We develop an abstract KAM theorem for systems of infinitely many interacting particles with decaying masses and all-to-all interactions. Using this framework, we construct full-dimensional KAM tori for infinite-dimensional mechanical systems exhibiting long range interactions.

Quantum chemistry calculations are often performed using atom-centered basis sets which are chosen to balance accuracy and cost. While they are systematically improvable, the total energy converges slowly with basis set size towards the complete basis set (CBS) limit. Common extrapolation methods require several intermediate-quality calculations to afford an estimate of the CBS energy. We propose combining a pairwise interaction model with a minimal complementary auxiliary basis set (CABS) baseline to estimate the CBS energy from a single quantum chemistry calculation in a minimal basis set via Kernel-Ridge-Regression (KRR), which is more efficient than both direct and $Δ$-machine learning. We show that KRR on standard molecular representations can be improved by approximating atom-wise local kernels using Chebyshev polynomials which allows us to train KRR models efficiently on moderate compute resources, further enabling a data-driven approach towards CBS combining physical baselines capturing leading order effects with data-efficient machine learning models.

For linear periodic finite-dimensional systems, it is well-known that, first, exponential stability is equivalent to the existence of a unique periodic positive definite solution to the Lyapunov equation, and second, the Lyapunov equation admits a unique periodic solution, if and only if the monodromy matrix has no reciprocal eigenvalues. In the present paper, we generalize these results to the case of periodic evolution families on a Hilbert space, with application to the stability theory of linear periodic systems with constant delays. More precisely, we first link the existence and uniqueness of a quadratic periodic Lyapunov functional with the existence and uniqueness of the solution to a discrete operator Lyapunov equation with the monodromy operator involved. Second, we show that the presented theory on a Hilbert space gives rise to an alternative definition of the delay Lyapunov matrix, the concept previously appeared in the construction of quadratic Lyapunov-Krasovskii functionals for a class of linear periodic delay systems. An explicit connection between the infinite-dimensional Hilbert setting and the previously developed delay Lyapunov matrix framework is established. An important consequence is the uniqueness theorem: the delay Lyapunov matrix exists and is unique, if and only if the monodromy operator has no reciprocal eigenvalues. As a by-product, our framework enables the construction of Lyapunov-Krasovskii functionals for periodic delay systems without a preliminary exponential stability assumption as in earlier theory.

Let $\mathbb{F}_{p^m}$ be the field containing $p^m$ elements where $p$ is an odd prime and $m \in \mathbb{N}$. In this article, we propose a unified approach to the study of skew constacyclic codes of length $np^s$ over the ring $R_k = \mathbb{F}_{p^m}[u]/\langle u^k \rangle,$ where $n, s, k \in \mathbb{N}$ and $\gcd(n, p)=1$. Consider the skew polynomial ring $R_k[x;Θ]$, where $Θ$ is an automorphism of $R_k$ such that $xa = Θ(a)x$ for all $a \in R_k$. Let $f(x)$ be a central irreducible divisor of $x^{np^s} - λ$ of degree $l$ and multiplicity $j$ in $R_k[x;Θ]$, where $λ$ is an invertible element in $R_k$. In this article, we study skew constacyclic codes of length \(np^s\) over \(R_k\), which reduces to the study of skew polycyclic codes of length $jl$ associated with a polynomial \(f(x)^j\). Using the fact that skew polycyclic codes associated with a polynomial \(f(x)^j\) can be described by the left ideal structure of the quotient ring $R_k[x;Θ]/\langle f(x)^{j}\rangle$, we investigate this class of codes for specific choices of $Θ$. In particular, if $λ$ is an invertible element of $\mathbb{F}_{p^m}$, we classify all left ideals and establish an isomorphism between skew cyclic and skew constacyclic codes, under suitable conditions. Furthermore, we provide a comprehensive analysis of skew constacyclic codes of length $3p^s$ over $R_k$. Finally, we examine skew cyclic and skew negacyclic codes of length $6p^s$ over $R_k$ using the factorization of $x^{6p^s} - 1$ and $x^{6p^s} + 1$, respectively; with a complete case-by-case analysis. Examples demonstrating codes with optimal parameters are also included.

