Single-cell RNA sequencing (scRNA-seq) frameworks lack explainable approaches for identifying cell subpopulations harboring strong pairwise monotonic gene-module relationships between a gene of interest (GOI) and its co-expressed genes. CEP-IP is introduced as a novel explainable machine learning framework to address this gap. In the primary dataset, TRPM4 served as the GOI and its co-expressed ribosomal genes (Ribo) were identified via Spearman-Kendall dual-filter (i.e., dual-filtered gene, DFG). Generalized additive modeling quantified TRPM4-Ribo relationship strength via deviance explained (DE), which was then mapped to individual cells via CEP classification to identify top-ranked explanatory power (TREP) cells. TRPM4-Ribo transcriptional space was then stratified into pre-IP and post-IP regions using inflection point (IP) analysis, producing four subpopulations per patient for pathway analysis. TRPM4-Ribo modeling outperformed alternative gene set modules (FDR<0.05). In each prostate cancer (PCa) patient, CEP-IP yielded four cell subpopulations, where pre-IP TREP cells showed enrichment of immune-related processes, and post-IP TREP cells were enriched for ribosomal, translation, and cell adhesion pathways. Validation was performed in the Allen middle temporal gyrus (MTG) and Neftel glioblastoma (GBM) datasets. In the MTG dataset (CARM1P1-DFG module), post-IP TREP cells showed enrichment of neuron projection ontologies. In the GBM dataset, FOXM1 was the sole GOI yielding mesenchymal-state DFGs, with FOXM1-DFG post-IP TREP cells enriched for cell division and microtubule pathways; 3D trajectory analysis demonstrated continuous trajectories of TREP cells that were obscured in 2D embeddings. CEP-IP identifies biologically distinct cell subpopulations in three independent scRNA-seq datasets, and it may be applicable to other pairwise GOI-DFG modules in single-cell transcriptomics.

Submarine cables play a critical role in global internet connectivity, energy transmission, and communication but remain vulnerable to accidental damage and sabotage. Recent incidents in the Baltic Sea highlighted the need for enhanced monitoring to protect this vital infrastructure. Traditional vessel detection methods, such as synthetic aperture radar, video surveillance, and multispectral satellite imagery, face limitations in real-time processing, adverse weather conditions, and coverage range. This paper explores Distributed Acoustic Sensing (DAS) as an alternative by repurposing submarine telecommunication cables as large-scale acoustic sensor arrays. DAS offers continuous real-time monitoring, operates independently of cooperative systems like the "Automatic Identification System" (AIS), being largely unaffected by lighting or weather conditions. However, existing research on DAS for vessel tracking is limited in scale and lacks validation under real-world conditions. To address these gaps, a general and systematic methodology is presented for vessel detection and distance estimation using DAS. Advanced machine learning models are applied to improve detection and localization accuracy in dynamic maritime environments. The approach is evaluated over a continuous ten-day period, covering diverse ship and operational conditions, representing one of the largest-scale DAS-based vessel monitoring studies to date, and for which we release the full evaluation dataset. Results demonstrate DAS as a practical tool for maritime surveillance, with an overall F1-score of over 90% in vessel detection, and a mean average error of 141 m for vessel distance estimation, bridging the gap between experimental research and real-world deployment.

Finding eigenstates of a given many-body Hamiltonian is a long-standing challenge due to the perceived computational complexity. Leveraging on the hardware of a quantum computer accommodating the exponential growth of the Hilbert space size with the number of qubits, more quantum algorithms to find the eigenstates of many-body Hamiltonians will be of wide interest with profound implications and applications. In this work, we advocate a quantum algorithm to find the ground state and excited states of many-body systems, without any penalty functions, variational steps or hybrid quantum-classical steps. Our fully quantum algorithm will be an important addition to the quantum computational toolbox to tackle problems intractable on classical machines.

