The pinching-antenna system (PASS) enables wireless channel reconfiguration through optimized placement of pinching antennas along dielectric waveguides. In this article, a unified analytical framework is proposed to characterize the maintainability of PASS. Within this framework, random waveguide failures and repairs are modeled by treating the waveguide lifetime and repair time as exponentially distributed random variables, which are characterized by the failure rate and the repair rate, respectively. The operational state of the waveguide is described by a two-state continuous-time Markov chain, for which the transition probabilities and steady-state probabilities of the waveguide being working or failed are analyzed. By incorporating the randomness of the waveguide operational state into the transmission rate, system maintainability is characterized using the probability of non-zero rate (PNR) and outage probability (OP). The proposed framework is applied to both a conventional PASS employing a single long waveguide and a segmented waveguide-enabled pinching-antenna system (SWAN) composed of multiple short waveguide segments under two operational protocols: segment switching (SS) and segment aggregation (SA). Closed-form expressions for the PNR and OP are derived for both architectures, and the corresponding scaling laws are analyzed with respect to the service-region size and the number of segments. It is proven that both SS-based and SA-based SWAN achieve higher PNR and lower OP than conventional PASS, which confirms the maintainability advantage of segmentation. Numerical results demonstrate that: i) the maintainability gain of SWAN over conventional PASS increases with the number of segments, and ii) SA provides stronger maintainability than SS.

One of the major conundrums in contemporary extragalactic astrophysics is the apparent overabundance of a remarkable population of UV-bright galaxies at redshifts $z\gtrsim 9$. We analyse galaxies spectroscopically observed by JWST/NIRSpec Prism and confirmed to lie at $z>9$, with sufficient signal-to-noise to carefully model their rest-frame UV to optical continua and line emission. In particular, we model the damped Lyman-$α$ (Ly$α$) absorption (DLA) features of each galaxy to place observational constraints on the gas assembly of neutral atomic hydrogen (HI) onto the galaxy halos at the onset of cosmic reionisation. Based on the derived HI column densities and star-formation rate (SFR) surface densities, we show that all galaxies are highly efficient at forming stars on rapid $\sim 10-100\,$Myr depletion timescales, greatly in excess compared to the canonical local universe Kennicutt-Schmidt relation and predictions from state-of-the-art galaxy formation simulations. The dense HI gas appears to also drive the offset from the fundamental-metallicity relation of these galaxies though its dust-to-gas ratio is seemingly consistent with values derived for local galaxies except for the lowest metallicity sight-lines. Our results provide the first robust observational constraints on the impact of pristine HI gas on early galaxy assembly, and imply that a combination of highly efficient star formation and low dust obscuration can likely explain the UV-brightness of galaxies at cosmic dawn.

We show that the space of Belyi maps admits a natural parametrization by an infinite-dimensional sphere arising from Voiculescu's theory of noncommutative probability spaces. We show that this sphere decomposes into sectors, each of which corresponds to a class of Belyi maps distinguished up to isomorphism by their monodromy, encoded by a finite-index subgroup of F2. For Galois Belyi maps, our correspondence between spectral sectors of the infinite sphere and algebraic quotients of F2 yields a genuine bijection. Within this framework, distinct sectors of the sphere capture the algebraic constraints imposed on the monodromy, thereby providing a geometric organization of Belyi maps according to their associated group-theoretic data.

Reservoir simulations help the energy industry make better decisions by predicting how fluids like oil, gas, water, hydrogen, and carbon dioxide will flow underground. To keep these predictions accurate, engineers often need to update geological models quickly as new information becomes available. pycopm is a tool designed to make this process faster and easier. It allows users to adjust geological models in several ways, such as simplifying complex grids, focusing on specific parts of a reservoir, or changing the shape and position of the model. These capabilities help engineers test different scenarios efficiently. Although pycopm was first used on two well-known public datasets, it has since become useful in many other situations because of its easy-to-use features and recent extensions. Today, it supports studies involving model refinement, comparing coarse and detailed models, analyzing interactions between nearby sites, and speeding up troubleshooting in large simulations.

