We prove that the locus of Noether-Lefschetz general polarized K3 surfaces of degree at most 8 defined over the rational numbers is Zariski dense in the moduli space. Previously, this was proved by van Luijk in the quartic case, and it follows from work of Elsenhans and Jahnel in the degree 2 case. Innovations on their methods, and employing Mukai's Hodge isogeny, suffices to handle the degree 8 case. New methods allow us to deal with the case of degree 6.

The existence of a new spin-zero particle with a mass below the electroweak scale is predicted by several theoretical models. Searches for resonant production of photon pairs at the LHC are able to probe these models. We present a search for a narrow resonance produced through gluon fusion that decays into a pair of photons with an invariant mass between 10 and 70 GeV, using a proton-proton collision data set from the CMS experiment. This data set, corresponding to an integrated luminosity of 54.4 fb$^{-1}$, was recorded in 2018 at a center-of-mass energy of 13 TeV using a newly introduced diphoton trigger that enabled exploration of the low-mass diphoton spectrum. No significant excess above the expected background is observed. Upper limits are set on the product of the gluon fusion production cross section and the branching fraction of the diphoton decay of a narrow resonance. An interpretation of these limits within an effective field theory framework for axion-like particles is also provided.

Emerging evidence suggests that physical systems operating as Maxwell demons, in which some subsystem of a larger system extracts heat energy from its environment in an apparent local violation of the second law, are commonplace throughout biology. Should these findings surprise us, or is Maxwell demon behavior inevitable in sufficiently large complex systems? In this Letter we pose the question of how likely it is that a random stochastic system with many degrees of freedom will operate as a Maxwell demon, considering null models for both continuous and discrete random dynamics. Our results show the probability of a finding a demon decreases at least exponentially, and in some cases double-exponentially, with the number of degrees of freedom, ultimately suggesting that large complex demons can only arise through a process of selection.

Estimating spatial extremes from sparse observational networks produces uncertain return level maps, but dense output from physics-based simulation models is often available as a complementary data source. We develop a two-stage frequentist frame-work for fusing observations and simulations. In Stage 1, generalized extreme value (GEV) distributions are fitted independently at each site, with a nonstationary location parameter where appropriate to accommodate observed trends. In Stage 2, the parameter estimates from all sources are modeled jointly as a high-dimensional spatial process through a linear model of coregionalization (LMC). Cross-source correlations, estimated from spatially interspersed networks without co-located sites, provide the mechanism for information transfer; an analytic gradient for the resulting likelihood keeps estimation computationally practical. We apply the framework to U.S. coastal sea levels over 1979-2021, fusing 29 NOAA tide gauge records with 100 ADCIRC hydrodynamic simulation sites. Leave-one-out cross-validation shows a 35% reduction in 100-year return level RMSE relative to a gauge-only model. Geographic block cross-validation confirms that fusion benefits persist under spatial extrapolation. The approach is implemented in the R package evfuse.

We study the stochastic heat flow with constant initial data and analyze its spatial average on the scale of $\varepsilon\ll1$. We prove that the logarithm of the averaged process satisfies a pointwise central limit theorem: After being centered by $-\tfrac{1}{2}\log\log \varepsilon^{-1}$ and scaled down by $\sqrt{\log\log \varepsilon^{-1}}$, it converges in distribution to a standard Gaussian.