Quantum sensing with solid-state spin defects has transformed nanoscale metrology, offering sub-wavelength spatial resolution with exceptional sensitivity to multiple signal types. Maximizing these advantages requires minimizing both the sensor-target separation and the detectable signal threshold. However, leading platforms such as nitrogen-vacancy (NV) centers in diamond suffer from performance degradation near surfaces or in nanoscale volumes, motivating the search for optically addressable spin sensors in atomically thin, two-dimensional (2D) van der Waals materials. Here, we present a comprehensive experimental framework to probe a 2D spin ensemble, including its Hamiltonian, coherent sensing dynamics, and noise environment. Using a central spin system in a hexagonal boron nitride (hBN) crystal, we fully map the hyperfine interactions with proximal nuclear spins, demonstrate switchable magnetic and electric noise sensing, and introduce a method to accurately reconstruct the environmental noise spectrum while explicitly accounting for quantum control imperfections. We achieve a record coherence time of $80~μ\mathrm{s}$ under dynamical decoupling, enabling sub-microtesla AC magnetic sensitivity at a $10~\mathrm{nm}$ target distance. Leveraging the broad opportunities for defect engineering in atomically thin hosts, these results lay the foundation for next-generation quantum sensors with ultrahigh sensitivity, tunable noise selectivity, and versatile functionalities.

Circulating-fuel reactors (CFRs) lose reactivity when delayed-neutron precursors (DNPs) drift out of the core and may regain part of it when the fuel re-enters the core. This paper formulates a physics-based description of both effects by combining DNP transport with residence-time theory. Then, treating the core and ex-core regions as two mixing volumes in series, closed-form expressions for (i) the static reactivity loss due to precursor drift and (ii) the zero-power transfer function that governs linearised dynamics are derived. When the gamma residence-time distributions are used, the new framework is shown to reduce to the plug-flow and Continuous-Stirred-Tank-Reactor limits as special cases, while generalising to intermediate mixing regimes via a single parameter: the degree of mixing. Performed parameter studies show that DNP recirculation has the highest impact when core and ex-core residence times are comparable and the product of the DNP decay constant and the in-core residence time is small. Benchmarks against the Molten-Salt Reactor Experiment are able to reproduce the measured static loss ($k_0 \approx 0.32$ \$) and its frequency response, with $\approx$20% of the steady-state DNP worth arising from recirculation. Additionally, for the EVOL reference Molten-Salt Fast Reactor the model is shown to agree well with the results of high-fidelity Serpent-2 calculations coupled with Computational Fluid Dynamics. Overall, the residence-time approach offers a computationally light yet versatile tool for sensitivity studies and generation of physical intuition for the behaviour of CFRs. Foundation for extensions to importance weighting of DNPs and application of the framework to time-domain analysis is also briefly sketched.

We revisit the thermal nature of the Unruh effect within a quantum thermodynamic framework. For a Unruh-deWitt (UDW) detector in $n$-dimensional Minkowski spacetime, we demonstrate that its irreversible thermalization to a Gibbs equilibrium state follows distinct trajectories on the Bloch sphere, which depend on the types of fields the detector interacts with, as well as the spacetime dimensionality. Using thermodynamic process functions, particularly quantum coherence and heat that form the quantum First Law, we characterize the Unruh thermalization through a complementary time evolution between the trajectory-dependent rates of process functions. Grounded in information geometry, we further explore the kinematics of the detector state as it "flows" along the trajectory. In particular, we propose two heating/cooling protocols for the UDW detector undergoing Unruh thermalization. We observe a quantum Mpemba-like effect, characterized by faster heating than cooling in terms of Uhlmann fidelity "distance" change. Most significantly, we establish the maximum fidelity difference as a novel diagnostic that essentially distinguishes between Unruh thermalization and its classical counterpart, i.e., classical thermal bath-driven thermalization of an inertial UDW detector. This compelling criterion may serve as a hallmark of the quantum origin of the Unruh effect in future experimental detection and quantum simulation. Finally, we conclude with a general analysis of Unruh thermalization, starting from equal-fidelity non-thermal states, and demonstrate that the detectors' fidelity and "speed" of quantum evolution still exhibit a Mpemba-like behavior.

