The ESA Euclid mission will measure the photometric redshifts of billions of galaxies in order to provide an accurate 3D view of the Universe at optical and near-infrared wavelengths. Photometric redshifts are determined by the PHZ processing function on the basis of the multi-wavelength photometry of Euclid and ground-based observations. In this paper, we describe the PHZ processing used for the Euclid Quick Data Release, the output products, and their validation. The PHZ pipeline is responsible for the following main tasks: source classification into star, galaxy, and QSO classes based on photometric colours; determination of photometric redshifts and of physical properties of galaxies. The classification is able to provide a star sample with a high level of purity, a highly complete galaxy sample, and reliable probabilities of belonging to those classes. The identification of QSOs is more problematic: photometric information seems to be insufficient to accurately separate QSOs from galaxies. The performance of the pipeline in the determination of photometric redshifts has been tested using the COSMOS2020 catalogue and a large sample of spectroscopic redshifts. The results are in line with expectations: the precision of the estimates are compatible with Euclid requirements, while, as expected, a bias correction is needed to achieve the accuracy level required for the cosmological probes. Finally, the pipeline provides reliable estimates of the physical properties of galaxies, in good agreement with findings from the COSMOS2020 catalogue, except for an unrealistically large fraction of very young galaxies with very high specific star-formation rates. The application of appropriate priors is, however, sufficient to obtain reliable physical properties for those problematic objects. We present several areas for improvement for future Euclid data releases.

PromptSource is a system for creating, sharing, and using natural language prompts. Prompts are functions that map an example from a dataset to a natural language input and target output. Using prompts to train and query language models is an emerging area in NLP that requires new tools that let users develop and refine these prompts collaboratively. PromptSource addresses the emergent challenges in this new setting with (1) a templating language for defining data-linked prompts, (2) an interface that lets users quickly iterate on prompt development by observing outputs of their prompts on many examples, and (3) a community-driven set of guidelines for contributing new prompts to a common pool. Over 2,000 prompts for roughly 170 datasets are already available in PromptSource. PromptSource is available at this https URL.

Large language models (LLMs) are increasingly being integrated into software engineering (SE) research and practice, yet their non-determinism, opaque training data, and evolving architectures complicate the reproduction and replication of empirical studies. We present a community effort to scope this space, introducing a taxonomy of LLM-based study types together with eight guidelines for designing and reporting empirical studies involving LLMs. The guidelines present essential (must) criteria as well as desired (should) criteria and target transparency throughout the research process. Our recommendations, contextualized by our study types, are: (1) to declare LLM usage and role; (2) to report model versions, configurations, and fine-tuning; (3) to document tool architectures; (4) to disclose prompts and interaction logs; (5) to use human validation; (6) to employ an open LLM as a baseline; (7) to use suitable baselines, benchmarks, and metrics; and (8) to openly articulate limitations and mitigations. Our goal is to enable reproducibility and replicability despite LLM-specific barriers to open science. We maintain the study types and guidelines online as a living resource for the community to use and shape (this http URL).

The star-forming main sequence (SFMS) is a tight relation observed between stellar masses and star formation rates (SFR) in a population of galaxies. This relation is observed at different redshifts, in various morphological, and environmental domains, and is key to understanding the underlying relations between a galaxy budget of cold gas and its stellar content. Euclid Quick Data Release 1 (Q1) gives us the opportunity to investigate this fundamental relation in galaxy formation and evolution. We complement the Euclid release with public IRAC observations of the Euclid Deep Fields, improving the quality of recovered photometric redshifts, stellar masses, and SFRs, as is shown both with simulations and a comparison with available spectroscopic redshifts. From Q1 data alone, we recover more than $\sim 30\,\mathrm{k}$ galaxies with $\log_{10} (M_\ast/M_\odot) > 11$, giving a precise constraint of the SFMS at the high-mass end. We investigated the SFMS, in a redshift interval between $0.2$ and $3.0$, comparing our results with the existing literature and fitting them with a parameterisation taking into account the presence of a bending of the relation at the high-mass end, depending on the bending mass, $M_0$. We find good agreement with previous results in terms of $M_0$ values, and an increasing trend for the relation scatter at higher stellar masses. We also investigate the distribution of physical (e.g. dust absorption, $A_V$, and formation age) and morphological properties (e.g., Sérsic index and radius) in the SFR--stellar mass plane, and their relation with the SFMS. These results highlight the potential of Euclid in studying the fundamental scaling relations that regulate galaxy formation and evolution in anticipation of the forthcoming Data Release 1.

