Newton's constant is the least well-measured among the fundamental constants of Nature, and, indeed, its accurate measurement has long served an experimental challenge. Levitated mechanical systems are attracting growing attention for their promising applications in sensing and as an experimental platform for exploring the intersection between quantum physics and gravitation. Here we propose a mechanical interferometric scheme of interacting levitated oscillators for the accurate estimation of Newton's constant. Our scheme promises to beat the current standard by several orders of magnitude.

The future Rubin Legacy Survey of Space and Time (LSST) is expected to deliver its first data release in the current of 2025. The upcoming survey will provide us with images of galaxy clusters in the optical to the near-infrared, with unrivalled coverage, depth and uniformity. The study of galaxy clusters informs us on the effect of environmental processes on galactic formation, which directly translates onto the formation of the brightest cluster galaxy (BCG). These massive galaxies present traces of the whole merger history of their host clusters, which can be in the shape of intra-cluster light (ICL) that surrounds them, tidal streams, or simply by the accumulated stellar mass that has been acquired over the past 10 billion years as they have cannibalized other galaxies in their surroundings. In an era where new data is being generated faster than humans can deal with, new methods involving machine learning have been emerging more and more in the most recent years. In the aim of preparing for the future LSST data release which will allow the observations of more than 20000 clusters and BCGs, we present in this paper different methods based on machine learning to detect these BCGs on LSST-like optical images. This study is done by making use of the simulated LSST Data Preview images. We find that the use of machine learning allows to accurately identify the BCG in up to 95% of clusters in our sample. Compared to more conventional red sequence extraction methods, the use of machine learning appears to be faster, more efficient and consistent, and does not require much, if any, pre-processing.

Recent wide-field galaxy surveys have led to an explosion in the number of galaxy-scale strong gravitational lens candidates. However, the vast majority of them feature massive luminous red galaxies as the main deflectors, with late-type galaxies being vastly under-represented. This work presents a dedicated search for lensing by edge-on late-type galaxies in the Ultraviolet Near Infrared Optical Northern Survey (UNIONS). The search covers $3600$ deg$^2$ of $r$-band observations taken from the Canada-France-Hawaii Telescope. We considered all sources with magnitudes in the range $17 < r < 20.5$, without any colour pre-selection, yielding a parent sample of seven million sources. We characterised our parent sample via the visual inspection of $120\,000$ sources selected at random. From it, we estimate, with a 68% confidence interval, that 1 in every $30\,000$ sources is an edge-on lens candidate, with at least eight high-quality candidates in the parent sample. Our search relied on a convolutional neural network (CNN) to select a reduced sample of candidates, which we followed with a visual inspection to curate the final sample. The CNN was trained from scratch using simulated $r$-band observations of edge-on lenses, and real observations of non-lenses. We found 61 good edge-on lens candidates using the CNN. Moreover, combining the CNN candidates with those found serendipitously and those identified while characterising the parent sample, we discovered 4 grade A, 20 grade B, and 58 grade C edge-on lens candidates, effectively doubling the known sample of these systems. We also discovered 16 grade A, 16 grade B, and 18 grade C lens candidates of other types. Finally, based on the characterisation of the parent sample, we estimate that our search found around 60% of the bright grade A and B edge-on lens candidates within the parent sample.

We derive exact equations governing the large-scale dynamics of hard rods, including diffusive effects that go beyond ballistic transport. Diffusive corrections are the first-order terms in the hydrodynamic gradient expansion and we obtain them through an explicit microscopic calculation of the dynamics of hard rods. We show that they differ significantly from the prediction of Navier-Stokes hydrodynamics, as the correct hydrodynamics description is instead given by two coupled equations, giving respectively the evolution of the one point functions and of the connected two-point correlations. The resulting equations are time-reversible and reduce to the usual Navier-Stokes hydrodynamic equations in the limit of near-equilibrium evolution. This represents the first exact microscopic calculation showing how ballistic dynamics generates long-range correlations, in agreement with general results from the recently developed ballistic macroscopic fluctuation theory, and showing how such long range-correlations directly affect the diffusive hydrodynamic terms, in agreement with, and clarifying, recent related results.

