The determination of the maximal length of maximum distance separable (MDS) codes arising from elliptic curves is a central problem in coding theory. For an elliptic curve $E$ over $\mathbb{F}_q$, let $\operatorname{MEC}(k,q)$ denote the maximal length of a $q$-ary MDS elliptic code of dimension $k$. It was recently shown that $\operatorname{MEC}(k,q)\le\frac{q+1}{2}+\sqrt{q}$ for $q\ge289$ and $3\le k\le(q+1-2\sqrt{q})/10$, with equality for odd $k$ when $q$ is an odd square. This paper investigates the remaining open cases, namely even dimension $k$, non-square $q$ and fields of characteristic $2$, and provides a complete resolution of the tightness question for the two natural parity regimes of $q+1+\lfloor 2\sqrt{q}\rfloor$. We prove that if the support of $G$ (used to define the code) consists of $\mathbb{F}_q$-rational points, the bound decreases to $\frac{q+1}{2}+\sqrt{q}-1$ for even $k$. Without this restriction, we construct MDS codes attaining $\frac{q+1}{2}+\sqrt{q}$ for even $k$. More generally, we establish $\operatorname{MEC}(k,q)=\frac{q+1+\lfloor2\sqrt{q}\rfloor}{2}$ when $q+1+\lfloor2\sqrt{q}\rfloor$ is even, and $\operatorname{MEC}(k,q)=\frac{q+\lfloor2\sqrt{q}\rfloor}{2}$ when it is odd.

We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a universal number that is solely determined by the largest coordination number on the lattice. Crucially, these bounds are tight in some cases such as the Honeycomb, Square, and Triangular lattices. We prove the bounds using the Feynman--Kac--Ward formalism, confirm their validity for a selection of over two hundred lattices, and construct a two-dimensional lattice with 24-coordinated sites and high critical temperature.

Short polymer chains exhibit clear deviations from Gaussian end-to-end distance statistics, yet the molecular mechanism by which Gaussian behavior is recovered in long chains remains unestablished. Atomistic molecular dynamics simulations of polyethylene melts reveal that conformational heterogeneity persists at the Kuhn scale across all chain lengths, consisting of a mosaic of slow-relaxing, extended aligned chain segments (ACS) and coiled segments -- random conformational sequences (RCS) and chain ends (CE). We show that the end-to-end distance distributions for both unentangled and entangled chains are accurately described by a $q$-Gaussian function, with the entropic index $q$ increasing systematically from $0.67$ (C50) to $0.99$ (C500). This evolution tracks the emergence and accumulation of RCS segments, which are absent in short chains, establishing $q$ as a quantitative ``heterogeneity index''. The $q < 1$ values are a signature of non-extensive statistics, with the ratio of Tsallis to Boltzmann-Gibbs entropy ($S_q/S_1$), computed directly from simulation data without fitting, decreasing from $1.80$ (C50) to $1.03$ (C500). Crucially, we demonstrate that Gaussian recovery does not result from the erasure of Kuhn-scale heterogeneities, as ACS domains persist in all chain lengths above the critical mass ($\approx 35\%$). Instead, the transition to Gaussian statistics is a statistical masking effect, where the accumulation of independent RCS segments progressively obscures the non-Gaussian signatures of the persistent ACS domains.

New particle formation (NPF) contributes to more than half of global aerosol number concentrations, with profound implications for human health and climate change. Observational studies have shown that the frequency of NPF events in urban Beijing during summer exceeds the global average. The prevailing paradigm attributes urban NPF primarily to sulfuric acid-base nucleation involving dimethylamine (DMA). However, recent field measurements in summer urban Beijing have identified several emerging amines emitted from carbon capture processes, including monoethanolamine (MEA), piperazine (PZ), diethanolamine (DEA) and N-methyldiethanolamine (MDEA), in addition to DMA. Here, we systematically evaluate the contributions of sulfuric acid-amine nucleation pathways to urban NPF. We found that emerging amines particularly DEA and PZ, can dominate nucleation pathways under polluted urban conditions, surpassing the contribution of DMA. These findings suggest that the current universal paradigm of urban nucleation should be revisited to explicitly account for the role of emerging amines. Moreover, emerging amine-mediated NPF will become increasingly important in the context of future co-control policies for air pollution and carbon reduction.

