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Driving the nuclear fusion reaction p+11B -> 3 alpha + 8.7 MeV in laboratory conditions, by interaction between high-power laser pulses and matter, has become a popular field of research, due to numerous applications that it can potentially allow: an alternative to deuterium-tritium (DT) for fusion energy production, astrophysics studies and alpha-particle generation for medical treatments. A possible scheme for laser-driven p-11B reactions is to direct a beam of laser-accelerated protons onto a boron sample (the so-called 'pitcher-catcher' scheme). This technique was successfully implemented on large, energetic lasers, yielding hundreds of joules per shot at low repetition. We present here a complementary approach, exploiting the high-repetition rate of the VEGA III petawatt laser at CLPU (Spain), aiming at accumulating results from many interactions at much lower energy, for better controlling the parameters and the statistics of the measurements. Despite a moderate energy per pulse, our experiment allowed exploring the laser-driven fusion process with tens (up to hundreds) of laser shots. The experiment provided a clear signature of the produced reactions and of the fusion products, accumulated over many shots, leading to an improved optimization of the diagnostic for these experimental campaigns In this paper we discuss the effectiveness of the laser-driven p-11B fusion in the pitcher-catcher scheme, at high-repetition rate, addressing the challenges of this experimental scheme and highlighting its critical aspects. Our proposed methodologies allow evaluating the performance of this scheme for laser-driven alpha particle production and can be adapted to high-repetition rate laser facilities with higher energy and intensity.

The study of algebraic curves $\cX$ with numerous automorphisms in relation to their genus $g(\cX)$ is a well-established area in Algebraic Geometry. In 1995, Irokawa and Sasaki \cite{Sasaki} gave a complete classification of curves over $\mathbb{C}$ with an automorphism of order $N \geq 2g(\mathcal{X}) + 1$. Precisely, such curves are either hyperelliptic with $N=2g(\cX)+2$ with $g(\cX)$ even, or are quotients of the Fermat curve of degree $N$ by a cyclic group of order $N$. Such a classification does not hold in positive characteristic $p$, the curve with equation $y^2=x^p-x$ being a well-studied counterexample. This paper successfully classifies curves with a cyclic automorphism group of order $N$ at least $2g(\mathcal{X}) + 1$ in positive characteristic $p \neq 2$, offering the positive characteristic counterpart to the Irokawa-Sasaki result. The possibility of wild ramification in positive characteristic has presented a few challenges to the investigation.

We present the first spectroscopic confirmation of a dust-obscured dwarf galaxy, CEERS-14821. The analysis is performed combining JWST NIRCam broad-band photometry and NIRSpec/PRISM spectroscopic data. From the detection of multiple rest-frame optical lines, we derive that CEERS-14821 is located at $z=4.883\pm0.003$. Moreover, from a secure detection of the $H_{\alpha}$ and $H_{\beta}$ we derived that the galaxy has a dust extinction ranging from Av=2.2 to Av=3.3, depending on the assumed reddening law. This value is extremely large given that we estimated a low stellar mass around log(M/Mo)=8.0-8.2. Moreover, using different metallicity tracers, we verify that the galaxy is also metal-rich, with 12+log(O/H)>8.3. This is well above the expectation from both the mass-metallicity relation and the fundamental mass-metalliticy relation. CEERS-14821 is going through a burst of star formation, there are no indications of a strong contribution from an active galactic nuclei (f(AGN)<0.5 with respect to the total dust luminosity). Based on the rest-frame optical images, this source has a size compatible with galaxies of similar stellar mass and redshift. Finally, with the current data, it seems that there are galaxies closely interacting with CEERS-14821., Comment: 14 pages, 11 figures. Submitted to A&A

We argue that the difference in infrared-to-radio luminosity ratio between local and high-redshift star-forming galaxies reflects {the alternative physical conditions} -- including magnetic field configurations -- of the dominant population of star-forming galaxies in different redshift ranges. We define three galactic types, based on our reference model, with reference to ages of stellar populations. ``Normal'' late-type galaxies dominate the star formation in the nearby Universe; ``starburst'' galaxies take over at higher redshifts, up to z ~1.5; while ``protospheroidal'' galaxies dominate at high redshift. A reanalysis of data from the COSMOS field combined with literature results shows that, for each population, the data are consistent with an almost redshift-independent mean value of the parameter q_IR, which quantifies the infrared-radio correlation. However, we find a hint of an upturn of the mean q_IR at z>~3.5 consistent with the predicted dimming of synchrotron emission due to cooling of relativistic electrons by inverse Compton scattering off the cosmic microwave background. The typical stellar masses increase from normal, to starburst, and to protospheroidal galaxies, accounting for the reported dependence of the mean q_IR on stellar mass. Higher values of q_IR found for high-z strongly lensed dusty galaxies selected at 500 micron might be explained by differential magnification., Comment: 9 pages, 4 figures, accepted for publication in A&A

