Understanding how neural population responses represent sensory information is a central problem in systems neuroscience. One approach is to define a representational geometry on stimulus space in which distances reflect how reliably stimuli can be distinguished from neural activity. However, different constructions of these distances can lead to qualitatively different conclusions about the neural code. Here, we show that a unique Riemannian representational geometry emerges from first principles governing how distances contract as stimulus resolution is lost through coarse-graining. This results in a multi-scale extension of the Fisher information metric, capturing encoding structure from fine stimulus details to coarse global distinctions. The resulting geometry is exactly related to the mutual information encoded by the population: well encoded stimulus directions - those contributing more to mutual information - are expanded, whereas poorly encoded directions are contracted. The metric tensor can be estimated using diffusion models, making the framework practical for large neural populations and high-dimensional stimuli. Applied to visual cortical responses to natural images, the eigenvectors of the metric tensor identify stimulus variations that contribute most to information transmission, yielding interpretable features that are robust to modelling choices. Together, these results provide a principled, information-theoretic framework for characterising neural population codes.

The strongly correlated phases of the homogeneous electron gas constitute the vocabulary of many-body condensed matter physics and find a natural realization in semiconductors. In this setting, recent neural-network variational Monte Carlo calculations discovered an unexpected quantum phase of matter in wide quantum wells: an electronic quasicrystal formed by a bilayer Wigner crystals with a 30-degrees twist. This state defies classical expectations and emerges in a regime dominated by quantum fluctuations. Here, we develop an analytical framework to reveal its origin. By computing zero-point energy corrections to bilayer Wigner crystal configurations, we show that quantum fluctuations qualitatively reshape the energetic landscape, destabilizing the classical honeycomb state and selecting the 30-degrees quasicrystalline ground state over a broad parameter range. Our results identify zero-point motion as the mechanism stabilizing the electronic quasicrystal and establish a route to spontaneous moiré physics driven by many-body quantum effects.

Higher-order interactions are increasingly recognized as a key component of ecological dynamics. However, we show that higher-order Lotka-Volterra dynamics can, in some scenarios, be accurately reproduced by effective pairwise models fitted to the same abundance time series. Consequently, higher-order interactions cannot, in general, be inferred from time-series data alone. We further identify a fundamental problem of mechanistic identifiability, whereby distinct interaction mechanisms generate nearly indistinguishable dynamics, potentially leading to accurate yet misleading ecological interpretations. Our results highlight the need to complement time-series data with additional ecological information to infer interaction structure reliably.

We propose an effect named the anomalous Thomson effect (ATE), analogous to the anomalous Hall effect and the anomalous Nernst effect (ANE). The anomalous Thomson coefficient (ATC) is derived as a function of the anomalous Nernst coefficient (ANC); hence, the ATC inherits the same mechanisms of the ANC. Specifically, we study a massive Dirac model for Fe3Sn2 to capture intrinsic Berry-curvature-driven transport. Our results show that the ATC is generally enhanced relative to the ANC. In the low-temperature limit, the ratio ATC/ANC approaches three. Since the relation between the ATE and the ANE is model-independent, we utilize experimental ANE data to infer experiment-related ATC for CoS2, Co3Sn2S2, and CeCrGe3. We find that the ATC for CeCrGe3 can be as large as fifteen times the ANC in the liquid-nitrogen temperature regime, making this effect highly attractive for solid-state thermoelectric refrigeration in this temperature range. It is important to emphasize that the proposed ATE can be directly verified using existing ANE data, without the need for additional equipment or measurements.

The cavity-mediated coupling between magnons in an yttrium-iron-garnet (YIG) sphere and a superconducting qubit has recently been demonstrated as a new platform for preparing macroscopic quantum states. Here, based on this system, we propose to entangle two magnon modes in two YIG spheres by driving the qubit with a two-tone field and by appropriately choosing the frequencies and strengths of the two driving fields. We show that strong entanglement can be achieved with fully feasible parameters. We further provide a detection scheme for experimentally verifying the entanglement. Our results indicate that macroscopic entanglement between two magnon modes in two millimeter-sized YIG spheres, involving more than $10^{18}$ spins, can be realized using currently available parameters, which finds promising applications in fundamental studies, such as macroscopic quantum mechanics and the test of unconventional decoherence theories.

