The knowledge gap hypothesis suggests that the diffusion of information tends to increase rather than reduce social inequalities. Subsequent research on the digital divide has extended this perspective by focusing on unequal access to and use of digital technologies. The emergence of generative artificial intelligence raises the question of whether these frameworks remain sufficient to describe current forms of informational inequality. While access to AI systems is increasingly widespread, differences may arise in how users engage with AI-generated content. This paper proposes a theoretical extension of the knowledge gap perspective by arguing that generative AI shifts the focus from access and usage to the critical evaluation of information. It is assumed that individuals with higher levels of education are more likely to question and contextualize AI-generated outputs, whereas individuals with lower levels of education may rely more directly on them. The contribution is conceptual and does not present empirical findings. It aims to provide a framework for future research on the relationship between education, AI use, and knowledge inequality.

Recently, Forré (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes a strong global Markov property connecting transitional conditional independencies with suitable graphical separation criteria for directed mixed graphs with input nodes (iDMGs), together with a version of causal calculus for iDMGs in a general measure-theoretic setting. These notes aim to further illustrate the motivations behind this framework and its connections to the literature, highlight certain subtlies in the general measure-theoretic causal calculus, and extend the "one-line" formulation of the ID algorithm of Richardson et al. (Ann. Statist. 51(1):334--361, 2023) to the general measure-theoretic setting.

Erg Chech 002 is an andesitic meteorite that formed early in the Solar System's history, and that is thought to have been formed in the primitive crust of an early accreted and differentiated planetesimal. It shows unique spectral features, and no known asteroid spectral type was initially found to match with its compositional type. In the literature, asteroids (10537) 1991 RY16, (7472) Kumakiri and (14390) 1990 QP10 were found to show peculiar spectra, and were not classified in any known existing spectral class. These objects were hypothesised to be fragments of differentiated planetesimals. In a previous study, the Gaia Data Release 3 dataset of visible reflectance spectra of Solar System Objects was exploited to search for potential analogues of Erg Chech 002 in the main belt. As a result, 142 asteroids were found to potentially match this meteorite. In this work, we present NASA's IRTF near-infrared observations of 20 main belt asteroids found as potential analogues of Erg Chech 002. We classified these asteroids based on their visible-near-infrared spectra, then studied and compared their diagnostic spectral features with those of the laboratory spectra of Erg Chech 002. We classified 16 of the 20 observed asteroids as V-types, one as S-complex and one as A-type, and conclude that none of the observed objects match with Erg Chech 002. In addition, we show that asteroids (10537) 1991 RY16 and (14390) 1990 QP10 are good spectral matches to Erg Chech 002 based on the study of their diagnostic spectral features. Asteroid (7472) Kumakiri could match a more olivine-rich Erg Chech 002-like material, and cannot be completely ruled out as a match of the meteorite. This possible link between the meteorite and these asteroids is consistent with the theories regarding their formation, and these asteroids could be part of a new spectral class of andesitic bodies in the main belt.

We determine the squarefree part of the scalar factor that arises when the quartic invariant of the generic binary form $F$ of odd degree $2n+1$ is expressed as the discriminant of the unique quadratic covariant $(F,F)_{2n}$. This squarefree part is exactly $p$ when $n+2$ is a power of an odd prime $p$, and $1$ otherwise. Equivalently, for each prime $p$: $v_2(S(n))$ is always even, and for odd $p$, $v_p(S(n))$ is odd if and only if $n+2$ is a power of $p$. This generalizes the classical identity $\operatorname{disc}(H(F))=-3\cdot\operatorname{disc}(F)$ for binary cubics, which dates back to the work of Cayley and Sylvester in the 1850s. The proof, which involves substantial explicit coefficient analysis and $p$-adic deformation arguments, was developed using an AI-assisted research workflow: the author's earlier partial attempts were completed through systematic collaboration with Claude Code (Anthropic) and Codex (OpenAI), and key arithmetic lemmas were formally verified in Lean~4 using Aristotle (Harmonic). We describe this workflow in detail as a case study in AI-assisted mathematical research. We also discuss representation-theoretic, geometric, and arithmetic interpretations of the quadratic covariant.