We study the mechanism design problem of facility location on a metric space in the learning-augmented framework, where mechanisms have access to imperfect predictions of the optimal facility locations. Our objective is to design strategyproof (SP) mechanisms that truthfully elicit agents' preferences over facility locations and, using the given prediction, select a facility location that approximately minimizes the maximum cost among all agents. In particular, we seek SP mechanisms whose approximation guarantees depend on the prediction error: they should achieve improved performance when the prediction is accurate (the property of \emph{consistency}) while still ensuring strong worst-case guarantees when the prediction is arbitrarily inaccurate (the property of \emph{robustness}). On the real line, we characterize all deterministic SP mechanisms with consistency strictly better than 2 and bounded robustness for the maximum cost. We show that any such mechanism must coincide with the MinMaxP mechanism, which returns the prediction if it lies between the two extreme agent locations and otherwise returns the agent location closest to the prediction. For any prediction error $η\ge 0$, we prove that MinMaxP achieves a $(1+\min(1, η))$-approximation and that no deterministic SP mechanism can obtain a better approximation ratio. In addition, for two-dimensional spaces with the $\ell_p$ distance, we analyze the approximation guarantees of a deterministic mechanism that applies MinMaxP independently on each coordinate, as well as a randomized mechanism that selects between two deterministic mechanisms with carefully chosen probabilities. We further extend these results to the $L_p$-norm social cost objective on the line metric and the maximum cost objective on the tree metric. Finally, we examine the group strategyproofness of the mechanisms.

We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Padé approximation of the Laplace transform and employs a highly efficient continued fraction technique to construct the corresponding rational approximant. We demonstrate the accuracy of this method through a variety of examples, including the Gaussian function, probability density functions of the lognormal and Gompertz-Makeham distributions, the hockey stick and unit step functions, as well as a function arising in the approximation of the gamma and Barnes $G$-functions.

We investigate the use of Berry curvature dipole in $n$-doped Tellurium as a mechanism for achieving terahertz amplification and lasing by applying a DC electric field. When the electrical bias and wave vector are aligned along the trigonal $c$-axis, the right-handed circularly polarized mode experiences amplification at relatively low bias, while the left-handed mode is attenuated. Furthermore, when the electrical bias and wave vector are orthogonal to the $c$-axis, the structure supports elliptically polarized eigenmodes that also exhibit gain under suitable bias conditions, where the degree of ellipticity is tunable by the applied bias. We also investigate lasing conditions for a Fabry-Perot cavity incorporating biased Te as an active medium. Due to the resonance in the dielectric permittivity of Tellurium, there are discrete lasing intervals. Our results show that bulk chiral Tellurium could be used as an electrically tunable, polarization-selective gain medium for micrometer-scale terahertz lasers, with lasing achievable at bias fields below the material's breakdown threshold, paving the way towards new terahertz devices.

In this paper, the recently developed differential homotopy approach is applied to the problem of disentangling dynamical and topological fields of the $3d$ higher-spin gauge theory at the linear level. This formalism allows us to reproduce all known disentangling solutions in a unified form, including both the solutions obtained previously within the shifted homotopy approach in \cite{Korybut:2022kdx} and that derived by hand in \cite{Vasiliev:1992ix}, as well as other solutions including those associated with the cohomology of the background covariant derivative $D_0$. Also, within the differential homotopy framework an alternative way of derivation of disentangled equations through a non-conventional solution for the field $S_1$ is suggested. The obtained results are important for further analysis of nonlinear corrections to HS equations in $AdS_3$.

