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1. Predicting Stellar Masses of the First Galaxies Using Graph Neural Networks

   https://doi.org/10.3847/2515-5172/ad40ad  

   Horvath, Vincent A.; Sethuram, Snigdaa S.; Wise, John H. (April 2024, Research Notes of the AAS)

   Abstract Theoretical models of galaxy formation and evolution are primarily investigated through cosmological simulations and semi-analytical models. The former method consumes $\mathcal{O}\left({10}^6\right)$core-hours explicitly modeling the dynamics of the galaxies, whereas the latter method only requires $\mathcal{O}\left({10}^3\right)$core-hours foregoing directly simulating internal structure for computational efficiency. In this work, we present a proof-of-concept machine learning regression model, using a graph neural network architecture, to predict the stellar mass of high-redshift galaxies solely from their dark matter merger trees, trained from a radiation hydrodynamics cosmological simulation of the first galaxies. 

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2. Tip of the Iceberg: Overmassive Black Holes at 4 < z < 7 Found by JWST Are Not Inconsistent with the Local $M_{\mathrm{BH}}-M_{\star }$ Relation

   https://doi.org/10.3847/1538-4357/ada603  

   Li, Junyao; Silverman, John D; Shen, Yue; Volonteri, Marta; Jahnke, Knud; Zhuang, Ming-Yang; Scoggins, Matthew T; Ding, Xuheng; Harikane, Yuichi; Onoue, Masafusa; et al (February 2025, The Astrophysical Journal)

   Abstract JWST is revealing a remarkable new population of high-redshift (z ≳ 4), low-luminosity active galactic nuclei in deep surveys and detecting the host galaxy's stellar light in the most luminous and massive quasars atz ∼ 6 for the first time. Recent findings claim that supermassive black holes (SMBHs) in these systems are significantly more massive than predicted by the local black hole (BH) mass–stellar mass ( ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$) relation and that this is not due to sample selection effects. Through detailed statistical modeling, we demonstrate that the coupled effects of selection biases (i.e., finite detection limit and requirements for detecting broad lines) and measurement uncertainties can largely explain the reported offset and flattening in the observed ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$relation toward the upper envelope of the local relation, even for those at ${\mathcal{M}}_{\mathrm{BH}}<10^8{M}_{\odot }$. We further investigate the possible evolution of the ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$relation atz ≳ 4 with careful treatment of observational biases and consideration of the degeneracy between intrinsic evolution and dispersion in this relation. The bias-corrected intrinsic ${\mathcal{M}}_{\mathrm{BH}}-{\mathcal{M}}_{\star }$relation in the low-mass regime ( ${\mathcal{M}}_{\star }\lesssim 10^{10}{M}_{\odot }$) suggests a large population of low-mass BHs ( ${\mathcal{M}}_{\mathrm{BH}}\lesssim 10^5{M}_{\odot }$), possibly originating from lighter seeds, may remain undetected or unidentified. These results underscore the importance of forward modeling observational biases to better understand BH seeding and SMBH–galaxy coevolution mechanisms in the early universe, even with the deepest JWST surveys. 

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3. Efficient Stochastic Template Bank Using Inner Product Inequalities

   https://doi.org/10.3847/1538-4357/ad7d87  

   Kacanja, Keisi; Nitz, Alexander_H; Wu, Shichao; Cusinato, Marco; Dhurkunde, Rahul; Harry, Ian; Dal_Canton, Tito; Pannarale, Francesco (November 2024, The Astrophysical Journal)

