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This paper studies asynchronous stochastic approximation (SA) algorithms and their application to reinforcement learning in semi-Markov decision processes (SMDPs) with an average-reward criterion. We first extend Borkar and Meyn's stability proof method to accommodate more general noise conditions, leading to broader convergence guarantees for asynchronous SA algorithms. Leveraging these results, we establish the convergence of an asynchronous SA analogue of Schweitzer's classical relative value iteration algorithm, RVI Q-learning, for finite-space, weakly communicating SMDPs. Furthermore, to fully utilize the SA results in this application, we introduce new monotonicity conditions for estimating the optimal reward rate in RVI Q-learning. These conditions substantially expand the previously considered algorithmic framework, and we address them with novel proof arguments in the stability and convergence analysis of RVI Q-learning., Comment: The materials in this paper extend the authors' results from 2023, reported in arXiv:2408.16262 and arXiv:2312.15091. This paper incorporates and subsumes the results of arXiv:2312.15091 and serves as Part II of arXiv:2408.16262

The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy., Comment: 16 pages, 2 figures

This paper analyzes reinforcement learning (RL) algorithms for Markov decision processes (MDPs) under the average-reward criterion. We focus on Q-learning algorithms based on relative value iteration (RVI), which are model-free stochastic analogues of the classical RVI method for average-reward MDPs. These algorithms have low per-iteration complexity, making them well-suited for large state space problems. We extend the almost-sure convergence analysis of RVI Q-learning algorithms developed by Abounadi, Bertsekas, and Borkar (2001) from unichain to weakly communicating MDPs. This extension is important both practically and theoretically: weakly communicating MDPs cover a much broader range of applications compared to unichain MDPs, and their optimality equations have a richer solution structure (with multiple degrees of freedom), introducing additional complexity in proving algorithmic convergence. We also characterize the sets to which RVI Q-learning algorithms converge, showing that they are compact, connected, potentially nonconvex, and comprised of solutions to the average-reward optimality equation, with exactly one less degree of freedom than the general solution set of this equation. Furthermore, we extend our analysis to two RVI-based hierarchical average-reward RL algorithms using the options framework, proving their almost-sure convergence and characterizing their sets of convergence under the assumption that the underlying semi-Markov decision process is weakly communicating.

We use JWST/NIRSpec observations from the Assembly of Ultradeep Rest-optical Observations Revealing Astrophysics (AURORA) survey to constrain the shape of the nebular attenuation curve of a star-forming galaxy at z=4.41, GOODSN-17940. We utilize 11 unblended HI recombination lines to derive the attenuation curve spanning optical to near-infrared wavelengths (3751-9550 \r{A}). We then leverage a high-S/N spectroscopic detection of the rest-frame ultraviolet continuum in combination with rest-UV photometric measurements to constrain the shape of the curve at ultraviolet wavelengths. While this UV constraint is predominantly based on stellar emission, the large measured equivalent widths of H$\alpha$ and H$\beta$ indicate that GOODSN-17940 is dominated by an extremely young stellar population <10 Myr in age such that the UV stellar continuum experiences the same attenuation as the nebular emission. The resulting combined nebular attenuation curve spans 1400-9550 \r{A} and has a shape that deviates significantly from commonly assumed dust curves in high-redshift studies. Relative to the Milky Way, SMC, and Calzetti curves, the new curve has a steeper slope at long wavelengths ($\lambda>5000$ \r{A}) while displaying a similar slope across blue-optical wavelengths ($\lambda=3750-5000$ \r{A}). In the ultraviolet, the new curve is shallower than the SMC and Calzetti curves and displays no significant 2175 \r{A} bump. This work demonstrates that the most commonly assumed dust curves are not appropriate for all high-redshift galaxies. These results highlight the ability to derive nebular attenuation curves for individual high-redshift sources with deep JWST/NIRSpec spectroscopy, thereby improving the accuracy of physical properties inferred from nebular emission lines., Comment: 21 pages, 6 figures, 1 table, submitted to ApJ

We study, from both a theoretical and observational perspective, the physical origin and spectroscopic impact of extreme nebular emission in high-redshift galaxies. The nebular continuum, which can appear during extreme starbursts, is of particular importance as it tends to redden UV slopes and has a significant contribution to the UV luminosities of galaxies. Furthermore, its shape can be used to infer the gas density and temperature of the ISM. First, we provide a theoretical background, showing how different stellar populations (SPS models, IMFs, and stellar temperatures) and nebular conditions impact observed galaxy spectra. We demonstrate that, for systems with strong nebular continuum emission, 1) UV fluxes can increase by up to 0.7~magnitudes (or more in the case of hot/massive stars) above the stellar continuum, which may help reconcile the surprising abundance of bright high-redshift galaxies and the elevated UV luminosity density at $z>10$, 2) at high gas densities, UV slopes can redden from $\beta\lesssim-2.5$ to $\beta\sim-1$, 3) observational measurements of $\xi_{ion}$ are grossly underestimated, and 4) UV downturns from two-photon emission can masquerade as DLAs. Second, we present a dataset of 58 galaxies observed with NIRSpec on JWST at $2.510$ galaxies, finding that UV slopes and UV downturns are in some cases redder or steeper than expected from SPS models, which may hint at more exotic (e.g. hotter/more massive stars or AGN) ionizing sources., Comment: 26 pages, 18 figures, submitted to The Open Journal of Astrophysics