In virtual reality environments, the alignment of perceptual modalities is crucial for immersion and presence. In the AR domain, it is difficult to create such alignments because elements in the physical world are often beyond the user's control. However, recent advances in generative AI enable on-demand content creation, enabling highly reactive AR experiences. Combined with contextual information about the physical world, it has become possible to design experiences that seamlessly align with the user's environment. In this reflection paper, I emphasize the importance of "synchronized" realities for context-aware AR experiences, particularly in mobility scenarios. I present several examples of existing synchronized experiences and examine their commonalities and distinctions. Finally, I discuss opportunities and pitfalls of synchronizing AR experiences with the physical world.

We consider the direct product of two symplectomorphisms, one of which exhibits a basic set and the other one a non-degenerate elliptic equilibrium. Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary of our construction we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic. To establish these results we develop perturbation techniques to create blender horseshoes in the real-analytic setting and import ideas from control theory which show that, typically, these objects have a large domain of influence.

We propose a new way to observe cosmic-ray-induced air showers by imaging the radio emission. With simulations we demonstrate key features for imaging the radio-wave emission from air showers, which show similarities to the well-established atmospheric imaging Cherenkov technique in gamma-ray astronomy. In addition, we find that imaging the emission with a camera, consisting of multiple antennas, resolves emission that is not accessible to a single antenna. Pursuing this technique, with a camera operating in the GHz frequency domain, might be beneficial ultra-high-energy gamma-ray astronomy and other studies that include detailed observations of air showers.

Extreme heat events are increasing in frequency and intensity under climate change, but the socio-behavioral mechanisms that shape community resilience remain insufficiently understood. This study uses a Large Language Model-enhanced agent-based model to simulate responses to a prolonged heatwave in a virtual society. One hundred heterogeneous agents were assigned a Heat Vulnerability Index based on demographic risk factors and observed over 13 simulated days covering baseline, heatwave, and recovery periods. The simulation shows that heat-related impacts are primarily psychosocial and unequally distributed. Agents with higher vulnerability experienced larger declines in perceived safety and social connection than agents with lower vulnerability. Vulnerability also shaped adaptive capacity. More resilient agents maintained routine self-care and protective behaviors, whereas highly vulnerable agents showed behavioral constriction, marked by reduced engagement in protective actions. At the collective level, risk-information diffusion followed a pattern of complex contagion, with adoption driven more by repeated social reinforcement within cohesive networks than by broad exposure alone. These findings suggest that LLM-enhanced simulation can help identify behavioral and social mechanisms of climate resilience and inform heat-risk interventions that combine targeted support for vulnerable groups with community-based information pathways.

Motivated by the inverse moment problem for convex polytopes, we study the pushforward to a line of the Lebesgue measure restricted to a convex $d$-polytope. Such pushforwards are spline densities of degree $d-1$, and their moments lead naturally to a family of ``higher'' univariate Prony systems, with the classical Prony system recovered when $d=0$. We describe the corresponding fixed-knot spline cone, give an explicit amplitude recovery criterion, record the rational generating function and recurrence satisfied by the normalized moments, and identify the directional moment variety with the Hankel determinantal variety appearing in the theory of moment varieties of measures on polytopes.

We study the abelian sandpile model in two dimensions on a directed cylindrical lattice with periodic transverse boundary conditions in the transverse direction and dissipation at one boundary. Recurrent configurations form a finite abelian group, and repeated grain addition at a specific site generates deterministic dynamics on this group. Using Dhar's formulation, the sandpile group is identified with the co-kernel of the reduced directed Laplacian. We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition. Our results establish a direct connection between the algebraic structure of the sandpile group and the periodicity of the driven dynamics, establishing the manner in which the underlying algebraic structure governs both deterministic and stochastic evolution in directed sandpile.

Subcellular protein complexes and organelles exhibit diverse dynamic behaviors that reflect the mechanical constraints and organization of the intracellular environment. Although some structures follow classical Brownian motion, many display anomalous dynamics. The transitions between these regimes are increasingly recognized as critical for subcellular organization, yet how they influence pattern formation remains unclear. Here, we investigate the spatial arrangement of cilia on the apical surface of multiciliated cells (MCCs) in developing Xenopus laevis embryos, where coordinated ciliary beating depends on the precise organization of hundreds of centriole-derived basal bodies (BBs). Using quantitative confocal, high-resolution and high-speed TIRF imaging together with theoretical modeling, we show that BB trajectories undergo time-resolved transitions between diffusive and anomalous motion, with distinct regimes that correlate with apical surface expansion. During the early stages, actin remodeling facilitates the dispersal of BBs by providing a permissive, low-confinement environment. As development progresses, the actin network becomes increasingly cross-linked that constrains BB movement and promotes uniform spacing across the apical domain. Disruption of $α$-actinin-1, a major actin cross-linking protein, impairs the integrity of the apical actin meshwork, weakens BB confinement, and disrupts regular spatial patterning, ultimately compromising the arrangement of BBs required for proper cilia alignment. Together, we show that progressive apical actin cross-linking coordinates BB positioning and regulates their dynamic state, guiding the shift from diffusive to confined motion. This transition in dynamics enables the emergence of a uniform BB pattern, which in turn ensures the aligned deployment of motile cilia necessary for effective directional fluid flow.