We develop a comprehensive theoretical framework that unifies quantum emission dynamics in one-dimensional Lieb lattices, bridging the gap between ideal flat-band coherence and realistic narrow-band dissipation. By coupling an emitter to sublattices with finite flat-band wavefunction overlap, we activate a collective, size-independent interaction fundamentally distinct from dispersive-band processes. Controllably breaking lattice symmetry transforms the flat band into a narrow dispersive band, enabling a continuous crossover from non-Markovian to Markovian dynamics governed by the competition between coupling strength and engineered bandwidth. Crucially, we derive explicit scaling laws that provide a quantitative blueprint for tuning spontaneous emission from coherent trapping to Markovian decay. Our work provides a unified framework that connects idealized flat-band physics to emerging narrow-band platforms such as moir$\rm\acute{e}$ photonic crystals, offering a practical toolkit for interpreting experiments and engineering quantum emission in structured photonic environments.

The fluctuations of ions in polar solvents remain poorly understood theoretically due to the complex coupling between ionic motion and solvent polarization. Indeed, while all-atom resolution can be achieved in numerical simulations, analytical approaches require suitable levels of coarse-graining. In this work, we describe ions and solvent molecules as interacting Brownian particles and use stochastic density functional theory to derive a generalized Langevin equation for the ionic charge density, explicitly accounting for solvent-mediated memory effects. In the regime where there is a clear timescale separation between fast solvent and slow ion dynamics, we obtain simple expressions for dynamical charge structure factors, which are validated by BD simulations. For slow solvents, we predict an emerging two-step relaxation in ionic dynamics. These results provide a mesoscopic approach for ion-solvent dynamics and open pathways to study fluctuation-induced phenomena in electrolytes.

Causal models, also known as Structural Equation Models (SEM), are a well-known formalism for representing and reasoning about causal dependencies between events. In this paper, we show that Temporal SEMs (TSEMs), which extend SEMs to support causal reasoning in temporal settings, can be interpreted as a model of computation. We prove that TSEMs can encode Linear Bounded Automata, and thus causal settings representable in context sensitive languages. We also prove that TSEMs with countably many variables are Turing complete. These results establish a formal connection between causal reasoning and classical models of computation, enabling the integration of counterfactual reasoning techniques from causal inference into the theory of computation.

Two-dimensional honeycomb lattice ferromagnet chromium tri-iodide (CrI$_3$) has attracted tremendous interest because it retains ferromagnetism down to the monolayer limit and hosts intriguing topological magnons. As a prototypical van der Waals magnet, CrI$_3$ provides an ideal platform for exploring the interplay between reduced dimensionality, magnetic order, and nontrivial spin excitations. Here, using inelastic neutron scattering together with improved sample quality, we uncover the magnon winding feature around the $K$-point of the hexagonal Brillouin zone, a key signature of Dirac magnons. In addition, we find that the magnon energy follows a $T^2$-renormalization behavior at elevated temperatures, consistent with magnon-magnon interactions. These results provide previously missing information on the magnon spectrum of CrI$_3$ and further consolidate the topological nature of its spin excitations.

This correspondence presents a convex-optimization-based evaluation framework of satellite-swarm-based apertures maintained by magnetic-field interactions. Spaceborne distributed apertures are composed of multiple satellites and are attractive for scientific and commercial missions because their scalability enables high-gain, narrow-beam, and large-aperture capabilities beyond the launch-size limitations. A key challenge is that the long-term maintenance of such virtual structures requires consistent formation control amid unstable orbital dynamics, and magnetic interactions generated by satellite-mounted magnetorquers offer a desirable propellant-free position-control strategy. However, the nonlinearities of the electromagnetic force and torque model lead to a nonconvex power-consumption constraint, making system-level configuration analysis difficult. To address this issue, we develop a convex optimization-based framework to analyze the power consumption of large magnetically actuated satellite swarms. The resulting analysis shows that increasing the number of satellites can improve formation-keeping power efficiency. This indicates that magnetically actuated swarm architectures provide a power-efficient alternative to the conventional few-satellite electromagnetic formation-flight concept for constructing large-scale space systems.

We generalize the unfolding of a Reed Muller distillation factory of Ruiz et. al. by exhibiting the algebraic structure that the unfolding is based on. We describe a 2D local layout for the Z stabilizers of a distance 4 Reed Muller distillation factory and a 3D local layout for the Z stabilizer of a distance 4 and a distance 7 Reed Muller distillation factory. Given input T states with infidelities $p=10^{-3}$, the 2D local distillation factory with distance 4 outputs a CCZ state with infidelity $p=8.256 \times 10^{-9}$ and the 3D local distillation factory with distance 7 outputs a T state with infidelity $p=1.1811 \times 10^{-17}$.