We present an analysis of JWST Ly$\alpha$ spectroscopy of $z\gtrsim6.5$ galaxies, using observations in the public archive covering galaxies in four independent fields (GOODS-N, GOODS-S, Abell 2744, EGS). We measure Ly$\alpha$ emission line properties for a sample of $210$ $z\simeq6.5-13$ galaxies, with redshifts confirmed independently of Ly$\alpha$ in all cases. We present $3$ new detections of Ly$\alpha$ emission in JWST spectra, including a large equivalent width (EW $=143\ \r{A}$) Ly$\alpha$ emitter with strong CIV emission (EW $=21\ \r{A}$) at $z=7.1$ in GOODS-N. We measure the redshift-dependent Ly$\alpha$ EW distribution across our sample. We find that strong Ly$\alpha$ emission (EW $>25\ \r{A}$) becomes increasingly rare at earlier epochs, suggesting that the transmission of Ly$\alpha$ photons decreases by $4\times$ between $z\simeq5$ and $z\simeq9$. We describe potential implications for the IGM neutral fraction. There is significant field to field variance in the Ly$\alpha$ emitter fraction. In contrast to the three other fields, the EGS shows no evidence for reduced transmission of Ly$\alpha$ photons at $z\simeq7-8$, suggesting a significantly ionized sightline may be present in the field. We use available NIRCam grism observations from the FRESCO survey to characterize overdensities on large scales around known Ly$\alpha$ emitters in the GOODS fields. The strongest overdensities appear linked with extremely strong Ly$\alpha$ detections (EW $>50\ \r{A}$) in most cases. Future Ly$\alpha$ spectroscopy with JWST has the potential to constrain the size of ionized regions around early galaxy overdensities, providing a new probe of the reionization process., Comment: 32 pages, 11 figures, submitted to ApJ

Strong gravitational lensing magnifies the light from a background source, allowing us to study these sources in detail. Here, we study the spectra of a $z = 1.95$ lensed Type Ia supernova SN~Encore for its brightest Image A, taken 39 days apart. We infer the spectral age with template matching using the supernova identification (SNID) software and find the spectra to be at 29.0 $\pm 5.0$ and 37.4 $\pm 2.8$ rest-frame days post maximum respectively, consistent with separation in the observer frame after accounting for time-dilation. Since SNe~Ia measure dark energy properties by providing relative distances between low- and high-$z$ SNe, it is important to test for evolution of spectroscopic properties. Comparing the spectra to composite low-$z$ SN~Ia spectra, we find strong evidence for similarity between the local sample of SN~Encore. The line velocities of common SN~Ia spectral lines, Si II 6355 and Ca II NIR triplet are consistent with the distribution for the low-$z$ sample as well as other lensed SNe~Ia, e.g. iPTF16geu ($z = 0.409$) and SN~H0pe ($z = 1.78$). The consistency in SN~Ia spectra across cosmic time demonstrates the utility of using SNe~Ia in the very high-$z$ universe for dark energy inference. We also find that the spectra of SN~Encore match the predictions for explosion models very well. With future large samples of lensed SNe~Ia, spectra at such late phases will be important to distinguish between different explosion scenarios., Comment: 9 pages, 8 figures, submitted to MNRAS. Comments welcome

While JWST has observed galaxies assembling as early as $z\sim14$, evidence of galaxies with significant old stellar populations in the Epoch of Reionisation (EoR) -- the descendants of these earliest galaxies -- are few and far between. Bursty star-formation histories (SFHs) have been invoked to explain the detectability of the earliest UV-bright galaxies, but also to interpret galaxies showing Balmer breaks without nebular emission lines. We present the first spectroscopic evidence of a $z\sim7.9$ galaxy, A2744-YD4, which shows a Balmer break and emission lines, indicating the presence of both a mature and young stellar population. The spectrum of A2744-YD4 shows peculiar emission line ratios suggesting a relatively low ionisation parameter and high gas-phase metallicity. A median stack of galaxies with similar emission line ratios reveals a clear Balmer break in their stacked spectrum. This suggests that a mature stellar population ($\sim 80$ Myr old) has produced a chemically enriched, disrupted interstellar medium. Based on SED-fitting and comparison to simulations, we conclude that the observed young stellar population is in fact the result of a rejuvenation event following a lull in star formation lasting $\sim 20$ Myr, making A2744-YD4 and our stack the first spectroscopic confirmation of galaxies that have rejuvenated following a mini-quenched phase. These rejuvenating galaxies appear to be in an exceptional evolutionary moment where they can be identified. Our analysis shows that a young stellar population of just $\sim 30 \%$ of the total stellar mass would erase the Balmer break. Hence, 'outshining' through bursty SFHs of galaxies in the early Universe is likely plaguing attempts to measure their stellar ages and masses accurately., Comment: 14 pages, 12 figures, 1 table. Submitted to MNRAS. Comments are welcome

