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Davide Bianchi

Publications and source records attributed to Davide Bianchi.

At least 19 recordsLinked to original sources

Uniform Chebyshev approximations of functions satisfying a variation-type condition: reconstruction of time-varying signals on graphs

We prove uniform approximation theorems for Chebyshev expansions of continuous functions of two variables. Under a variation-type condition on the square $[-1,1]^2$, a continuous function admits a uniformly convergent Chebyshev expansion in the first variable whose coefficients are continuous functions of the second variable. These results are applied to the spectral graph wavelet transform of time-varying signals on finite weighted graphs: the scaling and wavelet kernels are approximated by expansions with time-varying coefficients whose degrees do not depend on time, the composition of the approximate transform with its adjoint admits the same explicit coefficient formulas as in the time-independent case, and reconstruction by the pseudoinverse is stable, with explicit bounds in terms of the uniform kernel errors. Numerical experiments on a sensor network confirm the convergence and stability estimates. In a denoising problem, soft thresholding of the graph wavelet coefficients with a time-varying transform parameter improves over its time-independent, fixed-parameter counterpart.

math.NA

Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs

We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \[ (\partial_t + \Delta \Phi)u =0 \] where $\Delta$ is the non-negative formal graph Laplacian and $\Phi u =\phi \circ u$ with $\phi \colon \R\to\R$ nonconstant, continuous and increasing, stochastic completeness at infinity is equivalent to uniqueness of bounded pointwise solutions for every bounded initial datum. For \(\Phi=\id\), this recovers the classical heat equation characterization of stochastic completeness at infinity, and of stochastic completeness when the killing term is trivial, i.e., when \(\kappa=0\). If stochastic completeness at infinity fails, then every bounded initial datum admits infinitely many bounded pointwise solutions of the filtration equation. Admissible nonlinearities include the signed porous medium and fast diffusion powers $\phi(s)=s|s|^{m-1}$ for all $m>0$, as well as many others. Stochastic completeness at infinity is further characterized by a generalized mass balance: the total mass of a positive pointwise solution at time $t$, augmented by the mass $\int_0^t\sum_{x}\kappa(x)\phi(u(s,x)) \dd s$ dissipated by the killing term $\kappa$, equals the initial mass. This balance holds for every bounded positive solution on graphs of finite measure and for bounded finite-mass data on graphs of arbitrary measure under the sharp condition $\limsup_{r\to0^+}\phi(r)/r<\infty$. It also extends to positive pointwise solutions in $\ell^1$ that are bounded on every positive time interval. When the killing term is trivial, stochastic completeness at infinity reduces to stochastic completeness and generalized balance to conservation of mass.

math.PR

Luminosity function of quasars at $1.0<z<3.5$ from SDSS and DESI

We present a study of the evolution of type 1 quasars at $1.0<z<3.5$, covering the peak epoch of quasar activity. The quasar evolution has been extensively explored by a variety of previous works and the derived quasar luminosity functions (QLFs) are not well consistent with each other, presumably due to the complexities introduced by different quasar selection techniques and associated completeness corrections. We use a new strategy to construct QLFs based on a library of all known quasars. We focus on a wide region of $\sim$1700 deg$^2$ and a deep field of $\sim$265 deg$^2$ that have rich spectroscopic data primarily from SDSS and DESI. We then apply traditional color cuts in the rest-frame UV/optical to select quasar candidates and use the quasar library to identify them. Our final sample consists of 62,426 quasars at $1.0<z<3.5$, with a high completeness ($\sim$96%) and a high purity ($\sim$93%) in the color selection. Simple color cuts can potentially minimize selection biases for the study of quasar evolution. We derive binned QLFs and characterize them using a double power-law model. Sample incompleteness and contamination are considered as part of the uncertainties in the calculation. Compared to previous results, our QLFs are slightly higher at the faint end, and also higher at the bright end at $2.5<z<3.5$. The QLFs suggest that the quasar evolution at $1.0 < z < 2.5$ can be well described by the pure luminosity evolution model, while at $2.5 < z < 3.5$, it can be described by either the pure luminosity evolution or the pure density evolution model.

astro-ph.GA

Cosmic Pairs: A DESI Census of Dual and Offset AGN as Precursors to Massive Black Hole Binaries