The prospect of identifying axion signals due to axion-photon coupling induced changes to the polarization has now become a reality in view of near-horizon polarimetric observations by the Event Horizon Telescope (EHT). Axion-like particles (ALPs), motivated as dark matter candidates by the strong CP problem, induce frequency-independent birefringence in linearly polarized radiation, producing observable rotations of the electric vector position angle. While previous studies have focused exclusively on axion signatures in near-horizon accretion disk emission, the relativistic jet of M87 -- extending from 10 gravitational radii to kiloparsec scales -- remains unexplored as an axion probe despite offering extended path lengths through the putative dark matter distribution. In this study, we investigate the effects of an axion cloud around the jet in M87 on the Stokes maps of relativistic jets using a stationary, axisymmetric, self-similar model for the jet and a coherent, homogeneous soliton core in M87's galactic center for the axion background. At 230 GHz, for representative couplings in range $g_{a γ} \sim 5 \times 10^{-15} - 5 \times 10^{-14} GeV^{-1}$, we find that axion masses in the $10^{-21} eV $ range produce degree-level to multi-degree EVPA rotations, in some cases exceeding typical EHT measurement uncertainties, whereas masses in the $10^{-22} eV$ range yield predominantly sub-degree rotations. We identify a suite of morphological diagnostics that together constitute a framework for distinguishing axion-induced birefringence from plasma Faraday rotation in resolved jet polarimetry.

We study electron transport in a strained graphene sheet subjected to a sequence of $N$ electrostatic and magnetic barriers. Employing a modified and improved transfer-matrix framework, we examine how the transmission and reflection coefficients evolve with variations in uniaxial strain and in the number of barriers. The interplay of mechanical deformation and external magnetic fields is found to generate an anomalous Klein tunnelling, allowing the conductance to be effectively modulated through strain and barrier configurations. These findings highlight the role of strain engineering and magnetic field modulation as powerful tools for tailoring charge transport in two-dimensional materials. More broadly, they underscore how mechanical and electromagnetic control can be used to design next-generation solid-state devices with tunable electronic properties.

Spatial relationships in multi-species data can indicate and affect system outcomes and behaviors, ranging from disease progression in cancer to coral reef resilience in ecology; therefore, quantifying these relationships is an important problem across scientific disciplines. Persistent homology (PH), a key mathematical and computational tool in topological data analysis (TDA), provides a multiscale description of the shape of data. While it effectively describes spatial organization of species, such as cellular patterns in pathology, it cannot detect the shape relations between different types of species. Traditionally, PH analyzes single-species data, which limits the spatial analysis of interactions between different species. Leveraging recent developments in TDA and computational geometry, we introduce a scalable approach to quantify higher-order interactions in multi-species data. The framework can distinguish the presence of shape features or patterns in the data that are (i) common to multiple species of points, (ii) present in some species but disappear in the presence of other species, (iii) only visible when multiple species are considered together, and (iv) formed by some species and remain visible in the presence of others. We demonstrate our approach on two example applications. We identify (1) different behavioral regimes in a synthetic tumor micro-environment model, and (2) interspecies spatial interactions that are most significantly altered in colorectal cancer tissue samples during disease progression.

Learning diagnosis is a critical task that monitors students' cognitive state during educational activities, with the goal of enhancing learning outcomes. With advancements in language models (LMs), many AI-driven educational studies have shifted towards conversational learning scenarios, where students engage in multi-turn interactive dialogues with tutors. However, conversational learning diagnosis remains underdeveloped, and most existing techniques acquire students' cognitive state through intuitive instructional prompts on LMs to analyze the dialogue text. This direct prompting approach lacks a solid psychological foundation and fails to ensure the reliability of the generated analytical text. In this study, we introduce ParLD, a preview-analyze-reason framework for conversational learning diagnosis, which leverages multi-agent collaboration to diagnose students' cognitive state over multiple dialogue turns. Specifically, ParLD comprises three main components: (1) Behavior Previewer, which generates a student behavior schema based on previous states and learning content; (2) State Analyzer, which diagnoses the tutor-student dialogue and behavior schema to update the cognitive state; and (3) Performance Reasoner, which predicts the student's future responses and provides verifiable feedback to support ParLD's self-reflection with the Chain Reflector. They operate sequentially and iteratively during each interaction turn to diagnose the student's cognitive state. We conduct experiments to evaluate both performance prediction and tutoring support, emphasizing the effectiveness of ParLD in providing reliable and insightful learning diagnosis.