An exact gravitational instanton solution on a vacuum Kerr-like warped spacetime in conformal dilaton gravity is found. Remarkably, the metric solution results from a first-order PDE, allowing the connection with self-duality. The singular points are determined by a quintic polynomial. This suggests that this is the highest possible polynomial in describing the singularities of black holes of Petrov type D axially symmetric manifolds and don't fits the Plebanski-Demianski classification of black holes which is determined by a fourth order polynomial. The solution can be described by a locally conformal Kählerian manifold with Euclidean signature and a Kähler potential. This is possible for the effective 4D manifold, despite the fact that a Kähler manifold in 5D cannot be modelled. We are dealing with an effective 4D self-dual Kähler manifold with a recurrent conformal structure. This happened by the projected Weyl tensor of 5D on the brane. The topology of the gravitational instanton would be $S^3\times \mathbb{R}/\mathbb{Z}_2$. The antipodal boundary condition on the hyper-surface of a Klein bottle $\sim \mathbb{C}^1\times\mathbb{C}^1$ is applied to describe the Hawking particles during the evaporation process. We used the Hopf fibration to get $S^2$ as the black hole horizon, where the centrix is not in a torus but in the Klein bottle. The twist fits very well with the antipodal identification of the points on the horizon. No 'cut and past' is necessary, so the Hawing particles remain pure without instantaneous information transport. Finally, we reveal a connection between the description of the interior of our new black hole solution and the similar model proposed by Janis, Newman and Winicour some time ago of the Schwarzschild solution in complex coordinates with a zero rest mass scalar field, which develops an anomalous asymmetry.

We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complementing classical methods that use temporal and spatial diversity. The transformations under which a signal's statistics are invariant form a matched group; this group determines the natural transform for analysis, and averaging an estimator over the group action reduces variance without requiring additional snapshots. The viewpoint is broadened in five directions beyond the single-observation measurement of a companion paper. Rank promotion admits AD on scalar data streams and identifies the law of large numbers as the trivial-group case of a $(G, L)$ continuum combining sample-count with group-orbit averaging. An eigentensor hierarchy handles signals with nested symmetry. A blind group-matching methodology identifies the matched group from data via a polynomial-time generalized eigenvalue problem on the unitary Lie algebra, placing the DFT, DCT, and Karhunen--Loève transforms as distinguished points on a transform manifold. A cost-symmetry matching principle then extends AD from measurement to blind and adaptive signal processing generally; blind equalization is given as a detailed example, with the Constant Modulus Algorithm's residual phase ambiguity predicted analytically and matched within two degrees on 3GPP TDL multipath channels, and other blind problems in signal processing are mapped into the framework. Four theorems formalize a structural capacity $κ$, the Rényi-2 analog of Shannon and von Neumann's Rényi-1 entropies, quantifying how a signal's information is organized rather than how much information it contains. AD relationship to prior algebraic approaches including invariant estimation, minimax robust estimation, algebraic signal processing, and compressed sensing.

Reducing computational accuracy can lower energy consumption, and this principle is widely used to improve energy efficiency in computing. This raises a fundamental question: what is the quantitative relationship between error and thermodynamic cost in information processing? In this study, we derive the error-cost trade-off in the binary classifier by considering classification based on Markov processes. We obtain the lower bounds on the Bayes error in terms of thermodynamic costs such as entropy production and dynamical activity. Our results show that when entropy production or dynamical activity vanishes, the Bayes error reaches $1/2$, equivalent to random guessing, while greater thermodynamic costs enable lower error. This establishes a fundamental trade-off between error and cost in information processing by thermodynamic systems. Because the Bayes error provides the lowest achievable error among all possible classifiers, the classification error cannot fall below the obtained bounds given the entropy production or dynamical activity. We also discuss the quantum generalization and show that the Bayes error of the quantum classifier is bounded from below by the variance of the Hamiltonian.