We present a systematic census of dual and offset active galactic nuclei (AGN) using spectroscopic data from the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI). After correcting for observational systematics, our final sample contains $>7,000$ dual AGN and 27,000 galaxy pairs containing one AGN over the redshift range $0 \lesssim z \lesssim 3.6$. This sample expands the known dual AGN sample by $\sim 1-2$ orders of magnitude at $0.2 \lesssim z \lesssim 0.4$, includes $\sim 50$ dwarf dual AGN candidates in a regime where only a handful were previously known, and triples the census at $z>2$. Dual AGN are preferentially found at small separations, consistent with merger-driven triggering of AGN activity. The two members of a pair differ in their star formation response: the more massive (primary) host changes little with separation, while the less massive (secondary) lies $\sim 0.3$ dex above matched inactive and one-AGN companions at the same projected separation in main-sequence offset. Using ASTRID simulations, we predict that the fraction of DESI dual AGN whose central black holes will merge by $z \sim 0$ increases with redshift, reaching $\sim 76\%$ by $z \sim 2$, while the fraction producing LISA-detectable mergers peaks at $\sim 37\%$ near $z \sim 0.9$. These results provide the largest uniformly selected spectroscopic sample of kpc-scale dual and offset AGN candidates from a single survey, connecting their host-galaxy and AGN demographics to the progenitor population of massive black hole mergers detectable by LISA.

astro-ph.GA

The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation

We study the Cauchy problem for the generalized porous medium equation on infinite weighted graphs. For a general nonlinearity, we establish Dirichlet comparison and weak maximum principles on finite subgraphs and, through an exhaustion argument, construct minimal and maximal pointwise solutions for arbitrary $\ell^\infty$ initial data, controlled by explicit, possibly time-dependent, barriers. For the porous nonlinearity $\phi(s)=s|s|^{m-1}$, assuming a $\nu$-Sobolev inequality with $\nu>2$, we derive quantitative energy estimates for $\ell^1$-mild solutions. These yield finite-time extinction in the fast diffusion range $0 2/\nu$. Interestingly, we recover the Euclidean critical exponent for several model graphs. Finally, we prove an exact generalized mass balance for nonnegative $\ell^1$-mild solutions on graphs that are stochastically complete at infinity, allowing for an arbitrary killing term. The same balance is established for suitable classical and bounded pointwise solutions. In the absence of killing, these reduce to conservation of mass.

math.AP

Stacked Reverberation Mapping of High Redshift Quasars in DESI. I. Feasibility Analysis

The broad line region of quasars has long been probed by reverberation mapping techniques that measure time lags between continuum and broad emission line variations. Stacked reverberation mapping has been proposed as a less observationally expensive alternative to traditional methods. This ensemble approach also reduces biases from small-number statistics. The Dark Energy Spectroscopic Instrument (DESI) is conducting the most extensive spectroscopic survey of quasars to date. We create mock light curves emulating expected DESI quasar observations at redshifts $1.48<z<5.2$ and luminosities $ 44.68 \leq \log L_{1350} \lambda / \mathrm{erg\,s^{-1}} \leq 45.99 $ to test stacked reverberation mapping feasibility using sparse spectroscopic data paired with well-sampled photometric data. The pipeline, using the lag estimation code JAVELIN, successfully recovers the simulated C IV lags within one sigma of the true values using spectroscopic light curves composed of only a few spectral epochs (2-10) with irregular cadences. We investigate how observational factors, including C IV flux error magnitude, number of stacked quasars, and spectral epoch count, affect performance. This work motivates a pathway for future stacked reverberation mapping projects with large scale spectroscopic surveys of quasars having $\geq 2$ spectroscopic observations. Our results suggest an economical alternative for constraining and extending the radius-luminosity relation to higher redshifts and luminosities. Subsequently, this relation can be employed more reliably in single-epoch black hole mass measurements and quasar cosmology in these distant regimes.

