In their seminal works Herglotz (1905) and Wiechert and Zoeppritz (1907) have solved the so-called Travel Time Tomography Problem (TTTP) in the 1-D case. However, the question about stability estimates and uniqueness theorems for an n-D n>= 2 TTTP with formally determined incomplete input data still mostly stands open after more than one hundred years period. \textquotedblleft Formally determined input data" means that the number p of free variables in the input data equals the number $n$ of free variables in the unknown right hand side of the governing nonliniear eikonal PDE, p=n. Some previous publications demonstrate that it is possible to develop well performed numerical methods for the TTTP with formally determined input data, which indicates the importance of such data for practical applications. This is the first publication in which the above question is addressed. More precisely, we consider a semi-discrete case, in which a PDE generated by the eikonal equation is written in finite differences with respect to n-1 variables. In addition, it is assumed that the solution of that semi-discrete PDE is represented via a truncated Fourier-like series with respect to a special orthonormal basis of functions, which depend only on the position of the point source. Under these conditions, Lipschitz stability estimate is proven, and this estimate implies uniqueness. An important tool of this paper is a new Carleman estimate. Carleman Weighted Spaces are introduced. Carleman estimates were not applied previously to address questions about stability estimates and uniqueness theorems for the TTTP.

We present MaterialClusterGS, a palette-based material decomposition framework for 2D Gaussian Splatting that enables physically based relighting and material editing. Existing Gaussian inverse rendering methods typically assign independent BRDF parameters to individual primitives. While flexible, this local fitting strategy makes material recovery highly under-constrained: shadows, indirect illumination, geometric errors, and visibility residuals can be absorbed into thousands of slightly different local material estimates. Meanwhile, recent palette-based appearance methods operate solely in RGB space without modeling physical materials or illumination. To bridge this gap, we represent scene materials using a compact global palette of shared BRDF prototypes assigned via a continuous spatial material field. Without shared material structure, editing one region does not propagate consistently to others of the same material, making per-primitive decompositions impractical for editing. We jointly optimize the material field, palette prototypes, and environment lighting under a physically based rendering objective. The resulting framework recovers compact, spatially coherent attributes directly usable for material editing, relighting, and transfer.

In this paper, we consider the Ricci flow with prescribed curvature on infinite graphs, which reads as \begin{equation*}\label{flow-equation3} \frac{d}{dt}ω(t)=-(κ(t)-κ^*)ω(t),~~ t>0, \end{equation*} where $ω$ is the edge weight, $κ$ and $κ^*$ are Lin-Lu-Yau Ricci curvature and the prescribed curvature on the set of edges, respectively. First, we establish the existence and uniqueness of the solution to the Ricci flow. Furthermore, we prove the convergence of the Ricci flow for graphs with girth at least 6 under two different conditions. Our convergence result aligns with the conclusion of Rodin and Sullivan (J Differ Geom, 26(2) 1987) that a circle packing in the plane with the hexagonal pattern is the regular hexagonal packing.

This paper investigates the finite generation of the strict closure of rings in arbitrary dimension. For a Noetherian local ring $(R, \mathfrak{m})$, we provide a sufficient condition under which the strict closure $R^*$ is finitely generated as an $R$-module. Using this result, we characterize the finite generation of the strict closure over excellent rings.

This paper investigates the degenerate generalized Stirling operators of the first kind bridging a gap in the operational calculus of the generalized Heisenberg algebra GHA unified with degenerate calculus. As they are the inverse of the degenerate generalized Stirling operators of the second kind, these operators express the monomial operator products in terms of the degenerate factorial operators. We derive key structural and combinatorial properties for these operators, including an explicit product factorization, a fundamental recurrence relation, and an operational shifting identity. Furthermore, we establish the orthogonality relations between the degenerate generalized Stirling operators of the first and second kinds, providing a complete combinatorial framework for functional quantum algebras.