High-dimensional classification problems often rely on the Lasso-penalized linear Support Vector Machines (SVMs). However, the double non-smoothness induced by the hinge loss and Lasso penalty in this model makes statistical inference challenging and impedes computational efficiency. In this paper, we propose a unified inference framework in both offline and online settings. In the offline case, by applying a convolution smoothing technique to the hinge loss, we construct a debiased estimator that eliminates the shrinkage bias, thereby building a valid confidence interval. For online streaming data, we develop a real-time estimator and inference procedure that relies only on summary statistics of historical data. Theoretically, we provide rigorous proofs for the asymptotic normality of our offline and online debiased estimators. Simulation studies and real data applications demonstrate that our methods achieve valid statistical inference and improved computational efficiency.

A hard hadron-collider event is treated here as a single geometric object - the kinematics and the discrete object-type labels of all reconstructed final-state particles encoded in one multivector $\evMV\in\Cl(1,3)\otimes\Vflav$ - rather than as the customary list of four-momenta with separate label fields attached. The natural mathematical setting for this view is geometric algebra, whose grade decomposition is shown to organise essentially every observable in current use for collider analyses: inner products and invariant masses at grade zero, four-momenta at grade one, decay-plane bivectors at grade two, oriented three-volumes at grade three, and the CP-odd pseudoscalar at grade four. The high-level invariants, the low-level recipe, and the equivariant-network inputs are recovered as projections onto specific grades. An explicit per-grade dictionary of $34$ classical observables is provided, and the spacetime, discrete and approximate symmetries acting on $\evMV$ are listed. The Cayley--Menger lemma settles the question of new Lorentz-invariant scalars: none are unlocked beyond $\{p_i\!\cdot\!p_j,\,m_i^2\}$; the genuine non-trivial channel is the CP-odd sign of the pseudoscalar. The event-as-geometric-object representation is intended as a uniform input layer for foundation models of collider physics, and a grade-resolved pre-training strategy is outlined. The methodology is illustrated on the resonance-topology separation with a Lorentz-equivariant multivector transformer type whose per-particle grade-$0\!\oplus\!1$ tokens are complemented by event-level pairing tokens that surface the grade-two and grade-three candidate-pairing content of the multi-resonance topology at the input layer.

We introduce the notion of $π^2$-graded Hopf algebra, where the grading is by the double groupoid of commutative diagrams of a finite groupoid $π$. The finite dimensional representations of a $π^2$-graded Hopf algebra form a rigid monoidal category with a fibre functor to the category of $π$-graded vector spaces. The main example is given by the restricted quantum groups underlying the Andrews-Baxter-Forrester restricted solid-on-solid models of statistical mechanics and, more generally, the Jimbo-Miwa-Okado models associated to classical Lie algebras.

We introduce a class of Lévy-driven graph Ornstein-Uhlenbeck (grOU) models for edge-indexed network time series. The proposed framework extends generalized network autoregressive (GNAR) processes for edge-indexed network time series to continuous time and adapts graph Ornstein-Uhlenbeck dynamics, originally developed for node-indexed processes, to the edge-indexed setting. The model accommodates general Lévy noise and therefore captures both Brownian and jump behavior. We show that the model parameters can be estimated via a maximum-likelihood framework and derive the asymptotic properties of the estimator. We examine the finite-sample performance of the methodology through simulation studies and illustrate its practical relevance in an empirical application to high-frequency financial data. The results indicate that grOU models for edge-indexed network time series improve forecasting accuracy and reduce computational time relative to standard benchmarks while maintaining robustness through their network-based parametrization.