The International Telecommunication Union (ITU) identifies "Artificial Intelligence (AI) and Communication" as one of six key usage scenarios for 6G. Agentic AI, characterized by its ca-pabilities in multi-modal environmental sensing, complex task coordination, and continuous self-optimization, is anticipated to drive the evolution toward agent-based communication net-works. Semantic communication (SemCom), in turn, has emerged as a transformative paradigm that offers task-oriented efficiency, enhanced reliability in complex environments, and dynamic adaptation in resource allocation. However, comprehensive reviews that trace their technologi-cal evolution in the contexts of agent communications remain scarce. Addressing this gap, this paper systematically explores the role of semantics in agent communication networks. We first propose a novel architecture for semantic-based agent communication networks, structured into three layers, four entities, and four stages. Three wireless agent network layers define the logical structure and organization of entity interactions: the intention extraction and understanding layer, the semantic encoding and processing layer, and the distributed autonomy and collabora-tion layer. Across these layers, four AI agent entities, namely embodied agents, communication agents, network agents, and application agents, coexist and perform distinct tasks. Furthermore, four operational stages of semantic-enhanced agentic AI systems, namely perception, memory, reasoning, and action, form a cognitive cycle guiding agent behavior. Based on the proposed architecture, we provide a comprehensive review of the state-of-the-art on how semantics en-hance agent communication networks. Finally, we identify key challenges and present potential solutions to offer directional guidance for future research in this emerging field.

Purpose: Understanding a technical artifact requires grasping both its internal structure (Architecture) and its purpose and significance (Relevance), as formalized by Dual Nature Theory. This controlled experimental study investigates whether how explainers address these perspectives affects explainees' understanding. Methods: In a between-subjects experiment, 104 participants received explanations of the board game Quarto! from trained confederates in one of three conditions: Architecture-focused (A), Relevance-focused (R), or Integrated (AR). Understanding was assessed on comprehension (knowing that) and enabledness (knowing how). Results: The A and R conditions produced equivalent understanding despite different explanation content. The AR condition yielded significantly higher enabledness than the focused conditions combined $\mathrm{F}(1, 102) = 4.83$, $p = .030$, $η^2_p = .045$}, while no differences emerged for comprehension. Conclusion: Integrating Architecture and Relevance specifically enhances explainees' ability to apply their understanding in practice, suggesting that fostering agency with technical artifacts requires bridging both perspectives. This has implications for technology education and explainable AI design.

Self-Service Learning Analytics (SSLA) tools aim to support educational stakeholders in creating learning analytics indicators without requiring technical expertise. While such tools promise user control and trans- parency, their effectiveness and adoption depend critically on usability aspects. This paper presents a compre- hensive usability evaluation and improvement of the Indicator Editor, a no-code, exploratory SSLA tool that enables non-technical users to implement custom learning analytics indicators through a structured workflow. Using an iterative evaluation approach, we conduct an exploratory qualitative user study, usability inspections of high-fidelity prototypes, and a workshop-based evaluation in an authentic educational setting with n = 46 students using standardized instruments, namely System Usability Scale (SUS), User Experience Question- naire (UEQ), and Net Promoter Score (NPS). Based on the evaluation findings, we derive concrete design implications that inform improvements in workflow guidance, feedback, and information presentation in the Indicator Editor. Furthermore, our evaluation provides practical insights for the design of usable SSLA tools.

This article provides a survey of circuit complexity bounds for basic boolean transforms exploited in digital circuit design and efficient methods for synthesizing such circuits. The exposition covers structurally simple functions and operators, such as counters, adders, encoders, and multiplexors, and excludes more complex algebraic operations with numbers, polynomials, and matrices. Several applications to implementing more specific operations are also discussed.

We study the complexity of computing Bayes-Nash equilibria in single-item first-price auctions. We present the first efficient algorithms for the problem, when the bidders' values for the item are independently drawn from the same continuous distribution, under both established variants of continuous and finite bidding sets. More precisely, we design polynomial-time algorithms for the white-box model, where the distribution is provided directly as part of the input, and query-efficient algorithms for the black-box model, where the distribution is accessed via oracle calls. Our results settle the computational complexity of the problem for bidders with i.i.d. values.