This paper examines wireless-powered Internet of Things (IoT) networks involving multiple unmanned aerial vehicles (UAVs) equipped with backscatter and caching technologies to relay and transmit signals. For data communication and energy harvesting (EH), the source transmits information and power to UAVs using the dynamic time splitting (DTS) method. UAVs use harvested energy for passive communication (backscatter) and for active communication (transmitting information) to the destination. The primary objective is to maximize the total throughput by jointly optimizing the DTS ratio, trajectory, and transmission power, leveraging the UAVs' caching capability. This optimization problem is challenging due to its non-convexity. Therefore, an efficient alternating algorithm using the block coordinate descent (BCD) method is proposed to optimize each variable given the fixed values of the other parameters. By applying the Karush-Kuhn-Tucker (KKT) conditions, we derive a closed-form expression for the optimal DTS ratio, significantly reducing computation time. The optimal values for the other two parameters are determined using the BCD. In order to thoroughly assess the effectiveness of various solutions for the original problem, this paper introduces an approach leveraging a genetic algorithm (GA). The GA in this context employs a one-point crossover method, value mutation, and rank-based selection based on fitness values. Numerical results show that the BCD and GA achieve at least 31% throughput improvement over the benchmarks, with reduced computational time. These findings demonstrate the performance gain and practical feasibility of our solutions in caching-enabled UAV-aided IoT networks.

The influence of static electric fields on the electronic structure and dissociation behavior of the polar diatomics \ce{HF} and \ce{HCl} is investigated using quantum chemical calculations. Ground- and excited-state potential energy surfaces (PESs) are computed as a function of bond distance and external electric field strength to examine field-induced modifications of chemical bonding. The calculations reveal pronounced bond softening and progressive destabilization of both molecules with increasing field intensity. Notably, the ground-state PES of \ce{HCl} becomes entirely dissociative at field strengths of approximately 450 MV/cm, whereas \ce{HF} requires a substantially stronger field of nearly 700 MV/cm to induce dissociation. This difference reflects the greater polarizability and weaker bond localization in \ce{HCl} relative to \ce{HF}, providing a molecular-scale perspective on the contrasting macroscale acid strengths of the two species. Field-dependent dipole moments further demonstrate the stronger electronic response of \ce{HCl} to external perturbations, highlighting how molecular polarizability drives electric-field-induced bond activation. Ultimately, these results map out a detailed picture of field-controlled dissociation in hydrogen halides, supporting the view that local electric fields generated by surrounding hydrogen-bonding networks play a key role in modulating bond activation and condensed-phase acidity.

Calibration of gravitational-wave detectors reconstructs the strain h(t) from the detector output, and bias and uncertainty in this reconstruction directly affect downstream analyses. In ground-based interferometers, time-dependent correction factors (TDCFs) are estimated from calibration lines to track temporal variations of the detector response, while the underlying model parameters are periodically updated using broadband swept-sine calibration measurements (SSCMs). However, if a model-measurement bias exists between the measured transfer function and the reference model, the TDCFs inferred from calibration lines can introduce a systematic deviation into the reconstructed strain. We propose a statistical framework to estimate and correct this bias using repeated measurement-to-model ratios at the calibration-line frequencies. The bias correction factors are estimated with a rolling random-effects model based on restricted maximum likelihood (REML) and incorporated into the TDCF estimation, with their uncertainty propagated to the reconstructed response. Applying the method to KAGRA O4c data, we find that the uncorrected response shows deviations of up to approximately 7% in magnitude and 5 degrees in phase relative to the SSCM-based reference in representative examples. The correction reduces these deviations, with a modest increase in the propagated uncertainty due to the included correction-factor uncertainty. This framework provides a practical way to combine broadband reference models with calibration-line-based tracking when model-measurement bias is present.

The construction of Arf rings and strictly closed rings has been studied widely; however, there has been no clear description of the structure of the strict closure R^* when the integral closure of R is not a finitely generated R-module. In this paper, we investigate the construction and finite generation of the strict closure of rings. We determine its structure when R is a Cohen-Macaulay semi-local ring of dimension one, with dim R_M=1 for every Maximal ideal M in R. Using this, a characterization of the finite generation of the strict closure is given.

