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The Butterfly Effect, a concept originating from chaos theory, underscores how small changes can have significant and unpredictable impacts on complex systems. In the context of AI fairness and bias, the Butterfly Effect can stem from a variety of sources, such as small biases or skewed data inputs during algorithm development, saddle points in training, or distribution shifts in data between training and testing phases. These seemingly minor alterations can lead to unexpected and substantial unfair outcomes, disproportionately affecting underrepresented individuals or groups and perpetuating pre-existing inequalities. Moreover, the Butterfly Effect can amplify inherent biases within data or algorithms, exacerbate feedback loops, and create vulnerabilities for adversarial attacks. Given the intricate nature of AI systems and their societal implications, it is crucial to thoroughly examine any changes to algorithms or input data for potential unintended consequences. In this paper, we envision both algorithmic and empirical strategies to detect, quantify, and mitigate the Butterfly Effect in AI systems, emphasizing the importance of addressing these challenges to promote fairness and ensure responsible AI development., Comment: Cite as: Machine Learning with Applications, Volume 15, 2024, 100525 10.1016/j.mlwa.2024.100525

The star formation rate (SFR) in high redshift galaxies is expected to be time-variable due to competing physical processes. Such stochastic variability might boost the luminosity of galaxies, possibly explaining the over-abundance seen at $z\gtrsim 10$ by JWST. We aim at quantifying the amplitude and timescales of such variability, and identifying the key driving physical processes. We select 245 $z=7.7$ galaxies with stellar mass $5\times 10^{6}\lesssim M_\star/{\rm M}_\odot\lesssim 5\times 10^{10}$ from SERRA, a suite of high-resolution, radiation-hydrodynamic cosmological simulations. After fitting the average SFR trend, $\langle {\rm SFR} \rangle$, we quantify the time-dependent variation, $\delta(t) \equiv \log [\rm SFR/\langle {\rm SFR} \rangle]$ for each system, and perform a periodogram analysis to search for periodicity modulations. We find that $\delta(t)$ is distributed as a zero-mean Gaussian, with standard deviation $\sigma_\delta \simeq 0.24$ (corresponding to a UV magnitude s.d. $\sigma_{\rm UV} \simeq 0.61$) that is independent of $M_\star$. However, the modulation timescale increases with stellar mass: $t_\delta \sim (9, 50, 100)\, \rm Myr$ for $M_\star \sim (0.1, 1, 5)\times 10^9\, {\rm M}_\odot$, respectively. These timescales are imprinted on the SFR by different processes: (i) photoevaporation, (ii) supernova explosions, and (iii) cosmological accretion/merging dominating in low, intermediate, and high mass systems, respectively. The predicted SFR variations cannot account for the required $z\gtrsim 10$ UV luminosity function boost. Other processes, such as radiation-driven outflows clearing the dust, must then be invoked to explain the enhanced luminosity of super-early systems., Comment: 5 pages, 4 figures, accepted by A&A

This paper presents rigorous tests of pulsar timing array methods and software, examining their consistency across a wide range of injected parameters and signal strength. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms \texttt{Enterprise} and \texttt{PTMCMCSampler} are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster when the white noise parameters remain fixed. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis software. For the Bayesian analysis, we test prior recovery, injection recovery, and Bayes factors. For the frequentist analysis, we test that the cross-correlation-based optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both GWB detection and parameter estimation perspectives. The tests presented here validate current and future analyses of PTA data., Comment: 30 pages, 10 figures, 1 table; Companion paper to "The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background"; For questions or comments, please email comments@nanograv.org

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems., Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15-yr dataset, and show that this dataset has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data., Comment: 19 pages, 11 figures; submitted to Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

The NANOGrav 15-year data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15-year observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values, or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach sub-parsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations., Comment: Accepted by Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org. Edited to fix two equation typos (Eq.13 & 21), and minor text typos

The 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons., Comment: 74 pages, 31 figures, 4 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals., Comment: 67 pages, 73 figures, 3 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background., Comment: 90 pages, 74 figures, 6 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15-year pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings-Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law-spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of $10^{14}$, and this same model is favored over an uncorrelated common power-law-spectrum model with Bayes factors of 200-1000, depending on spectral modeling choices. We have built a statistical background distribution for these latter Bayes factors using a method that removes inter-pulsar correlations from our data set, finding $p = 10^{-3}$ (approx. $3\sigma$) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of inter-pulsar correlations yields $p = 5 \times 10^{-5} - 1.9 \times 10^{-4}$ (approx. $3.5 - 4\sigma$). Assuming a fiducial $f^{-2/3}$ characteristic-strain spectrum, as appropriate for an ensemble of binary supermassive black-hole inspirals, the strain amplitude is $2.4^{+0.7}_{-0.6} \times 10^{-15}$ (median + 90% credible interval) at a reference frequency of 1/(1 yr). The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black-hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings-Downs correlations points to the gravitational-wave origin of this signal., Comment: 30 pages, 18 figures. Published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