FIR and submm observations have established the fundamental role of dust-obscured star formation in the assembly of stellar mass over the past 12 billion years. At z between 2 and 4, the bulk of star formation is enshrouded in dust, and dusty star forming galaxies (DSFGs) contain about half of the total stellar mass density. Star formation develops in dense molecular clouds, and is regulated by a complex interplay between all the ISM components that contribute to the energy budget of a galaxy: gas, dust, cosmic rays, interstellar electromagnetic fields, gravitational field, dark matter. Molecular gas is the actual link between star forming gas and its complex environment, providing by far the richest amount of information about the star formation process. However, molecular lines interpretation requires complex modeling of astrochemical networks, which regulate the molecular formation and establishes molecular abundances in a cloud, and a modeling of the physical conditions of the gas in which molecular energy levels become populated. This paper critically reviews the main astrochemical parameters needed to get predictions about molecular signals in DSFGs. We review the current knowledge and the open questions about the interstellar medium of DSFGs, outlying the key role of molecular gas as a tracer and shaper of the star formation process., Comment: Review paper, 34 pages, accepted for publication on MPDI Galaxies special issue "Molecular gas in Dusty Star-Forming Galaxies at the Cosmic Noon"

In this paper, we investigate the benefits of teaming up data from the radio to the far- 1 infrared (FIR) regime for the characterization of Dusty Star-Forming Galaxies (DSFGs). These galaxies 2 are thought to be the star-forming progenitors of local massive quiescent galaxies, and play a pivotal 3 role in the reconstruction of the cosmic star formation rate density up to high redshift. Due to their 4 dust-enshrouded nature, DSFGs are often invisible in the near-infrared/Optical/UV bands. Therefore, 5 they necessitate observations at longer wavelengths, primarily the FIR, where dust emission occurs, 6 and radio, which is not affected by dust absorption. Combining data from these two spectral windows 7 makes it possible to characterize even the dustiest objects, enabling the retrieval of information about 8 their age, dust temperature, and star-formation status, and facilitates the differentiation between 9 various galaxy populations that evolve throughout cosmic history. Despite the detection of faint radio 10 sources being a challenging task, this study demonstrates that an effective strategy to build statistically 11 relevant samples of DSFGs would be reaching deep sensitivities in the radio band, even restricted to 12 smaller areas, and then combining these radio observations with FIR/submm data. Additionally, 13 the paper quantifies the improvement in the Spectral Energy Distribution (SED) reconstruction of 14 DSFGs by incorporating ALMA band measurements, in particular, in its upgraded status thanks to 15 the anticipated Wideband Sensitivity Upgrade.

Gravitational lensing, a compelling physical phenomenon, offers a unique avenue to investigate the morphology and physical properties of distant and faint celestial objects. This paper seeks to provide a comprehensive overview of the current state of observations concerning strongly lensed Dusty Star-Forming Galaxies. Emphasis is placed on the pivotal role played by cutting-edge facilities like the James Webb Space Telescope and the Square Kilometer Array Observatory. These advanced instruments, operating at disparate ends of the electromagnetic spectrum, in conjunction with the amplifying effect of gravitational lensing, promise significant steps in our understanding of these sources. The synergy between these observatories operating at two opposite ends of the spectrum, is poised to unlock crucial insights into the evolutionary path of high-redshift, dust-obscured systems and unravel the intricate interplay between Active Galactic Nuclei and their host galaxies., Comment: 21 pages, 1 figure, accepted on Galaxies