This paper investigates a class of partially dissipative viscoelastic Timoshenko systems with memory, where dissipation is induced by a Volterra-type memory term acting only on the shear variable. The well-posedness of weak and strong solutions is established on finite time intervals, including existence, uniqueness, stability, and higher-order regularity under compatibility conditions consistent with mixed boundary conditions. For the numerical approximation, a Fourier spectral fully discrete scheme is constructed: sine and cosine basis expansions are used in space for unknowns satisfying Dirichlet and Neumann boundary conditions, respectively; in time, a central difference scheme is applied to the second-order derivatives, and the composite trapezoidal rule is used to approximate the memory convolution term. Based on a discrete energy method, the positivity of the constructed discrete energy is proved, and the error estimate for the fully discrete scheme with second-order convergence in time and \(q\)-th order in space is established for any q \in \mathbb{N}. Numerical experiments are given to verify the theoretical convergence rates and to compare the dynamic responses of the local and nonlocal models, demonstrating that the memory term effectively captures energy dissipation and vibration attenuation behavior in viscoelastic materials.

We consider the interaction between centralized trading and decentralized Proof of Stake (PoS) blockchain ecosystems. Motivated by the increasing dominance of centralized exchanges and the institutionalization of crypto markets, we study how trading activities on centralized exchanges affect staking behavior, token allocation, and decentralization within a PoS blockchain. We formulate a continuous-time mean field model, where the miners simultaneously act as validators in the PoS protocol and traders in a centralized market with price impact. Under suitable assumptions, we establish the local well-posedness of the mean field system, and derive a semi-explicit characterization of the equilibrium trading strategy. Numerical results suggest that centralized trading activities may enhance staking participation, and promote decentralization of the staking distribution through market incentives. We also study the effects of transaction costs and token supply mechanisms on the equilibrium staking ratio and concentration profile. These results illustrate how market microstructure and centralized liquidity provision can exert significant influence on decentralized blockchain protocols.

Sparse linear systems from PDE discretizations are central to scientific computing, yet no existing JAX-ecosystem solver simultaneously provides GPU-accelerated algebraic multigrid (AMG), automatic differentiation (AD), and distributed multi-GPU execution. JAX-AMG fills this gap by wrapping the Nvidia AmgX solver suite as a native JAX primitive, exposing AMG and Krylov methods with configurable preconditioners through a unified interface compatible with JIT compilation, reverse-mode AD via adjoint methods, batched solves, and MPI-based distributed execution. Solver caching amortizes setup costs across repeated solves, making JAX-AMG practical for PDE-constrained optimization and inverse problems. The result is a robust, scalable sparse linear algebra layer that integrates seamlessly into differentiable simulation and scientific machine learning pipelines.

We present the transformation-response framework, an operational reformulation of quantum mechanics. A quantum state is not a Hilbert space object but the catalog of a system's responses to all physical transformations: for each operation $g$ from the system's local group $G$, an interference experiment gives a complex value $χ(g)$. The collection $\{χ(g): g\in G \}$ is the characteristic function and defines the state. The only postulate is that $χ$ is positive-definite, encoding the requirement that no superposition of transformations yields negative probability. From this single assumption, the entire standard formalism is derived: Hilbert space via GNS construction, Born rule via Bochner theorem, Schrödinger equation from group automorphisms, and especially Feynman path integral as a Trotter limit. The framework is background-independent and time-neutral: time is a coordinate along a one-parameter subgroup of $G$. It also reveals a new physical constraint, product order positivity, which may lead to testable predictions. The framework provides a unified, economical, and falsifiable foundation for quantum theory rooted in operational primitives.