Theories with radiative symmetry breaking (RSB) lead to first-order phase transitions and the production of gravitational waves as well as primordial black holes if the supercooling period lasted long enough. Here we explain how to efficiently reheat the universe after such period in the above-mentioned class of theories. Two cases are possible, depending on whether the RSB scale is much larger than the electroweak (EW) symmetry breaking scale or not. When it is, the dominant reheating mechanism can be the decays of the field responsible for RSB in the Standard Model (SM) sector. We point out that in a similar way dark matter (DM) can be produced and we analyze in some detail the case of a sterile-neutrino, finding that the full DM abundance is reproduced when this particle is at the $10^2$ MeV scale in a well-motivated SM completion. When the RSB scale is not much larger than the EW symmetry breaking scale, we find that efficient reheating always occurs when the energy density of the false vacuum is first entirely transferred to a dark photon and then to SM fermions via dark-photon decays.

A new version of the Teukolksy Master Equation, describing any massless field of different spin $s=1/2,1,3/2,2$ in the Kerr black hole, is presented here in the form of a wave equation containing additional curvature terms. These results suggest a relation between curvature perturbation theory in general relativity and the exact wave equations satisfied by the Weyl and the Maxwell tensors, known in the literature as the de Rham-Lichnerowicz Laplacian equations. We discuss these Laplacians both in the Newman-Penrose formalism and in the Geroch-Held-Penrose variant for an arbitrary vacuum spacetime. Perturbative expansion of these wave equations results in a recursive scheme valid for higher orders. This approach, apart from the obvious implications for the gravitational and electromagnetic wave propagation on a curved spacetime, explains and extends the results in the literature for perturbative analysis by clarifying their true origins in the exact theory.

Euclid will cover over 14000 $deg^{2}$ with two optical and near-infrared spectro-photometric instruments, and is expected to detect around ten million active galactic nuclei (AGN). This unique data set will make a considerable impact on our understanding of galaxy evolution and AGN. In this work we identify the best colour selection criteria for AGN, based only on Euclid photometry or including ancillary photometric observations, such as the data that will be available with the Rubin legacy survey of space and time (LSST) and observations already available from Spitzer/IRAC. The analysis is performed for unobscured AGN, obscured AGN, and composite (AGN and star-forming) objects. We make use of the spectro-photometric realisations of infrared-selected targets at all-z (SPRITZ) to create mock catalogues mimicking both the Euclid Wide Survey (EWS) and the Euclid Deep Survey (EDS). Using these catalogues we estimate the best colour selection, maximising the harmonic mean (F1) of completeness and purity. The selection of unobscured AGN in both Euclid surveys is possible with Euclid photometry alone with F1=0.22-0.23, which can increase to F1=0.43-0.38 if we limit at z>0.7. Such selection is improved once the Rubin/LSST filters (a combination of the u, g, r, or z filters) are considered, reaching F1=0.84 and 0.86 for the EDS and EWS, respectively. The combination of a Euclid colour with the [3.6]-[4.5] colour, which is possible only in the EDS, results in an F1-score of 0.59, improving the results using only Euclid filters, but worse than the selection combining Euclid and LSST. The selection of composite ($f_{\rm AGN}$=0.05-0.65 at 8-40 $\mu m$) and obscured AGN is challenging, with F1<0.3 even when including ancillary data. This is driven by the similarities between the broad-band spectral energy distribution of these AGN and star-forming galaxies in the wavelength range 0.3-5 $\mu m$.

Differences in forgery attributes of images generated in CNN-synthesized and image-editing domains are large, and such differences make a unified image forgery detection and localization (IFDL) challenging. To this end, we present a hierarchical fine-grained formulation for IFDL representation learning. Specifically, we first represent forgery attributes of a manipulated image with multiple labels at different levels. Then, we perform fine-grained classification at these levels using the hierarchical dependency between them. As a result, the algorithm is encouraged to learn both comprehensive features and the inherent hierarchical nature of different forgery attributes. In this work, we propose a Language-guided Hierarchical Fine-grained IFDL, denoted as HiFi-Net++. Specifically, HiFi-Net++ contains four components: a multi-branch feature extractor, a language-guided forgery localization enhancer, as well as classification and localization modules. Each branch of the multi-branch feature extractor learns to classify forgery attributes at one level, while localization and classification modules segment pixel-level forgery regions and detect image-level forgery, respectively. Also, the language-guided forgery localization enhancer (LFLE), containing image and text encoders learned by contrastive language-image pre-training (CLIP), is used to further enrich the IFDL representation. LFLE takes specifically designed texts and the given image as multi-modal inputs and then generates the visual embedding and manipulation score maps, which are used to further improve HiFi-Net++ manipulation localization performance. Lastly, we construct a hierarchical fine-grained dataset to facilitate our study. We demonstrate the effectiveness of our method on $8$ by using different benchmarks for both tasks of IFDL and forgery attribute classification. Our source code and dataset are available.