Fostered by upcoming data from new generation observational campaigns, we are about to enter a new era for the study of how galaxies form and evolve. The unprecedented quantity of data that will be collected, from distances only marginally grasped up to now, will require analysis tools designed to target the specific physical peculiarities of the observed sources and handle extremely large datasets. One powerful method to investigate the complex astrophysical processes that govern the properties of galaxies is to model their observed spectral energy distribution (SED) at different stages of evolution and times throughout the history of the Universe. To address these challenges, we have developed GalaPy, a new library for modelling and fitting SEDs of galaxies from the X-ray to the radio band, as well as the evolution of their components and dust attenuation/reradiation. GalaPy incorporates both empirical and physically-motivated star formation histories, state-of-the-art single stellar population synthesis libraries, a two-component dust model for attenuation, an age-dependent energy conservation algorithm to compute dust reradiation, and additional sources of stellar continuum such as synchrotron, nebular/free-free emission and X-ray radiation from low and high mass binary stars. GalaPy has a hybrid implementation that combines the high performance of compiled C++ with the flexibility of Python, and exploits an object-oriented design. It generates models on the fly without relying on templates, and exploits fully Bayesian parameter space sampling. In this first work, we introduce the project and showcase the photometric SED fitting tools already available to users. The library is available on the Python Package Index (PyPI) and comes with extensive online documentation and tutorials., Comment: 41 pages, 31 figures, 7 tables, to be published on A&A, links to documentation and PyPI available in the PDF, comments are very welcome

We present the first spectroscopic ALMA follow-up for a pilot sample of nine Radio-Selected NIRdark galaxies in the COSMOS field. These sources were initially selected as radio-detected sources (S(3GHz)>12.65 uJy), lacking an optical/NIR counterpart in the COSMOS2015 catalog (Ks>24.7 mag), with just three of them subsequently detected in the deeper COSMOS2020. Several studies highlighted how this selection could provide a population of highly dust-obscured, massive, and star-bursting galaxies. With these new ALMA observations, we assess the spectroscopic redshifts of this pilot sample of sources and improve the quality of the physical properties estimated through SED-fitting. Moreover, we measure the quantity of molecular gas present inside these galaxies and forecast their potential evolutionary path, finding that the RS-NIRdark galaxies could represent a likely population of high-z progenitors of the massive and passive galaxies discovered at z~3. Finally, we present some initial constraints on the kinematics of the ISM within the analyzed galaxies, reporting a high fraction (~55%) of double-peaked lines that can be interpreted as the signature of a rotating structure in our targets or with the presence of major mergers in our sample. Our results presented in this paper showcase the scientific potential of (sub)mm observations for this elusive population of galaxies and highlight the potential contribution of these sources in the evolution of the massive and passive galaxies at high-z., Comment: 18 pages, 9 figures (+2 in the appendix), 6 tables. Accepted by A&A

We consider skew products over subshifts of finite type in which the fibers are copies of the real line, and we study their mixing properties with respect to any infinite invariant measure given by the product of a Gibbs measure on the base and Lebesgue measure on the fibers. Assuming that the system is accessible, we prove a quantitative version of Krickeberg mixing for a class of observables which is dense in the space of continuous functions vanishing at infinity., Comment: 25 pages

Laser technologies improved after the understanding of the Chirped Pulse Amplification (CPA) which allows energetic laser beams to be compressed to tens of femtosecond (fs) pulse durations and focused to few $\mu$m. Protons of tens of MeV can be accelerated using for instance the Target Normal Sheath Acceleration (TNSA) method and focused on secondary targets. In such conditions, nuclear reactions can occur and radioisotopes relevant for medical purposes be produced. High repetition lasers can be used to produce enough isotopes for medical applications. This route is competitive to conventional methods mostly based on accelerators. In this paper we study the production of $^{67}$Cu, $^{63}$Zn, $^{18}$F and $^{11}$C currently used in positron emission tomography (PET) and other applications. At the same time, we study the reaction $^{10}$B(p,$\alpha$)$^{7}$Be and $^{70}$Zn(p,4n)$^{67}$Ga to put further constraints to the proton distributions at different angles and to the reaction $^{11}$B(p,$\alpha$)$^{8}$Be relevant for energy production. The experiment was performed at the 1 petawatt (PW) laser facility at Vega III located in Salamanca-Spain. Angular distributions of radioisotopes in the forward (with respect to the laser direction) and backward directions were measured using a High Purity Germanium Detector (HPGE). Our results are reasonably reproduced by the numerical estimates following the approach of Kimura et al. (NIMA637(2011)167)