Explanations are essential for helping users interpret and trust autonomous smart-home decisions, yet evaluating their quality and impact remains methodologically difficult in this domain. V-SHiNE addresses this gap: a browser-based smarthome simulation framework for scalable and realistic assessment of explanations. It allows researchers to configure environments, simulate behaviors, and plug in custom explanation engines, with flexible delivery modes and rich interaction logging. A study with 159 participants demonstrates its feasibility. V-SHiNE provides a lightweight, reproducible platform for advancing user-centered evaluation of explainable intelligent systems

This paper outlines a solution to the Straus Erdős Conjecture. Namely for each prime $p$ there exists positive integers $x \leq y \leq z$ so that $$ \frac{4}{p} = \frac{1}{x}+\frac{1}{y}+\frac{1}{z} $$

For a directed graph $G$, and a linear order $\ll$ on the vertices of $G$, we define backedge graph $G^\ll$ to be the undirected graph on the same vertex set with edge $\{u,w\}$ in $G^\ll$ if and only if $(u,w)$ is an arc in $G$ and $w \ll u$. The directed clique number of a directed graph $G$ is defined as the minimum size of the maximum clique in the backedge graph $G^\ll$ taken over all linear orders $\ll$ on the vertices of $G$. A natural computational problem is to decide for a given directed graph $G$ and a positive integer $t$, if the directed clique number of $G$ is at most $t$. This problem has polynomial algorithm for $t=1$ and is known to be \NP-complete for every fixed $t\ge3$, even for tournaments. In this note we prove that this problem is $Σ^\mathsf{P}_{2}$-complete when $t$ is given on the input.

In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions, we explicitly characterize the feasible set of admissible weights and introduce six optimization problems defined over this set, each corresponding to a different weight-selection strategy. These formulations provide representative solutions of the inverse problem and enable a systematic comparison of how different strategies influence the structure of the resulting weighted networks. We illustrate our framework using several real-world social network datasets, showing that different strategies produce different weighted graph structures while preserving the prescribed centrality. The results highlight the flexibility of the proposed approach and its potential applications in network reconstruction, and network design or network manipulation.

We address whether complex physical relations can be investigated through the synergy of automated high-volume experiments and the reduction of large datasets to a concise, representative subset of canonical examples -- a "textbook". To this end, we consider the unsteady aerodynamics of wing-gust interactions, which is characterized by its rich, high-dimensional physics. We take advantage of a purpose-built gust generator to systematically produce over 1,000 distinct random gust events and to measure the unsteady loads induced on a delta wing. We then employ a data summarization procedure to identify representative subsets of increasing size from the large-scale database, which then serve as training data for a machine-learning model of the aerodynamic loads from sparse pressure measurements. An appropriately selected "textbook" of a few events can achieve predictive accuracy comparable to random training sets up to two orders of magnitude larger, capturing the intrinsic diversity of the full-scale data and enhancing modeling efficiency and interpretability. Our methodology evidences the potential of distilling the essential information contained in large amounts of experimental observations.

We present a novel approach for efficient preparation of electronic ground states, leveraging the optimizer ExcitationSolve [Jäger et al., Comm. Phys. (2025)] and established variational quantum eigensolver-based operator selection methods, such as Energy Sorting. By combining these tools, we demonstrate a computationally efficient protocol that enables the construction of an approximate ground state from a unitary coupled cluster ansatz via a single sweep over the operator pool. Utilizing efficient classical pre-processing to select the majority of relevant operators, this approach reduces the computational complexity associated with traditional optimization methods. Furthermore, we show that this method can be seamlessly integrated with one-variational-parameter couple exchange operators, thereby further reducing the number of required CNOT operations. Overall, we empirically observe a quadratic convergence speedup beyond state-of-the-art methods, advancing the realization of quantum advantage in quantum chemistry.

