The Lagrange identity expresses the second derivative of the moment of inertia of a system of material points through kinetic energy and homogeneous potential energy, from which follows the Jacobi well-known result on the instability of a system of gravitating bodies. In this work, it is proven that if a Hamiltonian system satisfies the Lagrange identity, then it possesses additional tensor invariants that are not expressed through the basic invariants existing for all Hamiltonian systems. A new class of Hamiltonian systems with inhomogeneous potentials is considered, which also possess similar additional tensor invariants.

In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra $\mathcal{H}^f_{c}(n)$ is supersymmetric if $f=f^{(\mathtt{0})}_{\underline{Q}}$ and, symmetric if $f=f^{(\mathtt{s})}_{\underline{Q}}$ and an invertibility condition holds. In the semisimple case, we compute the Schur elements for both $\mathcal{H}^f_{c}(n)$ and the cyclotomic Sergeev algebra $\mathcal{h}^g_{c}(n)$. As applications, we define new symmetrizing forms on the Hecke-Clifford algebra $\mathcal{H}(n)$ and on the cyclotomic quiver Hecke algebras of types $A^{(1)}_{e-1}$ and $C^{(1)}_e$.

In this note, we construct invariant and coinvariant Morse chain complexes with integer coefficients for any compact effective orbifold. We show that the homologies of these two chain complexes are invariants of the orbifold. We conjecture that the homology of the coinvariant chain complex computes the singular homology of the underlying topological space with $\mathbb{Z}$-coefficients, thereby refining the construction by Cho-Hong, which recovers the homology over $\mathbb{Q}$. In contrast, the homology of the invariant Morse chain complex is sensitive to the orbifold structure.

Spectroscopic characterization of rocky exoplanets with the James Webb Space Telescope has brought the origin and evolution of their atmospheres into the focus of exoplanet science. Time-evolved models of the feedback between interior and atmosphere are critical to predict and interpret these observations and link them to the Solar System terrestrial planets. However, models differ in methodologies and input data, which can lead to significant differences in interpretation. In this paper, we present the experimental protocol of the Coupled atmospHere Interior modeL Intercomparison (CHILI) project. CHILI is an (exo-)planet model intercomparison project within the Climates Using Interactive Suites of Intercomparisons Nested for Exoplanet Studies (CUISINES) framework, which aims to support a diverse set of multi-model intercomparison projects in the exoplanet community. The present protocol includes the initial set of participating magma ocean models, divided into evolutionary and static models, and two types of test categories, one focused on Solar System planets (Earth & Venus) and the other on exoplanets orbiting low-mass M-dwarfs. Both test categories aim to quantify the evolution of key markers of the links between planetary atmospheres and interiors over geological timescales. The proposed tests would allow us to quantify and compare the differences between coupled atmosphere-interior models used by the exoplanet and planetary science communities. Results from the proposed tests will be published in dedicated follow-up papers. To encourage the community to join this comparison effort and as an example, we present initial test results for the early Earth and TRAPPIST-1 b, conducted with models differing in the treatment of energy transport in the planetary interior and atmosphere, surface boundary layer, geochemistry, and the in- and outgassing of volatile compounds.

Mathematical models support inference and forecasting in ecology and epidemiology, but results depend on the estimation framework. We compare Bayesian and Frequentist approaches across three biological models using four datasets: Lotka-Volterra predator-prey dynamics (Hudson Bay), a generalized logistic model (lung injury and 2022 U.S. mpox), and an SEIUR epidemic model (COVID-19 in Spain). Both approaches use a normal error structure to ensure a fair comparison. We first assessed structural identifiability to determine which parameters can theoretically be recovered from the data. We then evaluated practical identifiability and forecasting performance using four metrics: mean absolute error (MAE), mean squared error (MSE), 95 percent prediction interval (PI) coverage, and weighted interval score (WIS). For the Lotka-Volterra model with both prey and predator data, we analyzed three scenarios: prey only, predator only, and both. The Frequentist workflow used QuantDiffForecast (QDF) in MATLAB, which fits ODE models via nonlinear least squares and quantifies uncertainty through parametric bootstrap. The Bayesian workflow used BayesianFitForecast (BFF), which employs Hamiltonian Monte Carlo sampling via Stan to generate posterior distributions and diagnostics such as the Gelman-Rubin R-hat statistic. Results show that Frequentist inference performs best when data are rich and fully observed, while Bayesian inference excels when latent-state uncertainty is high and data are sparse, as in the SEIUR COVID-19 model. Structural identifiability clarifies these patterns: full observability benefits both frameworks, while limited observability constrains parameter recovery. This comparison provides guidance for choosing inference frameworks based on data richness, observability, and uncertainty needs.

