This note shows how Condition 1 in Okumura (2025) can be tested efficiently using a standard graph-theoretic algorithm. It also describes an efficient implementation of Okumura's mechanism.

The understanding of quantum many-body states in twisted bilayer graphene at the magic angle has been greatly improved both in experiment and in theory. However, away from the exactly solvable chiral limit and the sign-problem-free charge neutrality point, the calculation of the ground state properties and the identification of the phase diagram are challenging due to the exponential increase in the complexity, which has rendered explanations of experimentally observed insulating and superconducting phases restricted largely to the perturbative level. Here we focus on the filling factors $ν= \pm2$ away from charge neutrality and address the question of the strain dependence of the interacting ground state. We adjust our continuous field momentum-space quantum Monte Carlo (QMC) method to treat the sign problem approximately, and perform a quantum many-body study together with exact diagonalization (ED) and Hartree-Fock (HF) mean field. Leveraging this combined protocol of QMC, ED, and HF, we investigate the strain-tuned transition from the Kramers intervalley coherent (KIVC) state to the incommensurate Kekulé spiral state (IKS). Our computational protocol sheds light on the KIVC-IKS transition in a projected correlated flat-band setting, and opens the door for further understanding of the rich phase diagram of twisted bilayer graphene and other strongly-correlated flat-band systems.

Code smells signal violations of design principles that degrade the internal quality of evolving software systems. Although many tools detect such anomalies using static metrics, they often ignore the development context in which smells arise and are resolved. This limitation can lead to misleading warnings and weak support for refactoring decisions. To address this problem, we present SmellHunter, a context-aware tool that interprets scripts written in the SmellDSL domain-specific language to detect and contextualize code smells. SmellHunter integrates static code metrics with contextual information (such as team characteristics, project stage, and geographic metadata) to produce richer, more actionable analyses. The tool adopts an event-driven architecture in which a service bus orchestrates validation, interpretation, and persistence services through asynchronous events. This architecture enables scalable analysis while minimizing disruption to developers' workflows. SmellHunter is integrated into the Eclipse development environment via a dedicated plugin and provides aggregated insights via a mobile application, allowing developers to explore smell occurrences by type, severity, and location. By linking smell detection with contextual data and collaborative visualization, SmellHunter supports developers acting as smell hunters, helping teams identify recurring quality issues emerging from a particular location and assign refactoring tasks to developers with relevant expertise. We describe the architecture of SmellHunter, the interpretation process of SmellDSL scripts, and the integration of contextual data to support more informed refactoring decisions in modern software development environments.

Qualitative methods such as the linear sampling method and the factorization method reconstruct acoustic scatterers through sampling indicators. In practice, these indicators are gray-scale fields on a prescribed sampling window and a binary obstacle shape is obtained only after thresholding. The choice of threshold is usually empirical and may be unstable when the indicator contains noise-induced artifacts or when the scatterer has nontrivial topology, such as multiple components or holes. This paper proposes a topology-aware postprocessing framework based on persistent homology. Given any normalized qualitative indicator, we scan the persistent homology of its superlevel sets and use the resulting zero- and one-dimensional persistent features to estimate or impose the topology of the unknown scatterer. A topology-guided threshold is then selected by minimizing a Betti-number discrepancy together with mild geometric penalties. The method is indicator-agnostic: it can be applied to the linear sampling indicator, the factorization-method indicator, or a normalized fusion of indicators. The main formulation is single-frequency and therefore remains close to the classical qualitative inverse scattering setting. We present the mathematical construction, an automatic topology detection rule based on persistence lifetimes and lifetime gaps, and a detailed algorithmic protocol for numerical implementation. Numerical tests verify that the proposed method is effective.

This paper introduces Locally Adaptive Neural Context Estimation (LANCE), a novel extension for overfitted image compression (OIC) frameworks like Cool-Chic. While traditional OIC methods rely on lightweight autoregressive networks with globally signaled parameters, they struggle with non-stationary image statistics. LANCE addresses this by incorporating a forward-signaled spatial hyperprior that enables regional adaptation of the entropy model. To minimize overhead, we employ a predictive coding scheme that combines a static Median Edge Detector (MED) with a lightweight learned context model. Experiments demonstrate that LANCE achieves BD-rate reductions of 1.40% on the Kodak dataset and 1.97% on CLIC 2020 over Cool-Chic 4.0 at the high end of our decoder complexity range of 606-1481 MAC/pixel. At the low end of the complexity range, we outperform Cool-Chic 4.0 by 2.41% and 2.99% on Kodak and CLIC, respectively. Qualitative analysis reveals that the learned spatial hyperprior effectively segments image regions into areas of similar image statistics, providing an automated, content-aware adaptation layer.