An upper bound to the identification capacity of discrete memoryless wiretap channels is derived under the requirement of semantic effective secrecy, combining semantic secrecy and stealth constraints. A previously established lower bound is improved by applying it to a prefix channel, formed by concatenating an auxiliary channel and the actual channel. The bounds are tight if the legitimate channel is more capable than the eavesdropper's channel. An illustrative example is provided for a wiretap channel that is composed of a point-to-point channel, and a parallel, reversely degraded wiretap channel. A comparison with results for message transmission and for identification with only secrecy constraint is provided., Comment: ISIT 2023 version

CTA (Cherenkov Telescope Array) is the next generation ground-based observatory for gamma-ray astronomy at very-high energies. The Large-Sized Telescope prototype (LST-1) is located at the Northern site of CTA, on the Canary Island of La Palma. LSTs are designed to provide optimal performance in the lowest part of the energy range covered by CTA, down to $\simeq 20$ GeV. LST-1 started performing astronomical observations in November 2019, during its commissioning phase, and it has been taking data since then. We present the first LST-1 observations of the Crab Nebula, the standard candle of very-high energy gamma-ray astronomy, and use them, together with simulations, to assess the basic performance parameters of the telescope. The data sample consists of around 36 hours of observations at low zenith angles collected between November 2020 and March 2022. LST-1 has reached the expected performance during its commissioning period - only a minor adjustment of the preexisting simulations was needed to match the telescope behavior. The energy threshold at trigger level is estimated to be around 20 GeV, rising to $\simeq 30$ GeV after data analysis. Performance parameters depend strongly on energy, and on the strength of the gamma-ray selection cuts in the analysis: angular resolution ranges from 0.12 to 0.40 degrees, and energy resolution from 15 to 50%. Flux sensitivity is around 1.1% of the Crab Nebula flux above 250 GeV for a 50-h observation (12% for 30 minutes). The spectral energy distribution (in the 0.03 - 30 TeV range) and the light curve obtained for the Crab Nebula agree with previous measurements, considering statistical and systematic uncertainties. A clear periodic signal is also detected from the pulsar at the center of the Nebula., Comment: Accepted in ApJ. v3: updated author list and acknowledgements, fixed typos and other minor issues

Deterministic identification over K-input multiple-access channels with average input cost constraints is considered. The capacity region for deterministic identification is determined for an average-error criterion, where arbitrarily large codes are achievable. For a maximal-error criterion, upper and lower bounds on the capacity region are derived. The bounds coincide if all average partial point-to-point channels are injective under the input constraint, i.e. all inputs at one terminal are mapped to distinct output distributions, if averaged over the inputs at all other terminals. The achievability is proved by treating the MAC as an arbitrarily varying channel with average state constraints. For injective average channels, the capacity region is a hyperrectangle. The modulo-2 and modulo-3 binary adder MAC are presented as examples of channels which are injective under suitable input constraints. The binary multiplier MAC is presented as an example of a non-injective channel, where the achievable identification rate region still includes the Shannon capacity region., Comment: ISIT 2023 version

CONCERTO is the first experiment to perform a [CII] line intensity mapping survey to target $z>5.2$. Measuring the [CII] power spectrum allows us to study the role of dusty star-forming galaxies in the star formation history during the Reionization and post-Reionization. The main obstacle to this measurement is the contamination by bright foregrounds. We evaluate our ability to retrieve the [CII] signal in mock observations using the Simulated Infrared Dusty Extragalactic Sky. We compared two methods for dealing with the dust continuum emission from galaxies: the standard PCA and the arPLS method. For line interlopers, the strategy relies on masking low-redshift galaxies using external catalogues. As we do not have observations of CO or classical CO proxies ,we relied on the COSMOS stellar mass catalogue. To measure the power spectrum of masked data, we adapted the P of K EstimatoR and discuss its use on LIM data. The arPLS method achieves a reduction of the continuum background to a sub-dominant level of the [CII] at z=7 by a factor of>70. When using PCA, this factor is only 0.7. The masking lowers the power amplitude of line contamination down to $2 \times 10^2 Jy^2/sr$ This residual level is dominated by faint undetected sources. For our [CII] model, this results in a detection at z = 5.2 with a power ratio [CII]/(residual interlopers) = $62 \pm 32$ for a 22 % area survey loss. However, at z = 7, [C II ] / (residual interlopers)$=2.0 \pm 1.4$. Thanks to the large area covered by SIDES-Uchuu, we show that the power amplitude of line residuals varies by 12-15% for z=5.2-7. We present an end-to-end simulation of the extragalactic foreground removal that we ran to detect the [CII] at high redshift via its power spectrum. We show that dust continuum emission are not a limiting foreground for [CII] LIM. Residual CO and [CI] limits our ability to measure the [CII] power spectrum at z>7., Comment: 15 pages, 12 figures, to be published in Astronomy & Astrophysics