Cryo-electron microscopy (cryo-EM) enables the atomic-resolution visualization of biomolecules; however, modern direct detectors generate data volumes that far exceed the available storage and transfer bandwidth, thereby constraining practical throughput. We introduce cryoSENSE, the computational realization of a hardware-software co-designed framework for compressive cryo-EM sensing and acquisition. We show that cryo-EM images of proteins lie on low-dimensional manifolds that can be independently represented using sparse priors in predefined bases and generative priors captured by a denoising diffusion model. cryoSENSE leverages these low-dimensional manifolds to enable faithful image reconstruction from spatial and Fourier-domain undersampled measurements while preserving downstream structural resolution. In experiments, cryoSENSE increases acquisition throughput by up to 2.5$\times$ while retaining the original 3D resolution, offering controllable trade-offs between the number of masked measurements and the level of downsampling. Sparse priors favor faithful reconstruction from Fourier-domain measurements and moderate compression, whereas generative diffusion priors achieve accurate recovery from pixel-domain measurements and more severe undersampling. Project website: https://cryosense.github.io.

Large language models (LLMs) can generate executable code from natural language descriptions, but the resulting programs frequently contain bugs due to hallucinations. In the absence of formal specifications, existing approaches attempt to assess correctness using LLM-generated proxies such as tests or auto-formalized specifications. However, these proxies are produced by the same imperfect models and thus often corroborate rather than catch errors, especially when the model exhibits correlated errors. We introduce semantic triangulation, a theory-grounded framework that decorrelates model errors by transforming the original problem into a dissociative variant - one likely requiring a fundamentally different algorithm - and checks consistency between independently sampled solutions to both problems. We identify theoretical requirements for this framework, and we prove that under a formal model of LLM hallucinations, these properties confer higher confidence in program correctness. We instantiate the framework through four concrete triangulation methods based on problem inversion, decomposition, and solution enumeration. Evaluated on LiveCodeBench and CodeElo across GPT-4o, DeepSeek-V3, and Gemini 2.5 Flash, our tool increases the probability of selecting a correct program by 24% over baselines (test generation, metamorphic testing, and auto-formalized specifications) and achieves 26% higher F1 score in selection-or-abstention scenarios, while being the only method that consistently handles inexact problems admitting multiple valid solutions.

In this note, we make two methodical observations. $\bullet$ We prove in a simple explicit way that a necessary and sufficient condition for a Kähler manifold to be hyperkähler is $h_{i\bar k} h_{j\bar l } Ω^{\bar k \bar l} \ =\ C Ω_{ij}$, where $h_{i\bar k}$ is a complex metric, $Ω$ is a symplectic matrix and $C$ is a positive constant. $\bullet$ The procedure of Kähler reduction includes two stages. On the first stage, a Kähler manifold of dimension $2n$ is reduced to a $(2n-1)$ - dimensional manifold, while on the second stage, one arrives at a Kähler manifold of dimension $2(n-1)$. We note that this second stage has the meaning of Hamiltonian reduction. We illustrate the procedure by discussing a simple toy model when $\mathbb{R}^3 \times S^1$ is reduced down to $S^2$. We elucidate also hyperkähler reduction of $\mathbb{R}^7 \times S^1$ down to the Taub-NUT metric.