We show that the late-time dynamics of a minimal three-component mass-conserving reaction--diffusion system reduce to a scalar active field theory, Active Model B$^-$ (AMB$^-$), in which a density-dependent interfacial coefficient $κ(ϕ)$ turns negative at high density. This drives a finite-wavelength instability and stabilises microphase-separated patterns, in contrast to the unbounded coarsening of two-component mass-conserving systems. Unlike Active Model B$^+$, AMB$^-$ retains a chemical potential that remains a state function, inherited from the underlying conservation law, but admits no equation of state for the pressure.

The performance of tip-enhanced optical microscopy is often limited by inefficient coupling of the excitation field to the plasmonic tip apex, as well as by thermal drift and optical aberrations. Here, we demonstrate that adaptive wavefront shaping based on Zernike mode provides a practical approach to achieving robust near-field optimisation at the tip apex. Using a sequential feedback algorithm, initially using the near-field signal, we narrow the illumination point-spread function and suppress sidelobes. This demonstrates that Zernike-mode control can be used for both aberration correction and field engineering. In tip-enhanced Raman measurements of a Janus MoSSe monolayer, conventional near-field optimisation increases the signal intensity by around 1.4 fold. A second optimisation step based directly on the Raman-band intensity yields a further 5 to 15 fold enhancement, depending on the specific tips used. These results establish a systematic, optics-based strategy for optimising tip fields, providing a transferable framework for improving tip-enhanced and related near-field spectroscopies.

Variational neural network models have achieved remarkable success in solving ground-state problems of quantum many-body systems. However, addressing classical and quantum spin glasses remains challenging, as disorder and energy frustration give rise to an exponentially large number of local energy minima separated by high-energy barriers, hindering the efficiency of conventional Metropolis-based Monte Carlo methods. To bridge this gap, we introduce Deep Boltzmann Quantum States, a class of neural quantum states inspired by deep Boltzmann machines that inherit efficient block Gibbs sampling. We also propose two key advances in the training algorithm. Firstly, we combine natural-gradient updates with state-of-the-art stochastic optimizers. Secondly, we gradually tune the hardness of the problem Hamiltonian by interpolating from an easy to a hard regime, without the need to closely approximate the instantaneous adiabatic state at intermediate times. We match the exact solution or the best available estimate for several instances of classical and quantum Ising spin-glass models with infinite-range interactions and hundreds of spins. We also solve instances of the NP-hard Job Shop Scheduling Problem exceeding the current limitations of quantum annealing hardware. To summarize, deep neural architectures with efficient global update rules and trained within an annealing-like scheme, provide a powerful framework for solving real-world hard combinatorial optimization and for investigating disordered quantum many-body systems.

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed class of normal operators contains, in particular, the class of self-adjoint operators on Banach spaces known in the literature. In addition, we study several properties of self-adjoint operators on smooth Banach spaces, with emphasis on the norm, minimum modulus, numerical radius, and Crawford number, as well as the corresponding attainment properties and the relations among these quantities. Further, we obtain characterisations and spectral properties of the newly introduced classes of normal and unitary operators. Our results demonstrate close analogies with the corresponding theory of self-adjoint, normal, and unitary operators on Hilbert spaces.

The saturated, boosted, and disrupted magnetic braking (SBD MB) model is an empirical prescription that has recently gained support from close-binary observations. Different boosting ($K$) and disruption ($η$) parameters appear necessary for different systems, but their physical origins remain uncertain. We aim to identify the mechanisms that boost magnetic braking (MB) and cause its disruption at the fully convective boundary in cataclysmic variables (CVs). We modelled CV evolution with MESA and compared the results with observed CV properties. We computed the convective turnover time ($τ_c$) directly from the donor's structure rather than adopting empirical relations. We also included irradiation from the accreting white dwarf, which heats the donor's outer layers and can drive additional winds that enhance MB. The structure-based $τ_c$ calculation reveals a pronounced spike as the donor approaches full convection, which drives the disruption parameter $η$ and initiates the period gap in CVs. The outcome of irradiation is sensitive to the accretion, irradiation, and wind efficiencies, all of which are poorly constrained from observations. Despite these uncertainties, plausible parameter choices allow irradiation-driven winds to provide the required boost $K$ during accreting phases. We refer to the combined prescription as the i$τ$SBD MB model and find that it yields evolutionary tracks broadly consistent with the main CV properties. Our i$τ$SBD MB framework offers a physically motivated interpretation of the empirical boost and disruption factors in SBD MB for CV evolution. We suggest that the convective turnover time spike at the fully convective boundary may drive MB disruption for fast-rotating stars in the saturated regime, while irradiation-driven winds may be the dominant mechanism boosting MB in accreting binaries and other strongly irradiated close systems.