A superconducting diode effect is shown to arise in ferromagnetic superconductors through the nonreciprocal dynamics of magnetic domain walls. Specifically, we show that current-driven dynamics of a magnetic domain wall under a certain external field can exhibit a nonreciprocal Walker breakdown, possessing two distinct direction-dependent critical currents beyond which the domain wall precesses continuously. In ferromagnetic superconductors, the constant rotation of a domain wall is shown to give rise to phase slips, opening up dissipation channels, whereby the nonreciprocal Walker breakdown is mapped to the superconducting diode effect. For the nonreciprocal Walker breakdown of a magnetic domain wall, we analytically examine its dependence on the magnetic field and the Gilbert damping and verify the theoretical results with micromagnetic simulations. We then extend the analysis to ferromagnetic superconductors by considering additional effects from the superconductivity and identify criteria for experimental conditions to realize the predicted superconducting diode effect. Our work demonstrates that topological defects, such as domain walls, in magnetic superconductors can serve as an intrinsic nanoscale platform for nonlinear nonreciprocal superconducting functionalities within a single homogeneous material, circumventing the need for complicated engineered heterostructures and thereby enabling the miniaturization of superconducting devices down to the nanometer scale that is challenging to achieve with conventional Josephson junctions.

With the commissioning of the James Webb Space Telescope (JWST), near- and mid-infrared observations are rapidly extending into the wavelength regime where emission from small dust grains in circumplanetary disks (CPDs) is expected to dominate. We aim to systematically investigate how individual physical parameters of CPDs shape their infrared spectra and to improve the robustness of spectral fitting and physical interpretation of current and future observations. Building on our previous parametric CPD models, we employ a parameter-grid approach combined with radiative transfer simulations to explore the dependence of observable spectra on disk structure and dust properties. We identify the physical mechanisms responsible for the main spectral features and parameter degeneracies, and present the global trends emerging from the parameter study. We also demonstrate the applicability of the models by fitting representative observational data. Our results provide a structured theoretical framework for interpreting near- and mid-infrared observations of CPDs with JWST and related facilities.

We study the relativistic nature of the interactions that, at tree level, generate spin correlations between two electrons in Møller scattering, as well as in an extended process involving a witness particle $C$. The corresponding processes, $e^{-}e^{-}\rightarrow e^{-}e^{-}$ and $e^{-}e^{-}C\rightarrow e^{-}e^{-}C$, are analyzed both in the center-of-mass frame and, for the former process, in a Lorentz-boosted frame where Wigner rotations arise. It is found that, through a nonrelativistic approximation of the scattering amplitudes, dipole-dipole and current-dipole interactions are responsible for the emergence of these correlations. This is evidenced by the variation of the von Neumann entropy of one electron for initially separable states, and of $C$ for an initially prepared three-particle entangled W-state. In Wigner rotations, the invariance of entropy under local unitary transformations is maintained at the expense of the emergence of quantum coherence in the density matrix at large rapidities. As a consequence, the final states of both particles are evaluated and shown to encode information about the scattering process through their spin expectation values. This framework is then used to comment on the correlations in the inelastic process $e^{-}e^{+}\rightarrowμ^{-}μ^{+}$, for which some research has reported differing results.

We classify and count binary necklaces [w] for which the representative-independent minimum nontrivial rotational Hamming distance minDist(w) equals 2, the first positive layer after the periodic case. With a fixed priority convention, the set of nonzero shifts attaining distance 2 determines a classification into half-turn (HT), single-pair (SP), and subgroup-pattern (SUB) classes, while the residual multi-pair (MP) class is empty. We give closed formulas for the HT, SP, and SUB counts and an explicit Mobius-totient divisor-sum formula for |D_2(n)|. We also describe the larger subgroup-shaped branch, which contains the SUB cases together with boundary cases assigned by priority to HT and SP, by a quotient-background normal form and its boundary counts. For odd prime lengths p, every distance-2 necklace is rotation-equivalent to an arithmetic interval on the prime cycle, and |D_2(p)| = (p^2 - 4p + 7)/2.