Generative AI is rapidly reshaping how physicists teach, learn, and conduct research, yet little is known about how physics faculty are responding to these changes. We interviewed 12 physics professors at a major Scandinavian research university to explore their uses and perceptions of Generative AI (GenAI) in both teaching and research. Using the theoretical framework of epistemic framing, we conducted a thematic analysis that identified 19 overlapping practices, ranging from coding and literature review to assessment and feedback. From these practices, we derived six overlapping epistemic frames through which professors make sense of GenAI: as a threat to genuine learning and assessment, a source of knowledge, a discussion partner, a text-processing tool, a coding tool, and a labor-saving device. While the latter five position GenAI as a useful tool in the physicists' toolbox, the threat frame represented an overarching concern that colored all other frames. These findings reveal how GenAI is beginning to transform what it means to be a physicist, highlighting both opportunities for innovation and challenges for academic integrity and learning.

This paper proposes a definition of what has previously been coined a Wilson Spool in the case of three-dimensional gravity with vanishing cosmological constant. The definition builds upon a construction of the one-loop partition function of a massive, spinning field from a fixed background holonomy. While the background is taken to be a flat-space cosmology, the definition of the Wilson spool is expected to hold independently of the underlying geometry. Some comments are given towards possible connections to its two-dimensional incarnations at non-vanishing cosmological constant.

Medical image segmentation using deep learning (DL) has enabled the development of automated analysis pipelines for large-scale population studies. However, state-of-the-art DL methods are prone to hallucinations, which can result in anatomically implausible segmentations. With manual correction impractical at scale, automated quality control (QC) techniques have to address the challenge. While promising, existing QC methods are organ-specific, limiting their generalizability and usability beyond their original intended task. To overcome this limitation, we propose no-new Quality Control (nnQC), a robust QC framework based on a diffusion-generative paradigm that self-adapts to any input organ dataset. Central to nnQC is a novel Team of Experts (ToE) architecture, where two specialized experts independently encode 3D spatial awareness, represented by the relative spatial position of an axial slice, and anatomical information derived from visual features from the original image. A weighted conditional module dynamically combines the pair of independent embeddings, or opinions to condition the sampling mechanism within a diffusion process, enabling the generation of a spatially aware pseudo-ground truth for predicting QC scores. Within its framework, nnQC integrates fingerprint adaptation to ensure adaptability across organs, datasets, and imaging modalities. We evaluated nnQC on seven organs using twelve publicly available datasets. Our results demonstrate that nnQC consistently outperforms state-of-the-art methods across all experiments, including cases where segmentation masks are highly degraded or completely missing, confirming its versatility and effectiveness across different organs.

Orthogonal Time Frequency Space (OTFS) modulation has recently garnered attention for its robustness in high-mobility wireless communication environments. In OTFS, the data symbols are mapped to the Doppler-Delay (DD) domain. In this paper, we address low-overhead, scalable pilot-aided estimation of channel state information (CSI) for MIMO OTFS systems. Existing channel estimation techniques either require non-overlapping DD domain pilots with guard regions across multiple antennas, thus sacrificing significant communication rate as the number of transmit antennas increases, or allow pilots to overlap between antennas and rely on high-complexity methods to mitigate pilot pollution. We propose a novel pilot placement approach that embeds pilots within the time-frequency (TF) frame of each OTFS burst, along with a new use of TF and DD guard bins to preserve waveform orthogonality on the TF pilot bins and data integrity in the DD domain, respectively. The proposed pilot placement enables low-complexity coarse estimation of the channel parameters. Moreover, the pilot orthogonality allows the construction of a virtual array (VA), enabling the formulation of a sparse signal recovery (SSR) problem in which the coarse estimates are used to build a low-dimensional dictionary matrix. The SSR solution then yields high-resolution estimates of the channel parameters. Simulation results show that the proposed approach achieves good performance with very low overhead and is robust to pilot pollution. Importantly, the required overhead is independent of the number of transmit antennas, ensuring scalability to large MIMO arrays. The proposed approach accounts for practical rectangular transmit pulse shaping and receiver matched filtering, as well as fractional Doppler effects.

