Submillimeter astronomy is poised to revolutionize our understanding of the Universe by revealing cosmic phenomena hidden from optical and near-infrared observations, particularly those associated with interstellar dust, molecular gas, and star formation. The Xue-shan-mu-chang 15-meter submillimeter telescope (XSMT-15m), to be constructed at a premier high-altitude site (4813 m) in Qinghai, China, marks a major milestone for Chinese astronomy, establishing the China mainland's first independently developed, world-class submillimeter facility. Equipped with state-of-the-art instruments, XSMT-15m will address a diverse range of frontier scientific questions spanning extragalactic astronomy, Galactic structure, time-domain astrophysics, and astrochemistry. In synergy with current and forthcoming observatories, XSMT-15m will illuminate the formation and evolution of galaxies, unravel the physical and chemical processes shaping the interstellar medium, and explore transient phenomena in the submillimeter regime. These capabilities will advance our understanding across extragalactic astronomy, Galactic ecology, astrochemistry, and time-domain astrophysics, inaugurating a new era for submillimeter research in China and the northern hemisphere.

Landau levels (LLs) are the massively-degenerate discrete energy spectrum of a charged particle in a transverse magnetic field and lie at the heart of many intriguing phenomena such as the integer and fractional quantum Hall effects as well as quantized vortices. In this Letter, we consider coupling of LLs of a transversely driven, single charge-neutral particle in a synthetic gauge potential to a quantized field of an optical cavity -- a setting reminiscent of superradiant self-ordering setups in quantum gases. We uncover that this complex system can be surprisingly described in terms of two highly nonlinearly-coupled quantum harmonic oscillators, thus enabling a full quantum mechanical treatment. Light-matter coupling mixes the LLs and the superradiant photonic mode, leading to the formation of hybrid states referred to as "Landau polaritons". They inherit partially the degeneracy of the LLs and possess intriguing features such as non-zero light-matter entanglement and quadrature squeezing. Depending on the system parameters and the choice of initial state, the system exhibits diverse nonequilibrium quantum dynamics and multiple steady states, with distinct physical properties. This work lays the foundation for further investigating the novel, driven-dissipative Landau-polariton physics in quantum-gas--cavity-QED settings.

Human oversight of AI is promoted as a safeguard against risks such as inaccurate outputs, system malfunctions, or violations of fundamental rights, and is mandated in regulation like the European AI Act. Yet debates on human oversight have largely focused on its effectiveness, while overlooking a critical dimension: the security of human oversight. We argue that human oversight creates a new attack surface within the safety, security, and accountability architecture of AI operations. Drawing on cybersecurity perspectives, we model human oversight as an IT application for the purpose of systematic threat modeling of the human oversight process. Threat modeling allows us to identify security risks within human oversight and points towards possible mitigation strategies. Our contributions are: (1) introducing a security perspective on human oversight, (2) offering researchers and practitioners guidance on how to approach their human oversight applications from a security point of view, and (3) providing a systematic overview of attack vectors and hardening strategies to enable secure human oversight of AI.

This paper presents a detailed analysis of the three-body final state interactions in the $B^+\to D\bar{D}K^+$ process, whose phase space is sufficient small. To precisely extract the resonance parameters, for instance the $χ_{c0/2}(3930)$ in the $D\bar{D}$ invariant mass distributions, in this process, one has to take into account final state interaction, especially the three-body final state interaction. We employ the dispersive Khuri-Treiman formalism, combined with a parameterization of the $D\bar{D}$ interaction based on Heavy Quark Spin Symmetry. By performing a simultaneous fit to the experimental data from LHCb, BaBar, and Belle collaborations, the scheme with three-body interaction successfully describes the invariant mass distributions of the three two-body subsystems. We precisely extract the pole structures of $χ_{c0}(3930)$ and $ψ(3770)$ as $3.913-0.018i~\mathrm{GeV}$ and $3.764-0.002i~\mathrm{GeV}$ in $B^+$ decay. By performing the pole trajectory analysis on a uniformized complex plane, we find that both of them stem from the input bare state.