We present a conjecture for associated varieties of simple affine vertex algebras $L_k(\mathfrak{g})$ attached to a simple Lie algebra $\mathfrak{g}$ of simply-laced type and any rational level $k$ greater than the critical level. The key new ingredient compared to the integral case is the covering duality map introduced by Gao-Liu-Lo-Shahidi. We provide evidence for the conjecture.

Let \(G\) be a finite group and let \(χ\) be an ordinary irreducible character. We give an elementary algorithm which constructs explicit matrices affording \(χ\). The regular representation provides a canonical ambient representation, and the usual central idempotent projects onto the \(χ\)-isotypic component. The main step is then to maximize the squared norm of a diagonal matrix coefficient on the unit sphere of this component. The maximum is \(1/χ(1)\), and it is attained precisely by vectors whose cyclic span is an irreducible subrepresentation affording \(χ\). Thus the construction reduces the passage from characters to matrices to a concrete optimization problem. The same extraction method applies inside any smaller ambient representation containing \(χ\), such as an induced representation from a subgroup. We complement the theory with a discussion on dimension reduction, robust numerical implementation, and an explicit \(S_4\) example.

The Wisconsin H$α$ Mapper (WHAM) surveyed the entire Galactic sky in H$α$ ($\vert v_{\rm LSR}\vert \lesssim 100\, {\rm km\,s^{-1}}$) to approximately 0.1\,Rayleigh (R), albeit with a 1-degree beam. %The resulting WHAM Sky Survey, along with large area %imaging in [\ion{S}{2}] and [\ion{N}{2}], laid the foundation for Warm Ionized %Medium (WIM) science. \cite{rcm+05} reported ``point sources" which stood out against the Galactic background in space and velocity. Half of the sources are associated with plausible planetary nebulae and OB stars. Reynolds et al (2005) suggested sub dwarfs for one quarter of the sources. Here, we investigate one such source, WPS\,46, for which Reynolds et al (2005) suggested the sub-dwarf PG\,0931+691 to provide the source of ionization. With the Keck Cosmic Web Imager we found numerous nebular emission lines within the vicinity of WPS\,46, but we failed to find H$α$ emission in the arc-minute vicinity of PG\,0931+691. The line ratios (BPT diagram and [\ion{S}{2}]/H$α$) combined with the morphology are more consistent with AGN or LI(N)ER-like ionization than with pure warm ionized medium or \ion{H}{2} region-like photoionization. Separately, we offer compelling reasons to argue that PG\,0931+691 cannot be the source of ionizing power for WPS\,46. We suggest that WPS\,46 is associated with an intermediate velocity complex (IVC) and that H$α$ and nebula emission may arise as a result of a shock. We conclude by outlining a plan of action of using SDSS's Local Volume Mapper along with deep narrow band imagery obtained by amateur astronomers to explore and study the ionized sky on sub-degree scales, in general, and specifically studies of IVC and high-velocity complexes.

Misconceptions are "alternate hypotheses" that are incorrect according to established theories of how the world works. Often held with confidence by students, they are relatively context-insensitive, can seem like common-sense views, and are noted for being resistant to remediation using traditional instruction. To find misconceptions in Newtonian mechanics, we analyze ~34,000 administrations of the pioneering Force Concept Inventory using a flexible multidimensional item-response model for multiple-choice data. In contrast to most earlier work, we allow answer choices within each question to have different directions in the multidimensional space of student knowledge, essential for concept inventories in which distractors often codify distinct misconceptions. We uncover 22 robust, partly-overlapping dimensions whose distractors share a coherent theme identifiable with a misconception or misunderstanding. Motivated by the realization that many mirror previously-accepted theories of mechanics, we broadly sort these by historical era: Ancient (learned by infants but codified by Greeks), Medieval (reactions and extensions of Aristotelian ideas), and Post-Newtonian (including known modern misconceptions as well as two which appear novel). We also present a simple approach for computing "misconception scores" for students and classes. Examining these scores before and after instruction reveals surprisingly varied patterns of remediation in our sample: some misconceptions persist largely unchanged by instruction, while others are better remediated in below- or above-average students. In general, we find that many misconceptions are poorly remediated for students of average or lower ability. We hope our work will serve as a guide for developing, evaluating, and improving interventions for these while providing physics instructors with a valuable tool for class-level formative assessment.