Recent observations from JWST have revealed unexpectedly luminous galaxies, exhibiting stellar masses and luminosities significantly higher than predicted by theoretical models at Cosmic Dawn. In this study, we present a suite of cosmological zoom-in simulations targeting high-redshift ($z \geq 10$) galaxies with dark matter halo masses in the range $10^{10} - 10^{11}\ {\rm M}_{\odot}$ at $z=10$, using state-of-the-art galaxy formation simulation codes (Enzo, Ramses, Changa, Gadget-3, Gadget-4, and Gizmo). This study aims to evaluate the convergence of the participating codes and their reproducibility of high-redshift galaxies with the galaxy formation model calibrated at relatively low redshift, without additional physics for high-redshift environments. The subgrid physics follows the AGORA CosmoRun framework, with adjustments to resolution and initial conditions to emulate similar physical environments in the early universe. The participating codes show consistent results for key galaxy properties (e.g., stellar mass), but also reveal notable differences (e.g., metallicity), indicating that galaxy properties at high redshifts are highly sensitive to the feedback implementation of the simulation. Massive halos (${\rm M}_{\rm halo}\geq5\times10^{10}\,{\rm M}_{\odot}$ at $z=10$) succeed in reproducing observed stellar masses, metallicities, and UV luminosities at $10\leq z\leq12$ without requiring additional subgrid physics, but tend to underpredict those properties at higher redshift. We also find that varying the dust-to-metal ratio modestly affects UV luminosity of simulated galaxies, whereas the absence of dust significantly enhances it. In future work, higher-resolution simulations will be conducted to better understand the formation and evolution of galaxies at Cosmic Dawn.

The main purpose of this work is to present a SIMD-vectorized implementation of the symplectic 16th-order 8-stage implicit Runge-Kutta integrator based on collocation with Gauss-Legendre nodes (IRKGL16-SIMD), and to show that it can outperform state-of-the-art symplectic explicit integrators for high-precision numerical integrations (in double-precision floating-point arithmetic) of non-stiff Hamiltonian ODE systems. Our IRKGL16-SIMD integrator leverages Single Instruction Multiple Data (SIMD) based parallelism (in a way that is transparent to the user) to significantly enhance the performance of the sequential IRKGL16 implementation. We present numerical experiments comparing IRKGL16-SIMD with state-of-the-art high-order explicit symplectic methods for the numerical integration of several Hamiltonian systems in double-precision floating-point arithmetic.

High-temperature superconductivity in the cuprates emerges from an enigmatic metallic state, known as the pseudogap, characterized by a reconstructed Fermi surface, reduced carrier density, and the appearance of Fermi arcs, whose origin remains unresolved. Here, we show that these defining signatures naturally arise from a structural reconstruction observed experimentally that introduces a symmetry-enforced sublattice degree of freedom. In the presence of spin-orbit coupling, the Fermi surface is reconstructed into small closed pockets, effectively reducing the carrier density. The same sublattice structure gives rise to matrix-element interference in angle-resolved photoemission spectroscopy, leading to the manifestation of Fermi arcs. Density functional theory calculations support this mechanism. These results demonstrate that lattice symmetry provides a unifying and experimentally verifiable framework for understanding the pseudogap regime in the cuprates.

By the result of Artin--Tate--Van den Bergh, every $3$-dimensional cubic AS-regular algebra A can be expressed as a geometric algebra $A=\mathcal{A}(E,σ)$, where $E$ is either $\mathbb{P}^{1}\times \mathbb{P}^{1}$ or a curve of bidegree ($2$,$2$) in $\mathbb{P}^{1}\times \mathbb{P}^{1}$ and $σ\in \mathrm{Aut}_{k}E$. In particular, we treat the following three configurations: (1) a conic and two lines in a triangle, (2) a conic and two lines intersecting in one point, and (3) a quadrangle. For each of these cases, we (i) list all defining relations of the corresponding algebras $\mathcal{A}(E,σ)$, and (ii) classify them up to graded algebra isomorphism and graded Morita equivalence. Furthermore, we present explicit (twisted) superpotentials whose derivation-quotient algebras realize these algebras and verify that the resulting algebras are AS-regular. Combining our results with existing classifications for the remaining types (including Types P, S, T, WL, and TWL), we thereby complete the classification of 3-dimensional cubic AS-regular algebras whose point schemes are not integral.