The Atacama Cosmology Telescope (ATC) has recently released new measurements and constraints on inflationary observables. In this paper it is shown that a component of a dynamical affine connection, which is independent of the metric, can easily drive inflation in agreement with these observations. Such geometrical explanation of inflation is analysed in detail here in the minimal model, including the predictions for the scalar spectral index $n_s$ and its running $\alpha_s$, the amplitude of the scalar perturbations and the tensor-to-scalar ratio $r$. Furthermore, this minimal model is shown to provide an inflationary attractor: arbitrary initial values of the kinetic energy density are dynamically attracted down to negligible values compared to the potential energy density in homogeneous and isotropic metrics. The role of the Higgs boson during and after inflation is also briefly discussed.

The Near-Infrared Spectrometer and Photometer (NISP) on board the Euclid satellite provides multiband photometry and R>=450 slitless grism spectroscopy in the 950-2020nm wavelength range. In this reference article we illuminate the background of NISP's functional and calibration requirements, describe the instrument's integral components, and provide all its key properties. We also sketch the processes needed to understand how NISP operates and is calibrated, and its technical potentials and limitations. Links to articles providing more details and technical background are included. NISP's 16 HAWAII-2RG (H2RG) detectors with a plate scale of 0.3" pix^-1 deliver a field-of-view of 0.57deg^2. In photo mode, NISP reaches a limiting magnitude of ~24.5AB mag in three photometric exposures of about 100s exposure time, for point sources and with a signal-to-noise ratio (SNR) of 5. For spectroscopy, NISP's point-source sensitivity is a SNR = 3.5 detection of an emission line with flux ~2x10^-16erg/s/cm^2 integrated over two resolution elements of 13.4A, in 3x560s grism exposures at 1.6 mu (redshifted Ha). Our calibration includes on-ground and in-flight characterisation and monitoring of detector baseline, dark current, non-linearity, and sensitivity, to guarantee a relative photometric accuracy of better than 1.5%, and relative spectrophotometry to better than 0.7%. The wavelength calibration must be better than 5A. NISP is the state-of-the-art instrument in the NIR for all science beyond small areas available from HST and JWST - and an enormous advance due to its combination of field size and high throughput of telescope and instrument. During Euclid's 6-year survey covering 14000 deg^2 of extragalactic sky, NISP will be the backbone for determining distances of more than a billion galaxies. Its NIR data will become a rich reference imaging and spectroscopy data set for the coming decades.

An explicit realistic model featuring a supercooled phase transition, which allows us to explain the background of gravitational waves recently detected by pulsar timing arrays, is constructed. In this model the phase transition corresponds to radiative symmetry breaking (and mass generation) in a dark sector featuring a dark photon associated with the broken symmetry. The completion of the transition is ensured by a non-minimal coupling between gravity and the order parameter and fast reheating occurs thanks to a preheating phase. Finally, it is also shown that the model leads to primordial black hole production.

Extensions of the Standard Model and general relativity featuring a UV fixed point can leave observable implications at accessible energies. Although mass parameters such as the Planck scale can appear through dimensional transmutation, all fundamental dimension-4 operators can (at least approximately) respect Weyl invariance at finite energy. An example is the Weyl-squared term, whose consistency and observational consequences are studied. This quasi-conformal scenario emerges from the UV complete quadratic gravity and is a possible framework for inflation. We find two realizations. In the first one the inflaton is a fundamental scalar with a quasi-conformal non-minimal coupling to the Ricci scalar. In this case the field excursion must not exceed the Planck mass by far. An example discussed in detail is hilltop inflation. In the second realization the inflaton is a pseudo-Goldstone boson (natural inflation). In this case we show how to obtain an elegant UV completion within an asymptotically free QCD-like theory, in which the inflaton is a composite scalar due to new strong dynamics. We also show how efficient reheating can occur. Unlike the natural inflation based on Einstein gravity, the tensor-to-scalar ratio is well below the current bound set by Planck. In both realizations mentioned above, the basic inflationary formulae are computed analytically and, therefore, these possibilities can be used as simple benchmark models.

We derive nonparametric confidence intervals for the eigenvalues of the Hessian at modes of a density estimate. This provides information about the strength and shape of modes and can also be used as a significance test. We use a data-splitting approach in which potential modes are identified using the first half of the data and inference is done with the second half of the data. To get valid confidence sets for the eigenvalues, we use a bootstrap based on an elementary-symmetric-polynomial (ESP) transformation. This leads to valid bootstrap confidence sets regardless of any multiplicities in the eigenvalues. We also suggest a new method for bandwidth selection, namely, choosing the bandwidth to maximize the number of significant modes. We show by example that this method works well. Even when the true distribution is singular, and hence does not have a density, (in which case cross validation chooses a zero bandwidth), our method chooses a reasonable bandwidth.

