We consider a lattice model of Twisted Bilayer Graphene (TBG). The presence of incommensurate angles produces an emerging quasi-periodicity manifesting itself in large momenta Umklapp interactions that almost connect the Dirac points. We rigorously establish the stability of the semimetallic phase via a Renormalization Group analysis combined with number theoretical properties of irrationals, similar to the ones used in Kolmogorov-Arnold-Moser (KAM) theory for the stability of invariant tori. The interlayer hopping is weak and short ranged and the angles are chosen in a large measure set. The result provides a justification, in the above regime, to the effective continuum description of TBG in which large momenta interlayer interactions are neglected.

We investigate uncertainties in the estimation of the Hubble constant ($H_0$) arising from Gaussian Process (GP) reconstruction, demonstrating that the choice of kernel introduces systematic variations comparable to those arising from different cosmological models. To address this limitation, we introduce the Generalized Gaussian Process (Gen GP) framework, in which the Matérn smoothness parameter $\nu$ is treated as a free parameter, allowing for data-driven kernel optimization. Using the cosmic chronometer Hubble data, we find that while standard GP with $\Lambda$CDM mean function exhibits noticeable reconstruction differences between optimized and marginalized approaches, particularly at $z > 1$, Gen GP maintains methodological consistency. In Gen GP, slight increases in $\chi^2$ per degree of freedom relative to standard GP, for both the zero-mean and $\Lambda$CDM prior mean cases, reflect added flexibility rather than performance degradation. Our results emphasize that robust cosmological inference requires treating kernel parameters as free variables and implementing full Bayesian marginalization to avoid artificial precision from fixed hyperparameters. As machine learning becomes central to cosmological discovery, the Gen GP framework provides a principled approach to model-independent inference that properly accounts for methodological uncertainties while maintaining necessary flexibility for reliable parameter estimation.

We apply the general framework of multiple dispersive bounds, firstly discussed in the companion paper [1], to the study of sub-threshold branch-cuts. We propose the simultaneous application of a double dispersive bound as a proper way to take into account unitarity constraints within phenomenological analyses of hadronic form factors in the presence of sub-threshold branch-cuts. Accordingly, the standard $z$-expansion of hadronic form factors, commonly referred to as the Boyd-Grinstein-Lebed approach [2-5], is modified by including simultaneously the dispersive bounds related to the pair-production and to the sub-threshold regions. For the latter one the effects of above-threshold poles are described through a new resonance model and the possible choices of the outer function outside the pair-production region are discussed. A detailed numerical analysis of the experimental data or lattice QCD results in the spacelike region for the charged kaon form factor is presented as a direct application of the procedure of double dispersive bound. The comparison with other methodologies present in literature and with the $z$-expansion based on the single, total dispersive bound clearly shows that the $z$-expansion including the double dispersive bound provides the most precise extrapolation at large momentum transfer as well as the most stable results with respect to the choice of the outer function outside the pair-production region.

The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic Fourier transform seems to be an promising tool.

In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The two sets are apparently unrelated since of interest to independent parties, however they both account for (aspects of) the same world. We consider the case in which the agent is a reinforcement learning agent on the first set of features, while the restraining bolt is specified logically using linear time logic on finite traces LTLf/LDLf over the second set of features. We show formally, and illustrate with examples, that, under general circumstances, the agent can learn while shaping its goals to suitably conform (as much as possible) to the restraining bolt specifications.

In this paper we study the perturbations of the charged, dilaton black hole, described by the solution of the low energy limit of the superstring action found by Garfinkle, Horowitz and Strominger. We compute the complex frequencies of the quasi-normal modes of this black hole, and compare the results with those obtained for a Reissner-Nordström and a Schwarzschild black hole. The most remarkable feature which emerges from this study is that the presence of the dilaton breaks the \emph{isospectrality} of axial and polar perturbations, which characterizes both Schwarzschild and Reissner-Nordström black holes.