We present results on the emission-line properties of z=1.4-7.5 star-forming galaxies in the Assembly of Ultradeep Rest-optical Observations Revealing Astrophysics (AURORA) Cycle 1 JWST/NIRSpec program. Based on its depth, continuous wavelength coverage from 1--5 microns, and medium spectral resolution (R~1000), AURORA includes detections of a large suite of nebular emission lines spanning a broad range in rest wavelength. We investigate the locations of AURORA galaxies in multiple different emission-line diagrams, including traditional "BPT" diagrams of [OIII]/Hbeta vs. [NII]/Halpha, [SII]/Halpha, and [OI]/Halpha, and the "ionization-metallicity" diagram of [OIII]/[OII] (O32) vs. ([OIII]+[OII])/Hbeta (R23). We also consider a bluer rest-frame "ionization-metallicity" diagram introduced recently to characterize z>10 galaxies: [NeIII]/[OII] vs. ([NeIII]+[OII])/Hdelta; as well as longer-wavelength diagnostic diagrams extending into the rest-frame near-IR: [OIII]/Hbeta vs. [SIII]/[SII] (S32); and HeI/Pagamma and [SIII]/Pagamma vs. [FeII]/Pabeta. With a significant boost in signal-to-noise and large, representative samples of individual galaxy detections, the AURORA emission-line diagrams presented here definitively confirm a physical picture in which chemically-young, alpha-enhanced, massive stars photoionize the ISM in distant galaxies with a harder ionizing spectrum at fixed nebular metallicity than in their z~0 counterparts. We also uncover previously unseen evolution prior to z~2 in the [OIII]/Hbeta vs. [NII]/Halpha diagram, which motivates deep NIRSpec observations at even higher redshift. Finally, we present the first statistical sample of rest-frame near-IR emission-line diagnostics in star-forming galaxies at high redshift. In order to truly interpret rest-frame near-IR line ratios including [FeII], we must obtain better constraints on dust depletion in the high-redshift ISM., Comment: 17 pages, 8 figures, submitted to ApJ

We present the number densities and physical properties of the bright galaxies spectroscopically confirmed at $z\sim7-14$. Our sample is composed of 53 galaxies at $z_\mathrm{spec}\sim7-14$, including recently-confirmed galaxies at $z_\mathrm{spec}=12.34-14.32$ with JWST, as well as new confirmations at $z_\mathrm{spec}=6.583-7.643$ with $-24< M_\mathrm{UV}< -21$ mag using ALMA and Keck. Our JWST/NIRSpec observations have also revealed that very bright galaxy candidates at $z\sim10-13$ identified from ground-based telescope images before JWST are passive galaxies at $z\sim3-4$, emphasizing the necessity of strict screening and spectroscopy in the selection of the brightest galaxies at $z>10$. The UV luminosity functions derived from these spectroscopic results are consistent with a double power-law function, showing tensions with theoretical models at the bright end. To understand the origin of the overabundance of bright galaxies, we investigate their morphologies using JWST/NIRCam high-resolution images obtained in various surveys including PRIMER and COSMOS-Web. We find that $\sim70\%$ of the bright galaxies at $z\sim7$ exhibit clumpy morphologies with multiple sub-components, suggesting merger-induced starburst activity, which is consistent with SED fitting results showing bursty star formation histories. At $z\gtrsim10$, bright galaxies are classified into two types of galaxies; extended ones with weak high-ionization emission lines, and compact ones with strong high-ionization lines including NIV]$\lambda$1486, indicating that at least two different processes (e.g., merger-induced starburst and compact star formation/AGN) are shaping the physical properties of the brightest galaxies at $z\gtrsim10$ and are responsible for their overabundance., Comment: 32 pages, 22 figures, submitted to ApJ

Many reinforcement learning algorithms are built on an assumption that an agent interacts with an environment over fixed-duration, discrete time steps. However, physical systems are continuous in time, requiring a choice of time-discretization granularity when digitally controlling them. Furthermore, such systems do not wait for decisions to be made before advancing the environment state, necessitating the study of how the choice of discretization may affect a reinforcement learning algorithm. In this work, we consider the relationship between the definitions of the continuous-time and discrete-time returns. Specifically, we acknowledge an idiosyncrasy with naively applying a discrete-time algorithm to a discretized continuous-time environment, and note how a simple modification can better align the return definitions. This observation is of practical consideration when dealing with environments where time-discretization granularity is a choice, or situations where such granularity is inherently stochastic., Comment: RLC 2024

Properties of Riesz capacity are developed with respect to the kernel exponent $p \in (-\infty,n)$, namely that capacity is monotonic as a function of $p$, that its endpoint limits recover the diameter and volume of the set, and that capacity is left-continuous with respect to $p$ and is right-continuous provided (when $p \geq 0$) that an additional hypothesis holds. Left and right continuity properties of the equilibrium measure are obtained too.