In this study, we first heuristically construct the charges corresponding to the chiral transformation associated with the large U(1) gauge symmetry. We refer to these as the large chiral charges, and to the chiral transformation they generate as the large chiral transformations. Then, showing that these large chiral charges can be obtained based on Noether's theorem, we obtain the anomaly equation associated with these large chiral transformations. Subsequently, considering the one-loop diagrams of the fermionic field coupled to multiple classical gauge fields (which constitute the effective action of the model in this study with regard to the gauge field), we perform an axialization. Then, defining the BRS transformations for the large U(1) gauge symmetry (we refer to these as the large BRS transformations), we perform these transformations to these axialized one-loop diagrams, and demonstrate that the anomaly equations mentioned above can be derived by evaluating these diagrams. We further confirm that these anomaly equations can be derived using the Fujikawa method. Finally, we discuss the breaking of unitarity and the low-energy effective model associated with the large chiral anomaly in this study, and comment on potential future developments arising from them.

We explore the implications of finite-temperature quantum field theory effects on cosmological parameters within the framework of the $Ł$CDM model and its modification. By incorporating temperature-dependent corrections to the cosmological constant, we extend the standard cosmological model to include additional density parameters, $Ω_{Ł_2}$ and $Ω_{Ł_3}$, which arise from finite-T quantum gravitational effects. Using the Cosmic Linear Anisotropy Solving System (CLASS), we analyze the impact of these corrections on the cosmic microwave background power spectrum and compare the results with the Planck 2018 data. Through brute-force parameter scans and advanced machine learning techniques, including quartic regression, we demonstrate that the inclusion of $Ω_{Ł_2}$ and $Ω_{Ł_3}$ improves the model's predictive accuracy, achieving higher $R^2$ values, lower mean squared error, and lower AIC/BIC scores than those of the $Ł$CDM model. Despite identified methodological limitations, these findings establish an exploratory framework for incorporating finite-temperature quantum corrections into precision cosmology and open new avenues for data-driven parameter inference.

Both simulations and observations indicate that the so-called missing baryons reside in the intergalactic medium known as the warm-hot intergalactic medium (WHIM). In this study we employed the IllustrisTNG50-1 simulation to demonstrate that knowledge of the turbulence in the cosmic baryonic fluid is crucial for correctly understanding both the spatial distribution and the physical origins of the missing baryons in the Universe. First, we find that dynamical effects cause the gas to be detained in low-density and intermediate-density regions, resulting in high baryon fractions, and prevent the convergence of the gas in high-density regions, leading to low baryon fractions. Second, turbulent energy is converted into thermal energy, and the injection and dissipation of turbulent energy have essentially reached a balance from $z=1$ to $0$. This indicates that the cosmic fluid is in a steady state within this redshift range. Due to turbulent heating, as the redshift decreases, an increasing amount of warm gas is heated and converted into the WHIM, and some even into hot gas. We find that, compared with turbulence in the cosmic fluid, shocks are unimportant in intermediate-density regions and even negligible in high-density regions, both dynamically and thermodynamically. This finding accounts for the origin of the WHIM in terms of both dynamics and thermodynamics, calls into question the traditional view of shock-heating, and highlights the importance of turbulence in shaping the large-scale structure of the Universe, particularly in the evolution of galaxies and galaxy clusters. In addition to TNG50-1, we validated our key findings with TNG50-2, TNG100-1, WIGEON, and EAGLE simulations, demonstrating that the spatial resolution, box size, and sub-grid-physics variations do not affect our main conclusions.

In static, spherically symmetric spacetimes, the deflection angle of photons in the strong deflection limit exhibits a logarithmic divergence. We introduce an analytical framework that clarifies the physical origin of this divergence by employing local, coordinate-invariant geometric quantities alongside the properties of the matter distribution. In contrast to conventional formulations -- where the divergence rate $\bar{a}$ is expressed via coordinate-dependent metric functions -- our approach relates $\bar{a}$ to the components of the Einstein tensor in an orthonormal basis adapted to the spacetime symmetry. By applying the Einstein equations, we derive the expression \begin{align*} \bar{a}=\frac{1}{\sqrt{1-8πR_{\mathrm{m}}^2\left(ρ_{\mathrm{m}}+Π_{\mathrm{m}}\right)}}, \end{align*} where $ρ_{\mathrm{m}}$ and $Π_{\mathrm{m}}$ denote the local energy density and tangential pressure evaluated at the photon sphere of areal radius $R_{\mathrm{m}}$. This result reveals that $\bar{a}$ is intrinsically governed by the local matter distribution, with the universal value $\bar{a}=1$ emerging when $ρ_{\mathrm{m}}+Π_{\mathrm{m}}=0$. Notably, this finding resolves the long-standing puzzle of obtaining $\bar{a}=1$ in a class of spacetimes supported by a massless scalar field. Furthermore, these local properties are reflected in the frequencies of quasinormal modes, suggesting a profound connection between strong gravitational lensing and the dynamical response of gravitational wave signals.