Inspired by recent experiments of cells accumulating on anisotropic substrates, we study a two-dimensional, compressible, isotropic, active fluid in the presence of anisotropic friction. We find that regions of anisotropic friction that are patterned as positive topological defects may drive accumulation of an active fluid into a clump, but the robustness of this behavior depends on the initial configuration. If the initial azimuthal symmetry is sufficiently broken, we find that patterning asymmetry can instead lead to circular motion of accumulated clumps. We develop an approximate analytical model to qualitatively explain the motion. Finally, we use our simplified model to design a substrate pattern that creates directed motion of accumulated clusters along a given path.

We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from point and curve sources using piecewise-quadratic elements, exactly reproducing flat distances regardless of mesh quality while improving accuracy over existing approaches on curved meshes. The formulation naturally supports sources placed anywhere on the mesh, not just at vertices.

Multiparty quantum key agreement (MQKA) enables $n \geq 3$ mutually distrustful users to establish a shared secret key through collaborative quantum protocols. In this paper, we provide a comprehensive review where we argue that MQKA is best understood as a design space organized along three orthogonal but tightly coupled axes: (1) network architecture, which determines how quantum states flow between participants; (2) quantum resources, which encode the physical degrees of freedom used for implementation; and (3) security model, which defines trust assumptions about devices and infrastructure. Rather than treating MQKA as a linear sequence of isolated protocols, we develop this three-axis perspective to reveal recurrent patterns, sharp trade-offs, and unexplored design spaces. We classify MQKA protocols into structural families, map them to underlying quantum resources, and analyze how different security models shape fairness and collusion resistance. We further identify open challenges in composable security frameworks, network native integration, device-independent implementations, and propose a research roadmap toward hybrid-resource, bosonic-code-encoded, and fairness-aware MQKA suitable for the future quantum internet deployments in the post-NISQ era.

Machine learning interatomic potentials (MLIPs) evaluate potential energy surfaces orders of magnitude faster while maintaining accuracy comparable to first-principles calculations, and universal MLIPs that cover most of the periodic table are becoming increasingly commonplace. However, existing large-scale datasets have limited or no coverage of heavy elements such as minor actinides crucial in the nuclear field, and universal MLIPs are typically limited to 89 elements. Here, we constructed a heavy element dataset HE26 containing minor actinides, based on experimental and computational literature data. By integrating this with existing molecular and crystal datasets, we developed an open-source universal MLIP covering 97 elements, the broadest elemental coverage to date. The resulting model showed strong performance on the inorganic MPtrj and organic OFF23 test sets and promising accuracy on HE26. The dataset and model open a pathway toward the development of energy resources and the design of novel materials, such as actinide-based high-entropy ceramics, in the nuclear field.

A recent notion of geodesic flows which comes out of noncommutative geometry but which is also novel in the classical case is studied in detail for a Schwarzschild spacetime. In this framework, the geodesic velocity field is an independent concept which then defines the flow of a density $ρ$ on spacetime or possibly that of an amplitude wave function $ψ$ with $ρ= |ψ|^2$. The proper time flow parameter $s$ is generated collectively by the flow of matter. We show carefully how the $ρ$ evolution can be justified as modelling a large number of geodesics interpolated as a local density. Using Kruskal-Szekeres coordinates, we show that there are no issues crossing the horizon. A novel feature is that whereas two colliding Gaussian bumps in density $ρ$ merge into a single bump, two colliding wave function $ψ$ bumps of opposite phase merge into a dipole with a different density $|ψ|^2$ profile, providing a potential test of our wave-function hypothesis. We also revisit the Klein-Gordon flow or pseudo-quantum mechanics around a black-hole and find that previously found black-hole atom states and modes generated at the horizon when an area of disturbance approaches it are also present inside the black-hole in a reflected fashion. We argue that the behaviour of the horizon modes across the horizon as well as discretisation of the atomic spectrum depend on quantum gravity corrections at the horizon.