Warm starts are widely used to accelerate AC optimal power flow (ACOPF) solves, but the impact of different initialization strategies has received limited systematic study, particularly for the primal-dual interior-point methods that dominate large-scale ACOPF algorithms. This paper benchmarks initialization strategies for ACOPF solved with the interior-point solver IPOPT on 19 PGLib-OPF instances (5 to 30,000 buses), testing all 15 non-empty subsets of the primal blocks $\{P_g, Q_g, V_m, V_a\}$ under oracle conditions and three DC-seeded combinations in a practical setting. The experiments show that most partial primal-plus-dual restarts increase solve time or reduce convergence reliability. Among the oracle primal-plus-dual (O-PD) configurations, only the complete restart reliably converges on every baseline-convergent case, reaching a $47.6\%$ median solve-time speedup. Twelve of the 14 partial O-PD combinations have negative median speedups, and several fail repeatedly on larger networks. Decomposing the dual into constraint and bound multipliers shows that \emph{coverage}, not the presence of duals per se, governs robustness: the full bound-multiplier vector reaches 90.7\% convergence and a $+26.8$\% median speedup, whereas block-matched coverage (oracle multipliers on some bounds, defaults on the rest) drops to 70.4\% and $-31.1$\%. Practical DC seeding sometimes helps the AC solve, but the benefit is no longer statistically significant once the DCOPF presolve cost is included in the end-to-end comparison ($p = 0.4171$). For learned warm-start methods, the results support the following target ordering: predict the full primal vector first; if only partial coverage is possible, prioritize voltage variables; and avoid partial or inconsistent dual predictions unless the primal estimate is nearly complete.

Complex collective dynamics in cellular automata are usually associated with local-neighborhood combinatorics, yet it remains unclear whether long-lived dynamical organization requires such explicit local interaction structure. Here, we introduce a Separable-Field Cellular Automaton (SFCA), a normalized-field cellular automaton in which local neighbor counting is replaced by a rank-one-like row-column field. Each cell is updated according to a normalized field, with survival and birth governed by two threshold intervals. Systematic scans over interval widths and positions revealed four outcome classes: extinction, fixed points, cycles, and long transients. The outcome phase diagram was organized by the relative geometry of the survival and birth intervals: fixed points dominated when born interval was contained in survival interval, whereas long transients concentrated near the boundary between partial overlap and no overlap. A fine scan along this transition showed that the long-transient region forms a narrow but persistent ridge separating two qualitatively distinct cycle-dominated regimes. One side produced dense, high-change-rate cycles approximating global period-2 alternation, whereas the other produced sparse, low-change-rate, stripe-like cycles. Damage-spreading further supported a basin-competition interpretation, in which the long-transient ridge reflects delayed selection between two cyclic attractor families rather than random nonconvergence, while finite-size analysis shows that the long-transient ridge remains robust across tested grid sizes. These results show that structured long-transient dynamics can arise under compressed separable field coupling, suggesting that nontrivial collective organization does not necessarily require full local-neighborhood combinatorics.

Knowledge transfer across data sources holds great promise for improving the estimation of target population parameters by leveraging the growing availability of data from different sources. However, the effectiveness of knowledge transfer is often challenged by the complex and pervasive heterogeneity between data sources and the lack of access to individual-level data. This paper proposes the divide-and-shrink (dShrink) method, a transfer estimation method that estimates target population parameters in a closed form using summary statistics from a target population and some external source populations while accounting for population heterogeneity. The dShrink estimator is guaranteed to outperform the estimator based solely on the target population in terms of expected quadratic error under arbitrary population heterogeneity. The gain can be substantial when the target and source populations are similar, or the underlying true parameter values are near zero. Notably, dShrink is model-free, requires no user-specified tuning parameters, robust to various types of heterogeneity between data sources, and applies to a broad range of parameter estimation problems. dShrink remains effective even when the covariance matrix is not accessible for the external summary statistics and offers flexibility in incorporating side information and summary statistics from multiple source populations. Simulations and real data analyses demonstrate the superior performance of the dShrink estimator and its potential as a robust tool for transfer estimation.

