The Model Context Protocol (MCP) is emerging as a common interface connecting large language models (LLMs) with external services. Remote deployments are becoming increasingly important as agents connect to user-linked online services, such as social, productivity, and financial services. In such deployments, the authentication boundary between MCP clients and remote servers becomes security-critical, yet remains underexplored. We present the first measurement study of authentication security in real-world remote MCP servers. We identify 7,973 live remote MCP servers, finding that 40.55% expose tools without authentication. Among authenticated servers, OAuth is the dominant authorization mechanism for reaching remote services, and OAuth deployments in the MCP ecosystem commonly exhibit three characteristics: open client environments, dynamic client registration, and delegated authorization. These characteristics distinguish MCP deployments from traditional OAuth and introduce new attack surfaces. Guided by this observation, we derive a taxonomy of authentication flaws comprising three MCP-specific categories and conventional OAuth misconfigurations, for a total of four categories and nine concrete flaw types. To evaluate these flaws at scale, we implement a semi-automated detection framework that combines passive traffic inspection with active dynamic probing. Applying it to 119 testable real-world OAuth-enabled MCP servers, we find that each server exhibits at least one flaw, with a total of 325 flaws identified, among which dynamic client registration flaws affect 96.6% of tested servers. Many of these flaws can lead to sensitive information leakage and account takeover. Through responsible disclosure, we obtained 9 CVE IDs. Our findings expose pervasive authentication weaknesses in the MCP ecosystem and underscore the urgent need for hardened OAuth-based remote deployments.

Global fits of Beyond the Standard Model (BSM) physics often involve a two-way interplay between theory and experiment. Theoretical models provide guidance for experimental searches, while experimental results, in turn, constrain theoretical frameworks. A crucial aspect of this feedback loop is the direct inclusion of measurements and exclusion limits ``online'' global fits, i.e. during the parameter scans aspects of the global fits. However, incorporating the Large Hadron Collider (LHC) limits into such analyses has been computationally prohibitive, often due to time taken per parameter point exceeding the scales acceptable for global fit frameworks. In this study, we show that LHC limits can be incorporated ``online'' global fits by leveraging approximations derived from symbolic regression techniques. We utilize a dataset of ATLAS constraints from searches for electroweakino productions to derive a mathematical expression capable of classifying the phenomenological Minimal Supersymmetric Standard Model (pMSSM) parameter space as allowed or excluded. This is subsequently incorporated for making a global fit of the pMSSM to data, including the LHC Run-2 limits.

In post-disaster environments, damaged communication infrastructure severely limits coordination among emergency response teams. Cognitive radio networks (CRNs) enable rapidly deployable communication by allowing nodes to opportunistically access available spectrum. However, existing multihop rendezvous protocols typically rely on N-1 termination conditions, which can lead to premature termination, resulting in incomplete neighbour discovery and invalid network topology formation. This work identifies this limitation as a previously overlooked issue in multihop rendezvous protocols. This paper proposes a Multihop Reliable Dual-Modular Clock Algorithm (MR-DMCA) that eliminates premature termination and ensures reliable network formation. The proposed protocol introduces a coordinate-assisted neighbour validation mechanism and an autonomous termination strategy that guarantees complete neighbour and topology discovery before protocol termination. Although implemented within MR-DMCA, the proposed validation and termination approach is applicable to a wider class of multihop rendezvous protocols. Extensive simulations demonstrate that, in a worst-case scalable scenario with 20 nodes and 20 channels under high primary radio activity (m=2), MR-DMCA achieves 100% accurate neighbour and topology discovery while reducing rendezvous time by up to 76%, 37%, and 17% compared with baseline protocols. The results highlight that addressing premature termination is critical for reliable multihop rendezvous in cognitive radiobased emergency communication networks.