The Veneziano amplitude describing the tree-level scattering of four open superstrings is expected to be consistent with unitarity in ten spacetime dimensions. While this follows indirectly from the no-ghost theorem, a direct proof at the level of the amplitude has only been found for $D\leq 6$. In this article, we close this gap by providing a complete proof for the partial-wave positivity of the Veneziano amplitude in $D\leq 10$, derived directly from its definition in terms of the Euler beta function. We also demonstrate that this proof can be modified to show positivity of a wider family of amplitudes relevant to the $S$-matrix bootstrap.

Traced monoidal categories are used to model processes that can feed their outputs back to their own inputs, abstracting iteration. The category of finite dimensional Hilbert spaces with the direct sum tensor is not traced. But surprisingly, in 2014, Bartha showed that the monoidal subcategory of isometries is traced. The same holds for coisometries, unitary maps, and contractions. This suggests the possibility of feeding outputs of quantum processes back to their own inputs, analogous to iteration. In this paper, we show that Bartha's result is not specifically tied to Hilbert spaces, but works in any dagger additive category with Moore-Penrose pseudoinverses (a natural dagger-categorical generalization of inverses).

Blockchain technology has revolutionized financial markets by enabling decentralized exchanges (DEXs) that operate without intermediaries. Uniswap V2, a leading DEX, facilitates the rapid creation and trading of new tokens, which offer high return potential but exposing investors to significant risks. In this work, we analyze the financial impact of newly created tokens, assessing their market dynamics, profitability and liquidity manipulations. Our findings reveal that a significant portion of market liquidity is trapped in honeypots, reducing market efficiency and misleading investors. Applying a simple buy-and-hold strategy, we are able to uncover some major risks associated with investing in newly created tokens, including the widespread presence of rug pulls and sandwich attacks. We extract the optimal sandwich amount, revealing that their proliferation in new tokens stems from higher profitability in low-liquidity pools. Furthermore, we analyze the fundamental differences between token price evolution in swap time and physical time. Using clustering techniques, we highlight these differences and identify typical patterns of honeypot and sellable tokens. Our study provides insights into the risks and financial dynamics of decentralized markets and their challenges for investors.

The Highway Performance Monitoring System, managed by the Federal Highway Administration, provides data on average annual daily traffic volume across roadways in the United States, but it has limited representation of medium- and heavy-duty vehicle traffic on lower-volume roadways that are not part of the national highway system. This gap limits research and policy analysis on the community impacts of truck traffic, especially concerning air quality and public health. To address this, we use random forest regression to estimate medium- and heavy-duty vehicle traffic volumes on network links where these data are missing. The result is a comprehensive vehicle traffic dataset that covers 85.2% of public roadways in the United States. From these data, we also calculate traffic density values for each census block and vehicle class that can serve as a high-resolution surrogate for traffic-related air pollution exposure in public health studies and policy analysis. Our high-resolution spatial data products are rigorously validated and provide a more complete representation of truck traffic than any existing publicly available dataset. These datasets are valuable for transportation planning, public health research, and policy decisions aimed at understanding and mitigating the effects of truck traffic on communities that are disproportionately exposed to air pollution from vehicle traffic.

With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of stochastic systems, methods based on discrete, finite Markov approximations -- abstractions -- thereof have surged in recent years. These are found in contexts where: either a) one only has partial, discrete observations of the underlying continuous stochastic process, or b) the original system is too complex to analyze, so one partitions the continuous state-space of the original system to construct a handleable, finite-state model thereof. In both cases, the abstraction is an approximation of the discrete stochastic process that arises precisely from the discretization of the underlying continuous process. The fact that the abstraction is Markov and the discrete process is not (even though the original one is) leads to approximation errors. Towards accounting for non-Markovianity, we introduce memory-dependent abstractions for stochastic systems, capturing dynamics with memory effects. Our contribution is twofold. First, we provide a formalism for memory-dependent abstractions based on transfer operators. Second, we quantify the approximation error by upper bounding the total variation distance between the true continuous state distribution and its discrete approximation.