The cyclic hoist scheduling problem originates in electroplating lines, where a single or multiple hoists transport parts between processing tanks subject to technological constraints. The objective is typically to determine a cyclic sequence of hoist movements that minimizes the cycle time while satisfying travel and processing constraints. Although the problem has been widely studied for several decades, the literature contains a puzzling phenomenon: different studies often report different optimal cycle times for the same benchmark instances, which limits the comparability and reproducibility of computational results. In this paper, we revisit the modeling of cyclic hoist scheduling problems from a unified perspective. We introduce a consistent modeling approach for single-hoist problems and analyze several mixed-integer linear programming (MIP) formulations proposed in the literature. Our analysis identifies modeling inconsistencies and clarifies the relationships between existing formulations. Based on these observations, we propose straightforward constraint programming (CP) models that can serve as baseline approaches, and we also derive improved MIP~formulations. Extensive computational experiments compare the strength and performance of the investigated formulations. To support reproducible research, we also provide a publicly available library containing benchmark instances and implementations of several CP and MIP~formulations for single-hoist cyclic hoist scheduling.

We first fully implement, in Maple, the ingenious method of Robert Stoyan and Volker Strehl from 1995 to automatically derive generating functions for the number of Hamiltonian cycles in an m by n grid graph ,for a fixed width m, but general length n, and actually compute these generating functions for all m up to ten. We also show how to generate a uniformly-at-random such Hamiltonian cycle, and also derive more informative generating functions for other parameters besides the length of the grid graph.

This study presents a high-order finite volume scheme capable of large time-step integration for three-temperature radiation diffusion (3TRD) equations, where conservation is naturally achieved through energy update. To handle local large gradients and discontinuities in temperature, a central generalized ENO (GENO) reconstruction is developed for diffusion systems, which achieves essentially non-oscillatory reconstruction for discontinuous solutions. Compared to conventional nonlinear reconstruction methods, its most distinctive feature is the central-type symmetric sub-stencils, which ensure consistency between the numerics and the isotropic nature of thermal diffusion. Additionally, the central GENO method provides smooth states of temperature and temperature gradient at interfaces, facilitating the evaluation of numerical fluxes. Furthermore, interface flux evaluation for cases with discontinuous physical property parameters is modeled. To address the extremely small time-step issue caused by stiff diffusion and source terms, a dual-time-stepping method based on implicit time discretization is developed for the first time in 3TRD systems, with the advantage of decoupling temporal discretization from complex nonlinear spatial discretization. A series of numerical examples validates the high accuracy, physical property preservation, strong robustness, and large time-step integration capability of the present high-order central GENO scheme.

We introduce a zeta function counting imaginary quadratic number fields by their class numbers. It is proved that such a function is rational depending only on the eight roots of unity of degrees $1$ and $2$. As a corollary, one gets a lower bound $2p$ for the number of imaginary quadratic fields of the prime class number $p$. Our method is based on the study of periodic points of a dynamical system arising in the representation theory of the Drinfeld modules by the bounded linear operators on a Hilbert space.

Quantum magnets in the $M\mathrm{Nb_2O_6}$ and BaCo$_2$V$_2$O$_8$ families realise frustrated transverse-field Ising models whose competing ferromagnetic and antiferromagnetic couplings generate a sign problem provably intractable for quantum Monte Carlo at any system size, leaving their quantum phase boundaries numerically Inaccessible. Using a D-Wave Advantage2 quantum annealer at $L\leq27$ (729 spins), we obtain the large-$L$ critical points for this model family, measuring quantum-driven transitions at ${g_c^{\mathrm{QPU}}}\in\{0.286,\,0.210,\,0.156,\,0.093\}$ for $α\in\{1.0,\,0.7,\,0.5,\,0.3\}$, where the analytically exact classical threshold is ${g_c^{\mathrm{class}}}(α)=2α/3$. The suppression ratio $r(α)$ exhibits a sharp two-regime structure: the three quasi-1D geometries ($α\leq0.7$) are mutually consistent with a universal plateau $\bar{r}=0.450$ ($χ^2/\mathrm{dof}=1.10$, $p=0.33$), demonstrating that quantum fluctuations destroy approximately $55\%$ of the classical FM stability window independently of coupling anisotropy, while $r$ steps down to the 2D limit above the empirical crossover scale $α^*\approx0.7$. Inner Binder cumulant pairs, which converge fastest to the thermodynamic limit, resolve $r(1.0)\approx0.412$ and a step $Δr=0.038\pm0.015$ from the quasi-1D plateau. A four-point linear fit $r(α)=0.494-0.063\,α$ summarises both regimes; its $α\to0$ intercept recovers the exact 1D result of Pfeuty within 1.7 standard deviations, and its slope is a lower bound on the true crossover amplitude concentrated in $α\in[α^*,1]$. Two sequential blind predictions, confirmed at $0.2σ$ and $0.7σ$ before each measurement, validate the crossover law. All four geometries show a direct ferromagnet-to-paramagnet transition, complete quantum ergodicity ($f_{\rm uniq}=1.000$), and null valence-bond solid order.