Recently, Manolescu-Sarkar constructed a stable homotopy type for link Floer homology, which uses grid homology and accounts for all domains that do not pass through a specific square. We explicitly give the framings of the lower-dimensional moduli spaces of the Manolescu-Sarkar construction as well as the more general moduli spaces corresponding to the full grid. Though in the latter case the stable homotopy type is not known, the explicit framings are enough to construct a framed 1-flow category, a construction by Lobb-Orson-Schütz which contains enough information to find the second Steenrod square. Finally, we find an algorithm for computing the second Steenrod square for all versions of grid homology coming from the full grid.

We study the dynamics of a massive scalar field in the background of the Hayward black hole, which can be interpreted both as a regular spacetime and as an effective geometry arising from Asymptotically Safe gravity. The quasinormal spectrum and grey-body factors are computed using the WKB method with Padé improvements and confirmed through time-domain integration followed by Prony analysis. We find that the mass of the field significantly suppresses the damping rate of quasinormal oscillations, giving rise to long-lived modes that continuously approach arbitrarily long-lived states (quasi-resonances) at certain critical field masses. In the time domain, the standard exponentially decaying ringdown is replaced by oscillatory tails with a power-law envelope. The corresponding grey-body factors reveal a pronounced shift of the transmission peak toward higher frequencies and a suppression of the low-frequency part of the spectrum. Finally, we show that the correspondence between quasinormal modes and grey-body factors remains valid for massive fields, being highly accurate for large multipole numbers and gradually losing precision as either the field mass increases or the multipole number decreases.

The preparation of photonic qubits in the excited state is an integral part of the performance of an on-demand single photon source (SPS). Conventional resonant excitation, an excellent approach to maximize the coherence and indistinguishability of the SPS, often requires polarization filtering to remove the pump signal and isolate the qubit emission, but this results in an inherent 50\% hit to the efficiency. Recent excitation schemes strategically try to exploit pulses that excite the qubit while avoiding spectral overlap to bypass this required filtering. In this work, we compare three such pumping schemes to quantify the important SPS figures-of-merit for off-resonant quantum dot schemes, using: (i) a symmetrically detuned dichromatic pulse, (ii) a notch-filtered adiabatic rapid passage (NARP) pulse, and (iii) a swing up of the quantum emitter population (SUPER) pulse. Due to large instantaneous pulse strengths, the dichromatic pulse suffers from phonon-induced dephasing which can lower the SPS performance by up to 50\%. In contrast, the NARP and SUPER pulses are shielded from phonon coupling to differing degrees but both maintain excellent SPS performance. The SUPER pulse can lose significant efficiency if there is variance in its constituent pulses' amplitude, pulse width, or frequency, while the NARP pulse, though potentially more difficult to realize in experiments, is robust against variance in the pulse preparation.

Many new families of quasicrystal-forming magnetic alloys have been synthesized and studied in recent years. For small changes of composition, the alloys can go from quasiperiodic to periodic (approximant crystals) while conserving most of the local atomic environments. Experiments show that many of the periodic approximants order at low temperatures, with clear signatures of ferromagnetic or antiferromagnetic transitions, and also in some cases undergo non-equilibrium spin glass transitions. In contrast, the quasicrystals are mostly found to be spin glasses. Systematically studying these alloys could help elucidate the role played by quasiperiodicity in (de)stabilizing long range magnetic order. In this work, we study cluster spin models with the aim of understanding the mechanisms behind various types of long range magnetic ordering in approximants and quasicrystals. These models embody key features of real systems, and to some extent are analytically tractable, both for periodic and quasiperiodic cases. For the quasicrystal, we describe two novel magnetic phases with quasiperiodic ordering. Our results should serve to motivate further studies with detailed numerical explorations of this family of models.