Ultracold neutral atoms in an optical lattice and an optical tweezer array offer highly-controllable quantum many-body systems, utilized for various quantum science and technology such as quantum computing, quantum metrology, and quantum simulation. By combining high-fidelity imaging of individual atoms, one can further enhance the capability of such experimental platforms as quantum gas microscopes, tweezer clocks, and tweezer-array-based quantum computers. In this work, we propose a minimally destructive single-atom imaging by deterministic coherent excitation of atoms with alternately applied pi-pulses from counter-propagating directions, mitigating the fundamental heating effect associated with the stochastic absorption process. Using ytterbium-174 atoms trapped in an optical tweezer array, we experimentally demonstrate fast and low-loss single-atom imaging with a discrimination fidelity of 99.89(5) % and a survival probability of 98.80(44) % in 17.6 microseconds. Importantly, our scheme exhibits the lower heating rate, about half of that of the former scheme utilizing the incoherent excitation. This fast and minimally destructive imaging scheme is beneficial for relaxing the requirement on the trap depth, thereby enabling scalable atom imaging across a wide range of quantum science platforms.

Fractional polynomials (FP) are a standard tool for modelling nonlinear dose-response and covariate effects, implemented in the widely used mfp package. The conventional FP fit estimates its coefficients by ordinary least squares (OLS-FP), which is statistically inefficient when the regression errors are skewed or heavy-tailed, a common situation for survival times, concentrations and biomarkers. We present a drop-in replacement that keeps the identical FP model and design but estimates the coefficients with a moment-based score tuned to the residual skewness and kurtosis, giving a closed-form efficiency factor g2 = 1 - gamma3^2/(2+gamma4) relative to OLS-FP. Across skewed error laws the method reduces slope-coefficient variance by 10-20% for mildly skewed errors and up to roughly 60% for heavy-tailed log-normal errors, at realistic sample sizes, while keeping confidence-interval coverage close to nominal, and it reverts exactly to OLS-FP under symmetry, so it is never harmful when no gain is available. On the German Breast Cancer Study Group cohort it narrows the tumour-size confidence interval by 26% (bootstrap variance ratio 0.53 against the predicted 0.56), and a primary-biliary-cirrhosis cohort reproduces the gain. The estimator is closed-form, runs in milliseconds, and is released as a reproducible R package (pmm_fp in EstemPMM) with a one-command replication bundle; its core variance identity is machine-checked in Lean 4.

Living collectives and artificial swarms frequently employ a division of labor, wherein individuals take on different tasks or perform different amounts of work. However, the mechanisms used by collectives to divide labor remain poorly understood. Here, we study how workload inequality arises in collectives by monitoring excavation in Solenopsis invicta fire ants, whose coordination in constrained environments makes them an attractive system for studying division of labor. We vary group size (between 2 and 25 ants) and track digging activity to create Lorenz curves and corresponding Gini coefficients, which represent relative workload inequality. We find that that workload becomes more unequal as group size increases: the number of "active" ants scales with the square root of the group size. We implement a cellular automata (CA) model in which agents regulate their activity based on local crowding in the tunnel. The CA reproduces experimental Gini coefficients over a wide range of parameters and group sizes, indicating that local decisions emergently account for the scaling of workload inequality. An analytic rate equation model recovers the square root scaling with the assumption that individuals exit the tunnel at a rate which scales quadratically with the group size. Power law scalings in workload distribution have been observed in other systems, including social and natural sciences; however, these laws are primarily observational. Here, we provide a mechanistic explanation for the emergent workload scaling patterns in constrained biological collectives, offering insight into organization in both natural and future task capable engineered collectives and swarms.