Our work utilized a non-sequential simulation-based inference algorithm to provide an amortized neural density estimator, which approximates the posterior distribution for seven parameters of the adaptive exponential integrate-and-fire neuron model of the analog neuromorphic BrainScaleS-2 substrate. We constrained the large parameter space by training a binary classifier to predict parameter combinations yielding observations in regimes of interest, i.e. moderate spike counts. We compared two neural density estimators: one using handcrafted summary statistics and one using a summary network trained in combination with the neural density estimator. The summary network yielded a more focused posterior and generated posterior predictive traces that accurately captured the membrane potential dynamics. When using handcrafted summary statistics, posterior predictive traces match the included features but show deviations in the exact dynamics. The posteriors showed signs of bias and miscalibration but were still able to yield posterior predictive samples that were close to the target observations on which the posteriors were constrained. Our results validate amortized simulation-based inference as a tool for parameterizing analog neuron circuits.

Two-sided marketplaces embody heterogeneity in incentives: producers seek exposure while consumers seek relevance, and balancing these competing objectives through constrained optimization is now a standard practice. Yet real platforms face finer-grained complexity: consumers differ in preferences and engagement patterns, producers vary in catalog value and capacity, and business objectives impose additional constraints beyond raw relevance. We formalize two-sided fairness under these realistic conditions, extending prior work from soft single-item allocations to discrete multi-item recommendations. We introduce Conditional Value-at-Risk (CVaR) as a consumer-side objective that compresses group-level utility disparities, and integrate business constraints directly into the optimization. Our experiments reveal that the "free fairness" regime, where producer constraints impose no consumer cost, disappears in multi item settings. Strikingly, moderate fairness constraints can improve business metrics by diversifying exposure away from saturated producers. Scalable solvers match exact solutions at a fraction of the runtime, making fairness-aware allocation practical at scale. These findings reframe fairness not as a tax on platform efficiency but as a lever for sustainable marketplace health.

We study the Hermitian distance degree, a real enumerative invariant counting critical points of the squared Hermitian distance function, for matrix varieties invariant under left and right unitary actions. For such a variety \(M \subset \mathbb{C}^{n\times t}\), we prove that its Hermitian distance degree equals the real Euclidean distance degree of the associated absolutely symmetric variety of singular values. Equivalently, for a generic data matrix, Hermitian distance critical points on \(M\) are obtained by lifting Euclidean distance critical points from the singular-value slice. We also establish a Hermitian slicing theorem, paralleling the Bik--Draisma principle, which reduces the critical point count to a diagonal slice. As a motivating example, we recover a geometric Hermitian analogue of the Eckart-Young theorem.

Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study a variant in which the goal is to minimize a quantile of the cost, rather than the mean. For the semidiscrete setting, where one distribution is continuous and the other is discrete, we derive a complete characterization of the optimal transport plan and develop simulation-based methods to efficiently compute it. One particularly novel aspect of our approach is the efficient computation of a tie-breaking rule that preserves marginal distributions. In the context of geographical partitioning problems, the optimal plan is shown to produce a novel geometric structure.

Hons, Klimošová, Kucheriya, Mikšaník, Tkadlec, and Tyomkyn proved that, for every integer $\ell \ge 1$, every directed graph with minimum out-degree at least $3.23 \cdot \ell$ contains a $(2,\ell)$-spider (a $1$-subdivision of the in-star with $\ell$ leaves) as a subgraph. They also conjectured that the bound on the minimum out-degree can be further improved to $2 \ell$. In this note, we confirm their conjecture by showing that every directed graph with minimum out-degree at least $2\ell$ contains a $(2, \ell)$-spider as a subgraph. This result is best possible, as the complete directed graph with $2\ell$ vertices does not contain a $(2,\ell)$-spider.

A recent paper on SOL2012-06-03 reported the detection for the first time of two distinct phases of $>$100 MeV $γ$-radiation indicating separate acceleration processes. But such two-phase emission has been seen before and was first observed in SOL1982-06-03. The second phase is known as Late Phase Gamma-Ray Emission (LPGRE) and was cataloged for $>$40 solar eruptions, including SOL2012-06-03. Here we provide evidence that the second SOL2012-06-03 $π$-decay peak is the onset of LPGRE that lasted for $>$8 min. Its delay from the impulsive X-ray peak is consistent with the time it would take flare-produced suprathermal protons to overtake the expanding CME and be accelerated by its shock. The high accelerated ion-to-electron ratio in SOL2012-06-03 and other LPGRE events is consistent with the ratio observed in gradual SEP events produced by shocks and is inconsistent with ratios typically found in impulsive flares and solar energetic particle events produced by reconnection.