Landing methods have recently emerged in Riemannian matrix optimization as efficient schemes for handling nonlinear equality constraints without resorting to costly retractions. These methods decompose the search direction into tangent and normal components, enabling asymptotic feasibility while maintaining inexpensive updates. In this work, we provide a unifying geometric framework which reveals that, under suitable choices of Riemannian metric, the landing algorithm encompasses several classical optimization methods such as projected and null-space gradient flows, Sequential Quadratic Programming (SQP), and a certain form of the augmented Lagrangian method. In particular, we show that a quadratically convergent landing method essentially reproduces the quadratically convergent SQP method. These connections also allow us to propose a globally convergent landing method using adaptive step sizes. The backtracking line search satisfies an Armijo condition on a merit function, and does not require prior knowledge of Lipschitz constants. Our second key contribution is to analyze landing methods through a geometric parameterization of the metric in terms of fields of oblique projectors and associated metric restrictions. This viewpoint disentangles the roles of orthogonality, tangent and normal metrics, and elucidates how to design the metric to obtain explicit tangent and normal updates. For matrix optimization, this framework not only recovers recent constructions in the literature for problems with orthogonality constraints, but also provides systematic guidelines for designing new metrics that admit closed-form search directions.

One approach to studying the dynamics of a singular Lagrangian system is to attempt to regularize it, that is, to find an equivalent and regular system. In the case of time-independent singular Lagrangians, an approach due to \textit{A. Ibort} and \textit{J. Marín-Solano} is to use the coisotropic embedding theorem proved by \textit{M.J. Gotay} which states that any pre-symplectic manifold can be coisotropically embedded in a symplectic manifold. In this paper, we revisit these results and provide an alternative approach, also based on the coisotropic embedding theorem, that employs the Tulczyjew isomorphism and almost product structures, and allows for a slight generalization of the construction. In this revision, we also prove uniqueness of the Lagrangian regularization to first order. Furthermore, we extend our methodology to the case of time-dependent singular Lagrangians.

When dealing with stiff conservation laws, explicit time integration forces to employ very small time steps, due to the restrictive CFL stability condition. Implicit methods offer an alternative, yielding the possibility to choose the time step according to accuracy constraints. However, the construction of high-order implicit methods is difficult, mainly because of the non-linearity of the space and time limiting procedures required to control spurious oscillations. The Quinpi approach addresses this problem by introducing a first-order implicit predictor, which is employed in both space and time limiting. The scheme has been proposed in (Puppo et al., Comm. Comput. Phys., 2024) for systems of conservation laws in one dimension. In this work the multi-dimensional extension is presented. Similarly to the one-dimensional case, the scheme combines a third-order Central WENO-Z reconstruction in space with a third-order Diagonally Implicit Runge-Kutta (DIRK) method for time integration, and a low order predictor to ease the computation of the Runge-Kutta stages. Even applying space-limiting, spurious oscillations may still appear in implicit integration, especially for large time steps. For this reason, a time-limiting procedure inspired by the MOOD technique and based on numerical entropy production together with a cascade of schemes of decreasing order is applied. The scheme is tested on the Euler equations of gasdynamics also in low Mach regimes. The numerical tests are performed on both structured and unstructured meshes.