This study proposes a radar-centric integrated sensing and communication (ISAC) system utilizing a two-layer modulation scheme for vehicular networks. Frequency-modulated continuous wave (FMCW) chirps are jointly modulated via phase modulation (PM) and index modulation (IM) to transmit data while maintaining sensing as the primary function. To support this, a novel radar signal processing technique is developed to mitigate the impacts of IM and PM on sensing accuracy, alongside a communication receiver architecture designed to successfully demodulate IM and PM data within FMCW chirps. System performance is evaluated through simulations in the 2.4 GHz and 24 GHz bands under Doppler effects, achieving communication throughputs of 25 Mbps and 50 Mbps, respectively. Furthermore, a proof-of-concept hardware implementation is realized, and experimental measurements via a loopback cable are performed to verify the feasibility of the architecture. Finally, it evaluates the fundamental trade-off between communication throughput, sensing accuracy, and out-of-band emission, demonstrating the system's flexibility to dynamically adjust waveform parameters to meet varying operational requirements.

This study proposes a novel radar-centric signaling design and architecture for secure integrated sensing and communication (ISAC) systems. The proposed framework is designed to provide robust physical layer security for data transmission while simultaneously enhancing sensing privacy. It employs index modulation and phase coding over frequency-modulated continuous-wave radar (FMCW) chirps, where index modulation (IM) provides an outer layer of data security, and we explicitly design the phase coding (PC) to perturb the resulting signal's ambiguity function (AF) to enhance sensing privacy. This design reduces the risk of unauthorized surveillance by rendering target velocity estimation practically infeasible for unauthorized passive sensing hardware (i.e., a sensing eavesdropper, S-Eve) and significantly impairing its range estimation capabilities. Furthermore, this study also presents the transmitter and receiver architectures required for effective modulation and demodulation of the proposed ISAC signaling and for performing sensing at the legitimate sensing hardware. Simulation results show that the proposed approach achieves high data throughput while enhancing communication security and sensing privacy.

We present a Fourier--Galerkin asymptotic framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we apply a Fourier--Galerkin discretization to derive an explicit finite-dimensional effective matrix whose kernel characterizes the resonant frequencies. In the subwavelength regime, we obtain asymptotic expansions of this matrix in terms of $ω$ and the material contrast, identifying the leading-order operators and their kernel structure. This reduction transforms the resonance problem into a low-dimensional nonlinear eigenvalue problem, avoiding large-scale discretizations and global root-search procedures. The entries of the effective matrix are explicitly computable and admit fast evaluation using FFT-based quadrature. The resulting approach provides an efficient and robust computational framework for resonances in general smooth geometries.

We report the discovery of tidal disruption event (TDE) WFST250820mmsw/AT2025wet by the 2.5-meter Wide Field Survey Telescope (WFST). It exhibits a blue nuclear flare throughout the observed evolution with a g-band peak magnitude ~22, which is about 3 magnitudes brighter than its host galaxy. A Keck/LRIS spectrum taken near the optical peak reveals a featureless blue continuum, with no discernible emission lines. However, its redshift can be accurately determined to be 1.037 by its host galaxy absorption lines. Blackbody fits to the multiband spectral energy distribution (SED) of AT2025wet yield a constant temperature of ~19,000K and a peak luminosity of (8.27 +0.92 -0.71)*10^44 erg s^-1 while actually the SED likely peaks at a much shorter wavelength than a 19,000K blackbody. The SED modeling of the host galaxy implies a stellar mass of ~10^11.2 M_odot and an estimated central black hole mass of ~10^8 M_odot, with no evidence of significant active galactic nucleus activity prior to the flare. All of these observations are well consistent with a featureless TDE scenario, making it the highest-redshift non-jetted TDE known to date. TDEs at such high redshift provide us a unique opportunity to explore the intrinsic SEDs of TDEs, particularly to test whether they peak in the extreme-UV regime, thereby addressing the missing energy puzzle and the origin of optical emission in TDEs. Ongoing surveys represented by WFST and the Legacy Survey of Space and Time (LSST) are expected to discover an increasing number of TDEs at higher redshifts, which will extend our census of SMBHs across redshift space and help unravel the mysteries of optical TDEs through direct probes of their UV emission.