astro-ph.GA

Iterated graph Laplacian for image restoration problems

We study the graph Laplacian operator as a regularizer in a generalized Tikhonov framework for linear ill-posed problems. The Laplacian is updated iteratively from the current reconstruction, so that progressively sharper structural information about the solution is fed into the regularization term. We introduce three schemes: a standard one that rebuilds the Laplacian from each new iterate; an error-equation scheme that, following the error-based formulation of iterated Tikhonov regularization, builds the Laplacian from an estimate of the reconstruction error rather than of the image itself; and a mixed scheme combining the two. We establish convergence of all three schemes for noisy data under a priori parameter and stopping rules as the noise level tends to zero. Numerical experiments in two-dimensional computed tomography and image deblurring show consistent gains in reconstruction quality and sharper recovery of fine details.

math.NA

On the accretivity and m-accretivity of Laplacians and porous medium-type operators on graphs

We study the accretivity and m-accretivity of Laplacian and porous medium-type operators on weighted graphs. In particular, we give several conditions that imply these properties for maximal operators and investigate when these operators agree with various restrictions. For porous medium-type operators on $\ell^1$ and for Laplacians on $\ell^p$ for $p \in [1,\infty)$, we show that there always exists a dense subset of the domain on which the maximal operator is m-accretive. As a consequence, we establish that accretivity, m-accretivity and injectivity of the shifted operator are all equivalent for these maximal operators. Under additional conditions on the graph, we then prove that the maximal operators are m-accretive on the entire domain, not just a dense subset. We also investigate minimal operators and show that they are m-accretive if and only if the minimal and maximal operators agree and the maximal operator is accretive. We then give some conditions that imply this agreement. Furthermore, for the minimal Laplacian on $\ell^p$, we show that accretivity and m-accretivity are not equivalent. For the $\ell^2$ case, we give connections to Markov uniqueness and essential self-adjointness. For the $\ell^\infty$ case, we establish the equivalence of stochastic completeness at infinity, m-accretivity for the maximal Laplacian on $\ell^\infty$, and m-accretivity of the minimal Laplacian on $\ell^1$.

math.FA

Alleviating prior dependencies for DESI DR1 clustering fits through reparameterization

Bayesian analyses of the full-shape clustering of Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) exhibit prior-volume projection effects, whereby weakly constrained nuisance parameters of the Effective Field Theory of Large Scale Structure (EFTofLSS) shift marginalized cosmological posteriors away from the posterior maximum. We reanalyze DESI DR1 power spectrum multipoles using two complementary mitigation strategies: (i) nonlinear orthogonalization to decorrelate nuisance and cosmological parameter priors, and (ii) a fully reparameterization-invariant Jeffreys prior over all EFTofLSS coefficients, evaluated on-the-fly via closed-form Jacobians. Including data from DESI, Big-Bang Nuclesynthesis and a constraint on $n_{\mathrm{s}}$, baseline priors lead to multi-$\sigma$ projection in the Hubble parameter $H_{0}$ and dark energy equation of state parameters $w_{0}$ and $w_{a}$; the Jeffreys prior successfully recenters these posteriors to enclose the maximum a posteriori estimate within the 68\% credible regions, demonstrating clear mitigation of projection effects for these late-time expansion parameters. A hybrid Jeffreys+baseline-Gaussian configuration controls residual over-broad tails in the physical cold dark matter density $\omega_{\mathrm{c}}$ while preserving the volume correction, and is our favoured approach. We compare the credible intervals derived using our methodology to those obtained using Halo Occupation Distribution (HOD)-informed priors and to confidence intervals derived using frequentist profile likelihood analyses, finding agreement in both central values and degeneracy directions in the $w_{0}$--$w_{a}$ plane. This demonstrates that, once projection effects are properly controlled, we can make robust inferences about the late-time cosmological expansion independent of the statistical framework adopted.

astro-ph.CO

The 3D clustering of Lyman Alpha Emitters measured with DESI

We present a clustering analysis of Lyman-$\alpha$ emitters (LAEs) using spectroscopic observations from the Dark Energy Spectroscopic Instrument (DESI) of candidates selected from the Blanco/DECam Intermediate-Band Imaging Survey (IBIS). We measure the two-point correlation function and the power spectrum, including cross-correlations with DESI quasars. Using both analytical and halo occupation distribution (HOD) simulation-based modeling, we find a linear bias of $b \sim 2.31$--$2.62$ for LAEs over the redshift range $2.26 < z < 3.41$. The analytical modeling also provides constraints on the strength of radiative transfer effects, while the HOD analysis characterizes the LAE-halo connection across multiple models. Finally, we quantify the magnitude of non-perturbative clustering effects such as Fingers of God in the LAE population, providing essential input for the accurate modeling of LAE-based cosmological analyses in forthcoming high-redshift surveys such as DESI-II.