Security operations centers face persistent alert fatigue: in low-prevalence streams, even low false-positive rates generate substantial investigation load, while aggregate F1 scores obscure analyst burden. We introduce PACT, a Pareto-aware controller for triggered active learning, which wraps an already-deployed frozen XGBoost-Focal screener with an adaptive windowing score-shift trigger and a hybrid acquisition rule combining threshold-relative uncertainty with high-score sampling. On two public low-prevalence benchmarks, AIT-ADS (AIT Alert Data Set), and BOTSv1 (Boss of the SOC version 1), PACT attains the lowest benign-normalized false-positive (FP) burden among the adaptive methods tested. It reduces burden by 43% and 21%, respectively, relative to a frozen baseline, while using 3.8x and 5.2x fewer analyst queries than periodic uniform-random updating. A matched-trigger ablation controls trigger timing and shows that acquisition contributes beyond timing alone, at the cost of approximately ten percentage points of positive-window recall under free-running triggers. A frozen threshold-only baseline pushes FP lower still but collapses BOTSv1 recall by 55 percentage points. Under the evaluated workload assumptions, pure FP minimization trades unacceptable recall for that lower burden.

Magnetar short bursts (SBs) are hard X-ray transients of durations $0.01-1$ s peaking at $\sim 10-100$ keV, and are prime targets for new high-energy missions and polarimeters. The recent association of SBs with bright radio bursts in SGR 1935+2154 has broadened interest in SB physics. We present new advanced fireball models combining general relativistic light bending, polarized transport in magnetized photospheres, magnetic photon splitting attenuation, and magnetospheric vacuum birefringence. These models also have relevance to trapped fireballs in magnetar giant flare pulsating tails. We adopt confined flux tube geometries consistent with adiabatic fireballs, and anisotropic/polarized emergent intensities to produce spectra and polarizations, and energy-time Stokes impulse responses. We predict that most fireballs are highly linearly polarized, especially when vacuum birefringence is important. There is rich potential for diagnostics: coexisting direct and lensed delayed images, gaps by occultation of the neutron star surface, and Shapiro+Rømer delay with temporal caustics. These effects can imprint spin phase dependence of the spectral and polarization character of bursts. Predicted signatures depend strongly on viewing geometry, fireball configuration, and photon splitting assumptions, yielding large variance in model high-energy spectral shapes and cutoffs, and energy-dependent polarization. The models can reproduce established double-blackbody SB spectral phenomenology, and we find that the unusual April 2020 radio-associated SB from SGR 1935+2154 is broadly consistent with a footpoint close to the magnetic pole, and possibly near pole-on viewing geometry. Our models motivate reverberation-style analyses for SBs and suggest that high-quality data might constrain source geometry, burst crustal footpoints, and, potentially, neutron star masses and radii.

We develop a general theory of Cartesian and non-Cartesian polynomials on products of complex spaces $\mathbb{C}^{n_1} \times \cdots \times \mathbb{C}^{n_k}$. We prove that, for any fixed degree $d \ge 2$, a (Zariski) generic polynomial is non-Cartesian in a broad range of dimensions, establishing that Cartesian structure is highly exceptional. We further introduce effective sufficient criteria for a polynomial to be non-Cartesian. Moreover, we show that being (non)-Catersian can be decided algorithmically via Gröbner basis methods and quantitative forms of Hilbert's Nullstellensatz. As an application, we connect the non-Cartesian condition to incidence geometry, obtaining sharp intersection bounds and constructing extremal configurations that demonstrate the optimality of these estimates.

The discovery of altermagnetism offers new opportunities for exploring novel quantum states and developing spintronic devices for enabling momentum dependent spin splitting in compensated systems, while zero net magnetization limit its manipulability using conventional magnetic method. Here, we propose 2D alternating ferrimagnetism,a phase merging alternating momentum dependent spin splitting with a finite net magnetization. A tight binding model reveals that alternating ferrimagnetism originates from uncompensated magnetization in altermagnets, facilitating concurrent net magnetization and alternating spin splitting. First principles calculations and Monte Carlo simulations demonstrate stable alternating ferrimagnetism in strained and Cr substiting V2Te2O, which exhibit strain tunable net magnetization, reversable half metallicity and valley polarization, accompanied by long range magnetic order above room temperature. By combining altermagnetic and ferromagnetic properties, alternating ferrimagnetism expand the 2D magnetism landscape and offer pathways for energy efficient spintronic applications.