Retrieving evidence pages from visually rich long documents is a key challenge in document question answering. Existing page-level visual retrievers operate under an independent matching paradigm: each page is scored in isolation based on query-page similarity. This paradigm can under-rank evidence pages whose signals are localized in fine-grained chunks or depend on document-internal associations. We propose EviProp, a retrieval method that recovers such pages via seeded relevance diffusion. EviProp models each document as a multimodal Chunk-Page graph with hierarchical, sequential, and similarity links. Given a query, it combines dense visual page priors with sparse chunk seeds, then runs Personalized PageRank to diffuse relevance over the graph. Experiments on MMLongBench-Doc and LongDocURL show consistent gains in evidence-page retrieval over independent visual retrieval and text-visual fusion baselines. Downstream QA results further show that improved retrieval translates into better answer accuracy, with negligible online retrieval overhead. Our code is released at https://github.com/Flyecnu/EviProp.

The strong likelihood principle (SLP) is conventionally derived from the sufficiency principle and a conditionality principle in an argument due to Birnbaum, and much of the literature contests whether the derivation is sound. We take a different approach. We ask what the SLP says when its terms are read carefully, and argue that the principle as ordinarily stated reflects a confusion about the domain of the likelihood function. The likelihood is naturally defined as a function on a family of distributions $M$, not on a parameter space, and once it is so defined the SLP collapses into its weak counterpart, the weak likelihood principle. The diagnosis is illustrated by analogy with monetary value, developed concretely through a comparison of the binomial and negative binomial families that share a parameter, and connected to the geometric structure of $M$ through the Fisher information metric. The same standardization emerges from a statistical argument about comparing measurements across populations and from a geometric argument about manifold distance; this convergence supplies the positive content of the weak likelihood principle.

The sub-parsec proximity around the Sgr A$^\star$ supermassive black hole (SMBH) in the center of the Milky Way contains an inner cluster of eccentric S-stars with randomly oriented orbits, a midway-disk of clockwise-rotating stars (CWSs), and a surrounding population of off-the-disk stars (ODSs). Despite their diverse kinematic properties, all three-populations appear to be massive (WR/O/B types) and have similarly limited life span $τ_\star \sim 6-15$ Myr. Several scenarios, including star formation induced by SMBH's close encounters with one or more gas clouds as well as impulsive close scattering by a putative intermediate-mass companion (IMC) of Sgr A$^\star$ possible an intermediate-mass black hole (IMBH), have been proposed to explain piecemeal for the origin and dynamical evolution of S-stars, CWSs, ODSs, as well as hyper-velocity stars in the Galaxy. But, their coexistence and the origin of a recently discovered zone of avoidance in S-stars' eccentricity-peri-centric-distance distribution remain enigmatic. Here, we construct a unified model to comprehensively take into account these stars' interaction with each other, their single natal disk, and an independent IMC. We show their disparate present-day orbits would only be concurrently attainable, within their multi-Myr age, under the combined influence of IMC's secular perturbation and these stars' resonant relaxation in a depleting gaseous-disk environment.