The recent discovery of unconventional momentum-dependent magnetic orders has expanded the landscape of magnetism beyond conventional ferromagnetism and antiferromagnetism. Among them, $p$-wave magnets ($p$WMs) represent a novel class of odd-parity, non-collinear compensated magnetic order that generates spin-split electronic bands. In this work, our theoretical investigation establishes $p$WMs as a versatile platform for realizing intriguing superconducting phases including topological superconductivity (TSC), Bogoliubov Fermi surfaces (BFSs), and superconducting diode effect (SDE), within a unified microscopic framework. Employing a minimal model incorporating $p$-wave magnetic order, exchange coupling, and Zeeman fields, we perform a self-consistent mean-field analysis and uncover a rich phase diagram featuring unconventional finite-momentum Fulde-Ferrell (FF) and Larkin-Ovchinnikov (LO) superconducting phases. Remarkably, we also show that $p$WMs can undergo a transition to a TSC phase anchoring Majorana flat edge modes, a hallmark of two-dimensional TSCs, even without Rashba spin-orbit coupling and Zeeman field. Upon applying a Zeeman field, gapless FF and LO phases emerge with BFSs characterized by the appearance of finite zero-energy quasiparticle density of states. Furthermore, we demonstrate that SDE arises naturally in the asymmetric FF phase. Our analysis manifests that $p$WMs serve as a unique and novel platform to host TSC phase, gapless superconducting states, and non-reciprocal transport phenomena.

Detector dead time is typically treated as a fixed parameter in quantum key distribution (QKD) security analyses. In practice, however, the effective recovery time of single-photon avalanche photodiodes (SPADs) depends on the incident count rate. In this work, we demonstrate that this count-rate-dependent recovery nonlinearity constitutes a distinct attack primitive. We experimentally characterize the dead time shift of a free-running SPAD under controlled broadband loading and observe a substantial increase in effective recovery time as the detected rate rises into the high photon count regime. We show that recovery-induced availability reduction can be modeled as an adversarial erasure channel and derive a conservative bound on the signal detection probability under loading. Unlike previously studied detector-control or efficiency mismatch attacks, the proposed mechanism does not rely on deterministic blinding or timing discrimination. Instead, count-rate-dependent recovery asymmetry induces basis-dependent suppression of detection probabilities ($p_\perp<p_\parallel$), converting mismatch-induced errors into loss. Particularly, we show in active-basis BBM92 systems, this effect reduces the observed quantum bit error rate (QBER) below the abort threshold while increasing erasure probability. Using experimentally measured detector recovery data, we quantify the parameter regime in which such stealth suppression is achievable. These results establish count-rate-dependent detector recovery as a security-relevant vulnerability and show that countermeasures designed for timing-based efficiency mismatch do not directly address recovery-induced erasure (RIE) attack. Our findings underscore the need to incorporate detector recovery dynamics explicitly into practical QKD security models.

We introduce a tropical spherical measure on $\mathbb{R}^n$ that is based on the tropical metric and is an analogue of spherical Hausdorff measure. This measure is translation invariant but, unlike Lebesgue measure, is not invariant under rotations or reflections. It agrees with Lebesgue measure on $n$-dimensional (but not on $k$-dimensional, $k<n$) measurable subsets of $\mathbb{R}^n$, and on rectifiable curves it recovers tropical length. In dimension $2$ we prove a sharp tropical isoperimetric inequality, with equality precisely for tropical disks, and deduce a tropical honeycomb theorem. We also introduce a tropical analogue of Minkowski content and show that the tropical ball is the associated Wulff shape. This yields an anisotropic type of the tropical isoperimetric problem and consequently a tropical honeycomb theorem in $\mathbb{R}^n$. Finally, we describe the tropical dual norm and dual ball, compare the tropical spherical and Minkowski surface measures, and prove that they agree in the plane and on polytopes in $\mathbb{R}^n$ whose facets are parallel to facets of the tropical ball or its dual.