Tuning the electronic structures of two-dimensional (2D) material-based heterostructures is of crucial importance for their use in functional next-generation electronics. Here, through angle-resolved photoemission spectroscopy with nanoscale spatial resolution (nano-ARPES), we systematically track the evolution of the near-Fermi-level electronic structure of bilayer WSe2 over a large range of twist angle. While the momentum positioning of the valence band maxima is independent of twist angle, we find that the energetic separation between the hole bands at the K point of the Brillouin zone and the higher binding-energy hole band at Γ can be varied in excess of 100 meV. We explore the mechanisms underpinning this evolution and discuss the implications for tuning both the size of the band gaps, and the efficiency of the spin-dependent electron-phonon coupling channels in homobilayer transition metal dichalcogenide devices.

AI-enabled systems are increasingly introduced into educational contexts, yet their effectiveness depends less on technological sophistication than on the quality of pedagogical mediation, ethical constraints, and context-sensitive design. This paper proposes a replicable framework for AI-enabled pedagogical accompaniment, grounded in a human-in-command approach in which adult responsibility remains central and AI functions as an enabling, non-substitutive infrastructure. Building on the Amico project, we operationalize the concept of a relational bridge as a sequence of micro-mediations that lower the threshold of access to educational relationships and facilitate transitions toward meaningful human interaction with teachers, peers, and communities of practice. The contribution synthesizes a set of design principles, including transparency of system identity and limits, scaffolding toward human contact, maieutic questioning, prevention of dependency dynamics, and data minimization, and maps them to observable indicators suitable for real educational settings. The paper also outlines an initial cross-context exploration of the prototype in Italy and China and discusses how the two interaction modes, AmicoMio (structured, task-oriented) and AmicoTuo (reflective, supportive), can be used as complementary pedagogical mediations. Pilot observations and participant feedback suggested feasibility and perceived usefulness in vocational contexts, motivating the present framework, informing the subsequent doctoral research program, and supporting the proposed collaborative research agenda.

We propose a generalization of Hasse-Schmidt derivations that is equivalent to the notion of n-trivial extension introduced by Anderson-Bennis-Fahid-Shaiea, in the same way that derivations are equivalent to trivial extensions. We provide many examples of this generalization and prove some of its basic properties.

The study of ORR was inspired by Lázsló Babai in 1980 when he asked a question: Which [finite] groups admit an oriented graph as a DRR? And it has been solved by Joy Morris and Pablo Spiga through a series of papers in 2018. In this paper, we will extend the concept of ORR to $m$-partite oriented graphs for $m\geq 2$. We say that a finite group $G$ admits an \emph{$m$-partite oriented semiregular representation} ($m$-POSR) if there exists an $m$-partite oriented graph $\G$ such that its automorphism group is isomorphic to $G$ and acts semiregularly with the $m$ orbits giving the partition. Moreover, if $\G$ is regular, that is, each vertex has the same in- and out-valency, it can be viewed as the oriented version of an $m$-Haar graph of $G$ and we call $\G$ is an \emph{$m$-Haar oriented representation} ($m$-HOR) of $G$. Our main result is a complete classification of finite groups $G$ without $m$-HORs or $m$-POSRs for $m\geq 2$.

We extend the notion of conformal barycenter, recently introduced by Jačimović and Kalaj for the complex hyperbolic ball, to the quaternionic unit ball $\BH$. The quaternionic conformal barycenter of a measurable set $D$ with finite hyperbolic measure and finite first moment is defined as the unique point $c$ such that $\int_D Φ_c(q)\, \dLam(q) = \mathbf{0}$, where $Φ_c$ is the quaternionic Hua involution exchanging $0$ and $c$. Equivalently, it is the unique minimum of the energy functional $G(x) = \int_D \log\cosh^2\!\big(\frac12 d_H(x,y)\big)\, \dLam(y)$. We prove existence and uniqueness using the strict geodesic convexity of $G$, which is established by a direct computation along geodesics. The barycenter is invariant under the full isometry group $\mathrm{Sp}(n,1)$. We also treat finite point sets and provide explicit examples.