Flat bands, in which kinetic energy is quenched and quantum states become macroscopically degenerate, host a rich variety of correlated and topological phases, from unconventional superconductors to fractional Chern insulators. In Hermitian lattices, their formation mechanisms are now well understood, but whether such states persist, and acquire new features in non-Hermitian (NH) { crystals}, relevant to open and driven systems, has remained an open question. Here we show that the Hermitian principle for flat-band formation in bipartite lattices, based on a sublattice degeneracy mismatch, extends directly to the NH regime: whenever one sublattice hosts a momentum-independent eigenvalue with degeneracy exceeding that of its partner on the other sublattice, flat bands arise regardless of gain, loss, or complex couplings. Strikingly, at exceptional points, dispersive bands coalesce to form \emph{exceptional flat bands} (EFBs) that persist beyond these singularities, exhibiting biorthogonal eigenmodes spanning both sublattices, with energies and lifetimes tunable via sublattice asymmetry and non-reciprocal couplings. This general framework unifies Hermitian and NH flat-band constructions, and reveals dispersionless states with no closed-system analogue, as is the case of a bipartite lattice with imbalanced but constant sublattice chemical potentials. The proposed construction is applicable to synthetic platforms, from classical metamaterials, where flat bands can be directly emulated, to quantum-engineered systems such as photonic crystals and ultracold atom arrays, which should host correlated and topological phases emerging from such EFBs.

At the quantum level, the polynomial models of gravity with six and eight derivatives are superrenormalizable, but suffer from higher derivative ghost and/or tachyonic ghost states. On the other hand, these models may have advantages in the control of negative effects of ghosts, compared to the more common fourth-derivative theory. We explore the positiveness of energy of the individual plane wave solutions in the general models with six and eight derivatives. Different from the fourth-order gravity, the part of the energy which may be seen as the leading one in the UV, is positively defined in the tensor sector. We extend this investigation to the scalar sectors of the free theory.

We reconsider in modern terms the old discovery by A. Kirillov and M. Noumi, who devised peculiar operators adding columns to Young diagrams enumerating the Schur, Jack and Macdonald polynomials. In this sense, these are a kind of ``creation'' operators, representing Pieri rules in a maximally simple form, when boxes are added to Young diagrams in a regular way and not to arbitrary ``empty places'' around the diagram. Instead the operators do not commute, and one should add columns of different lengths one after another. We consider this construction in different contexts. In particular, we build up the creation operators $\hat B_m$ in the matrix and Fock representations of the $W_{1+\infty}$ algebra, and in the Fock representation of the affine Yangian algebra $Y(\widehat{gl}_1)$.

The selective control of specific momentum valleys lies at the core of valleytronics, a field that has thus far focused primarily on the $\mathbf{K}$ and $\mathbf{K'}$ valleys in transition metal dichalcogenides (TMDs). However, direct optical access to other low-lying yet conventionally inaccessible valleys such as the sixfold degenerate $\mathbf{Q}$ valleys has remained an outstanding challenge, fundamentally limiting the exploitation of the full valley degree of freedom for information processing. Here, we theoretically introduce an emergent light-wave valley selection rule that enables deterministic and high fidelity excitation of any single $\mathbf{Q}$ valley in monolayer TMDs. By coherently combining a circularly polarized pump pulse with a linearly polarized driver pulse, we engineer distinct quantum pathways that unambiguously excited electrons into a targeted $\mathbf{Q}$ valley, completely decoupled from the conventional $\mathbf{K}/\mathbf{K'}$ valleys. This all-optical scheme achieves near-unity ($\sim$100\%) valley polarization across an exceptionally broad ultrafast window, from the terahertz ($10^{12}$~Hz) to petahertz ($10^{15}$~Hz) regimes, enabling single $\mathbf{Q}$ valley polarization on femtosecond timescales. Our findings establish a new paradigm of light-wave quantum metrology in valleytronics, unlocking the $\mathbf{Q}$-valley subspace for scalable multi-state valley information processing.