A graph is chordal if it contains no induced cycle of length four or more. While finite chordal graphs are precisely those admitting tree-decompositions into cliques, this fails for infinite graphs. We establish two results extending the known theory to the infinite setting. Our first result strengthens sufficient conditions of Halin, Kříž-Thomas, and Chudnovsky-Nguyen-Scott-Seymour: We show that every chordal graph without a strict comb of cliques admits a tree-decomposition into maximal cliques. Our second result characterises the chordal graphs admitting tree-decompositions into finite cliques: a connected graph admits such a decomposition if and only if it is chordal, admits a normal spanning tree, and does not contain $\mathcal{H}$ $\unicode{x2013}$ an infinite clique with two non-adjacent dominating vertices $\unicode{x2013}$ as an induced minor. Combined with the characterisation of graphs with normal spanning trees, this yields a description by three types of forbidden minors. Both proofs proceed via greedy constructions of length $ω$, with the key new ingredient for the second result being an Extension Lemma that uses a finiteness theorem of Halin on minimal separators to produce suitable finite clique extensions at each step.

In this work we introduce a new method for the construction of minimal submanifolds of codimension two in even dimensional spheres and hyperbolic spaces. This is based on the theory of complex-valued harmonic morphisms. This gives the first explicit examples of such maps defined on the sphere $S^4$ and the hyperbolic space $H^4$.

In this short note, we study dg categories with homotopy kernels, whose homotopy categories are known to admit a natural left triangulated structure. Prototypical examples of such dg categories arise as dg quotients of exact dg categories. We demonstrate that the stablization of the homotopy category of such a dg category admits a canonical dg enhancement via its bounded derived dg category.

We study two-dimensional periodic metamaterials in which idealised cylindrical inclusions are modelled by boundary conditions. In the scalar time-harmonic setting, the background field satisfies the Helmholtz equation, and high-contrast inclusion limits reduce to Dirichlet or Neumann conditions, with direct analogues in dielectric and acoustic media. By switching the condition assigned to selected inclusions, we break point-group symmetries of the primitive cell and thereby lift symmetry-induced degeneracies in the Floquet--Bloch spectrum of hexagonal and square lattices, opening valley-type band gaps with Berry curvature localised near opposite valleys. To analyse infinite and finite structures within a unified framework, we derive matched-asymptotic point-scatterer approximations for mixed Dirichlet--Neumann arrays. For doubly periodic systems, this yields a finite-dimensional generalised eigenvalue problem for the Floquet--Bloch spectrum; for finite arrays, it yields a generalised Foldy multiple-scattering system. In both hexagonal and square lattices, geometrically identical crystals can realise distinct valley-Hall phases solely through boundary-condition assignment while retaining an overlapping bulk gap. Spatially varying this assignment therefore creates and relocates internal interfaces without altering the underlying geometry, enabling the associated valley-Hall interfacial modes to be repositioned within the same crystal.

A graph is called strongly $\Z_{2k+1}$-connected if for each boundary function $β: V(G)\mapsto \Z_{2k+1}$ with $\sum_{v\in V(G)}β(v)\equiv 0\pmod{2k+1}$, there exists an orientation $D$ of $G$ such that $d_D^+(v) - d_D^-(v) \equiv β(v) \pmod{2k+1}$ for each $v \in V(G)$. We show that every planar multigraph with $5$ edge-disjoint spanning trees is strongly $\Z_{5}$-connected. This verifies a special case of the Additive Base Conjecture when restricted to planar graphs. Hence, every $10$-edge-connected directed planar graph admits an antisymmetric $\Z_5$-flow. So, by duality, every orientation of a planar graph of girth at least $10$ admits a homomorphism to a $5$-vertex tournament. Our result also gives a new proof of the known result that every planar graph of girth at least $10$ has a homomorphism to the $5$-cycle.