The entangling power of a unitary operator quantifies its ability to generate entanglement from product states and provides a natural probe of quantum many-body dynamics. Entanglement extremization at points of enhanced symmetry has previously been observed in high-energy scattering. In this work we compute the time-averaged entangling power of anisotropic Heisenberg spin chains across two-site models and finite-size systems, as well as the entangling power of the two-magnon $S$-matrix in the thermodynamic limit. For two-site models we establish a monotonic hierarchy: the entangling power decreases as the symmetry group grows, reaching its minimum at the $SU(2)$ XXX point. Finite-size XXZ chains exhibit sharp dips at the $SU(2)$ points $Δ=\pm 1$ and the free-fermion point $Δ=0$, with the free-fermion dip decaying much more slowly with system size. In the thermodynamic limit, we decompose the two-magnon $S$-matrix into quantum logic gates -- Identity, SWAP, and $σ_z\otimesσ_z$ -- and show that the entangling power vanishes for all scattering energies at the $SU(2)$ points, where the $S$-matrix reduces to the Identity gate, while the free-fermion point achieves the maximum -- the opposite of the finite-size many-body behavior. The entangling power can serve as an {\em operator} diagnostic for symmetry and selected aspects of integrability in quantum simulations of spin-chain dynamics.

A Cayley (di)graph $\Cay(G,S)$ of a finite group $G$ is called CI if, for every Cayley (di)graph $\Cay(G,T)$ of $G$, $\Cay(G,S)\cong \Cay(G,T)$ implies that $S^σ=T$ for some $σ\in \Aut(G)$. The group $G$ is called an NDCI-group (resp. NCI-group) if every normal Cayley digraph (resp. graph) of $G$ is CI. It was shown that the generalized quaternion group $\Q_{4n}$ of order $4n$ ($n\geq 2$) is an NDCI-group if and only if either $n=2$ or $n$ is odd, but its NCI-group classification has been left as an open question. In this paper, we solve the question and prove that $\Q_{4n}$ is an NCI-group for every $n\geq 2$. A normal Cayley (di)graph of a group $G$ is called NNN if its automorphism group contains a non-normal regular subgroup isomorphic to $G$, and $G$ is called an NNND-group (resp. NNN-group) if it admits an NNN Cayley digraph (resp. graph). In this paper, we show that $\Q_{4n}$ is not an NNN-group for every $n\geq 2$, and is an NNND-group if and only if $n\geq 6$ and $n$ is even.

Understanding how complex entanglement structures emerge is a central problem in quantum many-body physics. Recent work by Zhang et al. has considered structured initial states prepared by evolving a product state under a chaotic Hamiltonian for a finite time before quenching to the target Hamiltonian. In this setup, total entanglement entropy growth in many-body localized systems exhibits two distinct regimes, first increasing and then decreasing as the initial entanglement is tuned. In this work, we identify the physical origin of this behavior by analyzing the dynamics of both the Rényi entanglement entropy and the Wehrl-Rényi entropy in the random-field XXZ model, the latter of which characterizes multipartite entanglement. We show that a similar non-monotonic dependence on the initial entanglement also appears in the net growth of the Wehrl-Rényi entropy for product states polarized along the $z$-direction. The first regime is governed by a finite magnetization associated with local integrals of motion, while the second reflects inter-site correlations. In contrast, for product states in the $x/y$-direction, the entanglement growth exhibits a monotonic decay. Our results provide a more fine-grained picture of how distinct initial-state properties shape entanglement dynamics in many-body localized systems.

Optically addressable spin defects in hexagonal boron nitride hold promise for room-temperature quantum technologies, but their microscopic identities remain largely unknown. Using first principles calculations, we show that coupled spin optical signals arise from interacting donor acceptor pairs, not the commonly believed isolated defects. Intra and inter pair separations control charge transfer, electronic structure, and spin coupling, thereby greatly modulating zero phonon lines, phonon sidebands, lifetimes, and the sign of optically detected magnetic resonance contrast. Importantly, we identify two distinct charge-state-dependent coupling regimes and extend this picture to correlated defect ensembles, explaining the wide diversity of experimental observations. Our results establish a microscopic framework for coupled defect behavior and provide design principles for spin-active quantum emitters in wide bandgap semiconductors.