Recent stellar chemical abundance measurements of a handful of $z\sim2$ quiescent galaxies have suggested these galaxies exhibit a remarkably strong $\alpha$-enhancement compared to their local and intermediate redshift counterparts. This apparent chemical evolution following quenching suggests that even the innermost regions of massive early-type galaxies may have experienced substantial mixing of stars in mergers, challenging a purely inside-out growth model. However, larger samples are needed to determine whether a high $\alpha$-enhancement ([Mg/Fe] $\approx 0.5$) is common in $z \sim 2$ quiescent galaxies, and a comparative analysis is needed to determine whether it is consistently inferred using different stellar population synthesis models. We report age and stellar chemical abundance measurements for a sample of four gravitationally lensed quiescent galaxies at $z\sim2.1-2.65$ based on Magellan/FIRE spectroscopy. For three of these galaxies we constrain the $\alpha$-enhancement, and in two cases we measure high values comparable to earlier results when the spectra are analyzed consistently. We also find that the choice of modeling approach can exert a significant effect on the measured abundances. This model dependence can be partly, but not entirely, explained by the complex abundance patterns of $\alpha$ elements in galaxies, which has been observed at lower redshifts and in one $z \sim 2$ quiescent galaxy. Our investigation highlights the importance of independently varying abundance of $\alpha$ elements when fitting the spectra of such galaxies. Observations with JWST will soon deliver precise and spatially resolved abundances of these and other quiescent galaxies at cosmic noon, opening a new window into their evolution., Comment: 10 pages, submitted to The Astrophysical Journal

We show that discounted methods for solving continuing reinforcement learning problems can perform significantly better if they center their rewards by subtracting out the rewards' empirical average. The improvement is substantial at commonly used discount factors and increases further as the discount factor approaches one. In addition, we show that if a problem's rewards are shifted by a constant, then standard methods perform much worse, whereas methods with reward centering are unaffected. Estimating the average reward is straightforward in the on-policy setting; we propose a slightly more sophisticated method for the off-policy setting. Reward centering is a general idea, so we expect almost every reinforcement-learning algorithm to benefit by the addition of reward centering., Comment: In Proceedings of RLC 2024

The ComPair gamma-ray telescope is a technology demonstrator for a future gamma-ray telescope called the All-sky Medium Energy Gamma-ray Observatory (AMEGO). The instrument is composed of four subsystems, a double-sided silicon strip detector, a virtual Frisch grid CdZnTe calorimeter, a CsI:Tl based calorimeter, and an anti-coincidence detector (ACD). The CsI calorimeter's goal is to measure the position and energy deposited from high-energy events. To demonstrate the technological readiness, the calorimeter has flown onboard a NASA scientific balloon as part of the GRAPE-ComPair mission and accumulated around 3 hours of float time at an altitude of 40 km. During the flight, the CsI calorimeter observed background radiation, Regener-Pfotzer Maximum, and several gamma-ray activation lines originating from aluminum.

JWST observations have recently begun delivering the first samples of Ly$\alpha$ velocity profile measurements at $z>6$, opening a new window on the reionization process. Interpretation of $z\gtrsim6$ line profiles is currently stunted by limitations in our knowledge of the intrinsic Ly$\alpha$ profile (before encountering the IGM) of the galaxies that are common at $z\gtrsim6$. To overcome this shortcoming, we have obtained resolved ($R\sim3900$) Ly$\alpha$ spectroscopy of $42$ galaxies at $z=2.1-3.4$ with similar properties as are seen at $z>6$. We quantify a variety of Ly$\alpha$ profile statistics as a function of [OIII]+H$\beta$ EW. Our spectra reveal a new population of $z\simeq 2-3$ galaxies with large [OIII]+H$\beta$ EWs ($>1200\ \r{A}$) and a large fraction of Ly$\alpha$ flux emerging near the systemic redshift (peak velocity $\simeq0$ km s$^{-1}$). These spectra indicate that low density neutral hydrogen channels are able to form in a subset of low mass galaxies ($\lesssim1\times10^8\ M_{\odot}$) that experience a burst of star formation (sSFR $>100$ Gyr$^{-1}$). Other extreme [OIII] emitters show weaker Ly$\alpha$ that is shifted to higher velocities ($\simeq240$ km s$^{-1}$) with little emission near line center. We investigate the impact the IGM is likely to have on these intrinsic line profiles in the reionization era, finding that the centrally peaked Ly$\alpha$ emitters should be strongly attenuated at $z\gtrsim5$. We show that these line profiles are particularly sensitive to the impact of resonant scattering from infalling IGM and can be strongly attenuated even when the IGM is highly ionized at $z\simeq 5$. We compare these expectations against a new database of $z\gtrsim6.5$ galaxies with robust velocity profiles measured with JWST/NIRSpec., Comment: 28 pages, 11 figures, accepted by ApJ

The majority of estimates of the social cost of carbon use preference parameters calibrated to data for North America and Europe. We here use representative data for attitudes to time and risk across the world. The social cost of carbon is substantially higher in the global north than in the south. The difference is more pronounced if we count people rather than countries.

