We present a catalogue of HI sources extracted from the MIGHTEE survey data cubes covering the COSMOS field. The catalogue contains 293 sources in the redshift range of 0.004 < z < 0.093. In addition to HI masses and velocity widths, the catalogue includes optical through near-infrared photometry and inferred stellar masses and star-formation rates. The quantity of sources in the HI catalogue acquired through untargeted source finding is greatly influenced by the source finding methods used. This study therefore also provides a well-characterised expected completeness of the detected sample of galaxies based on their properties, informing of any detection biases, inferred through a comparative study of different source finding algorithms. We have tested the performance of widely-used source finders: PyBDSF, ProFound and SoFiA, along with new source finder LESHI, focusing exclusively on HI source detection rather than source characterisation in the first instance. The source finders were tested by injecting a sample of simulated galaxies divided into narrow bins of mass, inclination and distance into a MeerKAT data cube. The results inform the source finding strategies for the MeerKAT International GigaHertz Tiered Extragalactic Exploration (MIGHTEE) survey, as well as upcoming SKAO surveys.

The hierarchy problem between the electroweak (EW) and Planck scales remains a central puzzle in modern physics. We discuss a promising solution operating through the cosmological selection of the EW vacuum in a multiverse landscape, where the EW scale is dynamically approached as the configuration that maximizes the vacuum energy. By extending the Standard Model with a complex scalar singlet and right-handed neutrinos, charged under a global $U(1)_{B-L}$ symmetry, the model not only explains the smallness of the EW scale. It can also account for neutrino masses via the seesaw mechanism and the matter-antimatter asymmetry via leptogenesis. In addition, it provides a viable dark matter candidate that is testable in future neutrino experiments.

We study hyperonic density-dependent three-body effects in cold neutron-star matter using a Skyrme energy-density-functional framework. In beta-equilibrated $npeμΛ$ matter, the effective $ΛNN$ and $ΛΛN$ terms are varied separately in the $(β,A_3)$ and $(γ,C_3)$ planes, and each tabulated equation of state is used in Tolman--Oppenheimer--Volkoff calculations. The calculated $P$--$\varepsilon$ branches are classified by monotonicity and extremum structure. The $ΛΛN$ term does not affect the $Λ$-onset condition, but modifies the finite-$Λ$ post-onset EOS: increasing $C_3$ generally stiffens the post-onset branch and raises $M_{\max}$ in mechanically admissible regions, whereas increasing $γ$ reduces this enhancement at fixed $C_3$. In contrast, the $ΛNN$ term shifts the $Λ$-onset density and modifies the post-onset EOS simultaneously, producing organized branch-limited and Maxwell-candidate regions for some reference interactions. Representative two-extrema cases are examined with Maxwell constructions. We also perform an exploratory Bayesian analysis using neutron-star mass--radius information alone and apply XGBoost--SHAP surrogate diagnostics to summarize parameter sensitivities. Within the adopted likelihood and prior ranges, the posterior weight tends to favor sizable hyperonic three-body repulsion, and the SHAP analysis identifies $A_3$ and $C_3$ as important controls of $M_\text{max}$ and $R_{2.0}$. These results show that maximum-mass recovery in hyperonic neutron stars is not a single mechanism: $M_\text{max}$ maps must be interpreted together with onset behavior, branch admissibility, and extremum-count diagnostics. *shortened due to the arXiv's word limit.

This article evaluates AI-enabled influence operations in synthetic social networks through controlled simulations of narrative release, amplification, and counter-messaging. We measure exposure and belief change in agentic audiences, showing that amplification maximizes reach, counter-messaging shifts opinions most, and narrative release requires larger attacker footprints.