   Abstract Gravitational wave searches are crucial for studying compact sources such as neutron stars and black holes. Many sensitive modeled searches use matched filtering to compare gravitational strain data to a set of waveform models known as template banks. We introduce a new stochastic placement method for constructing template banks, offering efficiency and flexibility to handle arbitrary parameter spaces, including orbital eccentricity, tidal deformability, and other extrinsic parameters. This method can be computationally limited by the ability to compare proposal templates with the accepted templates in the bank. To alleviate this computational load, we introduce the use of inner product inequalities to reduce the number of required comparisons. We also introduce a novel application of Gaussian Kernel Density Estimation to enhance waveform coverage in sparser regions. Our approach has been employed to search for eccentric binary neutron stars, low-mass neutron stars, primordial black holes, and supermassive black hole binaries. We demonstrate that our method produces self-consistent banks that recover the required minimum fraction of signals. For common parameter spaces, our method shows comparable computational performance and similar template bank sizes to geometric placement methods and stochastic methods, while easily extending to higher-dimensional problems. The time to run a search exceeds the time to generate the bank by a factor of $\mathcal{O}\left({10}^5\right)$for dedicated template banks, such as geometric, mass-only stochastic, and aligned spin cases, $\mathcal{O}\left({10}^4\right)$for eccentric and $\mathcal{O}\left({10}^3\right)$for the tidal deformable bank. With the advent of efficient template bank generation, the primary area for improvement is developing more efficient search methodologies. 

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4. Sums of linear transformations

   https://doi.org/10.1090/tran/9433  

   Conlon, David; Lim, Jeck (July 2025, Transactions of the American Mathematical Society)

   We show that if ${\mathcal{L}}_1$and ${\mathcal{L}}_2$are linear transformations from ${\mathbb{Z}}^d$to ${\mathbb{Z}}^d$satisfying certain mild conditions, then, for any finite subset $A$of ${\mathbb{Z}}^d$, $|{\mathcal{L}}_{1}A+{\mathcal{L}}_{2}A|\ge <\#comment/>{(|det({\mathcal{L}}_1){|}^{1/d}+|det({\mathcal{L}}_2\left){|}^{1/d}\right)}^d|A|-<\#comment/>o\left(|A|\right).$This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for certain choices of ${\mathcal{L}}_1$and ${\mathcal{L}}_2$. As an application, we prove a lower bound for $|A+\mathrm{\lambda <\#comment/>}\cdot <\#comment/>A|$when $A$is a finite set of real numbers and $\mathrm{\lambda <\#comment/>}$is an algebraic number. In particular, when $\mathrm{\lambda <\#comment/>}$is of the form $(p/q{)}^{1/d}$for some $p,q,d\in <\#comment/>\mathbb{N}$, each taken as small as possible for such a representation, we show that $|A+\mathrm{\lambda <\#comment/>}\cdot <\#comment/>A|\ge <\#comment/>(p^{1/d}+q^{1/d}{)}^d|A|-<\#comment/>o(|A|).$This is again best possible up to the lower-order term and extends a recent result of Krachun and Petrov which treated the case $\mathrm{\lambda <\#comment/>}=\sqrt{2}$. 

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5. No-boundary state for Klein space

   https://doi.org/10.1088/1751-8121/adc882  

   Melton, Walker; Sharma, Atul; Strominger, Andrew; Wang, Tianli (April 2025, Journal of Physics A: Mathematical and Theoretical)

   Abstract Analytic continuation from (3, 1) signature Minkowski to (2, 2) signature Klein space has emerged as a useful tool for the understanding of scattering amplitudes and flat space holography. Under this continuation, past and future null infinity merge into a single boundary ( $J$) which is the product of a null line with a (1, 1) signature torus. The Minkowskian $S$-matrix continues to a Kleinian $S$-vector which in turn may be represented by a Poincaré-invariant vacuum state $|C⟩$in the Hilbert space built on $J$. $|C⟩$contains all information about $S$in a novel, repackaged form. We give an explicit construction of $|C⟩$in a Lorentz/conformal basis for a free massless scalar. $J$separates into two halves $J_{\pm }$which are the asymptotic null boundaries of the regions timelike and spacelike separated from the origin. $|C⟩$is shown to be a maximally entangled state in the product of the $J_{\pm }$Hilbert spaces. 

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