This letter evaluates the performance of the slotted Aloha protocol defined by the European Telecommunication Standard Institute (ETSI) SmartBAN specification, under saturation conditions. For this purpose, we develop a two-dimensional Discrete Time Markov Chain (DTMC) to model the operational details of the protocol and assess its performance in terms of saturation throughput and average end-to-end delay. The accuracy of the proposed model is validated by means of simulation which reveals a very good match among theoretical and simulation results. The model can be used for protocol performance prediction and optimization purposes.

We show that the mutual coherence of a relativistic electron beam in a Coulomb-disordered medium is governed by an effective two-dimensional compact phase field with a logarithmic correlation function. The corresponding Gaussian free-field action exhibits a stiffness inversely proportional to the propagation length. When the compact nature of the phase is taken into account, the system supports vortex excitations that interact as a two-dimensional Coulomb gas. Renormalization-group analysis of this gas indicates the existence of a critical sample thickness $L_c$ at which a Berezinskii--Kosterlitz--Thouless (BKT) transition may occur, separating a regime of algebraic decoherence from one where free vortices proliferate and coherence is destroyed exponentially. The critical thickness is expressed through fundamental microscopic parameters and could be observed in transmission electron microscopy of liquid cells or cryogenic samples.

Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European options. We introduce a new Schwarz modulus-based splitting method for solving such linear complementarity problems, and further accelerate them using Modified Polynomial Extrapolation, a non-linear vector sequence acceleration technique, which is very much related to Krylov methods in the linear case. Numerical experiments on a model problem show that our new solver can have close to an order of magnitude lower iteration counts than the classically used modulus-based matrix splitting technique.

Answering a question of Goode, we show that $k$-triviality collapses to (1-)triviality among simple theories. In particular, every stable theory with quantifier elimination in a relational language of bounded arity is trivial. We use our collapse result, along with other facts about $k$-triviality and $k$-total triviality, to generate examples of (strongly) $k$-distal theories. The collapse result immediately implies that no stable theory can be strictly $k$-distal for some $k\geq 3$, partially answering a question of Walker. Moreover, all known examples of non-distal (strongly) $k$-distal theories are $k$-ary, rendering (strong) $k$-distality moot as a $(k+1)$-ary dividing line; we give four classes of examples that are not $k$-ary. We also show that just as distality is not preserved under taking reducts, neither is (strong) $k$-distality.

In this work, we report a new nanoscale phenomenon observed as photoemission intermittency (On-Off electron emission), manifested as stochastic bursts in electron yield at quasi-one-dimensional organic wires and silver nanoparticles interface. Energy-resolved measurements reveal that the emitted electrons carry out hybrid information, containing photoelectron yield enhancement associated with the nanoparticles and kinetic energies determined by the organic semiconductor. The intermittency results in a dynamic shift of the electron spectra correlating with the photoelectron yield. We attribute the observed behaviour to the photo-hole accumulation and stochastic gating of charge due to electron-hole separation at the nano interface. These findings introduces the photoemission intermittency as a nanoscale phenomenon indicating a new dynamic regime of charge assisted emission at organic-plasmonic interfaces. Keywords: rubrene, nanoparticle, PEEM, exciton, charge

This paper focuses on the application of time domain decomposition to solve partial differential equations constrained optimization problems and controllability problems. After clarifying the link between these two types of problems, we show that applying time domain decomposition to both problems leads to the same convergence behavior. Our numerical experiments also confirm these theoretical findings.