In April 2013, the TeV blazar Markarian~421 underwent one of its most powerful emission outbursts to date. An extensive multi-instrument campaign featuring MAGIC, VERITAS, and \textit{NuSTAR} provided comprehensive very-high-energy (VHE; $E > 100$\,GeV) and X-ray coverage over nine consecutive days. In this work, we perform a detailed spectral analysis of the X-ray and VHE emissions on sub-hour timescales throughout the flare. We identify several clockwise spectral hysteresis loops in the X-rays, revealing a spectral evolution more complex than a simple harder-when-brighter trend. The VHE spectrum extends beyond 10\,TeV, and its temporal evolution closely mirrors the behavior in the X-rays. We report the first evidence of VHE spectral hysteresis occurring simultaneously with the X-ray loops. To interpret these findings, we apply a time-dependent leptonic model to 240 broadband spectral energy distributions (SEDs) binned on a 15-minute scale, allowing us to self-consistently track the particle distribution's history. Our modeling shows that the majority of the sub-hour flux and spectral variations are driven by changes in the luminosity and slope of the injected electron distribution. The required variations in the electron slope are difficult to reconcile with magnetic reconnection but are consistent with a shock-acceleration scenario where the shock compression ratio evolves by a factor of $\sim2$. The model also points to a relatively stable magnetic field and emitting region size, favoring a scenario where the emission originates from a stationary feature in the jet, such as a recollimation shock. However, this scenario requires a jet Lorentz factor that significantly exceeds values from VLBI measurements to account for the high minimum electron energy implied by the lack of variability in the optical band.

Janus particles are functional particles with at least two surfaces showing asymmetric properties. We show at the interface between two magnetic regions with different antisymmetric exchange interactions, an alternative species of two-dimensional topological quasiparticles can emerge, in which different helicity structures can coexist. We name such an interfacial quasiparticle a "Janus skyrmion," in analogy to the Janus particle. As the Janus skyrmion shows helicity asymmetry, its size could vary with both the in-plane and out-of-plane magnetic fields. A vertical spin current could drive the Janus skyrmion into one-dimensional motion along the interface without showing the skyrmion Hall effect, at a speed which depends on both the in-plane spin-polarization direction and current density. Thermal fluctuations could also lead to one-dimensional random walk of a Brownian Janus skyrmion. This work uncovers unique dynamics intrinsic to interfacial quasiparticles with exotic helicity, which may be realized in interface-engineered magnetic layers.

We investigate the nature of low-energy excitations in a spin chain with antiferrmomagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and three-site $J_3$ interactions using the time-dependent density matrix renormalization group and the single mode approximation techniques. In the absence of the $J_2$ interaction, we identify clear distinctions in the spectral functions in the fully dimerized phase across the exactly dimerized line for different magnitudes of the spins. In contrast to the spin-$1/2$ chain, where the spinon continuum dominates the spectral functions, the magnon modes are prominent in the spectral functions of the spin-$1$ and spin-$3/2$ chains. Through single mode approximation and valence bond solid approaches, we disentangle magnon and spinon contributions to the spectral functions. After including the $J_2$ interactions, for the spin-$1$ chain we trace the evolution of the dynamical structure factor along the phase transition line between the Haldane phase and the fully dimerized phase. We find that the excitation spectrum is a continuum along this line and the spectral gap closes as the order of the transition changes from first order to second order. Along the line of first-order transitions, the spinon-like domain walls are deconfined, and the model exhibits their confinement into discrete bound states away from the transition line. A similar phenomenon occurs in the spin-$3/2$ chain across the phase transition between partially dimerized to fully dimerized phases, revealing a universal spinon confinement phenomenon across first-order phase transitions. This study presents the dynamical structure factor corresponding to the ground state phase diagram and establishes a unified quasiparticle framework for understanding the fundamental nature of excitations across distinct quantum phases in frustrated $J_1$-$J_2$-$J_3$ Heisenberg spin chains.

An edge of a graph dominates itself along with any edge that shares an endpoint with it. An efficient edge dominating set (also called a dominating induced matching, DIM) is a subset of edges such that each edge of the graph is dominated by exactly one edge in the subset. A perfect edge dominating set is a subset of edges in which every edge outside the subset is dominated by exactly one edge within it. In this article, we establish the NP-completeness of deciding whether a graph that does not admit any efficient edge dominating set has at least two perfect edge dominating sets. We also present a cubic time algorithm designed to identify a perfect dominating set of minimal cardinality for $P_6$-free graphs. Moreover, we show how this algorithm can be adapted to handle the weighted version of the problem and to count all perfect edge dominating sets as well as DIMs in a given graph, while preserving the same time complexity.