Learning effective feature interactions is central to modern recommender systems, yet remains challenging in industrial settings due to sparse multi-field inputs and ultra-long user behavior sequences. While recent scaling efforts have improved model capacity, they often fail to construct both context-aware and context-independent user intent from the long-term and real-time behavior sequence. Meanwhile, recent work also suffers from inefficient and homogeneous interaction mechanisms, leading to suboptimal prediction performance. To address these limitations, we propose HeMix, a scalable ranking model that unifies adaptive sequence tokenization and heterogeneous interaction structure. Specifically, HeMix introduces a Query-Mixed Interest Extraction module that jointly models context-aware and context-independent user interests via dynamic and fixed queries over global and real-time behavior sequences. For interaction, we replace self-attention with the HeteroMixer block, enabling efficient, multi-granularity cross-feature interactions that adopt the multi-head token fusion, heterogeneous interaction and group-aligned reconstruction pipelines. HeMix demonstrates favorable scaling behavior, driven by the HeteroMixer block, where increasing model scale via parameter expansion leads to steady improvements in recommendation accuracy. Experiments on industrial-scale datasets show that HeMix scales effectively and consistently outperforms strong baselines. Most importantly, HeMix has been deployed on the AMAP platform, delivering significant online gains over DLRM: +3.61\% GMV, +2.78\% PV\_CTR, and +2.12\% UV\_CVR.

When the sequence of regular polygons with consecutively increasing numbers of sides is joined edge-to-edge in a single direction while minimizing bending, the resulting structure assumes the shape of a logarithmic spiral. This paper proves that this spiral takes the form r=exp(4θ/π). Specifically, it is derived that the distances between the curve and the centers of the even-sided and odd-sided regular polygons converge to 5/6 and 7/12, respectively, with the centers extending outward along the inner side of the spiral. A similar analysis applied to the sequence of regular polygons with consecutively increasing odd numbers of sides reveals that it forms the same type of spiral, establishing that the distances to the centers converge to 7/24.

How do social animals make effective decisions in the absence of a leader? While coordination can improve accuracy, it also introduces delays as information propagates through the group. In changing environments, these delays can outweigh the benefits of globally coordinated decisions, even when local interactions remain tightly organized. This raises a key question: how can groups implement efficient collective decision-making without central coordination? We address this question using a collective foraging model in which individuals share information and rewards, but each must choose whether to bear the cost of exploring or to remain idle. We show that decentralized collectives can match the performance of centrally controlled groups through a division of labor: a small, heterogeneous subset explores even when expected rewards are negative, acquiring information to enable future foraging, while a coordinated majority forages only when expected rewards are positive. Information redundancy causes the optimal number of explorers to grow sublinearly with group size, so that larger groups need proportionally fewer explorers. The heterogeneity of the group is maximized at intermediate ecological pressures, but optimal groups are homogeneous when costs or fluctuations are extreme. Crucially, these group-level policies do not require central coordination, emerging instead from agents following simple threshold-based decision rules. We thus demonstrate a mechanism through which leaderless collectives can make effective decisions under uncertainty and show how ecological pressures can drive changes in the distribution of strategies employed by the group.

We report a normal-mode induced synchronization blockade in coupled quantum van der Pol oscillators under the influence of external drive. In this mechanism, the coupling hybridizes the oscillator modes into spectrally split normal modes. The destructive interference between the transitions to these modes blocks synchronization. We find that this blockade can be controlled simply by tuning the coupling strength and detuning allowing dynamic manipulation of quantum synchronization through collective mode dynamics. We analyze the phase-locking behaviour using perturbation analysis. Further, by deriving steady-state probability amplitudes we show how the energy redistribution and spectral splitting forms the basis of the blockade. Our results might provide new insights into how synchronization can be controlled in quantum systems.