Cosmological data from the cosmic microwave background (CMB), baryon acoustic oscillations, and Type Ia supernovae suggest that the component driving the accelerated expansion of the Universe may be dynamical at the $\sim 2.5$-$3σ$ CL. The best-fit CPL model produces a level of cosmic structure similar to that of $Λ$CDM, with both models exhibiting mild tension with redshift-space distortion data. In this {\it Letter}, we parametrize possible departures of the effective gravitational coupling from Newton's constant in the late Universe, below a comoving scale $λ_c$, using two redshift bins, $0 \leq z < 1$ and $1 \leq z \leq 3$. We then determine the optimal values of $λ_c$ and the amplitude of these deviations from General Relativity, assuming a background with dynamical dark energy in CPL form. We find that, in order to achieve the required suppression of structure growth at low redshifts while remaining consistent with CMB constraints -- primarily from the late-time ISW effect at low $\ell$ and lensing at high $\ell$ -- modified gravity effects must appear on scales smaller than $λ_c \sim \mathcal{O}(10)\,\mathrm{Mpc}$. Using Planck PR4, DESI DR2, Pantheon+ (or DES-Dovekie) and redshift-space distortions data we confirm that a CPL background with standard gravity is moderately preferred over $Λ$CDM; this preference strengthens to a mildly strong level when modified gravity effects are included. This enhancement leaves the CPL parameters largely unchanged, but shifts them slightly further into the quintom region.

In this paper we prove that every coefficient of twisted Alexander polynomials of torus knots associated with irreducible $\mathrm{SL}_n(\Bbb C)$-representations is an $\Bbb A$-valued locally constant function on the $\mathrm{SL}_n(\Bbb C)$-character variety, where $\Bbb A$ is the ring of all algebraic integers over $\Bbb C$. Moreover, as a generalization of a recent result of Kitano and Nozaki, we show that $\mathrm{SL}_n(\Bbb C)$-Reidemeister torsions are algebraic integers for many Seifert fibered spaces. Also, we discuss the power sums of Reidemeister torsions of torus knots for low-dimensional irreducible representations that provide a mysterious relation to TQFT.

The weak $k$-metric dimension of a graph is roughly understood as the cardinality of a smallest set of vertices $S$ of the graph with the property of uniquely recognizing all the vertices of the graph throughout summations of differences of distances to the vertices of $S$. The weak $k$-metric dimension of the direct product of two isomorphic complete graphs is considered in this work. Specifically, the value of such parameter is computed for almost all possibilities of these products and a bound is provided in the remaining case.

The fabrication of free-standing ultra-thin films from high-temperature (high-Tc) superconductors is of great interest for the development of superconducting nanowire single-photon detectors with high operating temperatures. We successfully fabricate a millimeter-sized, high-quality, ultra-thin YBa$2$Cu$3$O$_{7-x}$ (YBCO) film on an SrTiO$_3$/Sr$_{1.5}$Ca$_{1.5}$Al$_2$O$_6$ (STO/SCAO) bilayer using high-pressure sputtering. The STO nanomembranes with the YBCO films are released by dissolving the water-soluble SCAO sacrificial layer and transferred onto the SiO2/Si substrate. X-ray diffraction confirms that STO and YBCO crystallinity is preserved following transfer onto SiO2/Si substrates. Microbridges patterned from the transferred YBCO films exhibit a critical temperature of 88.8 K and a critical current density of 6.8 MA/cm2 at 77 K, demonstrating robust superconducting transport after transfer. The thermal boundary conductance across the van der Waals interface between the STO nanomembrane with YBCO film and the SiO2/Si substrate, measured over 15-75 K, is significantly reduced compared to that of epitaxial YBCO film on bulk STO leading to modified energy relaxation and enhanced stability of transient resistive states. These results establish ultra-thin YBCO films on optically transparent STO nanomembranes as a platform for integrating high-Tc superconducting devices with SiO2/Si-based photonic structures.