We present iHOMER, an iterative version of the HOMER method to extract Lund fragmentation functions from experimental data. Through iterations, we address the information gap between latent and observable phase spaces and systematically remove bias. To quantify uncertainties on the inferred weights, we use a combination of Bayesian neural networks and uncertainty-aware regression. We find that the combination of iterations and uncertainty quantification produces well-calibrated weights that accurately reproduce the data distribution. A parametric closure test shows that the iteratively learned fragmentation function is compatible with the true fragmentation function.

We present the first systematic study of explosive dispersal outflows (EDOs) as potential sources of high-energy emission in the Milky Way. EDOs are energetic outflows produced during dynamical interactions in young, massive star-forming regions, and their physical conditions make them promising environments for cosmic-ray acceleration. Using 16 years of $0.2$--$500$ GeV Fermi-LAT observations, we study the gamma-ray properties of seven EDOs. Three EDOs, DR21, G34.26$+$0.15, and G5.89$-$0.39 show spatially coincident GeV emission, while the remaining systems yield non-detections. Among the sample, DR21 stands out as the brightest candidate, with a detection significance $\geq 40σ$. Its spectrum is well described by a power law with an exponential cutoff, and the integrated luminosity in the $0.1$--$500$ GeV band is $L_γ\simeq 2\times10^{35}\ \mathrm{erg\ s^{-1}}$. When compared with the outflow's estimated kinetic energy, the inferred cosmic-ray acceleration efficiency is $\leq 15\%$, consistent with values for shocks in dense molecular environments. The energetics and morphology support an association between the DR21 molecular outflow and the observed gamma rays. Our results demonstrate that EDOs span a wide range of gamma-ray luminosities and efficiencies, suggesting they may contribute to the Galactic cosmic ray budget. This motivates searches for additional EDOs and improved multiwavelength characterization of their environments.

We introduce {\it (W')-specification} in terms of language decompositions of subshifts, and show that any recurrence set of a subshift with this property has full Hausdorff dimension. Our main result applies to a wide class of subshifts without specification, such as all $S$-gap shifts, some coded shifts, and the coding space of any transitive piecewise monotonic interval map with positive entropy. Further, for a wide class of piecewise expanding interval maps we show that any recurrence set has full Hausdorff dimension.

The equations for the photon surface in spherical symmetry are worked out, starting from arXiv:gr-qc/0005050, in the most general dynamical setting. We show that the condition for a timelike hypersurface to be a photon surface can be reformulated as a non-autonomous dynamical system, whose analysis reveals that the same condition also holds when the surface is generated by a null radial geodesic. As an application, we consider a well-known model of a spherical dust cloud undergoing gravitational collapse. Comparing our findings with those in arXiv:1910.13758 we establish that the photon surface uniquely extends in the interior spacetime as a null hypersurface, allowing us to analytically investigate whether it covers the singularity developing in the LTB model.

We present an energy conservative, quadrature based model reduction framework for the compressible Euler equations of Lagrangian hydrodynamics. Building on a finite element discretization of the governing equations, we develop reduced models using data based reduced basis functions and the empirical quadrature procedure (EQP). We introduce a strongly energy conservative variant of EQP that enforces exact energy conservation in the reduction process. Numerical experiments for four benchmark problems -- Sedov blast, Gresho vortex, triple point and Taylor-Green vortex -- demonstrate that the numerical implementation of our proposed method conserves total energy to near machine precision, while maintaining accuracy comparable to the basic EQP formulation.

Post-mortem analysis of compromised systems is a key aspect of cyber forensics, today a mostly manual, slow, and error-prone task. Agentic AI, i.e., LLM-powered agents, is a promising avenue for automation. However, applying such agents to cybersecurity remains largely unexplored and difficult, as this domain demands long-term reasoning, contextual memory, and consistent evidence correlation - capabilities that current LLM agents struggle to master. In this paper, we present the first systematic study of LLM agents to automate post-mortem investigation. As a first scenario, we consider realistic attacks in which remote attackers try to abuse online services using well-known CVEs (30 controlled cases). The agent receives as input the network traces of the attack and extracts forensic evidence. We compare three AI agent architectures, six LLM backends, and assess their ability to i) identify compromised services, ii) map exploits to exact CVEs, and iii) prepare thorough reports. Our best-performing system, CyberSleuth, achieves 80% accuracy on 2025 incidents, producing complete, coherent, and practically useful reports (judged by a panel of 25 experts). We next illustrate how readily CyberSleuth adapts to face the analysis of infected machine traffic, showing that the effective AI agent design can transfer across forensic tasks. Our findings show that (i) multi-agent specialisation is key to sustained reasoning; (ii) simple orchestration outperforms nested hierarchical architectures; and (iii) the CyberSleuth design generalises across different forensic tasks.