We propose a communication-efficient optimally structured gradient coding scheme to jointly address straggler resilience and communication efficiency in heterogeneous distributed learning. By establishing a unified framework that simultaneously optimizes gradient coding and quantization, we formulate an optimization problem to minimize residual error subject to an unbiasedness constraint. We rigorously establish the joint global optimum by deriving a closed-form code structure coupled with an optimal bit allocation strategy, while simultaneously proposing a low-complexity bit allocation algorithm that efficiently yields near-optimal performance. We provide rigorous convergence analysis for convex and smooth functions. Experiments on the COCO dataset demonstrate that our joint design significantly accelerates convergence and enhances communication efficiency compared to existing baselines.

The widespread of counterfeit integrated circuits (ICs) poses severe risks to the security, reliability, and trustworthiness of modern electronic systems. Federated learning (FL) offers a privacy-preserving paradigm for collaborative counterfeit detection across the semiconductor supply chain, but its vulnerability to byzantine data poisoning attacks limits practical deployment. This paper presents Federated Embedding Distribution Authentication (FedEDAuth), a lightweight, embedding level client authentication framework that detects and filters malicious participants before model aggregation. FedEDAuth leverages reference embedding distributions derived from a golden dataset and evaluates clients using outlier analysis, mean shift measurements, and micro-cluster behavior without requiring access to raw data or gradients. Integrated into standard FL pipelines, FedEDAuth consistently identifies all poisoned clients in experimental settings with 50 distributed participants under the byzantine data poisoning attack, achieving a 100% malicious client detection rate. After filtering, the federated model achieved a high counterfeit IC classification performance of 94.17% accuracy. These results not only validate FedEDAuth's effectiveness but also underscore the broader potential of secure, trustworthy FL frameworks as a critical advancement for next generation hardware security solutions, enabling robust, collaborative intelligence across the semiconductor supply chain.

Precise control of magnetic domain formation at the nanoscale remains constrained by stochastic defect-mediated and unstable pinning, limiting scalability and reproducibility in spintronic architectures. Here we demonstrate that spatially engineered anisotropy gradients provide a deterministic alternative. Using focused Ga+-ion irradiation, we pattern magnetic energy landscapes containing nanoscale "anisotropy wells" that confine magnetic domain walls and enable bidirectional sequential switching without reliance on difficult-to-control material disorder. An analytical framework describing domain-wall energetics in graded anisotropy profiles yields predictive design rules for depinning and stability, which are supported by micromagnetic simulations and experiments. We realize programmable multi-domain configurations in continuous ferromagnetic films and demonstrate robust, reproducible switching of 750 nm regions, while first results for 100 nm are shown, approaching the theoretical limit set by the domain-wall width. By replacing unstable pinning with engineered energy landscapes, this anisotropy landscape establishes a scalable materials strategy for deterministic magnetic-state programming and opens a pathway toward dense, energy-efficient spintronic and reconfigurable magnetic nanodevices.

Decoherence is usually described as the loss of local quantum coherence after tracing over environmental degrees of freedom. This reduced description, however, hides the reservoir state that carries the lost coherence. Here we show that spin-boson decoherence can write a postselectable nonclassical imprint into a structured bosonic reservoir. We map zero- and finite-temperature reservoirs to one-dimensional chains, evolve the joint qubit-reservoir state with tensor-network dynamics, and reconstruct the Wigner function of a time-adaptive leading collective reservoir coordinate after transverse qubit readout. The conditioned mapped-reservoir coordinate develops Wigner negativity and interference fringes that are strongly suppressed in the unconditional reservoir state. A parameter sweep shows that the spectral exponent and temperature control the visibility of this conditional nonclassicality, the mapped-chain excitation transport, and the degree to which a single collective coordinate captures the imprint. These results provide a branch-resolved phase-space picture of decoherence: the reservoir is not only a sink for qubit coherence, but can carry a measurement-conditioned nonclassical state in a collective mapped coordinate.

The available potential energy (APE) of a fluid can be defined locally in space, providing useful insights into both the energetics and dynamics of stratified flows ranging from three-dimensional turbulence to planetary scale circulations. Here we develop a framework for considering the multi-scale evolution of the local APE using a spatial filtering, or coarse-graining, approach. Evolution equations for the APE at scales larger, and smaller, than the filtering scale are derived -- including the cross-scale APE flux term. These results can be paired with existing frameworks for coarse-grained kinetic energy, offering the potential for examining a complete energy cycle that accounts for conversions between both spatial scales and energy reservoirs. An illustrative example of the application of this approach to a simulation of two-dimensional Kelvin-Helmholtz instability is provided.