We prove a structure theorem for finite perfect two-sided skew braces. The main tool is a central product theory for skew braces, developed here in both external and internal form; we show that these two constructions are equivalent. Our main result states that every finite perfect two-sided skew brace \(B\) admits the canonical decomposition $B=B^2\circ B^{2,\operatorname{op}},$ where \(B^2\) is almost trivial with perfect additive group, while \(B^{2,\operatorname{op}}\) is trivial with perfect additive group. Thus finite perfect two-sided skew braces are classified, up to central amalgamation, by trivial and almost trivial skew braces arising from perfect groups. This decomposition has strong consequences for the underlying groups: for finite two-sided skew braces, perfectness of the skew brace is equivalent to perfectness of either the additive or the multiplicative group. In the trivial-center case the central product becomes a direct product, recovering Trappeniers' classification of finite simple two-sided skew braces. We also show that quasi-simple two-sided skew braces are necessarily either trivial or almost trivial. Finally, we prove that this rigidity is genuinely two-sided by constructing a quasi-simple skew brace which is not two-sided and is neither trivial nor almost trivial.

Specifying a full Bayesian model that integrates multiple data sources can be challenging. One natural approach is to specify each individual model separately and join them afterwards. This is the approach adopted in Markov melding. However, when adjacent submodels share common quantities, as in chained Markov melding, posterior inference can be challenging for existing MCMC-based approaches. In this paper, we propose a new multi-stage sampler for chained Markov models involving an arbitrary number of submodels. The proposed sampler adopts a divide-and-conquer sequential Monte Carlo approach for the tree-structured model that fits naturally with the structure of chained Markov melding. The resulting multi-stage sampler provides a flexible alternative for sampling from complex joint models, as its separate sampling scheme for different submodels avoids the need for directly sampling from the full model. We demonstrate applications of the sampler through two examples. The first is a toy example involving 11 submodels of various types. The second example considers an ecologically integrated population model that combines multiple datasets to estimate immigration and reproduction rates.

We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare equation-based and data-driven SSM reductions, to illustrate the need for the latter. We then use the same algorithm to obtain purely data-driven, SSM-reduced, delay-free ODE models for several nonlinear delayed systems. Our approach requires no information about the form of the underlying DDE, or about the number and magnitude of the delays it contains. Our SSM-reduced, low-dimensional models remain predictive even for chaotic dynamics. We also illustrate the use of parametric SSM-reduction to capture bifurcations in systems with both distributed and discrete delays. Finally we extend the theoretical underpinning of delayed SSM-reductions to non-autonomous systems with periodic delays, and apply these results to experimental data from a control system with feedback delay and quantization.

Temporal ghost imaging (TGI) enables ultrafast signal reconstruction beyond electronic bandwidth limits. Extending this concept to the mid-infrared (MIR) regime through nonlinear frequency conversion offers new opportunities for high-fidelity temporal detection, but remains constrained by stringent phase-matching condition, limited spectral coverage, and intricate optical alignment. Here, we propose and demonstrate a broadband MIR TGI system based on non-degenerate two-photon absorption. A temporally encoded near-infrared pump transfers structured modulation onto a MIR signal directly at a silicon detector, which facilitates concurrent modulation and detection without external nonlinear crystals. The reconstructed temporal waveforms exceed the detector bandwidth by more than fortyfold, achieve a detection sensitivity of 0.05 pJ/pulse, allow compressed sensing with 80\% fewer measurements, and support broadband operation across 2.5-3.8 $μ$m. This compact, alignment-free, and room-temperature system establishes a practical route for fast and sensitive MIR time-domain analysis, holding great promise for applications in time-resolved molecular spectroscopy, high-precision infrared ranging, and high-speed free-space communication.

Context: Trans-Neptunian objects are distant bodies that retain valuable information about the origin and evolution of the Solar System. Many of these objects constitute binary systems. Studying binaries allows us to further characterise this primitive population and is critical for determining mass densities, a key but elusive physical property. Nevertheless, satellite detection can be challenging. Aims: This study aims to constrain the presence of close-in satellites around a selection of ten trans-Neptunian objects, including four known binary systems used for methodology validation. Methods: We developed a methodology independent of primary-secondary separation. We exploit the combination of occultation-derived sizes and thermal emission data from the "TNOs are Cool" Herschel Space Observatory key project. We model the thermal emission from a binary system to explain the thermal excess that cannot be reproduced by a single body of the occultation-derived size. Results: We obtain satisfactory constraints for the validation targets (208996) Achlys, (229762) G!kún{"hòmdímà, (38628) Huya and (174567) Varda. We find that (84522) 2002 TC302, (119951) 2002 KX14, and (307261) Máni are likely binary systems, which was previously unknown. We report size estimates for their putative satellites. For (84922) 2003 VS2, (28978) Ixion, and (470316) 2007 OC10 we find that no sizable satellite is needed to reconcile thermal and occultation data.