With the advancement of third-generation gravitational wave detectors, the identification of strongly lensed gravitational wave (GW) events is expected to play an increasingly vital role in cosmology and fundamental physics. However, traditional Bayesian inference methods suffer from combinatorial computational overhead as the number of events grows, making real-time analysis infeasible. To address this, we propose a deep learning model named Squeeze-and-Excitation Multilayer Perceptron Data-efficient Image Transformer (SEMD), based on Vision Transformers, which classifies strongly lensed GW events by modeling morphological similarity between time-frequency spectrogram pairs. By integrating Squeeze-and-Excitation attention mechanisms and multilayer perceptrons , SEMD achieves strong feature extraction and discrimination. Trained and evaluated on simulated datasets using Advanced LIGO and Einstein Telescope noise, the model demonstrates robustness and generalization across different detector sensitivities and physical conditions, highlighting the promise of deep learning for rapid identification of strongly lensed GW signals.

We present the first unified constraints on a broad class of extended dark matter compact objects (EDCOs) from interstellar gas heating. These include axion stars, Q-balls, axion miniclusters, dark fermion stars and primordial black holes surrounded by dark matter halos, which arise in a wide range of theories beyond the Standard Model. As such massive objects traverse the interstellar medium, their gravitational influence generates wakes and, if sufficiently compact, drives accretion flows that heat gas in their vicinity. Our general framework extends standard dynamical friction treatments by incorporating finite-size effects, internal density profiles, gas penetration through objects, and criteria for accretion disk formation. We perform detailed numerical calculations of wake formation and gas heating and apply our results to the Leo T dwarf galaxy, establishing new constraints on the dark matter fraction in EDCOs heavier than a solar mass spanning several orders of magnitude in both mass and abundance.

Multipole expansion plays an important role in the description of electromagnetic scatterers, allowing them to be accurately characterized by a small set of expansion coefficients. However, to describe electromagnetic excitations inside a scatterer, the current density in it should be decomposed into current multipoles, which include nonradiating current configurations (anapoles) that are absent in the classical field-based expansion. Unfortunately, the use of current multipoles has so far been limited by the absence of an exact and general expression for the current multipole moments beyond their point-multipole approximation. Here, we derive such an expression and present the exact mapping relations between the classical and current multipole moments. We use our theory to calculate the scattering and extinction cross sections for large, wavelength-scale, optical scatterers supporting multipole excitations up to the sixth order, showing perfect agreement with the Mie theory. We also demonstrate the ability of current multipole expansion to describe anapole excitations beyond the small-scatterer approximation, which allows us to derive the exact anapole condition and reveal the actual current configurations and their contributions to scattering. Our theoretical framework is valid for electromagnetic scatterers of arbitrary sizes and shapes without restrictions on the multipole orders, complementing the existing theory of electromagnetic multipole expansion. The minimalistic and universal character of current multipoles makes them a convenient tool for characterizing and designing diverse electromagnetic scattering systems of arbitrary complexity.

Treatment effect heterogeneity refers to the systematic variation in treatment effects across subgroups. There is an increasing need for clinical trials that aim to investigate treatment effect heterogeneity and estimate subgroup-specific responses. While several statistical methods have been proposed to address this problem, existing partitioning-based methods often depend on auxiliary analysis, overlook model uncertainty, or impose inflexible borrowing strength. We propose the Bayesian Hierarchical Adjustable Random Partition (BHARP) model, a self-contained framework that applies a finite mixture model with an unknown number of components to explore the partition space accounting for model uncertainty. The BHARP model jointly estimates subgroup-specific effects and the heterogeneity patterns, and adjusts the borrowing strengths based on within-cluster cohesion without requiring manual calibration. Posterior sampling is performed via a custom reversible-jump Markov chain Monte Carlo sampler tailored to partitioning-based information borrowing in clinical trials. Simulation studies across a range of treatment effect heterogeneity patterns show that the BHARP model achieves better accuracy and precision compared to conventional and advanced methods. We showcase the utilities of the BHARP model in the context of a multi-arm adaptive enrichment trial investigating physical activity interventions in patients with type 2 diabetes.

