosmic birefringence in constraining the distribution of axion parameters and uncovering possible correlations among them. We additionally offer predictions for "birefringence tomography," anticipating future measurements of birefringence from lower multipoles, and show how it can be used to rule out simpler versions of the Axiverse. Our findings contribute to the ongoing exploration of the Axiverse and its implications for cosmic birefringence., Comment: 47 pages, 17 figures; updated figures and extended discussion

We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation functions are calculated by the method of differential equations. This method can be used for Euclidean and Minkowskian signature alike. The lattice correlation functions have a power series expansion in $1/\sqrt{\lambda}$, where $\lambda$ is the coupling. We show that this series is convergent for all non-zero values of $\lambda$. At small coupling we quantify the accuracy of perturbative approximations. At the technical level we systematically investigate the interplay between twisted cohomology and the symmetries of the twist function., Comment: 31 pages, v2: version to be published

In this article we fully classify regular tubular surfaces in Euclidean, Lorentzian and hyperbolic 3-spaces whose Gaussian and mean curvatures $K$ and $H$ verify a polynomial relation. More precisely, we determine the set $S(Q)$ of all regular tubular surfaces whose curvatures verify a given polynomial relation $Q(K,H)=0$, and the set $Q(S)$ of all polynomial relations vanished by the curvatures of a given tubular surface $S$.

Besides the transient effect, the passage of a gravitational wave also causes a persistent displacement in the relative position of an interferometer's test masses through the \emph{nonlinear memory effect}. This effect is generated by the gravitational backreaction of the waves themselves, and encodes additional information about the source. In this work, we explore the implications of using this information for the parameter estimation of massive binary black holes with LISA. Based on a Fisher analysis for nonprecessing black hole binaries, our results show that the memory can help to reduce the degeneracy between the luminosity distance and the inclination for binaries observed only for a short time ($\sim$~few hours) before merger. To assess how many such short signals will be detected, we utilized state-of-the-art predictions for the population of massive black hole binaries and models for the gaps expected in the LISA data. We forecast from tens to few hundreds of binaries with observable memory, but only~$\sim \mathcal{O}(0.1)$ events in 4 years for which the memory helps to reduce the degeneracy between distance and inclination. Based on this, we conclude that the new information from the nonlinear memory, while promising for testing general relativity in the strong field regime, has probably a limited impact on further constraining the uncertainty on massive black hole binary parameters with LISA., Comment: 16 pages, comments are welcomed

We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential equations, supplemented with techniques from twisted cohomology. We derive differential equations for the variation with the coupling or -- more generally -- with the parameters of the action. Already simple examples show that the differential equation with respect to the coupling has an essential singularity at zero coupling and a regular singularity at infinite coupling. The properties of the differential equation at zero coupling can be used to prove that the perturbative series is only an asymptotic series., Comment: 6 pages, v2: version to be published

We propose a new method for the evaluation of intersection numbers for twisted meromorphic $n$-forms, through Stokes' theorem in $n$ dimensions. It is based on the solution of an $n$-th order partial differential equation and on the evaluation of multivariate residues. We also present an algebraic expression for the contribution from each multivariate residue. We illustrate our approach with a number of simple examples from mathematics and physics., Comment: 37 pages, matches published version, added ancillary files

We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose a novel, more efficient algorithm to compute Macaulay matrices, which are used to derive Pfaffian systems of differential equations. The Pfaffian matrices are then employed to obtain linear relations for ${\cal A}$-hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers., Comment: 51 page, 5 figures, matches published version

The recently reported non-zero isotropic birefringence angle in Planck 2018 polarization data provides a tantalizing hint for new physics of axions. In this paper, we explain this by a string theory motivated axion with a monodromy potential that plays the role of dark energy. Upon using the birefringence measurement and the constraint on the equation of state for dark energy in this scenario, we find an upper bound on the axion decay constant as $f_a \lesssim 10^{16}$ GeV. This naturally gives an energy scale of order GUT and can resolve the theoretical issue of super-Planckian field range of the conventional axion dark energy model. We further study the implications of cosmic birefringence for the underlying theory and its consequences for the string swampland conjectures. We finally discuss oscillatory features in the dark energy sector and the expected cosmic birefringence tomography., Comment: 18 pages, 5 figures

The structure of liquid water in the proximity of an interface can deviate significantly from that of bulk water, with surface-induced structural perturbations typically converging to bulk values at about ~1 nm from the interface. While these structural changes are well established it is, in contrast, less clear how an interface perturbs the dynamics of water molecules within the liquid. Here, through an extensive set of molecular dynamics simulations of supercooled bulk and interfacial water films and nano-droplets, we observe the formation of persistent, spatially extended dynamical domains in which the average mobility varies as a function of the distance from the interface. This is in stark contrast with the dynamical heterogeneity observed in bulk water, where these domains average out spatially over time. We also find that the dynamical response of water to an interface depends critically on the nature of the interface and on the choice of interface definition. Overall these results reveal a richness in the dynamics of interfacial water that opens up the prospect of tuning the dynamical response of water through specific modifications of the interface structure or confining material.

We present the computation of the massless three-loop ladder-box family with one external off-shell leg using the Simplified Differential Equations (SDE) approach. We also discuss the methods we used for finding a canonical differential equation for the two tennis-court families with one off-shell leg, and the application of the SDE approach on these two families., Comment: Contribution to the 15th International Symposium on Radiative Corrections (RADCOR) and the XIX Workshop on Radiative Corrections for the LHC and Future Colliders (LoopFest)