In the last decades, an increasing scientific interest has been growing in the elusive population of "dark" (i.e. lacking an optical/NIR counterpart) Dusty Star-Forming Galaxies (DSFGs). Although extremely promising for their likely contribution to the cosmic Star Formation Rate Density and for their possible role in the evolution of the first massive and passive galaxies around $z\sim3$, the difficulty in selecting statistically significant samples of dark DSFGs is limiting their scientific potentialities. This work presents the first panchromatic study of a sample of 263 Radio-Selected NIRdark galaxies discovered in the COSMOS field following the procedure by Talia+21. These sources are selected as radio-bright galaxies (S(3GHz)>12.65 uJy) with no counterpart in the NIR-selected COSMOS2020 catalog (Ks > 25.5 mag). For these sources, we build a new photometric catalog including accurate photometry from the optical to the radio obtained with a new deblending pipeline (PhoEBO: Photometry Extractor for Blended Objects). We employ this catalog to estimate the photo-zs and the physical properties of the galaxies through an SED-fitting procedure performed with two different codes (Magphys and Cigale). Finally, we estimate the AGN contamination in our sample by performing a series of complementary tests. The high values of the median extinction (Av ~ 4) and star formation rate (SFR ~ 500 Msun/yr) confirm the likely DSFG nature of the RS-NIRdark galaxies. The median photo-z (z~3) and the presence of a significant tail of high-z candidates (z>4.5) suggest that these sources are important contributors to the cosmic SFRD and the evolutionary path of galaxies at high redshifts., Comment: 22 pages, 9 figures, 3 tables. Accepted for publication in ApJ

We investigate the distribution and multiple occurrences of extreme events stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on $\mathbb{R}^n$. We do so by studying the action of an annealead transfer operators on ad-hoc spaces of probability densities. The spectral properties of such operators are obtained by employing a mixture of techniques coming from SDE theory and a functional analytic approach to dynamical systems.

About 12 billion years ago, the Universe was first experiencing light again after the dark ages, and galaxies filled the environment with stars, metals and dust. How efficient was this process? How fast did these primordial galaxies form stars and dust? We can answer these questions by tracing the Star Formation Rate Density (SFRD) back to its widely unknown high redshift tail, traditionally observed in the Near-InfraRed (NIR), Optical and UV bands. Thus, the objects with a high amount of dust were missing. We aim to fill this knowledge gap by studying Radio Selected NIR-dark (\textit{RS-NIRdark}) sources, i.e. sources not having a counterpart at UV-to-NIR wavelengths. We widen the sample by Talia et al. (2021) from 197 to 272 objects in the COSMic evolution Survey (COSMOS) field, including also photometrically contaminated sources, previously excluded. Another important step forward consists in the visual inspection of each source in the bands from u* to MIPS-24$\mu$m. According to their "environment" in the different bands, we are able to highlight different cases of study and calibrate an appropriate photometric procedure for the objects affected by confusion issues. We estimate that the contribution of RS-NIRdark to the Cosmic SFRD at 3$<$z$<$5 is $\sim$10--25$\%$ of that based on UV-selected galaxies.

We report ALMA high-resolution observations of water emission lines $p-{\rm{H_2O}} (2_{02}-1_{11}$), $o-{\rm{H_2O}} (3_{21}-3_{12})$, $p-{\rm{H_2O}} (4_{22}-4_{13})$, in the strongly lensed galaxy HATLASJ113526.2-01460 at redshift z $\sim$ 3.1. From the lensing-reconstructed maps of water emission and line profiles, we infer the general physical properties of the ISM in the molecular clouds where the lines arise. We find that the water vapor lines $o-{\rm{H_2O}} (3_{21}-3_{12})$, $p-{\rm{H_2O}} (4_{22}-4_{13})$ are mainly excited by FIR pumping from dust radiation in a warm and dense environment, with dust temperatures ranging from 70 K to $\sim 100$ K, as suggested by the line ratios. The $p-{\rm{H_2O}} (2_{02}-1_{11})$ line instead, is excited by a complex interplay between FIR pumping and collisional excitation in the dense core of the star-forming region. This scenario is also supported by the detection of the medium-level excitation of CO resulting in the line emission CO (J=8-7). Thanks to the unprecedented high resolution offered by the combination of ALMA capabilities and gravitational lensing, we discern the different phases of the ISM and locate the hot molecular clouds into a physical scale of $\sim$ 500 pc. We discuss the possibility of J1135 hosting an AGN in its accretion phase. Finally, we determine the relation between the water emission lines and the total IR luminosity of J1135, as well as the SFR as a function of water emission intensities, comparing the outcomes to local and high-$z$ galactic samples from the literature., Comment: 22 pages, 10 figures, final version to be published in Astrophysical Journal

Quantifying changes in galaxies' interstellar medium (ISM) abundance after quenching star formation is an important aspect of galaxy evolution, but it is poorly constrained beyond the local universe. We characterise the dust-related properties in 548 quiescent galaxies observed at $0.1