The discovery of high critical-temperature $T_{\mathrm{c}}$ superconductivity in La$_3$Ni$_2$O$_7$ under high pressure has led to a rapid expansion of the $T_{\mathrm{c}}$ range through lanthanide $Ln$ substitution, and to ambient-pressure superconductivity in strained thin films, yet the exploration of new bilayer nickelates remains strongly constrained by thermodynamic stability. Beyond the difficulty of synthesis of bulk single-crystals, here we report on the pressure-induced high-$T_{\mathrm{c}}$ superconductivity in epitaxially-stabilized Pr$_3$Ni$_2$O$_7$ thin films. While the Pr$_3$Ni$_2$O$_7$ films exhibit insulating behaviour at ambient pressure regardless of ozone-annealing treatment, they show $T$-linear metallic transport and superconductivity reaching an onset $T_{\mathrm{c}}$ of 66 K and zero-resistance at nearly 40 K at 22 GPa. Furthermore, Nd$_3$Ni$_2$O$_7$, with the smaller rare-earth ion Nd, can also be stabilized, however, superconductivity is not observed in the measured pressure range. Epitaxial stabilization enables us to examine the dependence of $T_{\mathrm{c}}$ and the critical pressure $P_{\mathrm{c}}$ for superconductivity on the $Ln$ ion in $Ln_3$Ni$_2$O$_7$ ($Ln$ = La, Pr, Nd). These results suggest that a higher $P_{\mathrm{c}}$ is required for smaller $Ln$ ions, consistent with trends observed in bulk studies of $Ln$ substitution. This study demonstrates that epitaxial stabilization is a powerful technique to further expand the family of superconducting bilayer nickelates.

Nonlinearity is an essential ingredient for encoding quantum states with non-uniform energy spacing, implementing coherent quantum gates, reading out qubits, amplifying, and mixing electromagnetic signals. In this work, we demonstrate the nonlinear behavior of a constriction fabricated from an amorphous, high-kinetic inductance material, tungsten silicide, embedded in a three-dimensional RF-SQUID. We find that the results are consistent with the weak link behaving as a Josephson junction with a sawtooth-like current-phase relation or a quantum phase slip element. Finally, we measure relaxation times of the metastable, persistent-current states trapped in the local minima of the potential.

We establish a priori regularity estimates for viscosity solutions of degenerate fully nonlinear elliptic equations with integrable right-hand sides. When the nonhomogeneous term belongs to $L^p$ with $p>n$, we prove optimal interior $C^{1,α}$ estimates. In the critical case, we obtain a log-Lipschitz modulus of continuity under the Lorentz condition $f\in L^{n,1}$. We utilize sliding paraboloid or cusp methods to develop uniform Hölder estimates for equations that are elliptic only in suitable gradient regimes. Finally, we establish an approximation lemma for integrable right-hand sides via a corrector argument, which allows us to deduce the corresponding Schauder-type estimates.

Achieving diffraction-limited focusing of high-power laser pulses to generate ultra-high intensities is crucial for developing compact laser-driven particle accelerators and exploring strong-field quantum electrodynamics. However, accurately diagnosing and optimizing the focal spots of petawatt (PW) laser pulses remains a significant challenge. In this work, we present an experimental methodology utilizing a twin-focus scheme to precisely characterize the intensity distribution and wavefront of focused PW femtosecond laser pulses, and employ it to elucidate their power-dependent evolution. Furthermore, we optimized the focal spots at full power via our in-situ wavefront correction method termed ``HotLoop', achieving a Strehl ratio of 0.80 for 1 PW laser pulses. Consequently, the cutoff proton energies in laser proton acceleration experiments were significantly enhanced. The success of this approach underscores the necessity of in-situ high-energy wavefront correction for ultra-high intensity laser-matter interactions.