We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_μ\textrm{-}$singularity. The semi-universal deformation of the $A_μ\textrm{-}$singularity is given by a certain deformation of the polynomial of type $A_μ$. In this paper, we consider the category of graded matrix factorizations associated to this deformed polynomial for a fixed parameter. To do so, we introduce a formal variable to make the polynomial homogeneous. As our main result, we construct a full strongly exceptional collection in this category for a generic parameter.

Affine Body Dynamics (ABD) within the Incremental Potential Contact (IPC) framework provides accurate simulation of extremely stiff solids exhibiting near-rigid behavior, with strict non-penetration guarantees. However, IPC's globally coupled barrier constraints hinder scalable execution across multiple GPUs and compute nodes. We propose a distributed formulation of ABD using a consensus-based ADMM scheme. Each compute node solves its local ABD subproblem in parallel, followed by a global consensus step that enforces consistency among shared boundary bodies. The proposed method preserves IPC-level robustness and global consistency under distributed execution. Experiments demonstrate stable convergence, non-penetration, and efficient scaling on large-scale scenes across multiple nodes.

Future wireless networks are moving toward autonomous service operation, where network control and resource management need to respond to time-varying radio conditions and evolving service objectives. To address this shift, this article develops an agent-native wireless communication framework that characterizes the interplay between agent intelligence and communication systems. In this framework, the coupling is organized around \emph{agents for communications} and \emph{communications for agents}. For agent-native operation, the architecture is organized around deployable computing infrastructure, programmable open radio access network (O-RAN) software, and controllable communication interfaces. Based on this architecture, \emph{agents for communications} addresses the use of agents in communication-system design and operation, including agent-generated communication software and agent-driven adaptive wireless optimization. On the other side, \emph{communications for agents} addresses wireless service support for agent operation, including network-supported single-agent loops and network-assisted multi-agent coordination. Finally, it outlines promising research directions for measurable, safe, and interoperable deployment of agent-native wireless communications.

Exact firing rate models, also known as next-generation neural mass models (NG-NMMs), provide a rigorous description of the dynamics of neural populations. While in its simplest form a single population only displays fixed-point activity, multi-population models may display a range of different behaviors. In this work, we study the dynamics of all-excitatory or all-inhibitory NG-NMMs coupled through sparse random networks with row-normalized network topology. Linear stability analysis of the homogeneous states of the system, representing asynchronous neural activity, provides a dispersion relation linking the emergence of spatiotemporal dynamics to the spectra of the connectivity matrix. Using bounds from random matrix theory, we identify the parameter regions where instabilities occur. In undirected networks, only inhibitory systems produce heterogeneous stationary patterns, corresponding to a winner-takes-all mechanism. In directed networks, exotic rhythmic states with high frequencies emerge in both, excitatory and inhibitory systems. Numerical simulations reveal that these hectic oscillatory states correspond to high-dimensional chaos with extensive properties.

The quantum Internet relies on the ability to distribute entangled quantum bits (ebits) between quantum memories at the end nodes, to perform applications like blind or distributed quantum computing that are impossible if end nodes are connected via a classical, i.e., non-quantum network. This need creates new challenges due to the fragile nature of entanglement, which decoheres over short timescales and cannot be amplified, buffered, or retransmitted. Two broad categories of approaches have been proposed in the scientific literature to realize such an entanglement distribution in a given path: one relying on a synchronous time-slotted model, and another one where intermediate nodes interact asynchronously. However, both of them implicitly assume a serial operation, where one ebit is established and made available to the application on end nodes before creating a new one. This is inefficient in long-range networks, with high transmission latencies, if the intermediate nodes have multiple memory qubits that could be used in parallel. To overcome this limitation, in this paper, we study the implications of multiplexing concurrent ebit requests on the same quantum, for both synchronous and asynchronous operation. Furthermore, for the latter, we define a novel distribution protocol, called HOPPER, where the intermediate nodes make autonomous and hop-by-hop decisions on the use of their local resources when establishing an ebit. With numerical simulations, we show that HOPPER is effective in handling multiple ebit requests in parallel, and it exhibits significantly better performance than a synchronous alternative in different scenarios.