The R package MixMashNet provides an integrated framework for estimating and analyzing single and multilayer networks using Mixed Graphical Models (MGMs), accommodating continuous, count, and categorical variables. In the multilayer setting, layers may comprise different types and numbers of variables, and users can explicitly impose a predefined multilayer topology. Bootstrap procedures are implemented to quantify sampling uncertainty for edge weights and node-level centrality indices. In addition, the package includes tools to assess the stability of node community membership and to compute community scores that summarize the latent dimensions identified through network clustering. MixMashNet also offers interactive Shiny applications to support exploration, visualization, and interpretation of the estimated networks.

The length $\mathsf{is}(π)$ of a longest increasing subsequence in a permutation $π$ has been extensively studied. An increasing subsequence is one that has no descents. We study generalizations of this statistic by finding longest subsequences with other descent restrictions. We first consider the statistic which encodes the longest length of a subsequence with a given number of descents. We then generalize this to restrict the descent set of the subsequence. Extending the classical result for $\mathsf{is}(π)$, we show how these statistics can be obtained using the RSK correspondence and the Schützenberger involution. In particular, these statistics only depend on the recording tableau of the permutation.

We study the thermodynamics of the isotropic Heisenberg XXX spin chain with negative spin, focusing on the case $s=-1$. The model is equivalent to the quantum lattice nonlinear Schrödinger (NLS) model and appears as an effective theory in deep inelastic scattering in high-energy quantum chromodynamics. Owing to its integrability, it admits a consistent Bethe Ansatz description and a well-defined thermodynamic limit. Using the thermodynamic Bethe Ansatz, we analyze the ground state, elementary excitations, and finite-temperature properties. In contrast to the conventional positive spin XXX chain, the negative spin model exhibits a distinct vacuum structure and excitation spectrum, leading to modified TBA equations and unconventional low-temperature behavior. Although the integral equations resemble those of the Lieb-Liniger Bose gas, the thermodynamics and scaling properties are qualitatively different and cannot be continuously connected. We derive the free energy, entropy, and specific heat, and identify a quantum phase transition separating different thermodynamic regimes. At zero temperature, the excitation spectrum becomes linear in the continuum limit and can be described by a conformal field theory. The low-temperature regime realizes a Luttinger-liquid like phase with features unique to the negative spin XXX chain.

Large language models (LLMs) can generate structured artifacts, but using them as dependable optimizers for scientific design requires a mechanism for iterative improvement under black-box evaluation. Here, we cast quantum circuit synthesis as a closed-loop, test-time optimization problem: an LLM proposes edits to a fixed-length gate list, and an external simulator evaluates the resulting state with the Meyer-Wallach (MW) global entanglement measure. We introduce a lightweight test-time learning recipe that can reuse prior high-performing candidates as an explicit memory trace, augments prompts with a score-difference feedback, and applies restart-from-the-best sampling to escape potential plateaus. Across fixed 20-qubit settings, the loop without feedback and restart-from-the-best improves random initial circuits over a range of gate budgets. To lift up this performance and success rate, we use the full learning strategy. For the 25-qubit, it mitigates a pronounced performance plateau when naive querying is used. Beyond raw scores, we analyze the structure of synthesized states and find that high MW solutions can correspond to stabilizer or graph-state-like constructions, but full connectivity is not guaranteed due to the metric property and prompt design. These results illustrate both the promise and the pitfalls of memory evaluator-guided LLM optimization for circuit synthesis, highlighting the critical role of prior human-made theoretical theorems to optimally design a custom tool in support of research.

Quantum mechanics predicts that unobserved systems may exist in a superposition of states, yet measurement produces definite outcomes, a tension at the heart of the quantum-to-classical boundary. How the transformation between these opposing regimes unfolds as observation strength increases has remained experimentally unexplored. Here, by continuously tuning the measurement strength on a superconducting qubit, we reveal that measurement-dominated dynamics emerge not gradually but through three distinct transitions: coherent oscillations abruptly halt; the system then freezes near a stable quantum state; and finally enters the quantum Zeno regime, where stronger observation paradoxically slows relaxation. Decoherence, rather than washing out this structure, reorganizes it, inverting the order in which transitions appear and decoupling signatures that coincide in idealized models. These results establish that the route from quantum dynamics to measurement-dominated behavior unfolds in sharp transitions governed by the interplay between observation and environment.