We construct a class of conformal boundary states in the $\mathrm{SU}(n)_1$ Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding $\mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1$. These boundary states are beyond the standard Cardy construction and possess $\mathrm{SO}(n)$ symmetry. The $\mathrm{SU}(n)$ Uimin-Lai-Sutherland (ULS) spin chains, which realize the $\mathrm{SU}(n)_1$ WZW model on the lattice, allow us to identify these boundary states as the ground states of the $\mathrm{SO}(n)$ Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the $\mathrm{SU}(n)$ ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.

Benford's law is the statement that in many real world data sets, the probability of having digit $d$ in base $B$ as the first digit is \log_{B}\!\left(\frac{d+1}{d}\right) for all $1 \leq d \leq B$. We sometimes refer to this as weak Benford behavior, and we say that a data set satisfies strong Benford behavior in base $B$ if the probability of having significand at most $s$ is \log_{B}\!\left(s\right) for all $1 \leq s < B$, . We examine Benford behaviors in two different probabilistic models: stick and box fragmentation models. Building on the work arXiv:1309.5603 on the single proportion stick fragmentation model, we employ combinatorial identities on multinomial coefficients to reduce the multi-proportion stick fragmentation model to the single proportion model. We then provide a necessary and sufficient condition for the lengths of the stick fragments to converge to strong Benford behavior along with a quantification of the discrepancy from uniform distribution on $[0,1]$ in terms of irrationality exponent. Then we answer a conjecture of arXiv:2304.08335 on the high-dimensional box fragmentation model. Using tools from Fourier analysis and order statistics, we prove that under some mild conditions, faces of any arbitrary dimension of the box have total volume converging to strong Benford behavior.

5G-Advanced (5G-A) has enabled the vibrant development of low altitude integrated sensing and communication (LA-ISAC) networks. As a core component of these networks, unmanned aerial vehicles (UAVs) have witnessed rapid growth in recent years. However, due to the lag in traditional industry regulatory norms, unauthorized flight incidents occur frequently, posing a severe security threat to LA-ISAC networks. To surveil the non-cooperative UAVs, in this paper, we propose a multi-domain supervised contrastive learning (MD-SupContrast) framework for UAV radio frequency (RF) open-set recognition. Specifically, first, the texture features and the time-frequency position features from the ResNet and the TransformerEncoder are fused, and then the supervised contrastive learning is applied to optimize the feature representation of the closed-set samples. Next, to surveil the invasive UAVs that appear in real life, we propose an improved generative OpenMax (IG-OpenMax) algorithm and construct an open-set recognition model, namely Open-RFNet. According to the unknown samples, we first freeze the feature extraction layers and then only retrain the classification layer, which achieves excellent recognition performance both in closed-set and open-set recognitions. We analyze the computational complexity of the proposed model. Experiments are conducted with a large-scale UAV open dataset. The results show that the proposed Open-RFNet outperforms the existing benchmark methods in terms of recognition accuracy between the known and the unknown UAVs, as it achieves 95.12% in closed-set and 96.08% in open-set under 25 UAV types, respectively.

We introduce the concept of temporal hierarchy forecasting (THieF) in predicting day-ahead electricity prices and show that reconciling forecasts for hourly products and 2- to 24-hour blocks can significantly (up to 13%) improve accuracy at all levels. These results remain consistent throughout a challenging 4-year test period (2021-2024) in the German and Spanish power markets and across model architectures, including linear regression, shallow feedforward neural networks, gradient-boosted decision trees, and a state-of-the-art, pretrained transformer. Given that (i) trading of block products is becoming more common and (ii) the computational cost of reconciliation is comparable to that of predicting hourly prices alone, we recommend using it in daily forecasting practice.