The Total Portfolio Approach and Strategic Asset Allocation are widely viewed as competing frameworks for institutional portfolio management. We argue they differ in a single governance parameter: the tracking error constraint. Using U.S. equity and bond data from 2000 to 2026, with portfolio simulations spanning 2004 to 2026, we show that Sharpe ratios are statistically indistinguishable across the full constraint spectrum while the volatility of realized tracking error varies approximately 12-fold. The cost of constraints spikes during crises, when forward returns are richest and governance pressure to de-risk is strongest. Dynamic tracking error subsumes both approaches and provides boards with a more productive framework for investment governance.

We present 225 and 350 GHz imaging of the iconic T Tauri system using the Atacama Large Millimeter submillimeter Array (ALMA). T Tauri is a hierarchical triple system, and the close binary T Tau Sa/Sb underwent periastron passage in March 2023. The ALMA images were obtained in epochs spanning November 2019 through June 2023, and therefore covered the time frame of the recent periastron passage. We clearly resolve the Sa-Sb binary in two epochs of high-resolution measurements with ALMA. We find increases in millimeter flux from heating of the Sa disk and the wider distribution of dust in the environment of the binary. This heating is likely in response to increased stellar accretion activity triggered by orbital motion during the dynamic periastron passage of T Tau Sb around Sa. Resolved, extended millimeter emission is also found to change morphology and increase in flux in the immediate environment of the Sa-Sb binary after periastron passage. This may suggest an increase in nonthermal emission from magnetic interaction, gravitational disruption of the circumstellar disks as the stars passed through periastron, or both of these phenomena. We also detected structures in the compact (24 au radius), thermal dust disk around T Tau N. In particular, we identify a crescent-shaped emission excess just outside a shallow gap at 12 au radius that appears to move at Keplerian speed. Future measurement of dust spectral indices can clarify the origin of increased and variable millimeter emission in the environment of the T Tau S binary.

In standard multi-field models, tachyonic isocurvature perturbations generally indicate the presence of an instability. We revisit the stability of some known counterexamples and show that, in a certain class of models that we call ultra slow-turn, an exponentially decreasing turn rate can shut off this potential instability. We argue that the stability of a given model can be correctly inferred by the total entropy perturbation, even if the effective mass squared of the isocurvature perturbation is negative. Several recent supergravity- or string-inspired models such as fibre inflation, SL(2,$\mathbb{Z}$) attractors and modular inflation fall into the ultra slow-turn class.

We point out a basic dichotomy between the shadowing and Lipschitz shadowing properties for one-sided shift spaces in two infinite-alphabet frameworks: the classical product-topology model $X\subseteq A^{\mathbb{N}}$ and the compact Ott--Tomforde--Willis (OTW) model obtained by adjoining finite words. In the product-topology setting, for the natural class of prefix ultrametrics, shadowing and Lipschitz shadowing coincide. However, since $A^{\mathbb{N}}$ is non-compact when $A$ is countably infinite, it remains unclear whether Lipschitz shadowing is stable under arbitrary uniformly equivalent changes of compatible metric in the product-topology model. In contrast, for OTW shift spaces the topology admits a canonical family of compatible ultrametrics indexed by enumerations of finite words, and these metrics are all uniformly equivalent. Using the Deaconu--Renault viewpoint and known shadowing results for local homeomorphisms on zero-dimensional compact spaces, we show that the OTW full shift has the shadowing property for every OTW metric. Nevertheless, Lipschitz shadowing can depend on the chosen OTW metric even within this fixed uniform equivalence class: we construct two uniformly equivalent OTW ultrametrics on the full shift for which Lipschitz shadowing holds in one case and fails in the other. Thus the OTW compactification provides a compact infinite-alphabet setting where the metric dependence of Lipschitz shadowing can be resolved explicitly, in sharp contrast with what is currently known for the product-topology model.