The intracluster light (ICL) permeating galaxy clusters is a tracer of the cluster's assembly history, and potentially a tracer of their dark matter structure. In this work we explore the capability of the Euclid Wide Survey to detect ICL using H-band mock images. We simulate clusters across a range of redshifts (0.3-1.8) and halo masses ($10^{13.9}$-$10^{15.0}$ M$_\odot$), using an observationally motivated model of the ICL. We identify a 50-200 kpc circular annulus around the brightest cluster galaxy (BCG) in which the signal-to-noise ratio (S/N) of the ICL is maximised and use the S/N within this aperture as our figure of merit for ICL detection. We compare three state-of-the-art methods for ICL detection, and find that a method that performs simple aperture photometry after high-surface brightness source masking is able to detect ICL with minimal bias for clusters more massive than $10^{14.2}$ M$_\odot$. The S/N of the ICL detection is primarily limited by the redshift of the cluster, driven by cosmological dimming, rather than the mass of the cluster. Assuming the ICL in each cluster contains 15% of the stellar light, we forecast that Euclid will be able to measure the presence of ICL in up to $\sim80000$ clusters of &gt;10^{14.2} M$_\odot$ between $z=0.3$ and 1.5 with a S/N&gt;3. Half of these clusters will reside below $z=0.75$ and the majority of those below $z=0.6$ will be detected with a S/N &gt;20. A few thousand clusters at $1.310^{14.7}$ M$_\odot$. Euclid will detect the ICL at more than 500 kpc distance from the BCG, up to $z=0.7$, in several hundred of these massive clusters over its large survey volume.

In the present paper we extend the Riemann-Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and pushforwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann-Roch theorem for moment graphs. As an application, we obtain the Riemann-Roch type theorem for equivariant $K$-theory of some Kac-Moody flag varieties.

A cornerstone theorem in the Graph Minors series of Robertson and Seymour is the result that every graph $G$ with no minor isomorphic to a fixed graph $H$ has a certain structure. The structure can then be exploited to deduce far-reaching consequences. The exact statement requires some explanation, but roughly it says that there exist integers $k,n$ depending on $H$ only such that $0

It has been suggested that logarithmically enhanced infra-red loop corrections arising in theories with four derivatives correspond to a physical running of couplings, rendering quadratic gravity asymptotically free. We find that these effects depend on the gauge and on the field parameterisation. We compute physical on-shell amplitudes and find genuine infra-red log-enhanced loop corrections, that are process-dependent and cannot be absorbed into running couplings. As a byproduct, we derive the effective action of quadratic gravity at tree level, showing that its ghost does not contribute to effective operators and thereby does not violate positivity bounds.

The planetary ephemerides play a crucial role for spacecraft navigation, mission planning, reduction and analysis of the most precise astronomical observations. The construction of such ephemerides is highly constrained by the tracking observations, in particular range, of the space probes collected by the tracking stations on the Earth. The present planetary ephemerides (DE, INPOP, EPM) are mainly based on such observations. However, the data used by the planetary ephemerides are not the direct raw tracking data, but measurements deduced after the analysis of raw data made by the space agencies and the access to such processed measurements remains difficult in terms of availability. The first part of the study deals with the analysis of the Mars Global Surveyor (MGS) tracking data. The tracking observations containing one-, two-, and three-way Doppler and two-way range are then used to reconstruct MGS orbit precisely. As a supplementary exploitation of MGS, we derived the solar corona model and estimated the average electron density along the line of sight separately for slow and fast wind regions. Fitting the planetary ephemerides, including additional data which were corrected for the solar corona perturbations, noticeably improves the extrapolation capability of the planetary ephemerides and the estimation of the asteroid masses (Verma et al., 2013). The second part of the thesis deals with the complete analysis of the MESSENGER tracking data. This analysis improved the Mercury ephemeris up to two order of magnitude compared to any latest ephemerides. Such high precision ephemeris, INPOP13a, is then used to perform general relativity tests of PPN-formalism. Our estimations of PPN parameters (? and ) are the most stringent than previous results (Verma et al., 2014).

Unimodular gravity addresses the old cosmological constant (CC) problem, explaining why such constant is not at least as large as the largest particle mass scale, but classically it is indistinguishable from ordinary gravity. Conversely, quantum physics may give us a way to distinguish the two theories. Thus, here the unimodular constraint is imposed on a non-perturbative and background-independent quantum version of quadratic gravity, which was recently formulated. It is shown that unimodularity does lead to different predictions for some inflationary quantum observables. Unimodular gravity per se does not solves the new CC problem (why the CC has the observed value?) even in this realization. To address this issue a multiverse made by different eras in a single big bang is considered and the observed scale of dark energy is explained anthropically.