Natural disasters not only cause large-scale physical destruction, but also cascading social consequences that are difficult to quantify with traditional surveys and reports. Social media platforms offer an alternative perspective that captures multimodal, real-time, and user-generated content that can be leveraged for disaster impacts. In this paper, we introduce DisImpact, a two-stage framework that systematically quantifies the physi-social impacts of disasters via a Multimodal Large Language Model (MLLM). The social media posts are first classified into ten disaster impact categories that cover both physical and social domains. We then construct a disaster impact index that integrates the relative prominence of each category with the intensity of public engagement on a weekly basis. This design provides a unified scale for representing disaster impacts across both individual disaster impact categories and the broader physical and social domains. The unified representation enables direct comparison across categories and allows the impacts to be flexibly aggregated to reveal higher-level patterns and overall trends. We validate the impact indices against authoritative ground-truth data, including FEMA Public Assistance data and NASA FIRMS fire detections, observing consistent lead-lag correlations that demonstrate strong validity across both social and physical impact dimensions. We further conduct temporal and spatial analyses, and the results show that physical impacts are often peak during the disasters and localized in regions that are directly affected by disasters, while social impacts often emerge later and spread more broadly across time and space. To the best of our knowledge, this is the first framework to comprehensively quantify disaster impacts across their physical and social dimensions using multimodal data from multiple social media platforms.

Distributed optimization has found widespread applications in smart grids, optimal control, and machine learning. This paper studies distributed consensus optimization. We extend the Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) framework to propose Consensus ALADIN (C-ALADIN) with a central coordinator, which directly handles consensus constraints. Our C-ALADIN algorithm admits both a first-order variant and a second-order variant that employs a Hessian approximation, avoiding direct transmission of second-order information while preserving fast local convergence. We then develop a decentralized version of C-ALADIN that operates over directed graphs with quantized communication, using a finite-time coordination protocol. For both versions, we establish global convergence guarantees for convex problems and local convergence guarantees for non-convex problems. For the decentralized case, the iterates converge to a neighborhood of the optimum determined by the quantization level. Numerical results demonstrate that our methods retain fast convergence while substantially reducing communication and computational costs compared to existing decentralized approaches.

We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary sample and shrinking bandwidth, to a vector of regression and second-moment statistics. Under stationarity, ergodicity, and finite second moments, the estimator is asymptotically normal and yields Wald confidence regions and simultaneous confidence intervals without direct long-run variance estimation or a parametric dependence model. For implementation, we introduce a scaled estimator with data-driven bandwidth selection and a mild truncation that improves finite-sample stability. Simulations under ARMA, ARFIMA, copula-based Markov errors, and fractional Gaussian noise, with Gaussian and heavy-tailed margins, show near-nominal coverage and competitive region volumes relative to Newey-West HAC and MAC. A winter Beijing PM2.5 application illustrates the procedure. Keywords: Random smoothing, Joint inference, Confidence regions, Dependent errors, Long memory, Regression inference

Propensity score (PS) methods are widely used in observational studies to reduce confounding and estimate causal treatment effects. However, the validity of PS-based causal estimators depends heavily on correct model specification, and model misspecification may lead to substantial bias and instability. In this study, we systematically evaluate the performance of commonly used causal estimators, including response surface modeling (RSM), inverse probability weighting (IPW), and augmented inverse probability weighting (AIPW), under varying levels of PS and outcome model misspecification. We compare classical logistic regression with several machine learning approaches for PS estimation, including random forests (RF), support vector machines (SVM), and linear discriminant analysis (LDA). Extensive simulation studies were conducted under multiple scenarios defined by combinations of correctly specified and misspecified PS and outcome models, varying sample sizes, and different covariate correlation structures. Estimator performance was assessed using bias, absolute bias, root mean squared error, empirical standard error, and confidence interval width. Results demonstrate that AIPW consistently provides robust and stable estimates across most scenarios due to its doubly robust property, whereas IPW is highly sensitive to PS misspecification and unstable PS estimates produced by flexible machine learning methods. RSM performs well only when the outcome model is correctly specified. Real-world applications using the ACTG175 clinical trial and the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset further illustrate the practical implications of estimator choice and PS modeling strategy. Overall, our findings highlight the importance of integrating flexible machine learning approaches within doubly robust frameworks to improve causal effect estimation in observational studies.