We present a sample of 341 "little red dots" (LRDs) spanning the redshift range $z\sim2-11$ using data from the CEERS, PRIMER, JADES, UNCOVER and NGDEEP surveys. These sources are likely heavily-reddened AGN that trace a previously-hidden phase of dust-obscured black hole growth in the early Universe. Unlike past use of color indices to identify LRDs, we employ continuum slope fitting using shifting bandpasses to sample the same rest-frame emission blueward and redward of the Balmer break. This approach allows us to identify LRDs over a wider redshift range and is less susceptible to contamination from galaxies with strong breaks that otherwise lack a rising red continuum. The redshift distribution of our sample increases at $z<8$ and then undergoes a rapid decline at $z\sim4.5$, which may tie the emergence, and obscuration, of these sources to the inside-out growth that galaxies experience during this epoch. We find that LRDs are 2-3 dex more numerous than bright quasars at $z\sim5-7$, but their number density is only 0.6-1 dex higher than X-ray and UV selected AGN at these redshifts. Within our sample, we have identified the first X-ray detected LRDs at $z=3.1$ and $z=4.66$. An X-ray spectral analysis confirms that these AGN are moderately obscured with $\log\,(N_{\rm H}/{\rm cm}^{2}$) of $23.3^{+0.4}_{-1.3}$ and $22.72^{+0.13}_{-0.16}$. Our analysis reveals that reddened AGN emission dominates their rest-optical light, while the rest-UV originates from their host galaxies. We also present NIRSpec follow-up spectroscopy of 17 LRDs that show broad emission lines consistent with AGN activity. The confirmed AGN fraction of our sample is $71\%$ for sources with F444W$<26.5$. In addition, we find three LRDs with narrow blue-shifted Balmer absorption features in their spectra, suggesting an outflow of high-density, low ionization gas from near the central engine of these faint, red AGN., Comment: 23 pages, 17 figures, submitted to ApJ

A family of discrete Schroedinger operators is investigated through scattering theory. The continuous spectrum of these operators exhibit changes of multiplicity, and some of these operators possess resonances at thresholds. It is shown that the corresponding wave operators belong to an explicitly constructed C*-algebra, whose K-theory is carefully analysed. An index theorem is deduced from these investigations, which corresponds to a topological version of Levinson's theorem in presence of embedded thresholds, resonances, and changes of multiplicity of the scattering matrices. In the second half of the paper, very detailed computations for the simplest realisation of this family of operators are provided. In particular, a surface of resonances is exhibited, probably for the first time. For Levinson's theorem, it is shown that contributions due to resonances at the lowest value and at the highest value of the continuous spectrum play an essential role., Comment: 44 pages

This study critically evaluates the impact of the Pradhan Mantri Ujjwala Yojana (PMUY) on LPG accessibility among poor households in India. Using Propensity Score Matching and Difference-in-Differences estimators and the National Family Health Survey (NFHS) dataset, the Average Treatment Effect on the interdedly Treated is a modest 2.1 percentage point increase in LPG consumption due to PMUY, with a parallel decrease in firewood consumption. Regional analysis reveals differential impacts, with significant progress in the North, West, and South but less pronounced effects in the East and North East. The study also underscores variance across social groups, with Schedule Caste households showing the most substantial benefits, while Scheduled Tribes households are hardly affected. Despite the PMUY's initial success in facilitating LPG access, sustaining its usage remains challenging. Policy should emphasise targeted interventions, income support, and address regional and community-specific disparities for the sustained usage of LPG.

We report first results from a deep near infrared campaign with the Hubble Space Telescope to obtain late-epoch images of the Hubble Ultra-Deep Field (HUDF), 10-15 years after the first epoch data were obtained. The main objectives are to search for faint active galactic nuclei (AGN) at high redshifts by virtue of their photometric variability, and measure (or constrain) the comoving number density of supermassive black holes (SMBHs), n_{SMBH}, at early times. In this Letter we present an overview of the program and preliminary results concerning eight objects. Three variables are supernovae, two of which are apparently hostless with indeterminable redshifts, although one has previously been recorded at a z\approx 6 object precisely because of its transient nature. Two further objects are clear AGN at z= 2.0 and 3.2, based on morphology and/or infrared spectroscopy from JWST. Three variable targets are identified at z = 6-7, which are also likely AGN candidates. These sources provide a first measure of n_{SMBH} in the reionization epoch by photometric variability, which places a firm lower limit of 3 \times 10^{-4} cMpc^{-3}. After accounting for variability and luminosity incompleteness, we estimate n_{SMBH} \gtrsim 8 \times 10{-3} cMpc{-3}, which is the largest value so far reported at these redshifts. This SMBH abundance is also strikingly similar to estimates of n_{SMBH} in the local Universe. We discuss how these results test various theories for SMBH formation., Comment: In press at ApJL