We study a nonequilibrium coherent effect generated by a finite chemical potential in a complex scalar field with a conserved $U(1)$ charge. The scalar excitation is treated as a probe coupled to an equilibrium thermal reservoir, so the self-energy is an equilibrium kernel and there is no backreaction on the bath. Solving the Schwinger-Keldysh-Kadanoff-Baym equations in the normal phase, when the chemical potential is smaller than the dispersion relation, we keep the particle and antiparticle quasiparticle poles separate. The source-driven inhomogeneous statistical propagator is fixed by the reservoir and relaxes to the usual decoherent equilibrium form. By contrast, the homogeneous solution carries initial-condition memory; finite chemical potential turns this memory into a transient particle-antiparticle interference pattern by splitting the two charge-sector phases. The effect is not a new equilibrium mode, but a phase-sensitive remnant of the initial data that is erased by damping as $t\to\infty$. We define a normalized interference contrast extracted from the mixed charge-sector terms, illustrate the relaxation using the plasmon damping rate of hot scalar $ϕ^4$ theory, and show that the same normal-phase solution displays the infrared enhancement that precedes Bose-Einstein condensation.

Variational Quantum Algorithms (VQAs) combine quantum circuits with classical optimization to tackle problems that may benefit from the capabilities of near-term quantum hardware. In knowledge graph embedding, recent proposals based on this approach follow a similar overall architecture but differ in the way they compute the score function and in the number of qubits they require. One design uses $n+1$ qubits and obtains the score through a switch test on an ancillary qubit, while another employs $2n+1$ qubits and applies a swap test between two registers. In both cases, entities and relations are represented in a Hilbert space of dimension $d = 2^n$, with comparable computational cost and the same mean squared error loss. This work introduces a unified framework that captures the two schemes and makes it possible to explore new variants. Within this setting, we propose an alternative that keeps the intuitive meaning of the score function while dispensing with ancillary qubits and entangled measurements. The result is a model better suited to current NISQ devices, reducing hardware demands without sacrificing interpretability.

Living cells are energy- and information-processing systems that sustain a nonequilibrium steady state (NESS) by continuously consuming energy and dissipating heat, as required by the second law of thermodynamics. The rate of heat dissipation, or the entropy production rate $σ$, is the universal primal life signal and a unique descriptor of the cellular state. Living matter dissipates $P_{\mathrm{life}} \sim 1$ Watt/kilogram (W/kg), a remarkably conserved value across scales, from molecular reactions to entire organisms. Surprisingly, this high power density is $10^{4}$ times larger than that of the Sun and comparable to the universe's average, $P_U = c^2 H_0 \sim 1$ W/kg, where $c$ is the speed of light and $H_0$ the Hubble constant, a striking coincidence that aligns with Dirac's large number hypothesis. We hypothesize that this large $P_{\mathrm{life}}$ sets the scale for generating negentropy, the negative contribution to the overall positive $σ$ that sustains biological organization, distinguishing animate from inanimate matter. Here, I introduce heatomics, the science of studying $σ$ at the cellular and molecular scales, and the Variance Sum Rule, an experimental--theoretical framework that extracts $σ$ from fluctuations of a dynamical probe combined with the equation of state for a NESS. The emerging field of heatomics aims to elucidate the fundamental principles governing heat power generation, optimization of energy resources, and negentropy in living systems.

Stellar obliquity ($λ$) and orbital eccentricity ($e$) trace the dynamical histories of close-in giant planets, but the current observational picture is assembled from heterogeneous analyses that have obscured population-level trends. In this work, we homogeneously refit systems with Rossiter-McLaughlin (RM) measurements by performing a joint global fit to spectral energy distributions, transit light curves, mid-transit times, out-of-transit and in-transit radial velocities, yielding self-consistent posterior distributions for the physical and orbital parameters of both stars and planets across 255 systems. Restricting to 145 single-star systems with reliable planet-mass measurements, we uncover pronounced structure in the $e-λ$ plane that depends on planet mass: (i) sub-Saturns ($M_{\rm p} \leq \sim0.3M_{\rm J}$) can be both eccentric and misaligned; (ii) Jupiters ($\sim0.3M_{\rm J}<M_{\rm p} \leq \sim3 M_{\rm J}$) are misaligned only on circular orbits; and (iii) super Jupiters and brown dwarfs ($M_{\rm p}>\sim3M_{\rm J}$) are aligned across the full eccentricity range. A two-dimensional Kolmogorov-Smirnov test shows that the joint $(e,λ)$ distributions differ significantly among these three mass regimes. These trends demonstrate that $λ$ depends jointly on eccentricity and planet mass, implying that obliquity alone is not a unique tracer of evolutionary history and underscoring the need for a unified framework for the origins of spin-orbit misalignment. The full catalog from this work is publicly available at https://www.stellarobliquity.com .