We derive the one-pion exchange potential (OPEP) in the presence of a homogeneous magnetic field using chiral perturbation theory with nonrelativistic nucleons. Our approach is applicable not only to weak magnetic fields but also to strong ones up to around the pion-mass scale. The Green's function of charged pions is modified by the magnetic field, leading to changes in the nuclear force. By numerically evaluating the modified OPEP incorporating its spin and isospin dependencies, we show that the range of the potential decreases in both directions parallel and perpendicular to the magnetic field as the field strength increases. We also compute the resulting energy shift of the deuteron due to the modified OPEP, which can reach the order of 1 MeV around $|eB| = m_π^2$, which is comparable to the deuteron binding energy.

In this contribution we present JosephsonCircuitsOptimizer.jl (JCO), a simulation and optimization framework based on the JosephsonCircuits.jl library for Julia. It models superconducting circuits that include Josephson junctions (JJs) and other nonlinear elements within a lumped-element approach, leveraging harmonic balance, a frequency-domain technique that provides a computationally efficient alternative to traditional time-domain simulations. JCO automates the evaluation of optimal circuit parameters by implementing Bayesian optimization with Gaussian processes through a device-specific metric and identifying the optimal working point to achieve a defined performance function. This makes it well suited for circuits with strong nonlinearity and a high-dimensional set of coupled design parameters. To demonstrate its capabilities, we focus on optimizing a Josephson Traveling-Wave Parametric Amplifier (JTWPA) based on Superconducting Nonlinear Asymmetric Inductive eLements (SNAILs), operating in the three-wave mixing regime. The device consists of an array of unit cells, each containing a loop with multiple JJs, that amplifies weak quantum signals near the quantum noise limit. By integrating efficient simulation and optimization strategies, the framework supports the systematic development of superconducting circuits for a broad range of applications.

The interstellar medium (ISM) is permeated by magnetic fields that affect gas dynamics and star formation. These fields correlate with supernova (SN)-driven turbulence, but whether the scaling is universal across galaxy properties, ISM phases, and energy budgets remains unclear. We quantify the dependence of magnetic fields on star formation activity including both regular and starburst galaxies. We analyse 19 spiral disks from the cosmological RTnsCRiMHD Azahar suite, deriving line-of-sight integrated maps to measure median magnetic-field strength ($B$), specific energies (thermal, turbulent, magnetic, and cosmic-ray), and star formation rate (SFR), star formation surface density ($Σ_{\mathrm{SFR}}$) and specific SFR (sSFR). We find an almost universal magnetic-field-SFR scaling with slope $α\approx 0.2$-$0.3$ across galaxy mass and ISM phases. The $B$-$Σ_{\mathrm{SFR}}$ slope ($α\approx 1/3$) supports an SN-driven, turbulence-regulated origin. Neutral gas is generally turbulence-dominated and in near equipartition with magnetic energy for systems with sSFR $\gtrsim 0.1$ Gyr$^{-1}$ and SFR $\gtrsim 1$ $M_\odot$ yr$^{-1}$. The simulated trends match observations with similar slopes ($α\approx 0.25$-$0.35$), indicating that SN-driven turbulence is the main amplification mechanism behind the near-universal $B$-SFR relation.