We study the $L^{\infty}$ discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective spaces. Using concentration inequalities and variance estimates for the number of points in metric balls, we derive general upper bounds for the discrepancy of homogeneous determinantal point processes. In the particular case of the harmonic ensemble, we show that the discrepancy of $N$ points is $O((N^{1-1/D})^{1/2}\log N)$ with high probability, where $D$ denotes the real dimension of the manifold. For the projective ensemble on $\mathbb{CP}^d$, we obtain the sharper bound $O((N^{1-1/D}\log N)^{1/2})$. These results extend previously known discrepancy estimates for determinantal point processes on the sphere to all compact, connected two-point homogeneous spaces.

Modular variables serve as a striking example of quantum nonlocality, particularly in superpositions of wave packets that are spatially well separated, where the relative phase between components cannot be accessed through conventional local measurements. In this work, we explore the time evolution of Hermitian modular operators for Gaussian wave-packet superpositions under the influence of a uniform gravitational field. We consider both unitary dynamics governed by the Schrödinger equation and open-system dynamics described by the Caldeira-Leggett master equation in the high-temperature limit. Adopting the Bohmian interpretation of quantum mechanics, we compute local expectation values of these modular operators along individual particle trajectories. Our analysis shows that gravitational acceleration induces a time-varying modular signal, the expectation value of the modular observable, that remains sensitive to the relative phase between the separated wave packets. In contrast, standard local quantities such as the probability density and probability current, while modified by gravity, become insensitive to the relative phase in the regime of negligible spatial overlap. For a pair of particles coupled to a shared environment, we find that environment-induced correlations can modify the local modular expectation value observed for one particle, yielding a clear signature of environmental influence. However, the transfer of phase sensitivity via environment-generated entanglement to the modular signal of the distant particle remains negligible within the regime considered. We further demonstrate that conventional measures of coherence and entanglement do not capture the relative phase information in this non-overlapping regime.

Electronic phases that lie outside the equilibrium ground state offer a route to explore competing configurations in correlated materials. In 1T-TaS2, ultrafast excitation accesses a metallic hidden phase that is distinct from the commensurate insulating ground state. Here we use angle-resolved photoemission spectroscopy to show that an equivalent electronic configuration is stabilized in exfoliated intermediate-thickness 1T-TaS2 flakes, where it persists up to room temperature before evolving through a different sequence of electronic transitions. This equilibrium hidden-phase-like state hosts a metallic band with finite Fermi-level spectral weight while retaining the characteristic hybridization gaps associated with the star-of-David band folding. These results establish a platform for controlling competing electronic states in layered materials, with implications for both quantum science and phase change technologies.

An $(r, s)$-${\textit set}$ in ${\rm PG}(n, q)$ is a set of points, say $\mathcal X$, such that each $s$-dimensional projective subspace contains at most $r$ points of $\mathcal X$. We investigate $(n, n-2)$-sets and $(n-2, n-3)$-sets in ${\rm PG}(n, q)$, $n \le 6$. We show that the trivial upper bounds on $(n, n-2)$-sets in ${\rm PG}(n, q)$, $4 \le n \le 6$, $(4, 3)$-sets in ${\rm PG}(6, q)$ and $(3, 2)$-sets in ${\rm PG}(5, q)$ are essentially sharp. A $(3, 2)$-set in ${\rm PG}(13, q)$ of size $\frac{q^6-1}{q-1}$ is also constructed.