Pulsar glitches are believed to originate from the dynamics of quantized vortices in the neutron superfluid interior. The outer core of a neutron star hosts a $^3\text{P}_2$ spin-triplet superfluid, whose half-integer quantum vortices (HQVs) are qualitatively different from the $^1\text{S}_0$ singly quantized vortices (SQVs) in the inner crust. It has recently been proposed that the coupling between these two vortex species gives rise to a large-scale vortex network, providing a candidate mechanism for the diversity of observed pulsar glitch phenomena. Using the Gross--Pitaevskii equations for the $^1\text{S}_0$ and $^3\text{P}_2$ condensates, we perform two-dimensional simulations of one SQV and two HQVs in a coexistence phase near the crust-core boundary, varying the density--density and Josephson coupling constants. We find that the Josephson term, arising from the relative phase between the two condensates, induces a strong attractive interaction between the two HQVs and the SQV, which dominates over the density--density coupling. When pinning potentials are applied to the HQVs and the SQV at spatially separated locations, this attraction is found to be sufficiently strong to drive vortex depinning. These results suggest that two HQVs and one SQV can form a tightly bound composite vortex at the crust-core boundary, with implications for the glitch mechanism in neutron stars.

Orbital eccentricity encodes key information about compact-binary formation channels and astrophysical environments, making it a critical target for gravitational-wave (GW) inference. We present parameter-estimation (PE) analyses of GWs from eccentric compact binaries with the SEOBNRv6EHM waveform model. Using long, highly eccentric numerical-relativity waveforms as synthetic signals, we compare parameter recovery across state-of-the-art eccentric models. We find that SEOBNRv5EHM and TEOBResumS-Dalí can yield biased estimates of eccentricity, masses, and spins in the most challenging configurations, while SEOBNRv6EHM significantly reduces these biases. Applying SEOBNRv6EHM to 26 GW events from the O1--O4 LIGO--Virgo--KAGRA observing runs -- including binary black hole, neutron-star--black-hole, and binary neutron-star mergers -- we identify five events with mild support for eccentricity over the quasi-circular precessing-spin hypothesis, with Bayes factors $\log_{10} \mathcal{B}^{\text{EAS}}_{\text{QCP}} > 0.5$. Since SEOBNRv6EHM is applicable to generic planar binaries, we reanalyze five high-mass events allowing for unbound initial conditions. For three of them -- including GW190521, previously claimed to originate from a dynamical capture -- a direct-capture configuration is comparable to, or marginally favored over, both the eccentric aligned-spin and quasi-circular precessing-spin hypotheses ($\log_{10}\mathcal{B}^{\rm unbound}_{\rm QCP} \approx 0.2$--$0.6$ for GW190521). The recovered configurations are, however, astrophysically unrealistic and cannot be confidently discriminated from highly eccentric bound orbits, so these results do not, by themselves, support an unbound origin for these events. SEOBNRv6EHM is approximately three times faster in PE analyses than SEOBNRv5EHM, while improving waveform accuracy, enabling efficient, large-scale GW inference with eccentric waveforms.