This paper investigates early legislative deliberations over Artificial Intelligence in the United States through a thematic analysis of the 2023-2024 Oversight of AI hearings held by the Senate Judiciary Committee's subcommittee on Privacy, Technology, and the Law. I focus on these hearings as a site where participants draw from, and renegotiate, accustomed ways of thinking about technology and society. First, I examine how participants, who overwhelmingly represent the technology industry, work to create narratives for understanding the past, present, and future impacts of AI. Second, I examine how these narratives are invoked to argue for particular forms of AI governance, while casting alternative approaches as everything from infeasible to anti-American. By tracing industry influence over dominant understandings of the impacts of AI and the proper role of government, I examine the arrangements of power enacted and upheld through these hearings. In all, I ask: what role to shared (mis)understandings of AI play in early attempts at governing this technology?

We study quasinormal modes of scalar, electromagnetic, and Dirac perturbations of four-dimensional regular black holes arising in non-polynomial quasi-topological gravity. Starting from a more general class of metric functions constructed within the same framework, from which two representative cases are selected for detailed analysis, we examine their spectral properties. While the fundamental mode changes smoothly with the regularization parameter, higher overtones display a markedly enhanced sensitivity to near-horizon modifications, leading to the characteristic outburst of overtones. Remarkably, pushing the WKB approximation to sufficiently high orders with Pade resummation already allows one to detect the onset of this effect. Time-domain analysis and the Leaver method confirm that the relative error of the higher-order WKB approach is much smaller than the observed effect. Our results indicate that overtone dynamics provides a sensitive probe of geometrically regular black holes and that high-order WKB methods remain capable of capturing nontrivial spectral features beyond the fundamental mode.

Semiconductor quantum dots host a rich manifold of excitonic complexes, including neutral excitons that emit anti-bunched single photons and charged exciton complexes capable of producing super-bunched photons via cascade emission. Accessing both emission regimes from a single emitter would open routes to novel quantum protocols, including advanced quantum imaging. In practice, however, emission from charged exciton complexes is intrinsically weak, often orders of magnitude dimmer than neutral excitons, placing simultaneous dual-mode operation out of reach. Here, we overcome this limitation by embedding the quantum dot in a dielectric Mie-resonant metasurface that provides order-of-magnitude photoluminescence enhancement across both neutral and charged exciton transitions of a single GaAs quantum dot. Under identical non-resonant pumping conditions, the emission from the neutral exciton yields anti-bunched emission ($g^{(2)}(0) < 0.5$) and the emission from positively charged exciton complexes shows super-bunched emission ($g^{(2)}(0) > 3.5$) with comparable count rates (~12 kHz). Crucially, super-bunching emerges only when charged exciton emission spectrally overlaps with the Mie resonances and vanishes in un-patterned slabs, demonstrating that photonic engineering, is essential for accessing these weak quantum light states. These results demonstrate a scalable, position-tolerant platform for harnessing the full excitonic structure of solid-state emitters.

Quantum non-Gaussian states and operations serve as fundamental resources for universal quantum computation, error correction, and high-precision metrology, extending beyond the Gaussian limits. While the stellar rank provides a rigorous hierarchical measure of non-Gaussianity, it remains challenging to determine experimentally. Conversely, witnesses of non-Gaussian features, based on the expectation values and variances of measurable observables, offer an accessible method for certifying non-Gaussian behavior but lack a direct connection to stellar rank. In this work, we establish a quantitative connection between these witnesses and stellar rank, demonstrating that the former can provide certifiable lower bounds on stellar rank. We introduce normalized expectation value and variance-based quantifiers and show that these witnesses form a consistent hierarchy of thresholds corresponding to stellar rank. Our results bridge the gap between abstract hierarchical measures and experimentally accessible quantifiers, enabling scalable certification of non-Gaussian states.