We present high-resolution ($\lesssim0.1$arcsec) ALMA observations of the strongly-lensed galaxy HATLASJ113526.2-01460 at redshift $z\sim3.1$ discovered in the Gama 12$^{\rm th}$ field of the Herschel-ATLAS survey. The gravitationally lensed system is remarkably peculiar in that neither the background source nor the foreground lens show a clearly detected optical/NIR emission. We perform accurate lens modeling and source morphology reconstruction in three different (sub-)mm continuum bands, and in the C[II] and CO(8-7) spectral lines. The modeling indicates a foreground lensing (likely elliptical) galaxy with mass $\gtrsim10^{11}\, M_\odot$ at $z\gtrsim1.5$, while the source (sub-)mm continuum and line emissions are amplified by factors $\mu\sim6-13$. We estimate extremely compact sizes $\lesssim0.5$ kpc for the star-forming region and $\lesssim 1$ kpc for the gas component, with no clear evidence of rotation or of ongoing merging events. We perform broadband SED-fitting and retrieve the intrinsic de-magnified physical properties of the source, which is found to feature a very high star-formation rate $\gtrsim10^3\, M_\odot$ yr$^{-1}$, that given the compact sizes is on the verge of the Eddington limit for starbursts; the radio luminosity at 6 cm from available EVLA observations is consistent with the star-formation activity. The galaxy is found to be extremely rich in gas $\sim10^{11}\, M_\odot$ and dust $\gtrsim10^9\, M_\odot$. The stellar content $\lesssim10^{11}\, M_\odot$ places the source well above the main sequence of starforming galaxies, indicating that the starburst is rather young with estimated age $\sim10^8$ yr. Our results indicate that the overall properties of HATLASJ113526.2-01460 are consistently explained by in-situ galaxy formation and evolution scenarios., Comment: 17 Pages, 12 Figures, 7 Tables. Submitted to ApJ

Scattered polynomials over finite fields attracted an increasing attention in the last years. One of the reasons is their deep connection with Maximum Rank Distance (MRD) codes. Known classification results for exceptional scattered polynomials, i.e. polynomials which are scattered over infinite field extensions, are limited to the cases where their index $\ell$ is small, or a prime number larger than the $q$-degree $k$ of the polynomial, or an integer smaller than the $k$ in the case where $k$ is a prime. In this paper we completely classify exceptional scattered polynomials when the maximum between $\ell$ and $k$ is odd, and give partial results when it is even, extending a result of Ferraguti and Micheli in 2021.

This errata fixes a mistake in the part of Giulietti, P.; Liverani, C.; Pollicott, M. Anosov flows and dynamical zeta functions. Ann. of Math. (2) {\bf 178} (2013), no. 2, 687--773, which proves a spectral gap for contact Anosov flows with respect to the measure of maximal entropy (Section 7). However, the first part of the paper, in which it is proved that the Ruelle zeta function is meromorphic, is unaffected.

The Star Formation Rate Density (SFRD) history of the Universe is well constrained up to redshift $z \sim 2$. At earlier cosmic epochs, the picture has been largely inferred from UV-selected galaxies (e.g. Lyman-break galaxies, LBGs). However, LBGs' inferred SFRs strongly depend on the assumed dust extinction correction, which is not well-constrained at high-$z$, while observations in the radio domain are not affected by this issue. In this work we measure the SFRD from a 1.4 GHz-selected sample of $\sim$600 galaxies in the GOODS-N field up to redshift $\sim 3.5$. We take into account the contribution of Active Galactic Nuclei from the Infrared-Radio correlation. We measure the radio luminosity function, fitted with a modified Schechter function, and derive the SFRD. The cosmic SFRD shows a rise up to $z \sim 2$ and then an almost flat plateau up to $z \sim 3.5$. Our SFRD is in agreement with the ones from other FIR/radio surveys and a factor 2 higher than those from LBG samples. We also estimate that galaxies lacking a counterpart in the HST/WFC3 H-band ($H$-dark) make up $\sim 25\%$ of the $\phi$-integrated SFRD relative to the full sample at z $\sim 3.2$, and up to $58\%$ relative to LBG samples., Comment: 20 pages, 11 figures. Accepted for publication in ApJ