We give conditions for topological and bi-Lipschitz equivalences within a class of mixed singularities of Pham-Brieskorn type. As a consequence, we construct infinite families that are topologically trivial but have distinct bi-Lipschitz types. We also investigate this problem in the context of mixed surfaces defined by these singularities in the case of two complex variables, deriving conditions for inner, outer, and ambient bi-Lipschitz equivalences. In particular, we obtain an invariant of the subanalytic outer geometry of the associated mixed surfaces, which is determined by the exponents.

This paper is a continuation of previous work of the author. We use the categorical trace formalism to give a construction of the categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we study the endomorphism algebra of the Gelfand-Graev representation and recover a result of Li and Shotton-Li.

This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between propagation-constant-offset and offset-frequency analytic signal and slowly-varying envelope assumption. (2) It contains complete derivations of the general formulations of several Fourier-transform relations. It shows the importance of having Fourier-transform constants as parameters, and helps clarify the arbitrary selection of Fourier-transform constants and conventions. (3) It also clarifies the correct Fourier-transform convention to be employed in ultrafast optics. (4) Moreover, multiple Fourier-transform aspects are discussed, involving convolution, aliasing, phase effect, and short-time Fourier transform. (5) In addition to the Fourier transform, a tutorial on the Hankel transform is provided. Its numerical implementation based on the fast Hankel transform with high accuracy (FHATHA) is also provided. Despite being a tutorial, I, for the first time, propose a new numerical scheme for the fast Hankel transform that outperforms both the original FHATHA and the discrete Hankel transform.

We study a novel production and decay mechanism for a bi-adjoint spin zero particle in the ($8,3,0$) representation of the Standard Model gauge groups. This work is part of a series studying new production processes for exotic particles in higher representations of Standard Model color and weak charge. Here, we study a specific new dimension 5 effective operator model which couples an exotic bi-adjoint scalar field to the SU(3) and SU(2) field strength tensors. The W-gluon resonant decay of the charged component of this new exotic field is explored. We discuss LHC production modes of both the charged and neutral bi-adjoint states and find a new single production mode for the charged state. This is the dominant LHC production mode for TeV-scale masses. We introduce a new HL-LHC search in which a single bi-adjoint is produced in association with a hard forward quark jet from asymmetric W-gluon fusion. This search yields a 5-sigma discovery potential for bi-adjoint masses up to 3 TeV for 10 TeV scalar effective operator cutoffs. We also find 2-sigma sensitivity at the HL-LHC for bi-adjoint masses up to 4 TeV and effective cutoffs in the 15 TeV range for the full 3 inverse atto-barn data set.

Let $k$ be a field, and let $\mathcal{C}$ be a Cauchy complete $k$-linear braided category with finite dimensional morphism spaces and ${{\rm End}(\bf 1)}=k$. We call an indecomposable object $X$ of $\mathcal C$ non-negligible if there exists $Y\in \mathcal{C}$ such that $\bf 1$ is a direct summand of $Y\otimes X$. We prove that every non-negligible object $X\in \mathcal{C}$ such that ${\rm dim}{\rm End}(X^{\otimes n})<n!$ for some $n$ is automatically rigid. In particular, if $\mathcal{C}$ is semisimple of moderate growth and weakly rigid, then $\mathcal{C}$ is rigid. As applications, we simplify Huang's proof of rigidity of representation categories of certain vertex operator algebras, and we get that for a finite semisimple monoidal category $\mathcal{C}$, the data of a $\mathcal{C}$-modular functor is equivalent to a modular fusion category structure on $\mathcal{C}$, answering a question of Bakalov and Kirillov. Finally, we show that if $\mathcal{C}$ is rigid and has moderate growth, then the quantum trace of any nilpotent endomorphism in $\mathcal{C}$ is zero. Hence $\mathcal{C}$ admits a semisimplification, which is a semisimple braided tensor category of moderate growth. Finally, we discuss rigidity in braided r-categories which are not semisimple, which arise in logarithmic conformal field theory. These results allow us to simplify a number of arguments of Kazhdan and Lusztig.