Surface-level reactor antineutrino experiments usually have substantial cosmic ray induced neutron backgrounds, particularly with shallow overburden. The Array of Lattice for Anti-neutrino Reactor Monitoring (ALARM) is a plastic scintillator based experiment designed for reactor power monitoring. It will be deployed about 44 m from the core of a reactor at the Taishan Nuclear Power Plant. Placed at a depth of 9.6 meters below the surface, cosmic ray induced fast neutrons constitute a significant background, making an effective neutron shielding system essential for the experiment. For the shielding design of ALARM, we tested the shielding performance of three materials water, HDPE, and 40\% boron-doped HDPE (BHDPE) against both fast and thermal neutrons. A thermal neutron detector composed of an EJ426 scintillator setup was first used to measure the shielding efficiency of these materials at various thicknesses using neutrons from an Am-Be source. A 30-cm thickness of BHDPE achieved a shielding efficiency exceeding 95\% for both fast and thermal neutrons. Monte Carlo simulations of the EJ426 setup yielded results consistent with the experimental data. Simulation results for the shielding performance of the full ALARM shielding assembly are also presented.

The structural properties of bosonic dark matter stars are systematically investigated, presenting precise scaling relations for the mass, radius, central density, and the properties of dark matter particles. The dark matter equation of state is derived from a complex scalar field theory with a quartic self-interaction potential $V(ϕ) = \fracλ{4} |ϕ|^4$, considering boson masses $m_ϕ$ ranging from $10^{-9}$ to $10^{3}$ GeV and self-coupling constants $λ$ ranging from $0.01π$ to $100π$. The scaling relation for the maximum mass of bosonic dark matter stars, the corresponding critical radius and critical central density are obtained as \[ M_{\text{max}} = 0.1 \frac{\sqrtλ}{m_ϕ^2} M_\odot, \qquad R(M_{\text{max}}) = 0.9 \frac{\sqrtλ}{m_ϕ^2} \ \text{km}, \qquad \varepsilon_{\text{max}} = 2.1 \times 10^5 \frac{m_ϕ^4}λ \ \mathrm{MeV/fm^3}, \] where $m_ϕ$ is in GeV, the relations for $R(M_{\text{max}})$ and $\varepsilon_{\text{max}}$ are first put forward. The fitting relative error is less than $4\%$. Based on these scaling relations, we further provide global analytical fits for the stable branch. The relationships between mass and central density as well as radius and central density can be described by a unified function of the form: \[ \tilde{Y} = \frac{A}{\left[1 + \left(5\tilde{\varepsilon}\right)^h\right]^s}, \] where for $Y=M$, $\tilde{M} \equiv M/M_{\text{max}}$, $A=1$, $h=-2$, $s=0.42$; for $Y=R$, $\tilde{R} \equiv R/R(M_{\text{max}})$, $A=1.634$, $h=1$, $s=0.28$; and $\tilde{\varepsilon} \equiv \varepsilon_0/\varepsilon_{\text{max}}$. The fitting relative error is less than $0.1\%$. Furthermore, we find a simple quadratic polynomial mass-radius relation for bosonic dark matter stars.

Class imbalance is common when developing clinical prediction models (CPMs) and is often assumed to lead to poor predictive performance. Several methods have been proposed to correct data imbalance during CPM development. However, it remains unclear whether correcting class imbalance improves or harms CPM performance. This study investigated how imbalance correction affects classification performance and prediction stability. We simulated the development and internal validation of CPMs using penalised logistic regression under different imbalance-correction strategies, including algorithm-level rebalancing, data-level rebalancing by oversampling, and combined over- and under-sampling. The simulation dataset was derived from the GUSTO-I trial, which included 40,830 patients and 2,851 events. All imbalance-correction strategies were evaluated across sample-size scenarios ranging from 500 to 40,830. Model performance and prediction stability were assessed using 200 bootstrap resamples, including discrimination, calibration, calibration stability, mean absolute prediction error (MAPE), and classification instability index (CII). Class imbalance correction did not meaningfully improve model discrimination. Both data-level and algorithm-level correction led to miscalibration, risk overestimation, and increased prediction instability, as shown by prediction stability, MAPE, and CII plots, compared with models developed without correction. These findings suggest that class imbalance correction does not necessarily improve CPM performance and may compromise calibration and prediction stability. Class imbalance should not be treated as a pathology that automatically requires correction. In clinical prediction modelling, routine imbalance correction by default is generally not advisable.