We explore the concept of antiflatness to characterize the structural fluctuations within the entanglement spectrum of a quantum state (i.e., the spectrum of its reduced density operator). As a measure of the interplay between entanglement and magic, two fundamental quantum resources, antiflatness provides second-order information about quantum correlations that standard average measures fail to capture. Recognizing that standard majorization theory fundamentally orders states by purity and is structurally blind to spectral fluctuations, we introduce a novel partial ordering known as antiflat majorization, based on the Rényi entropy spread. We define Flatness-Preserving Operations (FPOs), establishing new necessary conditions for state convertibility. Furthermore, we unify different measures of antiflatness-such as Capacity of Entanglement, Linear Rényi spread, and Logarithmic antiflatness-using the frameworks of escort distributions and Bregman divergences. We prove that the Capacity of Entanglement can be expressed as a second derivative of the Kullback-Leibler divergence along the escort trajectory, connecting it with the Quantum Fisher Information. Finally, we demonstrate that absolute maximal antiflatness is not achieved by a single universal state, but rather by a continuous Pareto frontier of extremal states with jump spectra, and we analyze the typicality of these spectral fluctuations using Haar, Bures-Hall and t-doped Clifford random state ensembles.

Let $s(n)$ denote the number of ones in the binary expansion of a natural number $n\in\mathbb{N}$. For any $t\in\mathbb{N}$ and $d\in\mathbb{Z}$, let $μ_t(d)$ denote the asymptotic density of the set of those natural numbers $n$ for which $s(n+t)-s(n)=d$. The $μ_t$ are properly defined probability measures on $\Z$, and the Cusick conjecture states that $μ_t(\mathbb{N})>\frac{1}{2}$ for any $t\in\mathbb{N}$. We investigate the properties of the family $\{μ_t\}_{t\in\N}$ by reindexing the odd integers via a suitable partial order. This construction leads to a nonautonomous dynamics on pairs of probability measures on $\Z$, which represents the process of growing a tree. The associated stopped random walk allows a transparent structural description of those measures, including their support, symmetries, variance, and an asymptotic dichotomy between the central limit theorem and the almost sure convergence. Next, we focus on the median-preserving property of this process, and show that the Cusick conjecture is a special case of a more general claim about the asymmetric evolution of the associated binary trees, which we support numerically.

Spin-orbit torque (SOT) enables efficient electrical control of magnetization, offering a pathway towards low-power spintronic devices. Magnetic topological insulators (TIs), with spin-momentum-locked surface states and intrinsic ferromagnetism, provide a unique platform for realizing SOT switching of edge current chirality in quantum anomalous Hall (QAH) insulators. In this work, we employ molecular beam epitaxy to synthesize a series of magnetic TI trilayers with controlled layer thicknesses on heat-treated SrTiO3(111) substrates. Electrical transport measurements reveal that SOT-driven magnetization reversal and the associated switching of edge current chirality are governed by the SrTiO3(111) substrate-induced charging effect, which generates an asymmetric chemical-potential alignment between the top and bottom magnetic TI layers. Furthermore, we demonstrate that the switching polarity and efficiency can be tuned through heterostructure design, gate voltage, and in-plane magnetic field, consistent with SOT symmetry. These findings identify chemical potential asymmetry as the origin of the large SOT switching ratio in magnetic TI trilayers and establish a route for electrical control of edge current chirality in QAH insulators. This work advances the understanding of SOT switching mechanism in magnetic topological materials and paves the way for next-generation, energy-efficient QAH-based logic and memory devices.

Practical quantum key distribution (QKD) systems operate under noise, but security of most protocols have been analyzed under ideal noiseless scenarios. In this work, we investigated security performance of BB84 protocol under effect of collective rotation noise. Using theoretical quantum information frameworks, we analyzed key security parameters including quantum bit error rate (QBER), mutual information and secret key rate (SKR). Security of protocol is studied under various eavesdropping scenarios based on intercept and resend attacks. Our results show that collective rotation noise has a significant impact on the information shared between the two parties. Particularly, we extended prior treatments by suggesting a noise engineering strategy where we identified a non-zero noise range where information accessed by Eve is minimized while corresponding SKR degradation remains relatively small. This analysis provide insights into robustness of BB84 protocol under realistic noisy channels and may contribute towards development of more resilient QKD systems.