This paper is the second part of a two-paper series, initiated in arXiv:2603.02163 for scalar PDEs on hypersurfaces, and is concerned with the well-posedness and $\mathrm{L}^p$-based Sobolev regularity of vector-valued PDEs of interest in fluid dynamics. This family of PDEs includes the (stationary) Bochner Laplace, tangent Stokes and Oseen, and tangent Navier--Stokes equations. We present several strong, weak and ultra-weak formulations of these problems on compact, connected $d$-dimensional manifolds without boundary embedded in $\mathrm{R}^{d+1}$. We prove $\mathrm{W}^{m,p}$-regularity for any $p \in (1,\infty)$ for manifolds of minimal regularity $C^{m+1}$ or $C^{m,1}$ for $m\ge1$. Building upon the $\mathrm{L}^p$-based scalar elliptic theory from arXiv:2603.02163, we develop a parametrization-free and purely variational approach that resorts to classical results such as the Banach--Nečas--Babuška theorem and the generalized Babuška--Brezzi theory in reflexive Banach spaces. In particular, by exploiting the manifold closedness, we decouple the velocity and pressure variables in the tangent Stokes problem to establish their higher-regularity $\mathbf{W}^{m,p} \times \mathrm{W}^{m-1,p}$ ($m \geq 2$) as a consequence of the $\mathrm{L}^p$-based well-posedness and regularity theory for the Laplace--Beltrami and Bochner--Laplace operators. We study spectral and regularity properties of an appropriate Stokes operator, and apply them to show existence of solutions for the Navier--Stokes equations for $p=2$ and $d \leq 4$. We next extend the well-posedness to $p > 2$ and prove higher-order $\mathrm{L}^p$-based regularity. We finally examine alternative choices to the Bochner Laplace operator that are useful in fluid dynamics.

The simulation of the spectra measured in nuclear magnetic resonance (NMR) spectroscopy experiments is a computationally non-trivial problem which, due to its natural interpretation as a quantum spin problem, maps in a straightforward way to a quantum computer. As such, it represents a problem for which such a device may provide some practical advantage over traditional computing methods. In order to understand the extent to which such problems may indeed provide examples of useful quantum advantage, it is important to understand the limitations of existing classical simulation methods. In this work, we benchmark our own classical solver designed to study such problems. This solver uses a clustering approximation to achieve a resource scaling which is linear in the total number of nuclear spins in a given molecule, for a fixed cluster size. The success of such an approximation would present a stark repudiation to the common claim that such problems require an exponential scaling of resources, the very claim which makes simulating an NMR spectra a candidate for quantum advantage. Our benchmarking results indicate that our approximation performs well throughout, and even somewhat beyond, the more typical experimental regimes. We discuss what implications this may have for future efforts to demonstrate quantum advantage in the context of NMR.

We prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin-Bona-Mahony, Korteweg-de Vries, Gardner, Kawahara, and Kuramoto-Sivashinsky equations, provided a smooth solution of the limiting problem exists. We only require weak (entropy) solutions of the hyperbolic approximations. Thereby, we provide a solid foundation for these approximations, which have been used in the literature without rigorous convergence analysis. We also present numerical results that support our theoretical findings.

The Sagittarius dwarf spheroidal galaxy provides us with the unique opportunity to study an ongoing Galactic cannibalistic event between our Milky Way Galaxy and a satellite dwarf galaxy. Understanding this event crucially requires memberships and high-precision metallicities. Here, we present the first major membership star catalog of the Sagittarius dwarf core ($\approx$140,000 sources) and Messier 54 ($\approx$2000 sources) with positions, proper motions, and parallaxes from $Gaia$ DR3, supplemented with metallicities from the Apache Point Observatory Galactic Evolution Experiment. We initially isolate the Sagittarius dwarf core and Messier 54 spatially from prior literature positions. Using evolutionary sub-samples separated within a color-magnitude diagram, we analyze the substructures of the Sagittarius core and infer its positional relationship with Messier 54 within 5D phase space. A sample of Milky Way stars from a similar galactic latitude were used to identify contaminants and separate member stars from the core of the Sgr dSph and Messier 54 using a Gaussian Mixture Model. We present the derived proper motion, parallaxes, and metallicities for these evolutionary sub-samples while demonstrating the precision of our sample using red clump standard candles. We find a distance modulus for the Sagittarius core and Messier 54 of $(m-M)_{0}=16.958^{+0.044}_{-0.044}$ mag and $(m-M)_{0}=16.94^{+0.047}_{-0.056}$ mag, corresponding to a heliocentric distance of $d=24.635^{+0.49}_{-0.49}$ kpc and $d=24.452^{+0.537}_{-0.602}$ kpc respectively. With red clump distance analysis, our results imply there is no separation between the Sagittarius core and Messier 54. Finally, we describe the metallicity distributions of the evolved stars within these two systems, finding evidence for the infall scenario.