The $q$-th moment ($q>0$) of electrostatic equilibrium measure is shown to be minimal for a centered ball among $3$-dimensional sets of given capacity, while among $2$-dimensional sets a centered disk is the minimizer for $0

Combining the public JWST/NIRCam imaging programs CEERS, PRIMER and JADES, spanning a total area of $\sim$500 arcmin$^2$, we obtain a sample of $>$30,000 galaxies at $z\sim4-9$ that allows us to perform a complete, rest-optical selected census of the galaxy population at $z>3$. Comparing the stellar mass $M_*$ and the UV-slope $\beta$ distributions between JWST- and HST-selected samples, we generally find very good agreement and no significant biases. Nevertheless, JWST enables us to probe a small population of UV-red galaxies that was missing from previous HST-based LBG samples. We measure galaxy stellar mass functions (SMFs) at $z\sim4-9$ and show that they are broadly consistent with existing literature results. However, UV-red galaxies dominate the high-mass end of the SMF at least out to $z\sim6$. In particular the most massive galaxies typically show very red colors between $\lambda_{obs}\sim1.5\mu$m and $\sim4.5\mu$m, and thus JWST's unprecedented resolution and sensitivity at these wavelengths yields more accurate constraints on their abundance and masses. The implied redshift evolution of the high-mass end of the SMF suggests a rapid build-up of massive dust-obscured as well as quiescent galaxies from $z\sim6$ to $z\sim4$ as well as an enhanced efficiency of star formation towards earlier times ($z\gtrsim6$). We find the SMFs to be steep over the entire redshift range, and slightly steepening with redshift from $z\sim 4-6$, reaching values of $\approx-2$ at $z\gtrsim6$. Finally, we show that the galaxy mass density grows by a factor $\sim20\times$ in the $\sim1$ Gyr of cosmic time from $z\sim9$ to $z\sim4$. Our results emphasize the importance of rest-frame optically-selected samples in inferring accurate distributions of physical properties and studying the mass build-up of galaxies in the first 1.5 Gyr of cosmic history., Comment: 29 pages, 17 figures, submitted to MNRAS

The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participate, Comment: 194 pages, 66 figures. Comments are welcome (wstelescope@gmail.com)

A new version of the database for the meta-analysis of estimates of the social cost of carbon is presented. New records were added, and new fields on the impact of climate change and the shape of the welfare function. The database was extended to co-author and citation networks., Comment: arXiv admin note: substantial text overlap with arXiv:2105.03656

JWST has recently sparked a new era of Ly$\alpha$ spectroscopy, delivering the first measurements of the Ly$\alpha$ escape fraction and velocity profile in typical galaxies at $z\simeq6-10$. These observations offer new prospects for insight into the earliest stages of reionization. But to realize this potential, we need robust models of Ly$\alpha$ properties in galaxies at $z\simeq5-6$ when the IGM is mostly ionized. Here we use new JWST observations from the JADES and FRESCO surveys combined with VLT/MUSE and Keck/DEIMOS data to characterize statistical distributions of Ly$\alpha$ velocity offsets, escape fractions, and EWs in $z\simeq5-6$ galaxies. We find that galaxies with large Ly$\alpha$ escape fractions (> 0.2) are common at $z\simeq5-6$, comprising 30 per cent of Lyman break selected samples. Comparing to literature studies, our census suggests that Ly$\alpha$ becomes more prevalent in the galaxy population toward higher redshift from $z\sim3$ to $z\sim6$, although we find that this evolution slows considerably between $z\sim5$ and $z\sim6$, consistent with modest attenuation from residual HI in the mostly ionized IGM at $z\simeq5-6$. We find significant evolution in Ly$\alpha$ velocity profiles between $z\simeq2-3$ and $z\simeq5-6$, likely reflecting the influence of resonant scattering from residual intergalactic HI on the escape of Ly$\alpha$ emission near line center. This effect will make it challenging to use Ly$\alpha$ peak offsets as a probe of Lyman continuum leakage at $z\simeq5-6$. We use our $z\simeq5-6$ Ly$\alpha$ distributions to make predictions for typical Ly$\alpha$ properties at $z\gtrsim8$ and discuss implications of a recently-discovered Ly$\alpha$ emitter at $z\simeq8.5$ with a small peak velocity offset (156 km s$^{-1}$)., Comment: 31 pages, 12 figures, accepted by MNRAS