Accurate and computationally efficient waveform models are required to infer the parameters of compact binaries from their gravitational wave (GW) emission. Among these parameters, orbital eccentricity serves as a smoking gun for dynamical formation channels and must be accounted for to avoid systematic errors in GW analyses. Here, we present SEOBNRv6EHM, a time-domain, multipolar waveform model for binaries on generic planar orbits, calibrated to quasi-circular (QC) numerical-relativity (NR) simulations from the SXS collaboration. In addition to the dominant $(2,2)$ mode, the model provides the $(2,1)$, $(3,3)$, $(3,2)$, $(4,4)$, and $(4,3)$ multipoles for the full inspiral-merger-ringdown process of coalescing binaries, as well as for dynamical captures and scattering encounters. The model is built within the effective-one-body (EOB) framework, and it employs novel resummations of the radiation-reaction force and waveform modes. We validate its accuracy through comparisons against 592 QC, 319 eccentric, one dynamical-capture, and two scattering SXS NR waveforms, and through scattering-angle comparisons against 61 SXS NR simulations. For QC and small-eccentricity binaries, its accuracy is comparable to previous-generation SEOBNRv5 models. For highly eccentric systems, however, SEOBNRv6EHM attains unprecedented accuracy, with waveform mismatches remaining below or close to $ 2\% $ across the total mass range $ 20-200\, \mathrm{M}_\odot $ for eccentricities up to $\sim 0.9$ at 14 periastron passages before merger. Additionally, SEOBNRv6EHM achieves waveform-generation walltimes that are $ 2 - 6 $ times faster than other state-of-the-art EOB eccentric models, enabling efficient and accurate applications in GW astronomy.

We construct prime Fano manifolds from spin representations of $Spin_n$ for $n\le 14$. In this range, and if $n\ne 13$, the projectivizations of these representations are prehomogeneous, and we deduce that our Fano manifolds are locally rigid and, up to a few exceptions, quasi-homogeneous under the action of their automorphism groups. For $n=13$ we obtain a non-trivial family of minimal compactifications of $SL_3\times SL_3$, modulo some finite group.

In 1974, Witsenhausen asked for the maximum possible density $α_n$ of a measurable subset $A$ of the unit sphere $\mathbb{S}^{n-1}\subset \mathbb{R}^n$ such that $A$ contains no pair of orthogonal vectors. For $n=3$, the best known lower bound is $1 - 1/\sqrt{2} = 0.29289\dots$, obtained from the natural "double cap" construction of two opposite spherical caps, which is conjectured to be optimal for all $n$ by Gil Kalai. In this paper, we use a novel approach to establish an upper bound of $α_3\le 0.2953$, improving the previous best known bound $0.2977$ due to Bekker et al. (2025). Our approach combines harmonic-analytic arguments with the geometric fractional chromatic number of finite graphs, recently introduced by Ambrus et al. (2024). In this framework, any finite subset of the sphere yields an upper bound for $α_n$, and we obtain our bound by identifying an appropriate 33-element point set through a large-scale computer search. The same method can also be used in higher dimensions to yield potential improvements of the best known bounds.

We study topological conditions ensuring the presence of rotational chaos for non-wandering or area-preserving annular homeomorphisms. Compared to previous criteria, our main result provides a simpler alternative that avoids the need to locate periodic points, requiring only knowledge of the behavior of certain open sets. This feature is crucial for enabling concrete applications to Poincaré return maps arising in Hamiltonian systems with two degrees of freedom. The resulting topological criterion admits straightforward numerical implementation: a computer can verify all the required conditions using a simple algorithm that relies solely on basic data from the map. We illustrate this approach with the so-called driven pendulum.