The thermal noise of mirror coatings for gravitational-wave detectors critically depends on the elastic properties of the constituent materials. Data analyses and theoretical models typically assume each material is homogeneous and isotropic, but isotropy has never been explicitly verified. Using Brillouin light scattering (BLS), we demonstrate for the first time that ion-beam-sputtered SiO2 -- a material still viable for future mirror coatings -- exhibits cylindrical elastic symmetry, with in-plane isotropy but a notable 6% compressive anisotropy along the film normal. This anisotropy remains unchanged after the post-deposition heat treatment currently used in ground-based detectors (500 $^\circ$C, 10 h) but is nearly eliminated at 900 $^\circ$C. Infrared reflectivity experiments support these findings by directly revealing heterogeneities in the distribution of bridging and non-bridging oxygen structures along the growth axis. While BLS measures the real part of the elastic constants at GHz frequencies, the data reveal negligible contributions from mechanical relaxations in the kHz-GHz range, making BLS a valid substitute for low-frequency properties obtained from standard anisotropy-insensitive techniques. Our results highlight that restoring isotropy through heat treatment -- by softening the material, enabling more than 7% out-of-plane expansion, and smoothing out structural heterogeneities -- may play a key role in reducing thermal noise. This proof-of-concept study extends beyond silica, providing critical insights for the design of future coatings.

In this note, we study the geometric structure of the parameter sets governing continuous embeddings between weighted Bergman-Orlicz spaces. First, for a fixed pair of growth functions, we show that the set of admissible weight exponents $(α, β)$ is convex, provided the growth functions satisfy specific log-convexity and log-concavity conditions of the inverses. Second, we consider the dual problem where the weight exponents are fixed. We prove that the collection of growth function pairs that yield such an embedding is log-convex under a natural interpolation of their inverses. We then obtain interpolated embeddings between Bergman-Orlicz spaces.

We study the origin of the non-monotonic magnetic-field dependence of the lowest charged pion excitation observed in lattice QCD. In a magnetic field, the charged pion mixes with the longitudinally polarized charged rho meson, which shares the same quantum numbers. Within the SU(2)$_f$ Nambu--Jona-Lasinio model supplemented by a gauge invariant tree-level $π-ρ$ mixing operator constrained by the experimental $ρ^\pm\rightarrowπ^\pmγ$ decay width, we compare four mass-extraction schemes: rest-mass reconstruction, local bosonization, direct determinant solving with Landau projection, and near-pole expansion. The rest-mass scheme cannot reproduce the lattice-type turnover, while in the local derivative-expansion scheme the turnover presence but is weak which occurs at large magnetic field. By contrast, the direct determinant and near-pole schemes both retain a robust non-monotonic lowest mode. The former is most faithful to the Landau-level kinematics of the charged excitation, while the latter most clearly shows that residue suppression enhances the effective mixing after canonical normalization. Our results indicate that the lattice behavior is a genuine quasiparticle mixing effect, but one whose robustness depends crucially on how the charged-meson pole structure is extracted in a magnetic field.

Transducers generalise automata by producing output word(s) for each input word, thereby defining a relation over words. A transducer is said to be finite-valued if, for every input word, it produces at most $k$ output words, for some constant $k$. If $k = 1$, then the transducer is said to be functional. The edit distance between two transducers is the minimal number of edits required to transform every output of one transducer into some output of the other, for each input word. This notion has been studied for functional transducers, where it is shown to be computable. However, it is uncomputable for transducers in general. In this work, we show the computability of the edit distance of finite-valued transducers, a class that is strictly more expressive than functional transducers.

Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of graded coalgebras-including graded distributive laws between graded monads-and we give conditions for the existence of terminal coalgebras. We define both branching-time and trace semantics, linking them to recent work on Feller-Dynkin processes. Finally, we develop coalgebraic modal logics for both process semantics and state criteria for invariance and expressivity.

In recent years, improvements in galaxy cluster observations have enabled a variety of tests of fundamental physics using these systems. In this work, we test the constancy of the speed of light, $c$, by combining X-ray gas mass fraction measurements from galaxy clusters with SNe Ia luminosity distance measurements from Pantheon+. We adopt the SH0ES prior on $H_0$ and the $Ω_b/Ω_m$ ratio from galaxy clustering observations, thereby minimizing the dependence of our analysis on any specific cosmological model. We explore different assumptions for the cluster mass calibration (mass bias), including \textsc{CLASH}, \textsc{CCCP}, and Planck-based estimates. We find no deviation from a constant $c$ when adopting \textsc{CLASH} or \textsc{CCCP} priors, while Planck-based calibration yields a mild tension, with the hypothesis of constant $c$ being only marginally consistent at the $2σ$ level, indicating a non-negligible sensitivity of the results to the adopted calibration scheme.

Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable systems, focusing on two complementary strategies to mitigate decoherence: Hamiltonian engineering and the exploitation of non-Markovian dynamics. By embedding squeezing directly into the system Hamiltonian, we show that the quantum Fisher information (QFI) may acquire a tunable higher-order time dependence, leading to enhanced sensitivity in the short-time regime. Moving beyond the Markovian approximation, we employ the quantum Brownian motion model to demonstrate that structured environments with finite memory can induce information backflow, temporarily restoring and even improving estimation precision relative to the unitary limit. We further assess the achievability of these bounds via Gaussian measurements, identifying regimes where homodyne, heterodyne, and optimized general-dyne measurements saturate the QFI, and noting that stronger squeezing widens the gap, potentially requiring non-Gaussian measurement strategies. Our results establish that jointly tailoring system Hamiltonian and environmental memory offers a viable route toward robust quantum-enhanced frequency estimation in open systems.

Treewidth is a well-studied decompositional parameter to measure the tree-likeness of a graph. While the propositional satisfiability problem (SAT) is known to be tractable when parameterized by the treewidth of the underlying primal graph, the evaluation of quantified Boolean formulas (QBFs) remains PSPACE-complete even on formulas of constant treewidth. Intuitively, this is because ordinary treewidth does not take into account the prefix of the QBF: it neither distinguishes between existential and universal variables, nor accounts for the order in which they are quantified. In the past, several weaker variants of treewidth have been devised to incorporate prefix-sensitive information. To establish tractability for QBFs under these notions, prior work has employed either strategy- or resolution-based techniques, thereby dividing the parameterized complexity landscape of QBF into two regimes that are incomparable in strength. We establish fixed-parameter tractability with respect to bilateral treewidth, a novel and strictly more powerful decompositional parameter that combines these rivaling approaches by simultaneously allowing for branching on strategies and performing Q-resolution. As in previous works in this direction, our algorithm assumes that a suitable tree decomposition is provided on the input.

Personalization is crucial for effective learning, yet online learning, designed for widespread availability and open access, lacks personalized guidance. Recent advancements in large language models (LLMs) offer opportunities to bridge this gap. We explore how LLM-driven tools may be designed to support personalized and adaptive learning and examine how they shape user experience and learning outcomes. We iteratively designed \tool{} to support online learning by providing personalized study plans, real-time contextual assistance, and adaptive learning activities. A preliminary study ($n=24$) assessed the effectiveness and usability of \tool{} and informed refinements in our system, which we then evaluated ($n = 16$) against a combination of a state-of-the-art online learning platform and an LLM for learning support. Results indicate that \tool{} advances AI pedagogy by improving both learning outcomes and user experience compared to existing online learning and support tools. This work advances our understanding of the design space of personalized, AI-driven educational tools and their potential impact on user experience.

In this paper, we propose a novel integrated sensing and communications (ISAC) framework for collaborative multi-static target localization in dense Industrial Internet-of-Things (IIoT) environments in the presence of environmental clutter. We first develop a lightweight temporal clutter-suppression learning method to mitigate persistent reflections. Building on this, we propose an iterative localization algorithm that integrates two key components introduced in this work: a sampling-based field-of-view-aware initialization (SFI) scheme and an empirical position error bound (PEB) scheme, which together adaptively identify the most informative subset of sensing nodes. A reliability-aware weighted least-squares estimator is then employed to fuse range and angle-of-arrival measurements from the selected sensing receivers for target localization. Numerical results demonstrate rapid convergence of the proposed method, reducing the localization RMSE by nearly two orders of magnitude within six sensing iterations to about 45 cm, while significantly outperforming all considered benchmarks under the same sensing-resource budget.

We present a novel procedure for generating synthetic well logs that simultaneously preserves multivariate correlations among petrophysical properties (Density, P-Sonic, S-Sonic) and vertical stacking patterns of electrofacies. The methodology integrates Markov chain models, autoencoder-based dimensionality reduction, and Markov chain Monte Carlo (MCMC) sampling in latent space. Application to a real turbidite reservoir dataset demonstrates that the framework successfully sustains fundamental rock physics relationships and generates geologically realistic vertical heterogeneity consistent with actual well log measurements. This technique addresses critical data scarcity in machine learning applications for seismic interpretation while enabling credible synthetic seismogram generation for scenario testing and uncertainty quantification in petroleum exploration and field development.