Astrometric measurements provide a unique avenue for constraining the stochastic gravitational wave background (SGWB). In this work, we investigate the application of two neural network architectures, a fully connected network and a graph neural network, for analyzing astrometric data to detect the SGWB. Specifically, we generate mock Gaia astrometric measurements of the proper motions of sources and train two networks to predict the energy density of the SGWB, $Ω_\text{GW}$. We evaluate the performance of both models under varying input datasets to assess their robustness across different configurations. We also perform a direct comparison with a likelihood-based approach using Markov chain Monte Carlo (MCMC) methods, finding out that the neural-network-based approach is significantly faster, taking on the order of minutes, compared to MCMC's order of days, while still capturing the same features in the data. Our results demonstrate that neural networks can effectively constrain the SGWB, showing promise as tools for addressing systematic uncertainties and modeling limitations that pose challenges for traditional likelihood-based methods.

Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to category $\mathcal{O}$. We use this to construct a collection of representations of $\mathbf{G}(\mathbb{F}_q)$ which we call the tilting representations. They form a generating collection of integral projective representations of $\mathbf{G}(\mathbb{F}_q)$. Finally we compute the character of these representations and relate their expression to previous calculations of Lusztig and we then use this to establish a conjecture of Dudas--Malle.

We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter $0\le p\le 1$) shapes the structure of the evolving network. We reveal the ability to seamlessly explore a vast landscape of scale-free networks, unlocking an entirely new class of complex networks that we call \textit{stars-with-filament} structure. Remarkably, the average degree $\bar k$ of these networks grows like $\log t$ to some power, where $t$ is time and the average shortest path length grows logarithmically with the system size for intermediate $p$ values, offering fresh insights into the structural dynamics of scale-free systems. Our approach is backed by a robust mean-field theory, which nicely captures the dynamics of $\bar{k}$. We further unveil a rich, $p$-dependent phase diagram, encompassing 47 real-world scale-free networks, shedding light on previously hidden patterns. This work opens exciting new avenues for understanding the universal properties of complex networks.

We study the problem of minimizing metric distortion in multi-winner elections, where a committee of size $k$ is selected from a set of candidates based on voters' ordinal preferences. We assume that voters and candidates are embedded on a line metric, and social cost is determined by the underlying metric distances. The distortion of a voting rule is the worst-case ratio between the social cost of the elected committee and an optimal committee. Previous work has focused on the $q$-cost model, in which a voter's cost is given by the distance to their $q$th closest committee member. Here, we study the additive cost, where a voter's cost is the sum of distances to all committee members. We introduce the Polar Comparison Rule and analyze its distortion under utilitarian additive cost. We show that it achieves a distortion of at most $2.33$ for all committee sizes $k>2$, improving upon the previously best-known upper bound of $3$. Moreover, for $k=2$ and $k=3$, we establish tight distortion bounds of $2.41$ and $2.33$, respectively. We also derive lower bounds that depend on the parity of $k$ and analyze the behavior of distortion for small and large committee sizes. Finally, we extend our results to the egalitarian additive cost.

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to π$ transition at zero momentum transfer, as well as the decay-constant ratio $f_K/f_π$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $α_s$. We review the determinations of nucleon charges from the matrix elements of both isovector and flavour-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model.

Daubechies-type theorems for localization operators are established in the multi-variate setting, where Hagedorn wavepackets are identified as the proper substitute of the Hermite functions. The class of Reinhardt domains is shown to be the natural class of masks that allow for a Daubechies-type result. Daubechies' classical theorem is a consequence of double orthogonality results for the short-time Fourier transform. We extend double orthogonality to the quantum setting and use it to establish Daubechies-type theorems for mixed-state localization operators, a key notion of quantum harmonic analysis. Lastly, we connect the results to Toeplitz operators on quantum Gabor spaces.

For an endofunctor $F\colon\mathcal{C}\to\mathcal{C}$ on an ($\infty$-)category $\mathcal{C}$ we define the $\infty$-category $\operatorname{Cart}(\mathcal{C},F)$ of generalized Cartier modules as the lax equalizer of $F$ and the identity. This generalizes the notion of Cartier modules on $\mathbb{F}_p$-schemes considered in the literature. We show that in favorable cases $\operatorname{Cart}(\mathcal{C},F)$ is monadic over $\mathcal{C}$. If $\mathcal{A}$ is a Grothendieck abelian category and $F\colon\mathcal{A}\to\mathcal{A}$ is an exact and colimit-preserving endofunctor, we use this fact to construct an equivalence $\mathcal{D}(\operatorname{Cart}(\mathcal{A},F)) \simeq \operatorname{Cart}(\mathcal{D}(\mathcal{A}),\mathcal{D}(F))$ of stable $\infty$-categories. We use this equivalence to construct a perverse t-structure on $\mathcal{D}(\operatorname{Cart}(\operatorname{Mod}(X), F_*))$ for any Noetherian $\mathbb{F}_p$-scheme $X$ with absolute Frobenius $F$. If $F$ is finite, this coincides with the perverse t-structure constructed by Baudin.