We study infinite-horizon robust Markov decision processes (MDPs) on continuous state spaces with structured rectangular ambiguity set. The proposed ambiguity set falls within the convex hull of unknown generating kernels. We utilize the dynamic formulation of the corresponding robust MDPs, and subsequently introduce a stochastic first-order method for robust policy evaluation. We establish its high probability convergence to the robust value function, which in turn leads to an $\widetilde{\mathcal O}(1/ε^2)$ sample complexity. This high probability accuracy certificate is then used in an approximate policy iteration method that finds an $ε$-optimal policy with $\widetilde{\mathcal O}(1/ε^2)$ samples. The obtained sample complexities for both robust policy evaluation and optimization appear to be new for robust MDPs with continuous state spaces. Of independent interest, the proposed method is also directly applicable to zero-sum Markov games, which seems to strictly improve the existing sample complexities for continuous state spaces.

We report neutron, X-ray absorption, and resonant X-ray spectroscopy of magnetic excitations in the new heavy-fermion van-der-Waals superconductor CeSiI. We determined effective Hamiltonians and ground states of crystal electric fields and magnons. Isotropic Heisenberg interactions on a quasi two dimensional lattice, including ferromagnetic nearest-neighbor exchange as the dominant interaction, provide an excellent account to the low-energy measured dynamics and stabilize a co-rotating spin cycloid. Our study provides the basis to model CeSiI from first principles, thereby laying the ground for microscopic understanding of heavy-fermion physics, their unconventional superconductivity, and quantum criticality.

The Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande (Hyper-K) will measure neutrino oscillation parameters with an unprecedented precision that requires neutrino energy estimation to be controlled at the few-MeV level. A central challenge in achieving this is the modelling of the reinteractions of hadrons produced in neutrino-nucleus scatters with the residual nuclear medium, or final-state interactions (FSI). In this work we use state-of-the-art neutrino interaction event generators to review the impact of FSI modelling on the kinematic and calorimetric neutrino energy estimators used by Hyper-K and DUNE respectively, considering both the semi-classical intranuclear cascades (INCs) that dominate current simulations and a microscopic treatment based on a relativistic mean field calculation. We find that plausible variations of the FSI model introduce uncertainties on the neutrino energy estimation proxies that are at or above the precision on the energy scale control required for Hyper-K and DUNE projected neutrino oscillation sensitivities, highlighting the importance of careful FSI modelling to allow robust near detector constraints. We further demonstrate that the two experiments are sensitive to different aspects of the FSI models. Neutrino energy estimation at Hyper-K is most impacted by pion absorption and nuclear effects beyond the semi-classical paradigm, whilst the DUNE energy estimation is more affected by the modelling of how hadronic energy is shared between sources of visible and invisible energy in the detector. We discuss the implications of these findings for neutrino oscillation analyses and outline some of the key experimental and theoretical developments needed to bring FSI modelling uncertainties under control.

Nonlinear optical light sources enable the generation of photons with quantum states that are intrinsically linked to underlying material dynamics, rather than imposed through external modulation. Here we investigate fundamental quantum communication metrics of four-wave-mixing signal fields generated by the two-dimensional perovskite (PEA)2PbI4. Using polarization-resolved interferometric measurements together with a microscopic nonlinear response model for the Bloch vector, we reconstruct effective single-photon polarization density matrices inferred from the experimental signal fields and evaluate the corresponding Holevo bound and effective secret-bit rates as a function of the coherence time, population time, and detection wavelength. We find that incorporating the coherence-time degree of freedom systematically lowers the Holevo bound by approximately 2.6-5.8% across the various excitonic resonances, indicating reduced distinguishability of the polarization states when the full multidimensional parameter space is sampled. To connect the polarization-state indistinguishability with experimentally achievable throughput, we further introduce an effective secret-bits-per-pulse metric that enables rapid evaluation of secure information throughput for candidate materials without requiring photon-number-resolved detection. For the present system, control of the population time via spin-dependent evolution yields substantially higher secret-bit rates than manipulation of the coherence time, while spectral regions associated with single-exciton and biexciton resonances define complementary operating regimes for secure communication. More broadly, this work positions nonlinear spectroscopy as a framework for exploring how emergent optical materials can generate and structure quantum states in ways that are advantageous for established quantum communication schemes.