A newborn, rapidly rotating magnetar may form in a binary neutron star merger and drive a Poynting-flux-dominated relativistic jet. As the jet propagates outward, a forward shock (FS) and a reverse shock (RS) are formed, inflating a pulsar wind nebula (PWN) between them. We present a systematic study of the emission from both the PWN and the jet, whose magnetic energy is subject to dissipation. By following the dynamics of the jet-ejecta-PWN system, we find that, in most cases, the RS is long-lived: it first lags behind the contact discontinuity and eventually coincides with both the contact discontinuity and the FS after the jet breakout into the external medium. As a result, the emission exhibits a characteristic temporal evolution. Depending on the optical depth, the emission is initially dominated by thermal radiation from the optically thick ejecta, then by a jet-powered X-ray plateau once the system becomes optically thin, and finally by synchrotron and inverse-Compton radiation from the PWN FS at late times. In particular, external inverse-Compton scattering of jet photons by the FS naturally produces a late-time GeV bump together with a substantial TeV component. Our model can simultaneously account for early thermal emission, X-ray plateaus, and late-time GeV excesses in merger-driven gamma-ray bursts, and also indicates that post-merger magnetar-driven PWNs are potential TeV photon sources.

The coherent lattice vibrations significantly impact physical and chemical processes in solids, such as heat transfer, displacive phase transitions, and thermal conductivity. Thus, probing lattice dynamics in real-space and real-time is essential for understanding ubiquitous phenomena in solids. High-harmonic spectroscopy (HHS) has emerged as a preferred technique for investigating static and dynamic properties of solids on ultrafast timescales. Yet, despite these accomplishments, the applicability of HHS to probe the influence of coherent lattice vibrations on electronic responses has remained unexplored. In this thesis, we explore the impact of coherent lattice dynamics on attosecond electronic responses in solids using HHS. We observe that coherent excitation of the in-plane phonon mode in graphene results in sidebands in the harmonic spectrum, separated by the frequency of the excited phonon mode. Additionally, we demonstrate the capability of HHS to characterize energy, polarization, phase difference, and the "chirality" of phonon modes. This thesis offers an avenue to probe phonon-driven processes in solids with sub-cycle temporal resolution. In the later segment, our focus shifts toward probing coherent lattice dynamics in real-space and real-time. We demonstrate that inelastic scattering techniques, combined with theoretical analysis, yield comparable results to those from time-resolved diffraction and imaging measurements within pump-probe configurations. Our findings exhibit excellent agreement with results from a time-resolved diffuse x-ray scattering experiment. Our proposed method serves as an alternative to time-resolved diffraction and imaging methods for probing lattice dynamics in real-space and real-time with atomic-scale spatiotemporal resolution.

This paper studies the problem of discrepancy estimates for pseudorandom vectors constructed by the elliptic curve congruential generator, particularly in the non-translational case. Two families of results are obtained. First, in a full-coset regime characterized by a relative maximal period condition (RMPC) on an induced one-dimensional linear congruential generator, one proves bounds of type $q^{1/2}/t$ for the discrepancy $D$, the serial discrepancy $D_s$, and, under the corresponding derived RMPC, the non-overlapping discrepancy $\widetilde D_s$. Second, in the general sub-period regime, one reduces bounds for $D$, $D_s$, and $\widetilde D_s$ to estimation of Fourier $\ell^1$ masses of admissible index sets attached to one-dimensional linear congruential generators. This isolates the arithmetic bottleneck for further improvement.

We present the results of a blind search for Lyman $α$ emitters (LAEs) in three deep archival $z\sim6$ quasar fields from VLT/MUSE using state-of-the-art detection algorithms. We explore their connection with absorbers-particularly C IV and Mg II-in the circumgalactic medium (CGM) from the E-XQR-30 survey. We detect 156 LAEs at $2.9<z<6.7$ with luminosities ranging from log $L[\text{ergs}^{-1}]=$ 41.3 to 43.2. We find 34 and 14 galaxy associations with C IV and Mg II absorption respectively at $3.4<z<5.8$ within a line of sight velocity window of $\pm1000~\text{km}^{-1}$ and impact parameter of $<250$ pkpc. These systems have a weak anti-correlation with respect to the absorber strength-impact parameter relation. No Mg II systems are found within the virial radii of any LAE while four C IV absorbers are located within the virial radii of an LAE suggesting that low ionisation gas has a lower covering fraction. The LAEs have mild overdensity ratios of 1.7 and 1.9 around C IV and Mg II respectively. The stellar mass upper limits of $\text{log}~M_*<10.7~\text{M}_\odot$ estimated using Keck/NIRC2 imaging indicate that a low-mass, faint population of galaxies pollutes the CGM with metals. This paper serves as a pilot analysis for the forthcoming REQUIEM survey, an ESO Large Program on high redshift deep quasar fields.