Identifying active galactic nuclei (AGN) is extremely important for understanding galaxy evolution and its connection with the assembly of supermassive black holes (SMBH). With the advent of deep and high angular resolution imaging surveys such as those conducted with the James Webb Space Telescope (JWST), it is now possible to identify galaxies with a central point source out to the very early Universe. In this study, we develop a fast, accurate and precise method to identify galaxies which host AGNs and recover the intrinsic AGN contribution to the observed total light ($f_{AGN}$). We trained a deep learning (DL) based method Zoobot to estimate the fractional contribution of a central point source to the total light. Our training sample comprises realistic mock JWST images of simulated galaxies from the IllustrisTNG cosmological hydrodynamical simulations. We injected different amounts of the real JWST point spread function (PSF) models to represent galaxies with different levels of $f_{AGN}$. We analyse the performance of our method and compare it with results obtained from the traditional light profile fitting tool GALFIT. We find excellent performance of our DL method in recovering the injected AGN fraction $f_{AGN}$, both in terms of precision and accuracy. The mean difference between the predicted and true injected $f_{AGN}$ is -0.002 and the overall root mean square error (RMSE) is 0.013. The relative absolute error (RAE) is 0.076 and the outlier (defined as predictions with RAE >20%) fraction is 6.5%. In comparison, using GALFIT on the same dataset, we achieve a mean difference of -0.02, RMSE of 0.12, RAE of 0.19 and outlier fraction of 19%. We applied our trained DL model to real JWST observations and found that 33% of X-ray-selected AGN and 15% of MIR-selected AGN are also identified as AGN using a cut at $f_{\rm AGN} > 0.1$.

Relationships among teachers are known to influence their teaching-related perceptions. We study whether and how teachers' advising relationships (networks) are related to their perceptions of satisfaction, students, and influence over educational policies, recorded as their responses to a questionnaire (item responses). We propose a novel joint model of network and item responses (JNIRM) with correlated latent variables to understand these co-varying ties. This methodology allows the analyst to test and interpret the dependence between a network and item responses. Using JNIRM, we discover that teachers' advising relationships contribute to their perceptions of satisfaction and students more often than their perceptions of influence over educational policies. In addition, we observe that the complementarity principle applies in certain schools, where teachers tend to seek advice from those who are different from them. JNIRM shows superior parameter estimation and model fit over separately modeling the network and item responses with latent variable models.

Let $G$ be a generically reductive group over a smooth projective curve $X$ over a finite field. For any finite set $I$, we show that nearby cycles commute with proper direct image from stacks of shtukas to $X^I$. This generalizes some results of Salmon and the authors.

The signature of a membrane is a sequence of tensors whose entries are iterated integrals. We study algebraic properties of membrane signatures, with a focus on signature matrices of polynomial and piecewise bilinear membranes. Generalizing known results for path signatures, we show that the two families of membranes admit the same set of signature matrices and we examine the corresponding affine varieties. In particular, we prove that there are no algebraic relations on signature matrices of membranes, in contrast to the path case. We complement our results by a linear time algorithm for the computation of signature tensors for piecewise bilinear membranes.

Measurements of the redshift drift -- the real time variation of the redshift of distance sources -- are expected in the next couple of decades using next generation facilities such as the ANDES spectrograph at the ELT and the SKAO survey. The unprecedented precision of such observations will demand precise theoretical and numerical modeling of the effect in the standard $Λ$CDM cosmology. In this work, we use the \texttt{Gadget4} $N$-body code to simulate the redshift drift and its fluctuations in $Λ$CDM cosmologies, deriving the corresponding power spectra from a simulation with $1024^3$ particles in a $1\textrm{Gpc}\,h^{-1}$ box. Our results represent an initial step toward deriving the redshift drift fluctuation power spectra from $N$-body simulations and establishing a methodology for the statistical analysis of the redshift drift effect using data from future large-scale surveys. However, further work is required to refine the approach and achieve an accurate modeling of the redshift drift fluctuation power spectra.