We study e+e- --> pi+pi-h_c at center-of-mass energies from 3.90 GeV to 4.42 GeV using data samples collected with the BESIII detector operating at the Beijing Electron Positron Collider. The Born cross sections are measured at 13 energies, and are found to be of the same order of magnitude as those of e+e- --> pi+pi-J/psi but with a different line shape. In the \pi^\pm h_c mass spectrum, a distinct structure, referred to as Z_c(4020), is observed at 4.02 GeV/c^2. The Z_c(4020) carries an electric charge and couples to charmonium. A fit to the \pi^\pm h_c invariant mass spectrum, neglecting possible interferences, results in a mass of (4022.9\pm 0.8\pm 2.7) MeV/c^2 and a width of (7.9\pm 2.7\pm 2.6) MeV for the Z_c(4020), where the first errors are statistical and the second systematic. No significant Z_c(3900) signal is observed, and upper limits on the Z_c(3900) production cross sections in \pi^\pm h_c at center-of-mass energies of 4.23 and 4.26 GeV are set.

We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power-law degreedistribution. Application of mean-field theory yields as main prediction that for symmetric disordered initial conditions the mean time to reach full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate to describe this problem.

The second Gravitational-Wave Transient Catalog reported on 39 compact binary coalescences observed by the Advanced LIGO and Advanced Virgo detectors between 1 April 2019 15:00 UTC and 1 October 2019 15:00 UTC. We present GWTC-2.1, which reports on a deeper list of candidate events observed over the same period. We analyze the final version of the strain data over this period with improved calibration and better subtraction of excess noise, which has been publicly released. We employ three matched-filter search pipelines for candidate identification, and estimate the astrophysical probability for each candidate event. While GWTC-2 used a false alarm rate threshold of 2 per year, we include in GWTC-2.1, 1201 candidates that pass a false alarm rate threshold of 2 per day. We calculate the source properties of a subset of 44 high-significance candidates that have an astrophysical probability greater than 0.5. Of these candidates, 36 have been reported in GWTC-2. If the 8 additional high-significance candidates presented here are astrophysical, the mass range of events that are unambiguously identified as binary black holes (both objects $\geq 3M_\odot$) is increased compared to GWTC-2, with total masses from $\sim 14 M_\odot$for GW190924_021846 to$\sim 182 M_\odot$ for GW190426_190642. The primary components of two new candidate events (GW190403_051519 and GW190426_190642) fall in the mass gap predicted by pair instability supernova theory. We also expand the population of binaries with significantly asymmetric mass ratios reported in GWTC-2 by an additional two events (the mass ratio is less than $0.65$ and $0.44$ at $90\%$ probability for GW190403_051519 and GW190917_114630 respectively), and find that 2 of the 8 new events have effective inspiral spins \chi_\mathrm{eff} > 0 (at $90\%$ credibility), while no binary is consistent with \chi_\mathrm{eff} < 0 at the same significance.

The Ashkin-Teller (AT) model is a generalization of Ising 2-d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four-spin interaction. It was conjectured long ago (by Kadanoff and Wegner, Wu and Lin, Baxter and others) that AT has in general two critical points, and that universality holds, in the sense that the critical exponents are the same as in the Ising model, except when the couplings of the two Ising layers are equal (isotropic case). We obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points. We find the somewhat unexpected feature that, despite universality holds for the specific heat, nevertheless nonuniversal critical indexes appear: for instance the distance between the critical points rescales with an anomalous exponent as we let the couplings of the two Ising layers coincide (isotropic limit); and so does the constant in front of the logarithm in the specific heat. Our result also explains how the crossover from universal to nonuniversal behaviour is realized.

Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed towards finding quantum algorithms that may provide a quantum advantage for this task, exploiting architectures that will become available in the near future. In this work we introduce a novel near-term quantum algorithm for computing one-particle Green's functions via their Lehmann representation. The method is based on a generalization of the quantum equation of motion algorithm that gives access to the charged excitations of the system. We demonstrate the validity of the present proposal by computing the Green's function of a two-site Fermi-Hubbard model on a IBM quantum processor.

We report on an improved measurement of the Cabibbo-Kobayashi-Maskawa {\it CP}-violating phase $\gamma$ through a Dalitz plot analysis of neutral $D$ meson decays to $K_S^0 \pi^+ \pi^-$ and $K_S^0 K^+ K^-$ in the processes $B^\mp \to D K^\mp$, $B^\mp \to D^* K^\mp$ with $D^* \to D\pi^0,D\gamma$, and $B^\mp \to D K^{*\mp}$ with $K^{*\mp} \to K_S^0 \pi^\mp$. Using a sample of 383 million $B\bar{B}$ pairs collected by the BABAR detector, we measure $\gamma=(76 \pm 22 \pm 5 \pm 5)^\circ$ (mod $180^\circ$), where the first error is statistical, the second is the experimental systematic uncertainty and the third reflects the uncertainty on the description of the Dalitz plot distributions. The corresponding two standard deviation region is 29^\circ < \gamma < 122^\circ. This result has a significance of direct {\it CP} violation ($\gamma \ne 0$) of 3.0 standard deviations.