Changepoints are essential for homogenizing categorical time series and analyzing their trends and variations. The original total cloud cover in Canada was recorded hourly in tenths (or eighths), exhibiting inherent seasonality and serial correlation. Lu and Wang (2012) introduced an extended cumulative logit model to detect shifts in the annual frequencies of cloud cover conditions. While annual aggregation mitigates seasonality and serial correlation, it shortens the time series and may lead to overdispersion. This article introduces a marginalized transition model to detect a single changepoint in periodic and serially correlated categorical time series. The model captures serial dependence using a first-order Markov chain and enables category-specific changepoint specification. To enhance computational efficiency, we develop a new parameter estimation procedure for obtaining maximum likelihood estimates. A maximally selected likelihood ratio test statistic is then proposed to test for sudden changes in categorical time series, and the method is illustrated using daily total cloud cover observations recorded at 9 a.m. and 3 p.m. at Fort St. John Airport, British Columbia, Canada.

We prove a complete realization theorem for multifractal entropy spectra of continuous potentials on a broad class of dynamical systems. More precisely, for every $H>0$ and every continuous concave function on a compact interval with maximum value $H$ attained at a unique point, each system in this class with topological entropy $H$ admits a continuous potential whose multifractal entropy spectrum is exactly that function. The same spectrum can moreover be realized by arbitrarily many pairwise non-cohomologous potentials. We also study the potential dependence of entropy spectra in the Hausdorff graph metric, proving general lower semicontinuity and dense failure of upper semicontinuity for non-trivial mixing subshifts of finite type. Finally, as an application of the realization theorem, we use the Legendre transform duality between multifractal entropy spectra and pressure functions to derive a pressure flexibility theorem for pressure functions defined on the whole real line, thereby giving an affirmative answer to a question of Kucherenko and Quas~\cite{KQ2022}.

We present a detailed chemical-abundance and kinematic analysis of four extremely metal-poor (EMP; [Fe/H] $\leq -3.0$) stars identified from \textit{Gaia} BP/RP data in our ongoing search for the most primitive stars. This includes a primary target, \textit{Gaia}~DR3~2563539603865382656 (hereafter G256353), a strongly $r$-process-enhanced star with [Eu/Fe]~$= +1.20$ and [Ba/Eu]~$= -0.64$. Our results are based on high-resolution, high-signal-to-noise GHOST spectra from Gemini-South. For the full sample, we statistically match the light-element abundances with those predicted from Population\,III supernova models. The ``best-fit'' model suggests massive progenitors with stellar masses of M$_{\star}\sim$ 20-30\,M$_\odot$. In addition, we determine orbital histories for all of the stars. We find that Gaia~DR3~2887334237669844480 appears to be kinematically associated with Atari, an accreted structure in the Galactic disk. This star has low abundance ratios of strontium ([Sr/Fe] = $-$1.09) and barium ([Ba/Fe] = $-$0.37), which supports an accretion origin. For G256353, we determine chemical abundances for 15 neutron-capture elements. We compare the observed heavy-element pattern for G256353 with that of the Sun, HD~222925, and two neutron star merger models. The $r$-process elements in G256353 align reasonably well with HD~222925, the scaled-Solar pattern (except for the first peak), and a recent predicted pattern associated with neutron star mergers. This consistency reinforces the universality of the main $r$-process across diverse astrophysical environments.

The gravitational entropy proposal of Clifton, Ellis and Tavakol (CET) is based on an effective energy momentum tensor formed by the algebraic decomposition of the 4th order Bel-Robinson tensor. So far the application of the CET proposal has been limited to spacetimes of Petrov types D and N for which this algebraic decomposition is unique. To address this limitation we examine in detail the effective energy momentum tensors that result from the algebraic decomposition of the Bel-Robinson tensor in Petrov type I spacetimes. As a test case we apply these results to the Szekeres models of class II, a Petrov type I analytic solution.