Triadic percolation turns bond percolation into a dynamical problem governed by an effective one-dimensional unimodal map. We show that the geometry of superstable cycles provides a direct, map-agnostic probe of local nonlinearity: specifically, the distance from the map's maximum to a distinguished next-to-maximum point on the attracting $2^n$-cycle (which coincides with a preimage of the maximum at $2^n$-superstability) scales as $|Δp|^γ$ with $γ= 1/z$, where $z$ is the nonflat order of the maximum. This prediction is verified across canonical unimodal families and heterogeneous triadic ensembles, with Lyapunov spectra corroborating the one-dimensional reduction. A derivative condition on the activation kernel fixes the local nonlinearity order $z$ (and thus, under standard unimodal-map hypotheses, the associated $z$-logistic universality class) and gives conditions under which $z>2$ can be realized. The diagnostic operates directly on orbit data under standard regularity assumptions, providing a practical tool to classify universality in higher-order networks.

I present derivation the BK equation for the dipole gluon density in momentum space, starting from its standard formulation in coordinate space. I review the equation for both proton and nuclear targets, and I also discuss the resummed BK evolution.The purpose of this paper is to consolidate derivations and formulas scattered across the literature, to show in detail how the structure of the triple-Pomeron vertex emerges in the unfolded form of the nonlinear term, and to establish a consistent notation throughout.

\texttt{aurel} is an open-source Python package designed to \emph{au}tomatically calculate \emph{rel}ativistic quantities. It uses an efficient, flexible and user-friendly caching and dependency-tracking system, ideal for managing the highly nonlinear nature of general relativity. The package supports both symbolic and numerical calculations. The symbolic part extends \texttt{SymPy} with additional tensorial calculations. The numerical part computes a wide range of tensorial quantities, such as curvature, matter kinematics and much more, directly from any spacetime and matter data arrays using finite-difference methods. Inputs can be either generated from analytical expressions or imported from Numerical Relativity (NR) simulations, with helper functions provided to read in data from standard NR codes. Given the increasing use of NR, \texttt{aurel} offers a timely post-processing tool to support the popularisation of this field.

As Open Radio Access Network (O-RAN) deployments expand and adversaries adopt 'store-now, decrypt-later' strategies, operators need empirical data on the cost of migrating critical control interfaces to post-quantum cryptography (PQC). This paper experimentally evaluates the impact of integrating a NIST-aligned module-lattice KEM (ML-KEM, CRYSTALS-Kyber) into IKEv2/IPsec protecting the E2 interface between the 5G Node B (gNB) and the Near-Real-Time RAN Intelligent Controller (Near-RT RIC). Using an open-source testbed built from srsRAN, Open5GS, FlexRIC and strongSwan (with liboqs), we compare three configurations: no IPsec, classical ECDH-based IPsec, and ML-KEM-based IPsec. The study focuses on IPsec tunnel-setup latency and the runtime behaviour of Near-RT RIC xApps under realistic signalling workloads. Results from repeated, automated runs show that ML-KEM integration adds a small overhead to tunnel establishment, which is approximately 3~5 ms in comparison to classical IPsec, while xApp operation and RIC control loops remain stable in our experiments. These findings indicate that ML-KEM based IPsec on the E2 interface is practically feasible and inform quantum-safe migration strategies for O-RAN deployments.

We characterise non-Hermitian Fabry-Pérot resonances in high-contrast resonator systems and study the properties of their associated resonant modes from continuous differential models. We consider two non-Hermitian effects: the exceptional point degeneracy and the skin effect induced by imaginary gauge potentials. Using the propagation matrix formalism, we characterise these two non-Hermitian effects beyond the subwavelength regime. This analysis allows us to (i) establish the existence of exceptional points purely from radiation conditions and to (ii) prove that the non-Hermitian skin effect applies uniformly across resonant modes, yielding broadband edge localisation.