We give a cohomological interpretation of the geodesic simplices of the pseudo-hyperbolic space of signature $(p,q)$ and formulate a necessary and sufficient condition for such a simplex to have finite volume. As a corollary, we obtain that every ideal geodesic polytope in the pseudo-hyperbolic space of signature $(2,2)$ has finite volume.

We characterize the Artin invariant of a smooth K3 hypersurface in terms of quasi-$F$-splitting. As an application, we obtain an explicit formula for this invariant.

We consider the kinematic axioms of quantum mechanics projectively. Instead of normalized (pure) states up to global phase, states become one-dimensional subspaces of vector spaces. This process of projectivization is functorial and lax monoidal. For qubits it identifies the Bloch sphere with the Riemann sphere. We interpret a fragment of the ZXW-calculus projectively and thereby provide an alternate derivation of the arithmetic GHZ/W-calculus of Coecke et al. We find meromorphic functions that characterize the coherent behaviour of circuits for logical state preparation of quantum codes and magic state distillation.

Differential phase shift keying (DPSK) constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances in the security of DPSK have proven its security against general adversaries, albeit requiring limitations, including strong repetition rate constraints at the security proof and costly statistical estimators. In this work, we overcome said limitations by leveraging recent techniques in variable-length general security by using entropy accumulation techniques based on Rényi leftover hashing, together with conic optimization methods. Our approach achieves secret key rates with $10^5$ signals beyond 12 dB, constituting a robust proof of the experimental implementability of industrial-grade DPSK.

As the $q$-analog of Chebyshev polynomials, $q$-Hermite polynomials form a cornerstone in the family of $q$-orthogonal polynomials, which play a fundamental role in quantum algebra and mathematical physics. Recently, Andrews obtained a series of Rogers-Ramanujan type identities by constructing Bailey pairs from Chebyshev polynomials. In this paper, by applying the expansion formula of Chebyshev polynomials in terms of $q$-Hermite polynomials and using the orthogonality relations, we derive a series of Rogers-Ramanujan type identities on double sums, which further generalized the known results due to Andrews, Shi, Sun and Yao.

Multimodal Emotion Recognition (MER) has attracted growing attention with the rapid advancement of human-computer interaction. However, different modalities exhibit substantial discrepancies in semantics, quality, and availability, leading to highly heterogeneous modality combinations and posing significant challenges to achieving consistent and reliable emotion understanding. To address this challenge, we propose the Modality-Aware Contrastive and Uncertainty-Regularized (MCUR) framework, which approaches MER from the perspective of representation consistency, aiming to enable robust emotion prediction across heterogeneous modality combinations. MCUR incorporates two core components: (1) Modality Combination-Based and Category-Based Contrastive Learning mechanism (MCB-CL), which encourages samples with the same emotion category and the same available modalities to be close in the representation space; and (2) Sample-wise Uncertainty-Guided Regularization (SUGR), which adaptively assigns sample-wise uncertain weights to samples to optimize training. Extensive experiments demonstrate that MCUR consistently outperforms existing methods, achieving average F1 gains of 2.2% on MOSI, 2.67% on MOSEI, and 4.37% on IEMOCAP.

In open quantum systems with strong symmetries, the global scaled cumulant generating function (SCGF) is generally nonanalytic, so the Gärtner-Ellis theorem cannot directly yield the genuine large-deviation rate function. To address this issue, we propose that the theorem remains valid within blocks of the systems' operator space: we first obtain local rate functions for each block via the theorem and then recover the global one by minimization. This approach is justified by the dissipative freezing phenomenon in such systems. We demonstrate the scheme in an analytical model and a three-spin model with XX interaction. In the latter, we find that the vanishing of a nonanalytic point in the global SCGF under dephasing appears as an avoided ``level'' crossing, and we quantify this behavior using a degenerate perturbation theory.

In evolutionary biology, phylogenetic networks are now widely used to represent the historical relationships between species and population, when this history includes reticulation events such as hybridization, gene flow and admixture between populations. Semidirected phylogenetic networks are appropriate models when the direction of some edges and the root position are not identifiable from data. Comparing semidirected networks is important in many applications. For rooted and directed networks, a $μ$-representation was originally introduced to distinguish tree-child networks, and has since been extended in two different directions: to the larger class of orchard directed networks by adding an extra component that counts paths to reticulations; and to semidirected networks, through an edge-based variant. However, the latter does not provide a distance between semidirected and orchard networks. We introduce here a new edge-based $μ$-representation capable of distinguishing distinct orchard binary semidirected networks. For this class, we provide a reconstruction algorithm and therefore obtain a true distance that is computable in polynomial time.