Ward and Szabó [WS94] have shown that a complete graph with $N^2$ nodes whose edges are colored by $N$ colors and that has at least two colors contains a bichromatic triangle. This fact leads us to a total search problem: Given an edge-coloring on a complete graph with $N^2$ nodes using at least two colors and at most $N$ colors, find a bichromatic triangle. Bourneuf, Folwarczný, Hubácek, Rosen, and Schwartzbach [Bou+23] have proven that such a total search problem, called Ward-Szabó, is PWPP-hard and belongs to the class TFNP, a class for total search problems in which the correctness of every candidate solution is efficiently verifiable. However, it is open which TFNP subclass contains Ward-Szabó. This paper will improve the computational complexity of Ward-Szabó. We prove that Ward-Szabó is a complete problem for the complexity class PPP, a TFNP subclass of problems in which the existence of solutions is guaranteed by the pigeonhole principle.

Silicon carbide is a wide-bandgap semiconductor with an emerging CMOS technology platform and it is widely deployed in high power and harsh environment electronics. This material is also attracting interest for quantum technologies through its crystal defects, which can act as spin-based qubits or single-photon sources. In this work, we assess the cryogenic performance of commercial power MOSFETs to evaluate their suitability for CMOS-compatible quantum electronics. We perform a statistical study of threshold voltage and subthreshold swing from 300 K down to 650 mK, focusing on reproducibility and variability. Our results show significant performance degradation at low temperatures, including large gate hysteresis, threshold voltage shifts, and subthreshold swing deterioration. These effects suggest instability in electrostatic control, likely due to carrier freeze-out and high interface trap density, which may pose challenges for the reliable use of this transistor technology towards the realisation of quantum devices or cryo-CMOS electronics.

Surgical resection is the primary treatment option for brain tumor patients, but it carries the risk of postoperative cognitive impairments. This study investigates how tumor-induced alterations in presurgical neural dynamics relate to postoperative working memory outcome assessed by Spatial Span (SSP) test. We analyzed functional magnetic resonance imaging (fMRI) of brain tumor patients before surgery and extracted energy landscapes of high-order brain interactions. We then examined the relation between these energy features and postoperative working memory performance using statistical and machine learning (random forest) models. Patients with lower postoperative SSP Scores (2 to 5) exhibited fewer but more extreme transitions between local energy minima and maxima, whereas patients with higher SSP Scores (6 to 9) showed more frequent but less extreme shifts. Furthermore, the presurgical high-order energy features were able to accurately predict postoperative working memory outcome with a mean accuracy of 90%, F1 score of 87.5%, and an AUC of 0.95. Our study suggests that the brain tumor-induced disruptions in high-order neural dynamics before surgery are predictive of postoperative working memory outcome. Our findings pave the path for personalized surgical planning and targeted interventions to mitigate cognitive risks associated with brain tumor resection.

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is the sum of the $\ell_1$-norm and nuclear norm. In this paper we detail the iterative algorithms and its associated computations for solving this convex optimization problem. We present various efficient implementation strategies, with attention to practical cases where $H$ is circulant, separable, or block structured. Notably, we propose a preconditioning technique that drastically improved the performance of our algorithms in terms of efficiency, accuracy, and robustness. While this paper serves as an illustrative algorithm implementation manual, we also provide theoretical guarantee for our preconditioning strategy. Numerical results demonstrate the effectiveness of the proposed approach.

We show the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal to ensure the finiteness. Our proof of finiteness is based on the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu.

This study offers a forensic assessment of a widely circulated photograph featuring Andrew Mountbatten-Windsor, Virginia Giuffre, and Ghislaine Maxwell, an image that has played a pivotal role in public discourse and legal narratives. Numerous inconsistencies emerge across multiple published versions, including irregularities in lighting, posture, and physical interaction, which are more consistent with digital compositing than with an unmanipulated original. The analysis includes a 3D reconstruction of the scene geometry and a search of reference images matched to the identified camera model. Because no original print is available, and no verifiable chain of custody exists for the original, definitive conclusions remain unattainable. Even so, the technical and contextual anomalies indicate that the photograph may have been deliberately fabricated, particularly since two probable source image unrelated to the case were identified. In the absence of further evidence, it remains an unresolved yet symbolically charged artifact within a complex story of abuse, memory, and contested truth.