Modern equality saturation systems excel at expression-level rewrites by exploring large spaces of equivalent programs without suffering from the phase-ordering problem. How- ever, these systems struggle to represent equivalence directly over arbitrary control-flow graphs, often requiring normal- ization into structured or tree-like forms before optimization can occur. We present the E-Path data structure, a prototype frame- work for equality-saturation-style optimization over control- flow graphs. Instead of representing congruence between individual expressions, the E-Path records equivalence be- tween instruction sequences embedded within a compiler intermediate representation. In this prototype, E-Path is in- stantiated over a restricted ANF-based control-flow graph used in a compiler backend, but the model itself is intended to be IR-agnostic. By treating instruction sequences as the fundamental unit of congruence, the E-Path enables non-destructive optimiza- tion of loops and other control-flow structures while preserv- ing multiple equivalent program variants simultaneously. This allows classical CFG optimizations to be expressed as rewrite-driven transformations without destructive mutation of the underlying graph.

We study a class of nested path problems, in which every path-based variable can be decomposed into a sequence of subpaths. Subpaths must satisfy local resources, while paths must satisfy additional global resources. This paper develops a new exact pricing algorithm in column generation for these problems that avoids the enumeration of non-dominated subpaths. The algorithm relies on adaptive partitioning of subpaths into buckets characterizing the consumption of global path resources. The algorithm represents each bucket by its subpath of minimum reduced cost, and iterates between pessimistic and optimistic pricing steps to combine subpaths into paths while maintaining upper and lower bounds on the minimum reduced cost. An adaptive refinement procedure closes the gap in a finite number of iterations. We demonstrate the effectiveness of the algorithm on two applications. For the balanced multi-period capacitated vehicle routing problem, we obtain speed-ups of up to a factor of 13 over a state-of-the-art column generation benchmark, and the resulting branch-price-and-cut algorithm solves three times as many instances to optimality as a subpath-based baseline. For the robust railway crew scheduling problem, we obtain speed-ups of up to a factor of three and produce primal solutions within 1% of optimality.

Periodically poled lithium niobate (PPLN) nanophotonic waveguides that simultaneously feature low propagation-loss and uniform periodic poling are essential for a wide range of applications ranging from classical nonlinear frequency-conversion to scalable integrated quantum technology. However, fabrication imperfections have frequently limited the propagation loss of fully domain-inverted PPLN nanophotonic waveguides to a few dB/cm, primarily due to anisotropic etching issue, thereby restricting the absolute conversion efficiency and scale of photonic integration. Here, we present a fabrication approach that overcomes this challenge, yielding a 1.2-cm-long PPLN nanophotonic waveguide with low propagation loss via femtosecond-laser photolithography-assisted chemo-mechanical etching (PLACE). By carrying out domain inversion on a planar thin-film prior to waveguide definition, electric-field distortion is minimized during poling, while isotropic etching of the waveguide is achieved by PLACE with an average surface roughness of only 0.34 nm, resulting in uniform poling of duty cycle of 50% and a record-low propagation loss of 0.042 dB/cm in the telecom band. Under continuous-wave pumping at 1525 nm, the device demonstrates a high normalized quasi-phase-matched SHG conversion efficiency of 2021%/W, and an absolute conversion efficiency of 64% at a pump power of 86 mW which represents the state of the art for single-period PPLN nanophotonic waveguides.

We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order, there is an established axiomatisation in terms of a G-crossed braided fusion category. We lay the foundations for a generalisation of this notion. By condensing an arbitrary algebra of charges in a quantum double model, we demonstrate that the category of localised excitations in the resulting theory forms a hypergroup-graded extension of the category of deconfined excitations. For every element in the hypergroup, the associated domain wall acts in a typically non-invertible way on these localised excitations. Both this action and the monoidal structure are compatible with the hypergroup grading. The actual categorical action is encoded in a Hopf monad on the category of localised excitations, and gauging the non-invertible symmetry amounts to computing the category of modules over this Hopf monad. Finally, we outline how this framework naturally extends to theories obtained by condensing algebras in a generic string-net model.