We give new upper bounds for the number of nonconstant holomorphic maps depending only on the genus. Our estimates improve previously known bounds. The proof is based on the study of pullbacks of holomorphic differentials, together with techniques from the geometry of numbers and the theory of Jacobian varieties.

When multiple hydraulic fractures propagate simultaneously from a horizontal wellbore, elastic stress-shadow interactions generate complex non-planar three-dimensional geometries whose effect on subsequent reservoir drainage has infrequently been quantified, because the propagation and production solvers have historically been incompatible stand-alone tools. This paper presents HyFrac.fun, a cloud-native platform that bridges this gap by exploiting a structural isomorphism between the two SGBEM--FEM governing operator systems. The platform enables automated zero-conversion handoff of the evolved 3D fracture mesh directly to the steady-state Darcy production solver for realizing a fully integrated lifecycle simulation of multi-stage non-planar hydraulic fractures. The lifecycle analysis reveals a double shadow phenomenon: the mechanical stress shadow that suppresses inner-fracture growth during stimulation mirrors a fluid pressure shadow that reduces the inner fracture's drawout rate at small cluster spacing. Critically, switching to a shear-thinning power-law fracturing fluid leaves the fracture trajectories and production rates almost unchanged, demonstrating that stress-shadow-controlled fracture geometry instead of fluid rheology is the primary determinant of long-term production efficiency at equal injection rates. These physics findings are accessible from integrated fracture propagation and production simulations.

Vertical Take-Off and Landing (VTOL) vehicles are gaining traction in both the delivery drone market and passenger transportation, driving the development of Urban Air Mobility (UAM) systems. UAM seeks to alleviate road congestion in dense urban areas by leveraging urban airspace. To handle UAM traffic, vertiport terminals (vertiminals) play a critical role in supporting VTOL vehicle operations such as take-offs, landings, taxiing, passenger boarding, refueling or charging, and maintenance. Efficient scheduling algorithms are essential to manage these operations and optimize vertiminal throughput while ensuring safety protocols. Unlike fixed-wing aircraft, which rely on runways for take-off and climbing in fixed directions, VTOL vehicles can utilize multiple surface directions for climbing and approach. This flexibility necessitates specialized scheduling methods. We propose a Mixed Integer Linear Program (MILP) formulation to holistically optimize vertiminal operations, including taxiing, climbing (or approach) using multiple directions, and turnaround at gates. The proposed MILP reduces delays by up to 50%. Additionally, we derive equations to compute upper bounds of the throughput capacity of vertiminals, considering its core elements: the TLOF pad system, taxiway system, and gate system. Our results demonstrate that the MILP achieves throughput levels consistent with the theoretical maximum derived from these equations. We also validate our framework through a case study using a well-established vertiminal topology from the literature. Our MILP can be used to find the optimal configuration of vertiminal. This dual approach, MILP and throughput analysis, allows for comprehensive capacity analysis without requiring simulations while enabling efficient scheduling through the MILP formulation.

We derive logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on \RCD\, metric measure spaces, which contains the class of Riemannian manifolds with Ricci curvature bounded below. These estimates are applicable for equations satisfying subcritical index condition,which recover many classical results even on Euclidean spaces. In certain case, these estimates are optimal even on \RCD\,\,spaces with $K<0$. Two direct corollaries of these estimates are Harnack inequality and Liouville theorem. In addition to these estimates, we also establish fundamental relations among the universal boundedness estimate, the logarithmic gradient estimate, and Harnack inequality. Under certain and wild assumptions for the nonlinear term, we prove that these estimates are $κ$-equivalent on \RCDO\,spaces for any $κ>1$.