astro-ph.CO

Disentangling the Distant Stellar Halo Using K-Giants in the DESI Year 3 Data

We present a sample of 88,959 K-giants from DESI Milky Way Survey Year 3 data, which we use to characterize the chemo-dynamical properties of the stellar halo at Galactocentric distances of 12 to ~100 kpc. Using HDBSCAN, we identify five prominent stellar halo substructures: Aleph, the Sagittarius stream, Gaia Sausage-Enceladus (GSE), Cetus-Palca and the Orphan-Chenab stream. We present the properties of each of these structures as they appear in our catalog, and examine how uncertainties on distance affect the characterization of substructure with this approach. We also examine regions associated with previously reported overdensities (such as the Virgo Overdensities and the Sagittarius spur) that we do not recover with HDBSCAN. The size and distance range of our catalog allows us to explore in detail the residual stellar halo, comprising stars that we do not associate with any substructure. We find that samples of ~2000 outer halo stars with both highly prograde and highly retrograde angular momenta have similar metallicity distribution functions (MDFs), which do not resemble the MDFs of either GSE or Sagittarius. Both the prograde and retrograde residual halo MDFs are bimodal, with a metal-poor peak at [Fe/H] ~ -2 and a metal-rich peak at [Fe/H] ~ -1.3 (prograde) or -1.5 (retrograde). The MDF for lower angular momentum residual halo K-giants does not show clear evidence for a metal-poor peak, and broadly resembles the MDF of GSE, even at much lower binding energies than GSE itself. We discuss possible interpretations of these findings for GSE accretion scenarios.

astro-ph.GA

Augmented Correlation Functions for Spectroscopic Galaxy Surveys

Galaxy redshift surveys encode a wealth of information generated by nonlinear gravitational evolution, galaxy bias, and redshift-space distortions, only part of which is accessible through standard two-point statistics. Motivated by the need for flexible and computationally efficient alternatives, we introduce the augmented correlation function, a general framework in which an arbitrary transformation of the galaxy field defines additional ``latent'' dimensions that extend the standard two-point correlation function and isolate clustering properties averaged out in conventional analyses. As a proof of concept, we study a latent variable constructed from the pairwise gradient of the inverse Laplacian of the galaxy density field, showing that the resulting statistics naturally distinguish clustering regimes associated with infalling and outflowing pairs. Using Fisher forecasts based on $z=1$ halo catalogues from the Quijote simulations within $\nu\Lambda\mathrm{CDM}$ cosmology, we find that the augmented correlation systematically yields tighter constraints on all cosmological parameters considered. Although these improvements should be regarded as indicative given the exploratory nature of the analysis and the limitations of Fisher forecasts and simulations, our results demonstrate the potential of augmented correlations as a flexible framework for extracting additional information from spectroscopic galaxy surveys.

astro-ph.CO

Constraining the Galactic bar using the M92 stellar stream

Stellar streams are excellent probes of the gravitational potential in which they evolve. In the Milky Way (MW), globular cluster (GC) streams are routinely used to infer properties about time-dependent perturbations of the underlying potential. This implies that streams with Galactocentric radii small enough to be perturbed by the MW bar should offer constraints on it, such as its pattern speed, which currently has a wide range of values reported in the literature and is important when studying stellar kinematics. The GC M92 has a small pericentre and should be affected by the bar. It has a diffuse stellar stream, but confirming stream members has previously been hindered by a lack of spectroscopic data. In this paper, we use Dark Energy Spectroscopic Instrument (DESI) observations together with photometric and astrometric data to obtain spectroscopic members of the M92 stream for the first time. We identify a clear spatial distribution and gradients in distance moduli, proper motions, and radial velocities that confirm the stream's existence. We compare the observed stream to mock streams generated in different barred potentials and estimate the MW bar's pattern speed $\Omega = 29.1^{+0.7}_{-0.4}$ km s$^{-1}$ kpc$^{-1}$ and $\dot \Omega = 0.7^{+3.5}_{-2.3}$ km s$^{-1}$ kpc$^{-1}$ Gyr$^{-1}$. This is the first time a stellar stream is used to probabilistically infer these bar properties, and it opens up an exciting realm of inner Galactic potential characterisation using stellar streams.