We classify $1+1$d bosonic SPT phases with non-invertible symmetry $\mathrm{Rep}(G)\times G$, equivalently the fusion-category symmetry $\mathcal{H}=\mathrm{Rep}(G)\times\mathrm{Vec}_G$. Focusing on \emph{intrinsically mixed} phases (trivial under either factor alone), we use the correspondence between $\mathcal{H}$-SPTs, $\mathcal{H}$-modules over $\mathrm{Vec}$, and fiber functors $\mathcal{H}\to\mathrm{Vec}$ to obtain a complete classification: such phases are parametrized by $ϕ\in\operatorname{End}(G)$. For each $ϕ$ we identify the associated condensable (Lagrangian) algebra $\mathcal{A}_ϕ$ in the bulk $\mathcal{Z}(\mathcal{H})\simeq\mathcal{D}_G^2$. We further provide an explicit lattice realization by modifying Kitaev's quantum double model with a domain wall $\mathcal{B}_ϕ$ and smooth/rough boundaries, and then contracting to a 1D chain, yielding a (possibly twisted) group-based cluster state whose ribbon-generated symmetry operators encode the same $ϕ$.

In compressible turbulent boundary layers (TBLs), roughness drag is typically characterised by first applying a velocity transformation to account for compressibility, after which the momentum deficit $ΔU^+$ (Hama, 1954) and the equivalent sand-grain roughness $k_s$ are inferred. In practice, $k_s$ is often obtained from measurements at a single Mach number $M$ and Reynolds number $Re$, effectively forcing the roughness into the $ΔU^+$--$\log(k_s)$ relation of Nikuradse (1933). This raises a key question: if a rough surface has a known $k_s$ in incompressible flow, under what conditions can this value be used in compressible flows? This question is explored using data obtained through a series of experiments of TBLs on rough walls (P60- and P24-grit sandpapers) over $0.3 \leq M \leq 2.9$ and $7427 \leq Re_τ \leq 30292$, including independent variation of $Re_τ$ at $M=2$. Results show that $ΔU^+$ is largely insensitive to the velocity transformation, but the fully rough regime exhibits a Mach-number-dependent shift in the logarithmic relation. Three empirical scalings are examined: an equivalent incompressible $k_s$, a viscosity-scaled roughness $k_{*} = k/ν_\infty^+$ with $ν_\infty^+ = ν_\infty/ν_w$, and a correction factor $\sqrt{1/F_c}$ where $F_c$ depends on $T_\infty/T_w$. The last provides the most consistent improvement across datasets, although all corrections remain empirical and rely on smooth-wall compressibility transformations. This paves the way for future work to develop custom transformation for a rough-wall TBL that can account for roughness properties and other parameters including wall conditions.

We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.

Robustness of higher-order networks is often quantified by the instantaneous smallest positive eigenvalue of the Hodge $1$-Laplacian under simplex deletion. We show that this observable is generically ill-defined: along a deletion trajectory, eigenvalue branches can switch, so the quantity being monitored may correspond to different nonharmonic modes at different steps. The primary issue is therefore definitional rather than algorithmic. We resolve it by fixing the first nonharmonic branch of the intact complex and following that same branch throughout the damage process, which defines a branch-consistent functional robustness. Triangle sensitivities then follow directly from first-order perturbation theory, making the resulting mode-sensitive deletion protocol a consequence of the observable itself rather than an independent heuristic. Across synthetic and empirical clique complexes, removing only a small fraction of triangles is sufficient to drive the tracked mode to collapse, while graph-level observables remain unchanged because the $1$-skeleton is exactly preserved. The same framework also reveals bridge-like localization of functionally critical simplices and provides a compact predictor of dynamical timescales.

Colloidal perovskite nanocrystals (NCs) are a well-proven platform for growing anisotropic structures. Nanowires (NWs) exhibiting a quantum confinement phenomenon and microwires (MWs), which enable lasing, are of particular interest for optoelectronic devices. Synthesis of the latter is challenging. Herein, we report a straightforward access to high-quality CsPbBr3 MW lasers. We utilize a diphenyl ether (DPE) solvent for the hot-injection synthesis. DPE coordinates strongly to Pb2+ and allows to reduce an excess of oleic acid/oleylamine ligand pair well established for PbBr2 dissolution and inhibition of as-formed NCs regrowth. Therefore, a rapid injection of Cs-oleate into the PbBr2-containing solution yields lead-depleted Cs4PbBr6 NCs which slowly release perovskite precursors and produce CsPbBr3 counterparts. The latter transform into NWs through an oriented-attachment mechanism, which in turn evolve into laser MWs. To demonstrate spectrally tunable lasing in MWs we employ YCl3 for ion exchange in perovskite lattice. Resultant CsPb(Cl,Br)3 MWs show high-Q coherent emission in the 485-540 nm range. To highlight the potential of synthesized MWs for integrated optoelectronics, we assemble a device comprising a CsPb(Cl,Br)3 MW laser coupled to MoO3 lossless nanowaveguide, which delivers coherent light to a CsPbBr3 MW photodetector. The device exhibits a nonlinear optoelectronic response applicable for on-chip neuromorphic computing.