Asymptotically flat balanced configurations of two spinning black holes with synchronised scalar hair (2sBHs) are possible (arXiv:2305.15467). These are constructed within a generalized Bach-Weyl framework and arise from two spinning boson stars (2sBSs) by placing a horizon at the center of each component. Here, we investigate the effects of quartic scalar self-interactions on this family of solutions, comprising the 2sBSs, the 2sBHs, and an intermediate configuration--single spinning black hole with quadrupolar scalar hair (1sBHs). For 2sBSs, the additional repulsive force introduced by the self-interactions drives a topological transition of the ergoregion, from a single torus to a double torus, in the strong-gravity regime. For 1sBHs, as the self-interaction coupling strength increases, the solutions become "hairier" but their horizons cannot become heavier; moreover, the self-interactions broaden the regime in which an analytical effective model accurately describes these solutions. For 2sBHs, increasing the coupling reshapes the bifurcation structure of the solution sequences and, as in the 1sBH case, repulsive self-interactions cannot make the horizons heavier; horizons carrying a larger mass fraction are obtained only when attractive self-interactions are considered.

Accurate timekeeping relies on feedback that continually steers a local clock toward a higher-grade reference. We evaluate first-order sliding-mode control (SMC) for steering an atomic clock and benchmark it against two standards: linear-quadratic-Gaussian (LQG) control and the bang-bang (BB). All three are tested in a common numerical framework using the standard two-state clock model driven by white and random-walk-frequency noise. To ensure the conclusions are not tied to a single noise realization and a single time period, we repeat the accuracy analysis over 100 independent random seeds for four different time periods, reusing the same seed across controllers within each trial. The time periods considered are one week, one month, one year, and ten years to cover short-, mid-, and long-term analyses of accuracy. Our results show that SMC remains competitive with LQG across the tested timescales and reference-clock qualities. Both SMC and LQG substantially outperform BB over the same time periods. Over the full averaging-time range studied, SMC's stability is almost identical to LQG's, whereas BB shows the characteristic short-term instability. Together, our results indicate that SMC is a promising clock-steering policy that can remain close to LQG in accuracy while avoiding the short-term instability seen in BB.

Yield-stress fluids are ubiquitous and encountered in diverse fields ranging from natural muddy flows to industrial applications such as secondary battery electrode slurries and direct ink writing. Despite the proposal of various constitutive equations, few models have been shown to successfully predict both steady and transient rheological behaviors in yield-stress fluids. In this study, a constitutive equation is hereby proposed, offering a comprehensive description of the rheological characteristics observed in simple yield-stress fluids, excluding thixotropy, such as the Carbopol dispersion. The constitutive equation is derived from a Zener-type viscoelastic solid element combined with an additional linear dashpot connected in parallel, together with a nonlinear viscosity model, a flow rule, an evolution equation for the back stress, and the Kroner-Lee decomposition. This combination satisfies the principle of material frame invariance. The proposed model successfully reproduces the rheological characteristics qualitatively in a manner consistent with experimental observations conducted during start-up shear, creep, and stress relaxation tests. In particular, the present viscoelastic solid-based constitutive equation is shown to accurately predict stress overshoot during start-up shear. Importantly, the overshoot is found to originate from a homogeneous mechanism in which normal stress difference enhances the stress invariant and thereby accelerates the plastic response, rather than from isotropic hardening or spatially heterogeneous microstructural evolution. This study is expected to facilitate a deeper understanding of the intricate dynamics governing the flow of yield-stress fluids.

The challenge presented by computing actions for eccentric orbits in axisymmetric potentials is discussed. In the limit of vanishing angular momentum about the potential's symmetry axis, there is a clean distinction between box and loop orbits. We show that this distinction persists into the regime of non-zero angular momentum. In the case of a Staeckel potential, there is a critical value I_{3crit}(E) of the third integral I_3 below which I_3 does not contribute to the centrifugal barrier. An orbit is of box or loop type according as its value of I_3 is smaller or greater than I_{3crit}. We give algorithms for determining I_{3crit}(E) and the critical action Jzcrit below which orbits in any given potential are boxes. It is hard to compute the actions and especially the frequencies of orbits that have Jz ~ Jzcrit using the Staeckel Fudge. A modification of the Fudge that alleviates the problem is described.