In this paper, we have systematically explored the mass spectrum of fully strange tetraquark candidates within the framework of QCD sum rules, focusing on states with quantum numbers $J^{PC}=0^{++}$, $0^{-+}$, $0^{--}$, $1^{--}$, $1^{+-}$, and $1^{++}$. The analysis reveals the existence of fully strange tetraquark states with masses ranging from approximately $2.07$ to $3.12$ GeV. These predictions are confronted with existing experimental observations of potential fully strange tetraquark resonances, notably the $X(2300)$ recently reported by the BESIII Collaboration, which may be interpreted as a fully strange tetraquark state. Furthermore, the possible decay modes of these fully strange tetraquark states are analyzed, providing guidance for their identification in current and future high energy experiments such as BESIII, Belle II, and LHCb.

In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are shown to be not equivalent to Reed-Solomon(RS) codes. Moreover, our construction offers more flexible parameters than existing twisted generalized Reed-Solomon(TGRS) code designs. For a large odd prime power $q$, systematically constructed TGRS codes are known to be limited to length $\frac{q+1}{2}$. By contrast, our column TRS construction supports code lengths up to $\frac{q+3}{2}$. Finally, we present the dual codes of column TRS codes. Overall, this work introduces a new method for constructing MDS codes by appending column vectors to some generator matrix of an RS code.

We propose a multi-field fibre inflation scenario in type IIB perturbative large volume compactifications, showing that the multi-field dynamics suppresses trans-Planckian displacements of the canonical inflaton. Considering a concrete K3-fibred Calabi-Yau (CY) threefold with $h^{1,1}({\rm CY})=3$ and having certain underlying symmetries, we show that the presence of multi-fibre moduli creates an assisted inflation scenario where multiple moduli collectively help in producing the cosmological observables consistent with the current experimental bounds. We further argue that individual field range excursions $(Δϕ_n)$ corresponding to each of the inflaton fields can be estimated as $Δϕ_n = Δϕ/\sqrt{n}$, where $Δϕ$ denotes the effective single-field inflaton range needed to generate the desired cosmological observables, and $n$ is the number of moduli assisting the multi-fibre inflation. We also present various numerical benchmark models consistently producing cosmological observables in light of the recent ACT experiments.

We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while generating results with similar visual quality. Our contribution is a full algorithmic pipeline that makes cloth simulation using quadratic B-spline surfaces faster than standard linear FEM in practice while consistently improving accuracy and visual fidelity. Using quadratic B-spline basis functions, we obtain a globally $C^1$-continuous displacement field that supports consistent discretization of both membrane and bending energies, effectively reducing locking artifacts and mesh dependence common to linear elements. To close the performance gap, we introduce a reduced integration scheme that separately optimizes quadrature rules for membrane and bending energies, an accelerated Hessian assembly procedure tailored to the spline structure, and an optimized linear solver based on partial factorization. Together, these optimizations make high-order, smooth cloth simulation competitive at scale, yielding an average $2\times$ speedup over linear FEM in our tests. Extensive experiments demonstrate improved accuracy, wrinkle detail, and robustness, including contact-rich scenarios, relative to linear FEM and recent higher-order approaches. Our method enables realistic wrinkling dynamics across a wide range of material parameters and supports practical garment animation, providing a new promising spatial discretization for high-quality cloth simulation.

We introduce two classes of junctions in a toric code, a prototypical model of a $\mathbb{Z}_2$ quantum spin liquid, and study the nature of anyonic transport across them mediated by Zeeman fields. In the first class of junctions, termed potential barrier junctions, the charges sense effective static potentials and a change in the band mass. In a particular realization, while the junction is completely transparent to the electric charge, magnetic charge transmission is allowed only after a critical field strength. In the second class of junctions we stitch two toric codes with operators which do not commute at the junction. We show that the anyonic transmission gets tuned by effective pseudospin fluctuations at the junction. Using exact analytical mappings and numerical simulations, we compute charge-specific transmission probabilities. Our work, apart from uncovering the rich physical mechanisms at play in such junctions, can motivate experimental work to engineer defect structures in topologically ordered systems for tunable transport of anyonic particles.