In this paper, we investigate a multi-cell six-dimensional movable antenna (6DMA) network for enhancing downlink communication performance under inter-cell interference (ICI). Each base station (BS) is equipped with multiple 6DMA surfaces, and the 6DMA rotations affect both the desired-signal enhancement for in-cell users and the interference leakage toward neighboring cells, which makes the antenna-rotation design and transmit precoding intrinsically coupled across BSs. To address this issue, we formulate an average weighted sum-rate maximization problem for the multi-cell system by jointly optimizing the short-term downlink precoders and long-term 6DMA rotations under practical antenna geometric constraints. To tackle the resulting nonconvex problem, we propose a distributed two-timescale design based on inter-cell interference power constraint (IPC) coordination among neighboring BSs, under which each BS performs local short-term precoder optimization based on instantaneous channel state information (CSI) and long-term 6DMA rotation update according to statistical CSI with limited inter-BS information exchange. In particular, an edge-wise IPC coordination mechanism based on two-stage one-dimensional grid search and random maximal matching is developed to enable scalable distributed implementation. A centralized offline benchmark is also provided for performance comparison. Numerical results show that the proposed distributed design achieves performance close to the centralized benchmark under different interference conditions, while maintaining favorable scalability as the network size increases.

The moveEZ (pronounced move easy) R package provides tools for constructing animated PCA biplots that reveal how multivariate structure evolves across the ordered levels of a categorical variable. Built as an extension to the biplotEZ package, moveEZ offers three animation frameworks of increasing methodological complexity: a fixed variable frame, in which variable vectors remain constant and only sample positions are animated; and two dynamic frames, in which both sample positions and variable vectors are recomputed and animated at each level. The dynamic frames support Procrustes alignment and reflection to ensure visual continuity across levels, and are compatible with high-dimensional datasets including grouped structures. The package integrates with gganimate to produce high-quality animations suitable for publications and presentations, and supports both animated and static faceted displays via a single argument. Although originally motivated by tracking shifts in African climate indicators, moveEZ is domain-agnostic and applicable wherever multivariate measurements are recorded repeatedly across an ordered categorical variable, including economic, ecological, and biological settings.

Rhombohedral (ABC) graphite hosts a surface-localized flat band that supports correlated and topological electronic phases, but its experimental study is limited by the scarcity of ABC stacking in natural graphite, which is dominated by Bernal (AB) stacking. Here we show that the routine mechanical exfoliation step itself enriches the rhombohedral content of graphite flakes, and that a simple blade-assisted exfoliation step, which introduces additional shear, amplifies the effect further. Using large-area Raman 2D-band skewness mapping we measure ABC content at area fractions of 3\% in the pristine source crystal, 16\% after conventional exfoliation, and 26\% after blade-assisted exfoliation for thick flakes. In thin flakes ($<20$ layers) the per-flake area fraction reaches 75\% in the upper tail of the distribution. Tracking individual flakes before and after blade-assisted exfoliation shows that wrinkles seed AB-ABC domain walls, and uniaxial strain can move these walls. Blade-assisted mechanical exfoliation therefore removes one of the bottlenecks to the preparation of ABC-rich graphite samples for studies of correlated and topological phases in rhombohedral graphite.

LSQR and LSMR are iterative methods, based on the Golub-Kahan bidiagonalization algorithm, widely used for large-scale linear least squares problems. FLSQR and FLSMR are flexible variants of LSQR and LSMR, respectively, based on a flexible Golub-Kahan (Arnoldi-like) factorization algorithm, which naturally allow modifications of the solution approximation subspace and/or handling inexact matrix-vector multiplications with the (transpose of the) coefficient matrix, thereby enabling to enforce prior information into the computed solution. The goal of this paper is to introduce sFLSQR and sFLSMR, i.e., sketched variants of FLSQR and FLSMR, respectively, where randomization becomes particularly effective, as it allows to recover short recurrences for the solution approximation. In particular, this paper explores applications to large-scale inverse problems, showing the ability of the new randomized solvers to alleviate computational bottlenecks while preserving reconstruction quality. A theoretical analysis of sFLSQR and sFLSMR is provided, and their performance is validated through numerical experiments.