Metal-poor stars are crucially important for understanding the early Galaxy, first stars, and the Universe. In this series of papers, we present a homogeneous non-local thermodynamic equilibrium (NLTE) abundances analysis of 12 elements for 103 very/extremely metal-poor (VMP/EMP) stars with metallicity down to $-4.3$ dex. The sample was selected from the LAMOST survey and observed by the high-resolution spectroscopy of Subaru. In this paper, we present the NLTE abundances and evolution of lithium in these stars. We report different lithium behaviors corresponding to different evolutionary stages and their signatures: 1) The Spite Plateau shows a slightly positive slope, indicating increasing lithium abundance with increasing metallicity. Most significantly, it appears to extend to lower metallicities as previously suggested, calling into question the reality of the so-called 'meltdown' at low metallicity; 2) We confirm a lithium plateau for lower red giant branch (LRGB) stars with A(Li) $= 1.13$ dex in our sample, while lithium abundance drops rapidly to A(Li)$<0.5$ as stars continue to evolve to higher stage. 3) We identify four Li-rich stars in our sample across different evolutionary stages, showing complex and multiple lithium production mechanisms in VMP/EMP stars. These findings suggest that early Galactic lithium enrichment results from a complex interplay between depletion and production processes.

Purpose: Access to electroencephalography (EEG) remains limited across low- and middle-income countries (LMICs) due to cost, infrastructure requirements, and a shortage of trained staff. This study evaluated the feasibility and clinical utility of a smartphone-based EEG system in a real-world setting. Methods: We conducted a multicenter observational study (November 2023 to April 2026) across 29 clinical sites in Kenya. A smartphone-based 27-lead EEG system enabled trained healthcare workers to acquire standardized recordings with remote expert interpretation. Results: 3,036 EEG sessions were performed. Male patients constituted 57.8% of the cohort, with representation across pediatric and adult populations. The most common referral indication was seizures or convulsions (68.5%). Overall, 2,915 (96%) recordings were interpretable, while 121 (4%) were uninterpretable, primarily due to high electrode impedance and insufficient recording duration. Uninterpretable recordings were significantly shorter than interpretable recordings (mean 18.5 vs. 33.8 minutes; median 15.1 vs. 31.6 minutes; p < 0.0001). Mean turnaround time for interpretation was 107 minutes. Among interpretable recordings, 917 (30.2%) were abnormal, including 701 (76.4%) with epileptiform abnormalities, 215 (23.4%) with non-epileptiform findings, and 1 (0.1%) indeterminate finding. Epileptiform abnormalities were highest in children aged 4-9 years (33.1%) and less frequent in adults (14-21%). Non-epileptiform abnormalities were more common in patients aged 60+ years (19.2%) compared to younger age groups (3-9%). Conclusion: Large-scale, point-of-care EEG acquisition by non-specialist operators in a resource-limited setting is feasible. Expansion of smartphone-based EEG systems may improve equitable access to neurological diagnosis and care in LMICs.

We characterize single-mode vacuum squeezing generated by a SNAIL Parametric Amplifier (SPA) operated under conditions representative of practical sensing and qubit-readout experiments. Motivated by prior expectations that Kerr-induced distortion limits squeezing in degenerate parametric amplifiers, we varied external flux and pump power to explore operating points where Kerr nonlinearity is theoretically minimized. We find that for practical applications where the squeezing frequency is fixed, the Kerr was variable by about a factor of two and the achievable squeezing showed no significant dependence on Kerr. Theoretical modeling supports this observation and indicates that baseline Kerr values in state-of-the-art SPAs are already too small to impose a practical limitation. Instead, squeezing was dominated by internal resonator loss and insertion loss in the microwave chain. These results indicate that, in practical SPAs, reducing loss, rather than suppressing Kerr, is the primary route to improved squeezing performance.

The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a network-based approach in which nodes represent communities of interacting agents holding one of two competing opinions, and links represent avenues of migration. Agents adapt to the dominant opinion within a community or migrate toward other communities. Using a master stability function approach, we analytically derive conditions for diffusion-driven pattern formation and identify structural features of the community network that sustain opinion diversity. Our model shows that even under minimal opinion rules, the interaction between local dynamics and community structure generates spatial patterns that allow minority opinions to persist by gaining local dominance.