astro-ph.GA

A Natural $\gtrsim 100\times$ Telescope: Discovery of the Strongly Lensed Type II SN 2025mkn at $z=1.37$

We present the discovery of SN 2025mkn, a gravitationally lensed Type II supernova. First detected as a blue transient in ZTF, 0.83$^{\prime\prime}$ from a $z=0.42$ elliptical galaxy, follow-up SNIFS/UH2.2m and LRIS/Keck spectra revealed absorption lines at $z=1.371$. Later JWST NIRCam imaging shows that the bright transient is a close pair of point sources separated by $\sim 0.07^{\prime\prime}$, and a 30 times fainter counterimage opposite the lens, for which NIRSpec reveals strong H$\alpha$ emission also at $z=1.371$. The light curves and spectra are consistent with the Type II supernova source being magnified $\gtrsim 100$ times, with $\sim 250$ required to reconcile its luminosity with that of nearby events such as SN 2023ixf. Lens models are consistent with such high magnifications, and always show that the faint image arrived first (undetected in earlier ZTF imaging), consistent with the later spectral phase of this fainter image. A fourth image is also predicted and possibly detected in the NIRSpec data. Light-curve-based time-delay measurements are not possible due to the first image being the faintest; however, the resolved NIRSpec spectra offer a future opportunity for time-delay cosmography through supernova phase measurements.

astro-ph.CO

The velocity field of our Milky Way outer stellar halo based on DESI DR2

Using 64,000 halo K giants from Dark Energy Spectroscopic Instrument (DESI) second Data Release (DR2), we decompose the Milky Way (MW) stellar halo between 3 and 160 kpc into metal-rich (MR) and metal-poor (MP) components via a Gaussian mixture model (GMM). The two populations are nearly equal in number but chemically and kinematically distinct: MR stars occupy highly radial orbits with velocity anisotropy of beta ~0.94 and metallicity dispersion sigma([Fe/H]) ~0.17 dex, without obvious dependence on distance, and are mainly contributed by Gaia-Sausage/Enceladus (GSE) debris. MR component dominates the inner 30 kpc and re-emerges beyond 50 kpc, implying GSE debris can extend to ~70-80 kpc. MP stars exhibit a weaker radial bias of beta ~0.46, decreasing to -0.5 beyond 80 kpc, and with a larger metallicity dispersion of sigma([Fe/H]) ~0.46 dex, showing signatures of multiple minor mergers. Both components exhibit net prograde rotation at ~10-30 kpc with a stronger azimuthal signal in the MP population. The non-equilibrium motions of the outer halo (>50 kpc) are quantified with a dipole-plus-contraction velocity field. We find that the outer halo is simultaneously contracting (~-19 km/s, distance-independent) and subject to reflex motions (increases from -19 to -44 km/s with radius), reflecting the perturbation from the Large Magellanic Cloud (LMC). We also confirm a linear dependence of mean polar velocity for the outer stellar halo on the dipole velocity field, a direct consequence of the LMC and MW interaction. Our results provide a quantitative distance-resolved description of the MW's last major accretion event and its ongoing response to the first infall of the LMC.

astro-ph.GA

Nonlinear Information from DESI Luminous Red Galaxies: An Emulator-Based Analysis of Pre- and Post-Reconstruction Power Spectra