The practical utilization of MnP in chiral spintronic devices is fundamentally constrained by its low helical ordering temperature ($T_{\rm S}$). Here, we demonstrate that Ru substitution in Mn$_{1-x}$Ru$_x$P single crystals drives a highly anisotropic lattice expansion, where the $b$-axis elongation is one-quarter that of the $a$- and $c$-axes ($\sim$ 0.04 Å). This structural distortion profoundly stabilizes the helical ground state, elevating $T_{\rm S}$ from 51~K to 215~K and the critical field along the [010] direction at 5~K from 2.3 to 30.0~kOe, while suppressing the Curie temperature ($T_{\rm C}$) from 291~K to 215~K. Synthesizing these results with reported data on Mo- and W-doped analogues reveals that $T_{\rm S}$ and $T_{\rm C}$ are governed primarily by the $b$-axis parameter, exhibiting universal linear scaling relationships ($dT_{\rm S}/db = 1.59 \times 10^4\ \text{KÅ}^{-1}$, $dT_{\rm C}/db = 0.69 \times 10^4\ \text{KÅ}^{-1}$) far greater than those associated with the $a$- or $c$-axes. First-principles calculations reveal that the lattice expansion selectively attenuates ferromagnetic coupling while preserving antiferromagnetic interactions between nearest-neighbor Mn atoms, thereby enhancing magnetic frustration and stabilizing helimagnetism. These findings establish chemical pressure via directed $b$-axis engineering as a robust, generalizable paradigm for stabilizing helimagnetism in MnP.

The Talbot effect -- a near-field diffraction phenomenon in which a periodic wavefront self-images at regular distances -- can be transposed to the time--frequency domain via the space--time duality between diffraction and dispersive broadening. We exploit this analogy to define the time--frequency (TF) Talbot effect and show that it implements different Clifford operations on TF Gottesman-Kitaev-Preskill (TF-GKP) qubits (Phys. Rev. 102, 012607), a class of qubit states encoded in the discretised frequency and time-of-arrival degrees of freedom of entangled photon pairs, whose logical basis corresponds to even and odd components of an entangled frequency combs. These states are intrinsically robust against small frequency and temporal displacements, which can be further corrected by linear or nonlinear quantum error-correction schemes. We analyse the role of the comb envelope and peak width relative to the free spectral range, and show that a compromise must be made between the gate fidelity of the Clifford gates induced by TF-Talbot operation and the error-correction capacity of the code. We then demonstrate that the signature of the TF-Talbot effect is directly accessible via the generalised Hong-Ou-Mandel interferometer: all six logical GKP states can be unambiguously distinguished by introducing a frequency shift of half the comb periodicity in one interferometer arm. We conclude with a feasibility analysis based on current experimental technology, identifying the comb finesse as the key figure of merit for both gate performance and correctability. This conclusion extends naturally to quadrature GKP states, where a shear in quadrature phase space is precisely a Talbot effect.

The visit probability, quantifying whether a particle has reached a given point for the first time by a specified time, provides access to various extreme value statistics and serves as a fundamental tool for characterising active matter models. However, previous studies have largely neglected how the visit probability depends on the internal degree of freedom driving the active particle. To address this, we calculate the "state-dependent'' visit probability for a Run-and-Tumble particle, that is the probability that the particle first passes through $x$ before time $t$, keeping track of its internal state during first passage. This process may be thought of as the particle "painting'' the positions it passes through for the time in the colour of its self-propulsion state. We perform this calculation in one dimension using Doi-Peliti field theory, by extending the tracer mechanism from previous works to incorporate such "polar deposition'' and demonstrate that state-dependent visit probabilities can be elegantly captured within this field-theoretic framework. We further derive the total volume covered by a right- (or left-) moving Run-and-Tumble particle and compare our results with known expressions for Brownian motion.