Symplectic quantization is a functional approach to quantum field theory that allows sampling of quantum fluctuations directly in Minkowski space time by means of a Hamiltonian dynamics in an intrinsic time $τ$ which samples a microcanonical ensemble, in close analogy with the standard microcanonical approach to lattice field theory. In this contribution we present constrained symplectic quantization for relativistic quantum field theory, generalizing from the quantum mechanical case. The method is based on the analytic continuation of fields and action from $\mathbb{R}$ to $\mathbb{C}$ and on constraints that select stable intrinsic time trajectories and that simultaneously define convergent integration cycles for the microcanonical partition function. In the continuum limit we recover the Feynman generating functional with the correct real time prescription. We test the construction for a free scalar field in $1+1$ dimensions on a periodic lattice by measuring real time two point functions and by verifying Dyson Schwinger identities with the correct contact term.

We give a purification and fidelity formulation of the projection method for mixed Hartree data. For the mean-field evolution of $N$-particle density matrices, we prove quantitative propagation of chaos for all fixed marginals, first in squared Uhlmann fidelity and then in trace norm via the Fuchs--van de Graaf inequality. The argument applies a rank-one Pickl-type counting estimate in a purified one-particle space and uses monotonicity of fidelity under partial trace to return to the physical variables. The result allows singular interactions satisfying a projected-square bound, including $L^{2r}$ interactions and the Coulomb potential.

For any acyclic quiver $Q$ without multiple edges, we construct a monoidal category $\mathcal{R}_Q$ whose indecomposable objects are tensor products (over the base field) of finite-dimensional modules over the path algebra of $Q$. We show the existence and uniqueness up to homotopy of certain distinguished chain complexes satisfying good homological properties (higher almost split complexes) preserved under tensoring by objects in $\mathcal{R}_Q$. As a crucial ingredient for this construction, we establish the existence of a family of complete exceptional sequences in $\mathrm{mod}\,\mathbf{k}Q$ satisfying many good properties, which we believe might be of independent interest. We then prove that when $Q$ admits a height function, the Euler characteristics of (the images under certain additive functor of) these complexes coincide with the truncated $q$-characters of the standard modules in Hernandez-Leclerc's category $\mathcal{C}^{(1)}$. Applying our results to the case where the underlying graph of $Q$ is a Dynkin diagram of type $A_n, n \geq 1$, we also interpret the cluster characters of all cluster variables in the finite type cluster algebra $\mathcal{A}_Q$ as Euler characteristics of certain chain complexes in $\mathcal{R}_Q$.

We study the large-scale behaviour of a family of stochastic reaction-diffusion equations driven by long-range correlated noise in a weakly nonlinear regime. Depending on the decay of correlations of the noise and the strength of the nonlinearity, the universal behaviour is governed by a version of the dynamical $Φ^p$ model with long-range correlated noise, and with a coupling constant determined by the reaction term of the microscopic model. Our main result establishes the stochastic estimates and convergence of models required in the theory of regularity structures. We adapt the multiindex-based approach to regularity structures using a suitable expansion of the reaction term tailored to the law of the noise. This yields a systematic weak universality result, allowing for a particularly simple identification of the macroscopic limit throughout the full subcritical regime and beyond Gaussian noise. The method appears robust and applicable to a broader class of singular stochastic PDEs.