The X-ray pulsar RX J0440.9+4431 went through a giant outburst in 2022 and reached a record-high flux of 2.3 Crab, as observed by Swift/BAT. We study the evolution of different spectral and timing properties of the source using NICER observations. The pulse period is found to decrease from 208 s to 205 s, and the pulse profile evolves significantly with energy and luminosity. The hardness ratio and hardness intensity diagram (HID) show remarkable evolution during the outburst. The HID turns towards the diagonal branch from the horizontal branch above a transition (critical) luminosity, suggesting the presence of two accretion modes. Each NICER spectrum can be described using a cutoff power law with a blackbody component and a Gaussian at 6.4 keV. At higher luminosities, an additional Gaussian at 6.67 keV is used. The observed photon index shows negative and positive correlations with X-ray flux below and above the critical luminosity, respectively. The evolution of spectral and timing parameters suggests a possible change in the emission mechanism and beaming pattern of the pulsar depending on the spectral transition to sub- and super-critical accretion regimes. Based on the critical luminosity, the magnetic field of the neutron star can be estimated in the order of 10$^{12}$ or 10$^{13}$ G, assuming different theoretical models. Moreover, the observed iron emission line evolves from a narrow to a broad feature with luminosity. Two emission lines originating from neutral and highly ionized Fe atoms were evident in the spectra around 6.4 keV and 6.67 keV (higher luminosities)., Comment: Published in Monthly Notices of the Royal Astronomical Society

We propose CHRT (Control Hidden Representation Transformation) - a controlled language generation framework that steers large language models to generate text pertaining to certain attributes (such as toxicity). CHRT gains attribute control by modifying the hidden representation of the base model through learned transformations. We employ a contrastive-learning framework to learn these transformations that can be combined to gain multi-attribute control. The effectiveness of CHRT is experimentally shown by comparing it with seven baselines over three attributes. CHRT outperforms all the baselines in the task of detoxification, positive sentiment steering, and text simplification while minimizing the loss in linguistic qualities. Further, our approach has the lowest inference latency of only 0.01 seconds more than the base model, making it the most suitable for high-performance production environments. We open-source our code and release two novel datasets to further propel controlled language generation research., Comment: Accepted at ACL 2023 as a long paper (Findings)

News articles are driven by the informational sources journalists use in reporting. Modeling when, how and why sources get used together in stories can help us better understand the information we consume and even help journalists with the task of producing it. In this work, we take steps toward this goal by constructing the largest and widest-ranging annotated dataset, to date, of informational sources used in news writing. We show that our dataset can be used to train high-performing models for information detection and source attribution. We further introduce a novel task, source prediction, to study the compositionality of sources in news articles. We show good performance on this task, which we argue is an important proof for narrative science exploring the internal structure of news articles and aiding in planning-based language generation, and an important step towards a source-recommendation system to aid journalists., Comment: 13 pages

The final phase of the reionization process can be probed by rest-frame UV absorption spectra of quasars at z>6, shedding light on the properties of the diffuse intergalactic medium within the first Gyr of the Universe. The ESO Large Programme "XQR-30: the ultimate XSHOOTER legacy survey of quasars at z~5.8-6.6" dedicated ~250 hours of observations at the VLT to create a homogeneous and high-quality sample of spectra of 30 luminous quasars at z~6, covering the rest wavelength range from the Lyman limit to beyond the MgII emission. Twelve quasar spectra of similar quality from the XSHOOTER archive were added to form the enlarged XQR-30 sample, corresponding to a total of ~350 hours of on-source exposure time. The median effective resolving power of the 42 spectra is R~11400 and 9800 in the VIS and NIR arm, respectively. The signal-to-noise ratio per 10 km/s pixel ranges from ~11 to 114 at $\lambda \simeq 1285$ \AA rest frame, with a median value of ~29. We describe the observations, data reduction and analysis of the spectra, together with some first results based on the E-XQR-30 sample. New photometry in the H and K bands are provided for the XQR-30 quasars, together with composite spectra whose characteristics reflect the large absolute magnitudes of the sample. The composite and the reduced spectra are released to the community through a public repository, and will enable a range of studies addressing outstanding questions regarding the first Gyr of the Universe., Comment: 21 pages, 10 figures. Final version accepted by MNRAS