We present joint measurements of the pre- and post-reconstruction power spectra, $P_{\rm pre}$ and $P_{\rm post}$, together with their cross-power spectrum, $P_{\rm cross}$, for the Luminous Red Galaxies (LRGs) in the DESI Data Release 1 (DR1). We jointly analyse these observables with an emulator-based full-shape modeling framework, thereby, for the first time, we extract complementary nonlinear information from the galaxy density field before and after reconstruction in real survey data. Specifically, including $P_{\rm post}$ and $P_{\rm cross}$ in addition to $P_{\rm pre}$ (hereafter $P_{\rm all}$) yields an improvement of approximately $18$-$27\%$ in the $\sigma_8$ constraint in both $\Lambda$CDM and $w$CDM, depending on the redshift bin, relative to the $P_{\rm pre}$-only analysis with the cosmic microwave background distance priors (hereafter CMB). In $w$CDM, the joint CMB+$P_{\rm all}$ analysis can tighten the constraints on $w$ by approximately $5$-$15\%$ across the two LRG redshift bins, compared to the CMB+$P_{\rm pre}$ combination. Further incorporating the Type Ia supernova dataset and comparing the cosmological constraints in $w$CDM from each individual power-spectrum component with those from the full combination, we find that $P_{\rm all}$ consistently provides the tightest constraints. From the joint CMB+$P_{\rm all}$+DES-Dovekie dataset, we obtain $\Omega_m = 0.314 \pm 0.0048$ and $w = -0.988 \pm 0.023$ for the \texttt{LRG1} sample, and $\Omega_m = 0.318 \pm 0.0046$ and $w = -0.988 \pm 0.025$ for \texttt{LRG2}. These results demonstrate that combining pre- and post-reconstruction power spectra with their cross-correlation enables DESI to harvest additional nonlinear information, leading to tighter constraints on cosmological parameters.

astro-ph.CO

ODIN: Confirmation and 3D Reconstruction of Six Massive Protoclusters at Cosmic Noon

Protoclusters represent sites of accelerated galaxy formation and extreme astrophysical activity characteristic of dense environments. Identifying massive protoclusters and mapping their spatial structures are therefore crucial first steps in understanding how the large-scale environment influences galaxy evolution. We combine wide-field Ly$\alpha$ imaging from the ODIN survey with extensive DESI and ancillary spectroscopy across the extended COSMOS and XMM-LSS fields ($\approx$14 deg$^2$) to search for massive protoclusters. We confirm six systems at $z\approx 2.4$ and $z\approx 3.1$, reconstruct their three-dimensional structures, estimate descendant halo masses, and, for one structure at $z\approx 3.12$, demonstrate that overlapping narrowband filters ($NB497$ and $N501$) provide accurate redshift tomography for emission-line galaxies. One protocluster at $z\approx 2.45$ overlaps with one of the LATIS tomographic fields, enabling direct comparison between galaxy and H {\sc i} overdensities traced by Ly$\alpha$ forest absorption. Another at $z\approx 3.12$ hosts a massive quiescent galaxy ($M_{\ast} \approx 1.2 \times 10^{11}M_\odot$), indicating early quenching in a dense environment. By comparing Ly$\alpha$ emission properties across environments, we find that protocluster galaxies exhibit higher median line fluxes and a deficit of faint emitters relative to the field. The effect is strongest when both 2D and 3D density information are combined, indicating that galaxies in the densest protocluster cores are most affected by environmental processes. This effect is stronger at $z\approx3.1$ than at $z\approx2.4$, suggesting possible redshift evolution.

astro-ph.GA

Extremely Metal-Poor Galaxies in DESI DR1: Connections to Galaxies in the Early Universe

Extremely Metal-Poor Galaxies (XMPGs), defined as having metallicities below 10\% of the solar value, are considered possible local analogs to primordial systems and offer a unique window into early galaxy evolution. This study presents a large-scale search for XMPGs using data from the Dark Energy Spectroscopic Instrument DR1, systematically evaluating their resemblance to high-redshift galaxies. From a parent sample of over 14 million galaxies, we identify 656 (551 new) confirmed XMPGs and 767 (670 new) high-quality candidates via the direct $T_{\mathrm{e}}$ method. Results reveal that XMPGs follow a distinct star-forming main sequence (SFMS) that is elevated and shallower than that of the comparing star-forming galaxies. Notably, at higher stellar masses ($M_{\star} > 10^{7.5} M_{\odot}$), the XMPG SFMS converges with the sequence observed in high-redshift galaxies by James Webb Space Telescope (JWST), indicating that mature XMPGs sustain star formation rates comparable to their primordial counterparts. Furthermore, XMPGs consistently deviate below the local fundamental metallicity relation, mirroring high-redshift galaxy behavior. These findings demonstrate that XMPGs not only exhibit low metallicities but also preserve scaling relations characteristic of the early Universe, confirming their potential value as local laboratories for studying early galaxy formation processes.

astro-ph.GA