We present the particle method for simulating the solution to the path-dependent McKean-Vlasov equation, in which both the drift and the diffusion coefficients depend on the whole trajectory of the process up to the current time t, as well as on the corresponding marginal distributions. Our paper establishes an explicit convergence rate for this numerical approach. We illustrate our findings with numerical simulations of a modified Ornstein-Uhlenbeck process with memory, and of an extension of the Jansen-Rit mean-field model for neural mass.

This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD student to deformations of compact complex manifolds, from the very beginning to some recent (i.e. at that time not yet published) results. The goal of these lectures is to give a soft introduction to extended deformation theory. In view of the aim (and the hope) of keeping this paper selfcontained, user friendly and with a tolerating number of pages, we consider only deformations of compact complex manifolds. Anyhow, most part of the formalism and of the results that we prove here will apply to many other deformation problems.

Coupled cosmologies can predict values for the cosmological parameters at low redshifts which may differ substantially from the parameters values within non-interacting cosmologies. Therefore, low redshift probes, as the growth of structure and the dark matter distribution via galaxy and weak lensing surveys constitute a unique tool to constrain interacting dark sector models. We focus here on weak lensing forecasts from future Euclid and LSST-like surveys combined with the ongoing Planck cosmic microwave background experiment. We find that these future data could constrain the dimensionless coupling to be smaller than a few $\times 10^{-2}$. The coupling parameter $\xi$ is strongly degenerate with the cold dark matter energy density $\Omega_{c}h^2$ and the Hubble constant $H_0$.These degeneracies may cause important biases in the cosmological parameter values if in the universe there exists an interaction among the dark matter and dark energy sectors.

We combine recent measurements of Cosmic Microwave Background Anisotropies, Supernovae luminosity distances and Baryonic Acoustic Oscillations to derive constraints on the dark energy equation of state w in the redshift range 0

We introduce a class of composite axion models that provide a natural solution to the strong CP problem, and possibly account for the observed dark matter abundance. The QCD axion arises as a composite Nambu-Goldstone boson (NGB) from the dynamics of a chiral gauge theory with a strongly-interacting and confining SU(N) factor and a weakly-interacting U(1), with no fundamental scalar fields. The Peccei-Quinn (PQ) symmetry is accidental and all the mass scales are generated dynamically. We analyze specific models where the PQ symmetry is broken only by operators of dimension 12 or higher. We also classify several other models where the PQ symmetry can be potentially protected up to the dimension 15 or 18 level. Our framework can be easily extended to a scenario where the Standard Model (SM) is unified into a simple gauge group, and we discuss the case of non-supersymmetric SU(5) unification. The GUT models predict the existence of additional pseudo NGBs, parametrically lighter than the GUT and PQ scales, which could have an impact on the cosmological evolution and leave observable signatures. We also clarify the selection rules under which higher-dimensional PQ-violating operators can generate a potential for the axion in the IR, and provide a discussion of the discrete symmetries in composite axion models associated to the number of domain walls. These results can be of general interest for composite axion models based on a QCD-like confining gauge group.

We propose the implementation of two novel ingredients in the standard $z$-expansion of hadronic form factors, commonly referred to as the Boyd-Grinstein-Lebed (BGL) approach [1-4]. The first new ingredient is the explicit addition of a unitarity filter applied to a given known set of input data for the hadronic form factors. This further constraint is not usually taken into account in the phenomenological applications of the BGL $z$-expansion. We show that it brings to a formulation of the BGL approach fully equivalent to the Dispersion Matrix (DM) method [5], which describes hadronic form factors in a completely model-independent and non-perturbative way. The second key ingredient is represented by the introduction of suitable kernel functions in the evaluation of unitarity bounds, leading to the application of multiple dispersive bounds to hadronic form factors, whenever data and/or (non-)perturbative techniques allow to do so. This idea may be useful for the investigation of many physical processes, from the analysis of the electromagnetic form factors of mesons and baryons to the study of weak semileptonic decays of hadrons. An explicit numerical application will be presented in the companion paper [6], where the effects of sub-threshold branch-cuts are analyzed.