We investigate the radio-far infrared (FIR) correlation for a sample of $28$ bright high-redshift ($1 \lesssim z \lesssim 4$) star-forming galaxies selected in the FIR from the Herschel-ATLAS fields as candidates to be strongly gravitationally lensed. The radio information comes either from high sensitivity dedicated ATCA observations at $2.1$ GHz or from cross-matches with the FIRST survey at $1.4$ GHz. By taking advantage of source brightness possibly enhanced by lensing magnification, we identify a weak evolution with redshift out to $z\lesssim 4$ of the FIR-to-radio luminosity ratio $q_{\rm FIR}$. We also find that the $q_{\rm FIR}$ parameter as a function of the radio power $L_{1.4\,\rm GHz}$ displays a clear decreasing trend, similarly to what is observed for optically/radio selected lensed quasars found in literature, yet covering a complementary region in the $q_{\rm FIR}-L_{1.4\,\rm GHz}$ diagram. We interpret such a behavior in the framework of an in-situ galaxy formation scenario, as a result of the transition from an early dust-obscured star-forming phase (mainly pinpointed by our FIR selection) to a late radio-loud quasar phase (preferentially sampled by the optical/radio selection)., Comment: 12 pages, 6 figures. Minor changes and references updated to match the published version

We establish an abstract quenched linear response result for random dynamical systems, which we then apply to the case of smooth expanding on average cocycles on the unit circle. In sharp contrast to the existing results in the literature, we deal with the class of random dynamics that does not necessarily exhibit uniform decay of correlations. Our techniques rely on the infinite-dimensional ergodic theory and in particular, on the study of the top Oseledets space of a parametrized transfer operator cocycle., Comment: Electronic copy of final peer-reviewed manuscript accepted for publication in Communications in Mathematical Physics

Time-Of-Flight (TOF) technique coupled with semiconductor detectors is a powerful instrument to provide real-time characterization of ions accelerated because of laser-matter interactions. Nevertheless, the presence of strong electromagnetic pulses (EMPs) generated during the interactions, can severely hinder its employment. For this reason, the diagnostic system must be designed to have high EMP shielding. Here we present a new advanced prototype of detector, developed at ENEA-Centro Ricerche Frascati (Italy), with a large area (15 mm x 15 mm) polycrystalline diamond sensor having 150 microns thickness. The tailored detector design and testing ensure high sensitivity and, thanks to the fast temporal response, high energy resolution of the reconstructed ion spectrum. The detector was offline calibrated and then successfully tested during an experimental campaign carried out at the PHELIX laser facility at GSI (Germany). The high rejection to EMP fields was demonstrated and suitable calibrated spectra of the accelerated protons were obtained.

We present the ALMA view of 11 main-sequence DSFGs, (sub-)millimeter selected in the GOODS-S field, and spectroscopically confirmed to be at the peak of Cosmic SFH (z = 2-3). Our study combines the analysis of galaxy SED with ALMA continuum and CO spectral emission, by using ALMA Science Archive products at the highest spatial resolution currently available for our sample (< 1 arcsec). We include galaxy multi-band images and photometry (in the optical, radio and X-rays) to investigate the interlink between dusty, gaseous and stellar components and the eventual presence of AGN. We use multi-band sizes and morphologies to gain an insight on the processes that lead galaxy evolution, e.g. gas condensation, star formation, AGN feedback. The 11 DSFGs are very compact in the (sub-)millimeter (median r(ALMA) = 1.15 kpc), while the optical emission extends tolarger radii (median r(H)/r(ALMA) = 2.05). CO lines reveal the presence of a rotating disc of molecular gas, but we can not exclude either the presence of interactions and/or molecular outflows. Images at higher (spectral and spatial) resolution are needed to disentangle from the possible scenarios. Most of the galaxies are caught in the compaction phase, when gas cools and falls into galaxy centre, fuelling the dusty burst of star formation and the growing nucleus. We expect these DSFGs to be the high-zstar-forming counterparts of massive quiescent galaxies. Some features of CO emission in three galaxies are suggestive of forthcoming/ongoing AGN feedback, that is thought to trigger the morphological transition from star-forming disks to ETGs., Comment: 18 pages, 6 figures, 7 tables

A $k$-server Private Information Retrieval (PIR) code is a binary linear $[m,s]$-code admitting a generator matrix such that for every integer $i$ with $1\le i\le s$ there exist $k$ disjoint subsets of columns (called recovery sets) that add up to the vector of weight one, with the single $1$ in position $i$. As shown in \cite{Fazeli1}, a $k$-server PIR code is useful to reduce the storage overhead of a traditional $k$-server PIR protocol. Finding $k$-server PIR codes with a small blocklength for a given dimension has recently become an important research challenge. In this work, we propose new constructions of PIR codes from combinatorial structures, introducing the notion of $k$-partial packing. Several bounds over the existing literature are improved.