We study the spatially resolved outflow properties of CSWA13, an intermediate mass ($M_*=10^{9}~\mathrm{M}_{\odot}$), gravitationally lensed star-forming galaxy at $z=1.87$. We use Keck/KCWI to map outflows in multiple rest-frame ultraviolet ISM absorption lines, along with fluorescent Si II$^*$ emission, and nebular emission from C III] tracing the local systemic velocity. The spatial structure of outflow velocity mirrors that of the nebular kinematics, which we interpret to be a signature of a young galactic wind that is pressurizing the ISM of the galaxy but is yet to burst out. From the radial extent of Si II$^*$ emission, we estimate that the outflow is largely encapsulated within $3.5$ kpc. We explore the geometry (e.g., patchiness) of the outflow by measuring the covering fraction at different velocities, finding that the maximum covering fraction is at velocities $v\simeq-150$ km$\,$s$^{-1}$. Using the outflow velocity ($v_{out}$), radius ($R$), column density ($N$), and solid angle ($\Omega$) based on the covering fraction, we measure the mass loss rate $\log\dot{m}_{out}/(\mathrm{M}_{\odot}\text{yr}^{-1}) = 1.73\pm0.23$ and mass loading factor $\log\eta = 0.04\pm0.34$ for the low-ionization outflowing gas in this galaxy. These values are relatively large and the bulk of the outflowing gas is moving with speeds less than the escape velocity of the galaxy halo, suggesting that the majority of outflowing mass will remain in the circumgalactic medium and/or recycle back into the galaxy. The results support a picture of high outflow rates transporting mass and metals into the inner circumgalactic medium, providing the gas reservoir for future star formation., Comment: Submitted to ApJ. Comments welcome (17 pages, 10 figures, 1 table)

In the era of sustainability, firms grapple with the decision of how much to invest in green innovation and how it influences their economic trajectory. This study employs the Crepon, Duguet, and Mairesse (CDM) framework to examine the conversion of R&D funds into patents and their impact on productivity, effectively addressing endogeneity by utilizing predicted dependent variables at each stage to exclude unobservable factors. Extending the classical CDM model, this study contrasts green and non-green innovations' economic effects. The results show non-green patents predominantly drive productivity gains, while green patents have a limited impact in non-heavy polluting firms. However, in high-pollution and manufacturing sectors, both innovation types equally enhance productivity. Using unconditional quantile regression, I found green innovation's productivity impact follows an inverse U-shape, unlike the U-shaped pattern of non-green innovation. Significantly, in the 50th to 80th productivity percentiles of manufacturing and high-pollution firms, green innovation not only contributes to environmental sustainability but also outperforms non-green innovation economically.

Quantitative technology forecasting uses quantitative methods to understand and project technological changes. It is a broad field encompassing many different techniques and has been applied to a vast range of technologies. A widely used approach in this field is trend extrapolation. Based on the publications available to us, there has been little or no attempt made to systematically review the empirical evidence on quantitative trend extrapolation techniques. This study attempts to close this gap by conducting a systematic review of technology forecasting literature addressing the application of quantitative trend extrapolation techniques. We identified 25 studies relevant to the objective of this research and classified the techniques used in the studies into different categories, among which growth curves and time series methods were shown to remain popular over the past decade, while newer methods, such as machine learning-based hybrid models, have emerged in recent years. As more effort and evidence are needed to determine if hybrid models are superior to traditional methods, we expect to see a growing trend in the development and application of hybrid models to technology forecasting.

The social cost of carbon (SCC) serves as a concise gauge of climate change's economic impact, often reported at the global and country level. SCC values are disproportionately high for less-developed, populous countries. Assessing the contributions of urban and non-urban areas to the SCC can provide additional insights for climate policy. Cities are essential for defining global emissions, influencing warming levels and associated damages. High exposure and concurrent socioenvironmental problems exacerbate climate change risks in cities. Using a spatially explicit integrated assessment model, the SCC is estimated at USD$137-USD$579/tCO2, rising to USD$262-USD$1,075/tCO2 when including urban heat island (UHI) warming. Urban SCC dominates, with both urban exposure and the UHI contributing significantly. A permanent 1% reduction of the UHI in urban areas yields net present benefits of USD$484-USD$1,562 per urban dweller. Global cities have significant leverage and incentives for a swift transition to a low-carbon economy, and for reducing local warming.

This study investigates the long-term economic impact of sea-level rise (SLR) on coastal regions in Europe, focusing on Gross Domestic Product (GDP). Using a novel dataset covering regional SLR and economic growth from 1900 to 2020, we quantify the relationships between SLR and regional GDP per capita across 79 coastal EU & UK regions. Our results reveal that the current SLR has already negatively influenced GDP of coastal regions, leading to a cumulative 4.7% loss at 39 cm of SLR. Over the 120 year period studied, the actualised impact of SLR on the annual growth rate is between -0.02% and 0.04%. Extrapolating these findings to future climate and socio-economic scenarios, we show that in the absence of additional adaptation measures, GDP losses by 2100 could range between -6.3% and -20.8% under the most extreme SLR scenario (SSP5-RCP8.5 High-end Ice, or -4.0% to -14.1% in SSP5-RCP8.5 High Ice). This statistical analysis utilising a century-long dataset, provides an empirical foundation for designing region-specific climate adaptation strategies to mitigate economic damages caused by SLR. Our evidence supports the argument for strategically relocating assets and establishing coastal setback zones when it is economically preferable and socially agreeable, given that protection investments have an economic impact.