The origin of quasi-periodic oscillations (QPOs) in black hole accretion flow remains uncertain, particularly regarding the role of magnetic field configurations in shaping disk structure and variability signatures. We investigate this using global two- and three-dimensional (2D and 3D) general relativistic magnetohydrodynamic (GRMHD) simulations of geometrically thin disks initialized with different multi-loop magnetic field configurations. These configurations naturally produce a puffed-up inner region. We find that QPO-like variability arises in the effective viscosity and mass accretion rate, with frequencies following the local radial epicyclic frequency and its harmonics. Time-series diagrams show coherent, inclined stripe-like patterns associated with inertial-acoustic perturbations, while power spectra exhibit narrow bands of enhanced variability linked to truncation radii associated with magnetic fields. Cross-correlation analysis reveals a finite lag between pressure and Maxwell stress at these interfaces, consistent with viscous-epicyclic overstability. The magnetic topology regulates both the truncation radius and the location of resonant cavities that sustain oscillations. As the disk becomes thicker, increased turbulent diffusion suppresses the overstability and the associated QPO signals. We find that the QPO frequency ranges and their evolution are consistent with observations of black hole X-ray binaries during outbursts. These results suggest that magnetic field configurations play a pivotal role in shaping disk structure and variability in accreting black holes.

We introduce the concept of disjunctive sum of squares for certifying nonnegativity of polynomials. Unlike the popular sum of squares approach where nonnegativity is certified by a single algebraic identity, the disjunctive sum of squares approach certifies nonnegativity with multiple algebraic identities which can be found in parallel. Our main result is a disjunctive Positivstellensatz proving that we can keep the degree of each algebraic identity as low as the degree of the polynomial whose nonnegativity is in question. Based on this result, we construct a semidefinite programming based converging hierarchy of lower bounds for the problem of minimizing a polynomial over a compact basic semialgebraic set, where the size of the largest semidefinite constraint is fixed throughout the hierarchy. We further prove a second disjunctive Positivstellensatz which leads to an optimization-free hierarchy for polynomial optimization. We specialize this result to the problem of proving copositivity of matrices. Finally, we describe how the disjunctive sum of squares approach can be combined with a branch-and-bound algorithm and we present numerical experiments on polynomial, copositive, and combinatorial optimization problems.

We have developed a methodology for analyzing multi-frequency oscillating magnetic fields using neutron spin interferometry. A theoretical formulation was derived of the contrast and the phase of the interference pattern for an input oscillating magnetic field consisting of a series of sine functions with multiple frequencies. According to the formulation, the contrast decays due to the dispersion of the Larmor precession induced by an oscillating field. The formulation also predicts that the phase of the interference pattern does not constant in contrast to single-frequency cases. We conducted an experiment in JRR-3 C3-1-2-2 beam port to confirm the formulation in the cases of two-frequency oscillating fields in the frequency range from 2500 Hz to 10000 Hz. The measured interference patterns showed reasonable agreement with the theoretical predictions.

Understanding how nitrogen dioxide (NO2) varies both within and across cities is essential for assessing urban health inequalities, yet the joint influence of city size and internal structure remains poorly quantified. While it is expected that agglomeration size increases NO2 concentrations and that distance from major urban activities reduces them, the magnitude and form of their combined effect have not been established. Our objective is to move beyond city-specific local context effects and to characterize the general structural form of NO2 distributions, understood as their systematic variation with distance from the center across cities of different sizes. Using both ground monitoring stations and satellite data for 378 European Functional Urban Areas, we estimate parallel models for each measurement type and show that the same structural relationships hold in both cases. We find that NO2 concentrations increase with population size as a power law (with an exponent between 0.14 and 0.22) and decrease with distance from the city center (with an exponent between -0.12 and -0.18), with consistent results across measurement types and robust to local and regional controls. These effects combine into a scalable radial profile, where the total air pollution over a city is proportional to (N/r)^0.16, which generalizes the spatial distribution of NO2 in European cities. This formulation clarifies how total and per-capita pollution depend on the extent to which pollution is integrated and provides a simple framework for evaluating the health implications of urban growth.