An $n$-plat 1-knot is one isotopic to the plat closure of some $2n$-braid, which is also called an $n$-bridge 1-knot. Schubert classified 2-bridge 1-knots by considering their double branched covers which are homeomorphic to lens spaces. A 2-knot is a 2-sphere smoothly embedded in 4-space or 4-sphere. An $n$-plat 2-knot is one isotopic to the plat closure of some 2-dimensional $2n$-braid. The aim of this paper is to classify 2-plat 2-knots. By a result of Montesinos, double branched covers do not distinguish 2-plat 2-knots. Thus, we introduce a new invariant to classify them. Our invariant serves as an analogue of a torsion invariant. Furthermore, it is an obstruction to invertibility of 2-knots.

This paper investigates the orbital dynamics and gravitational wave radiation characteristics of neutral test particles around a static spherically symmetric charged black hole (BH) in 4D Einstein-Gauss-Bonnet (4D-EGB) gravity theory. We analyze the dependence of the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO) on the Gauss-Bonnet coupling parameter $α$ and charge $Q$. The results indicate that the orbital radius, angular momentum, and energy all decrease with increasing $α$ or $Q$, with the corresponding bound orbit region shifting leftward in the $(E, L)$ parameter space. By combining observational data from the BH shadows of M87* and Sgr A* as well as the orbital precession of the S2 star, we constrain the model parameters and find that existing observations can limit the ranges of $α$ and $Q$ to a certain extent. Furthermore, we investigate the characteristics of periodic orbits corresponding to different rational numbers $q$ and the gravitational waveforms they excite, finding that variations in $α$ and $Q$ can lead to distinguishable differences in periodic orbit structures and gravitational wave phases. This study contributes to understanding the effects of Gauss-Bonnet corrections on BH spacetimes, and the results may provide theoretical references for future gravitational wave observations of extreme mass ratio inspirals (EMRIs).

Sedimentation of particulate suspensions in horizontal pipes can lead to formation, growth and consolidation of a solid-like bed which can severely retard pipeline performance. As stagnant flow conditions frequently arise during industrial processes, critical operational questions are: (i) at what rate and extent does sedimentation proceed, and (ii) can the sedimentation dynamics be predicted from conventional suspension characterisation methods? We address these questions by characterising the sedimentation properties of an aqueous Kaolin suspension via batch settling tests and comparing predictions from 1D sedimentation theory with experiments in a horizontally oriented cylindrical pipe. We show that particulate sedimentation can be accurately predicted, indicating that the estimated sedimentation properties are representative material properties, and that transient effects such as gravity currents are not significant. Conversely, we find that the consolidation of the sediment is not well predicted by 1D theory, suggesting that the stress state is not 1D and likely involves contributions from the pipe walls. These stagnant cylindrical pipe results provide a basis for the development of methods to predict pipeline sedimentation under more general (laminar and turbulent) flow conditions.

A graph is even-degenerate if one can iteratively remove a vertex of even degree at each step until at most one edge remains. Recently, Janzer and Yip showed that the Erdős--Renyi random graph $G(n,1/2)$ is even-degenerate with high probability, and asked whether an analogous result holds for any general $G(n,p)$. In this paper, we answer this question for any constant $p\in (0,1)$ in affirmation by proving that $G(n,p)$ is even-degenerate with high probability.

Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff problems, that assumption is often violated, and a problematic degradation in accuracy, known as order reduction, can arise. Methods with high stage order, e.g., Gauss-Legendre and Radau, are known to avoid order reduction, but they must be fully implicit. For the broad class of semilinear ODEs, which consist of a stiff linear term and non-stiff nonlinear term, we show that weaker conditions suffice. Our new semilinear order conditions are formulated in terms of orthogonality relations and can be enumerated by rooted trees. Finally, we prove global error bounds that hold uniformly with respect to stiffness of the linear term.