Glioblastoma (GBM) is one of the most aggressive and lethal human cancers. Intra-tumoral genetic heterogeneity poses a significant challenge for treatment. Biopsy is invasive, which motivates the development of non-invasive, MRI-based machine learning (ML) models to quantify intra-tumoral genetic heterogeneity for each patient. This capability holds great promise for enabling better therapeutic selection to improve patient outcomes. We proposed a novel Weakly Supervised Ordinal Support Vector Machine (WSO-SVM) to predict regional genetic alteration status within each GBM tumor using MRI. WSO-SVM was applied to a unique dataset of 318 image-localized biopsies with spatially matched multiparametric MRI from 74 GBM patients. The model was trained to predict the regional genetic alteration of three GBM driver genes (EGFR, PDGFRA, and PTEN) based on features extracted from the corresponding region of five MRI contrast images. For comparison, a variety of existing ML algorithms were also applied. The classification accuracy of each gene was compared between the different algorithms. The SHapley Additive exPlanations (SHAP) method was further applied to compute contribution scores of different contrast images. Finally, the trained WSO-SVM was used to generate prediction maps within the tumoral area of each patient to help visualize the intra-tumoral genetic heterogeneity. This study demonstrated the feasibility of using MRI and WSO-SVM to enable non-invasive prediction of intra-tumoral regional genetic alteration for each GBM patient, which can inform future adaptive therapies for individualized oncology., Comment: 36 pages, 8 figures, 3 tables

In this paper, we study asynchronous stochastic approximation algorithms without communication delays. Our main contribution is a stability proof for these algorithms that extends a method of Borkar and Meyn by accommodating more general noise conditions. We also derive convergence results from this stability result and discuss their application in important average-reward reinforcement learning problems., Comment: Corrected typos and a minor error; parts of this material will be included in a separate future arXiv preprint

The bubble transform is a procedure to decompose differential forms, which are piecewise smooth with respect to a given triangulation of the domain, into a sum of local bubbles. In this paper, an improved version of a construction in the setting of the de Rham complex previously proposed by the authors is presented. The major improvement in the decomposition is that unlike the previous results, in which the individual bubbles were rational functions with the property that groups of local bubbles summed up to preserve piecewise smoothness, the new decomposition is strictly space-preserving in the sense that each local bubble preserves piecewise smoothness. An important property of the transform is that the construction only depends on the given triangulation of the domain and is independent of any finite element space. On the other hand, all the standard piecewise polynomial spaces are invariant under the transform. Other key properties of the transform are that it commutes with the exterior derivative, is bounded in L^2, and satisfies the stable decomposition property.

Carbon abatement decisions are usually based on the implausible assumption of constant social preference. This paper focuses on a specific case of market and non-market goods, and investigates the optimal climate policy when social preference for them is also changed by climate policy in the DICE model. The relative price of non-market goods grows over time due to increases in both relative scarcity and appreciation of it. Therefore, climbing relative price brings upward the social cost of carbon denominated in terms of market goods. Because abatement decision affects the valuation of non-market goods in the utility function, unlike previous climate-economy models, we solve the model iteratively by taking the obtained abatement rates from the last run as inputs in the current run. The results in baseline calibration advocate a more stringent climate policy, where endogenous social preference to climate policy raises the social cost of carbon further by roughly 12%-18% this century. Moreover, neglecting changing social preference leads to an underestimate of non-market goods damages by 15%. Our results support that climate policy is self-reinforced if it favors more expensive consumption type.

We investigate optimal carbon abatement in a dynamic general equilibrium climate-economy model with endogenous structural change. By differentiating the production of investment from consumption, we show that social cost of carbon can be conceived as a reduction in physical capital. In addition, we distinguish two final sectors in terms of productivity growth and climate vulnerability. We theoretically show that heterogeneous climate vulnerability results in a climate-induced version of Baumol's cost disease. Further, if climate-vulnerable sectors have high (low) productivity growth, climate impact can either ameliorate (aggravate) the Baumol's cost disease, call for less (more) stringent climate policy. We conclude that carbon abatement should not only factor in unpriced climate capital, but also be tailored to Baumol's cost and climate diseases.

We prove a general Levinson's theorem for Schr\"odinger operators in two dimensions with threshold obstructions at zero energy. Our results confirm and simplify earlier seminal results of Boll\'e, Gesztesy et al., while providing an explicit topological interpretation. We also derive explicit formulas for the wave operators, and so show that they are elements of a $C^*$-algebra introduced by Cordes. As a consequence of our approach, we provide an evaluation of the spectral shift function at zero in the presence of $p$-resonances., Comment: 27 pages

The social cost of carbon is the damage avoided by slightly reducing carbon dioxide emissions. It is a measure of the desired intensity of climate policy. The social cost of carbon is highly uncertain because of the long and complex cause-effect chain, and because it quantifies and aggregates impacts over a long period of time, affecting all people in a wide range of possible futures. Recent estimates are around $\$$80/tCO$_2$.