A novel modular modeling and control framework based on Lagrangian mechanics is proposed for multibody systems, motivated by the challenges of modular control of systems with closed kinematic chains and by the need for a modeling framework that remains locally updatable under reconfiguration of body-level geometric and inertial properties. In the framework, modularity is defined with respect to the degrees of freedom of the multibody system, represented in the model by the minimal generalized coordinates, and the inertial properties of each body are partitioned with respect to how they are reflected in the kinetic energy of the system through the motion induced by each degree of freedom. By expressing body contributions through body-fixed-frame Jacobians and spatial inertia matrices, the dynamic model remains locally updatable under changes in geometric and inertial parameters, which is advantageous for reconfigurable multibody systems. For multibody systems in which a mapping between the auxiliary and minimal generalized coordinates is available, the approach accommodates closed kinematic chains in a minimal-coordinate ordinary-differential-equation form without explicit constraint-force calculation or differential-algebraic-equation formulation. Based on the resulting modular equations of motion, a robust model-based controller is designed for trajectory tracking, and practical boundedness of the tracking error is analyzed under bounded uncertainty and external disturbance. The proposed framework is implemented in simulation on a three-degree-of-freedom series-parallel manipulator, where uncertainties and disturbances are introduced to assess robustness. The results are consistent with the expected stability and tracking performance, indicating the potential of the framework for trajectory-tracking control of reconfigurable multibody systems with closed kinematic chains.

Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting, the performance of QML models can be significantly affected by the limited access to the underlying data set. Previous studies have focused on proving generalization error bounds for any QML models trained on a limited finite training set. We focus on the optimal QML models obtained by training them on a finite training set and establish a tight prediction error bound in terms of the number of trainable gates and the size of training sets. To achieve this, we derive covering number upper bounds and packing number lower bounds for the data re-uploading QML models and linear QML models, respectively, which may be of independent interest. We support our theoretical findings by numerically simulating the QML strategies for function approximation and quantum phase recognition.

Motivated by single-particle cryo-electron microscopy, we study the sample complexity of the multi-target detection (MTD) problem, in which an unknown signal appears multiple times at unknown locations within a long, noisy observation. We propose a patching scheme that reduces MTD to a non-i.i.d. multi-reference alignment (MRA) model. In the one-dimensional setting, the latent group elements form a Markov chain, and we show that the convergence rate of any estimator matches that of the corresponding i.i.d. MRA model, up to a logarithmic factor in the number of patches. Moreover, for estimators based on empirical averaging, such as the method of moments, the convergence rates are identical in both settings. We further establish an analogous result in two dimensions, where the latent structure arises from an exponentially mixing random field generated by a hard-core placement model. As a consequence, if the signal in the corresponding i.i.d. MRA model is determined by moments up to order $n_{\min}$, then in the low-SNR regime the number of patches required to estimate the signal in the MTD model scales as $σ^{2n_{\min}}$, where $σ^2$ denotes the noise variance.

We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary density near a boundary of its support. We demonstrate the practical use in numerical examples.

We revisit an ingenious argument of K. Ball to provide sharp estimates for the volume of sections of a convex body in John's position. Our technique combines the geometric Brascamp-Lieb inequality with a generalised Parseval-type identity. This lets us complement some earlier results of the first two named authors, as well as generalise the classical estimates of Meyer-Pajor and Koldobsky regarding extremal sections of $B_p^n$ balls to a broader family of norms induced by a John's decomposition of the identity in $\mathbb{R}^n$.

We investigate the influence of an anonymous leader on a collective of self-propelled robots using Kilobot experiments and numerical simulations. A single leader alternated deterministically between clockwise and counterclockwise motion, while the other robots followed a stochastic majority rule. Although the leader does not change global order, it induces correlations with the collective response that peak at intermediate perturbation levels, resembling stochastic resonance. Simulations confirm that this resonance occurs when the leader's reversal period matches the mean residence time of the unperturbed system. Our results contribute to understanding decision-making in active matter and suggesting principles for steering robotic swarms with minimal leadership input.

A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a linear combination of inelastic and elastic (or resonant) collisions, and its basic properties are discussed. Then, in the case where the elastic collisions are dominant, fluid dynamic equations of Euler and Navier--Stokes type including two temperatures, i.e., translational and internal temperatures, as well as relaxation terms are systematically obtained by means of the Chapman--Enskog expansion. The obtained equations are different depending on the degree of weakness of the interaction between the translational and internal modes.