A framework of continuous-aperture array (CAPA)-based integrated sensing and communications (ISAC) under a fading communication channel is proposed. A continuous operator-based signal model is developed, and the statistics of the communication channel gain are characterized via Landau's eigenvalue theorem. On this basis, the performance of the CAPA-based ISAC system is analyzed by considering three continuous beamforming designs: i) the sensing-centric (S-C) design that optimizes sensing performance, ii) the communication-centric (C-C) design that optimizes communication performance, and iii) the Pareto-optimal design that balances the sensing-communication trade-off. For the S-C and C-C design, closed-form expressions for the sensing rate (SR), ergodic communication rate (CR), and outage probability are derived, and high-signal-to-noise ratio asymptotic analysis is conducted to obtain the multiplexing and diversity gains. For the Pareto-optimal design, the Pareto-optimal beamformer achieving the Pareto boundary is derived, and the achievable SR-CR region is characterized. Numerical results demonstrate that the proposed CAPA-ISAC scheme outperforms both conventional spatially discrete arrays-based ISAC and CAPA-based frequency-division sensing and communications.

We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric polynomials in logarithmic mass ratios, normalized by the external momentum squared, with coefficients determined by analytic series expansions. For the equal-mass case, we establish a dimension-raising relation expressing the $L$ loop sunset integrals in $D+2$ as the one in $D$ dimensions acted on a differential operator of order $L-1$. These representations are free of complicated transcendental functions, making them well-suited to both formal analysis and high-precision numerical evaluation. The two-dimensional results serve as boundary conditions for dimension-shifting relations, enabling systematic reconstruction of four-dimensional sunset integrals via analytic continuation to $D = 4 - 2ε$.

We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms the receiver's share of a bipartite state that can be used for entanglement-assisted communications, both in the noiseless and noisy ebit error models. In the case of degenerate codes, we show that the receiver's share of the bipartite state can sometimes be compressed, at the cost of potentially reduced error-correction ability in the noisy ebit error model. We also give examples of permutation-invariant and XP-stabilizer entanglement-assisted codes, the first outside of the stabilizer and codeword-stabilized frameworks.

Mesozooplankton aggregations undergoing vertical migrations in the upper ocean have been hypothesized to have an important role in the redistribution of carbon, nutrients, and oxygen via biogenic hydrodynamic transport (BHT). While laboratory studies have demonstrated how swarm-induced hydrodynamic instabilities can drive large-scale transport in strongly stratified environments, measurements are usually performed with model organisms that differ in morphology and swimming mode from ecologically relevant marine species. To bridge this gap, we conducted experiments with copepods and analyzed upward and downward trajectories to identify differences in flow fields, force distribution, and BHT for these two scenarios. Using two-dimensional bright-field Particle Image Velocimetry (PIV), we quantified the near-body velocity field and found that the average downward swimming speed significantly exceeds the average upward swimming speed, with the flow fields exhibiting direction-dependent characteristics. We incorporated these findings into a continuum squirmer model to estimate the swimmer-induced drift volume and mixing efficiency, focusing on the effects of the reduced gravity of the swimmers and the density stratification of the surrounding fluid. Our simulations reveal that both the excess weight of the organisms and the fluid stratification strongly constrain the net BHT. This study provides a critical step toward integrating lab-based models of marine mesozooplankton with remote sensing data to incorporate vertical migrations into global ocean models with realistic biogeochemistry and assess their ecological significance in actively sustaining local ecosystems.

Let $d\in\mathbb{N}$ and $φ\colon(0,1)\to[0,d]$. We prove there exists a set $F\subset\mathbb{R}^d$ whose lower spectrum $\operatorname{dim}^θ_{\mathrm{L}} F$ satisfies $(1-θ)\operatorname{dim}^θ_{\mathrm{L}} F = φ(θ)$ for all $θ\in(0,1)$ if and only if for all $λ,θ\in(0,1)$, \begin{equation*} φ(θ) \leq φ(λθ) - θφ(λ) \leq (1-θ) d. \end{equation*} We also obtain a similar classification result for $\underline{\operatorname{dim}}^θ_{\mathrm{L}} F$. In contrast to the case for Assouad spectra, it is insufficient to consider homogeneous (or uniform) sets. Instead, we follow the approach introduced by Orgoványi--Rutar in arXiv:2510.07013 and proceed via a more general classification result for appropriate two-scale branching functions.