Two-body gravitational interactions will occasionally lead to a stellar-mass compact object entering a very highly eccentric orbit around a massive black hole at the center of a galaxy. Gravitational radiation damping will subsequently result in an extreme mass ratio inspiral. Much of the inspiral time of these events is spent with the compact object on a long-period orbit, with a brief burst of gravitational wave emission at periapsis firmly in the mHz band. Burst orbits have been previously modeled as parabolic, with a focus on extreme examples that could be detectable by space-based gravitational wave detectors. This work focuses on the recurring bursts called ``peeps". Peeps are not likely to be individually resolvable; however, it is also important to consider them as possible sources of signal confusion noise because they do generate a signal within the LISA band with every pericenter passage. To account for peeps, we must utilize estimates for EMRI capture parameters along with tracking the massive black hole population out to a redshift of 3 using the Illustris Project. Then, this population is combined with an EMRI formation rate to estimate the number of EMRI events per unit volume for LISA. In this study, we model four different assumptions for the gravitational wave background produced by these highly eccentric peeps. We find that with our two most likely backgrounds, the signal may result in a slight rise of the LISA noise floor (SNR $\sim 0.3-2.4$); however, in two more abundant cases, the background generated by these sources would be detectable on their own and likely obscure many potentially detectable sources (SNR $\sim77-145$).

Understanding magnetoelectric coupling in emerging van der Waals multiferroics is crucial for developing atomically thin spintronic devices. Here, we present a comprehensive first-principles investigation of magnetoelectric coupling in orthorhombic CrI$_2$. Monte Carlo simulations based on DFT-calculated magnetic exchange interactions suggest a proper-screw helimagnetic ground state with a Néel temperature consistent with experimental observations. A ferroelectric switching pathway driven by interlayer sliding is predicted, featuring a low switching energy barrier and out-of-plane ferroelectric polarization. To quantitatively characterize the magnetoelectric effect in orthorhombic CrI$_2$ and its microscopic origin, we evaluate the spin-driven polarization using the paramagnetic phase as a reference alongside the magnetoelectric tensor method. The extracted spin-driven polarization aligns along the $z$-axis, with its origin dominated by the exchange-striction mechanism. Although in-plane components of the total polarization in the bulk vanish due to global symmetry constraints, each CrI$_2$ single layer exhibits local electric polarization along the $x$ direction, arising from the generalized spin-current mechanism, which couples spin chirality to the electric polarization. As a result, we further predict that a proper-screw helimagnetic state may persist in monolayer CrI$_2$, with its charity reversable by switching the in-plane electric polarization through applying external electric field, providing another promising candidate for electrical control of two-dimensional multiferroics.

We consider an inverse initial-data problem for the compressible anisotropic Navier--Stokes equations, in which the goal is to reconstruct the initial velocity field from noisy lateral boundary observations. In the formulation studied here, the density, pressure, anisotropic viscosity tensor, and body force are assumed known, while the initial velocity is the quantity to be recovered. We introduce a new computational framework based on Legendre time-dimensional reduction, in which the velocity field is projected onto an exponentially weighted Legendre basis in time. This transformation reduces the original time-dependent inverse problem to a coupled system of time-independent elliptic equations for the Fourier coefficients of the velocity field. The resulting reduced model is solved using a combination of quasi-reversibility and a damped Picard iteration. Numerical experiments in two dimensions show that the proposed method accurately and robustly reconstructs initial velocity fields, even in the presence of significant measurement noise, geometrically complex structures, and anisotropic effects. The method provides a flexible and computationally tractable approach for inverse fluid problems in anisotropic media.

We review and develop the classical theory of moments of configurations of weighted points with a focus on systems with an identically vanishing first moment. The latter condition produces equations for equilibrium configurations of systems of interacting particles under the sole condition that interactions are between pairs of particles and along the lines connecting such pairs. Complying external forces are admitted, so the description of some dynamical equilibrium configurations, such as relative equilibria in Celestial Mechanics, is included in our approach. Moments provide a unified framework for equilibrium problems in arbitrary dimensions. The equilibrium equations are homogeneous and invariant by isometries (for interactions depending only on mutual distances), and are obtained through simple algebraic procedures requiring neither reduction by isometries nor a variational principle for their determination. Our equations include the renowned set of $n$-body central configuration equations by A. Albouy and A. Chenciner. These equations are extended to a rather broad class of equilibrium problems, and new equilibrium equations written in terms of mutual distances are introduced. We also apply moments to the theory of constraints for mutual distances of configurations of fixed dimension, and for co-spherical configurations, thus re-obtaining and adding to classical results by A. Cayley and successors. For the sake of concreteness, novel sets of central configurations equations are provided.