The monodromy of the $\sl(3)$ Casimir flat connection around root hyperplanes is studied. For the computation of the traces of the root monodromy operators, acting on the parabolic Verma modules, we deduce branching rules w.r.t. the corresponding root $\sl(2)$ subalgebras. We show that the traces of the monodromy operators are partial theta functions of special type.

We introduce a symmetric tridiagonal matrix-valued process ($β$-TMP) $H(t)$ whose diagonal entries $H_{k,k}(t)$ evolve independently via an Ornstein-Uhlenbeck process starting at the origin and the off-diagonal entries $H_{k,k+1}(t)$ evolve independently via the Cox-Ingersoll-Ross process, starting at the origin and with parameters that depend on the row index $k$. We show that the joint distribution of the entries of the matrix can be computed exactly at all times and moreover, the joint distribution of its $N$ real eigenvalues can be computed exactly at all times too. We then subject this time-evolving matrix-valued process to stochastic resetting with rate $r$ in two different settings: (i) simultaneous resetting of the matrix entries to the origin with rate $r$ ($β$-SRTMP process) and (ii) independent resetting of the matrix entries to the origin with rate $r$ ($β$-IRTMP process). We show that the joint distribution of the eigenvalues of the $β$-SRTMP process at long times can be computed analytically and it coincides with the joint distribution of the positions of the resetting Dyson Brownian motion in its stationary state for arbitrary $β>0$. For the $β$-IRTMP stationary ensemble, computing analytically the joint distribution of eigenvalues or even the average density of eigenvalues is difficult. However, generating the stationary $β$-IRTMP ensemble numerically is relatively straightforward and we compare its numerical average eigenvalue density to the corresponding analytical results for the $β$-SRTMP stationary ensemble with same parameter values, showing that they are quite different from each other. Finally, we provide a simple and concrete application of this tridiagonal matrix-valued process in computing the annealed partition function of a disordered quantum tight-binding Hamiltonian on a one-dimensional lattice.

Low Earth Orbit (LEO) satellite constellations are emerging as a key component of non-terrestrial networks due to their low-latency and high-capacity communication capabilities. However, satellites in these orbits are characterized by a small coverage footprint and high orbital velocity compared to those in higher orbits. This results in constantly changing and dynamic constellations that require smart design of orbital parameters to ensure continuous coverage. Existing constellation deployments are typically optimized either for low- and mid-latitude regions or for full polar coverage, leaving high-latitude regional scenarios such as the North Atlantic insufficiently explored. This work provides insights into the key characteristics associated with the deployment of satellites in LEO for North Atlantic coverage. Therefore, we investigate how constellation inclination, minimum elevation angle, altitude, and satellite footprint jointly affect visibility probability, revisit time, path loss, and coverage continuity. Results show that the minimum elevation angle is a critical design parameter since a Walker Delta constellation with 64 satellites at 1000 km altitude can provide continuous coverage above 55°N for elevations below 20°, whereas coverage probability degrades drastically for larger elevation angles. Similarly, inclinations above approximately 70° are required to achieve robust North Atlantic coverage with medium-size constellations. Thus, these results provide practical guidelines on how a satellite constellation should be designed to achieve an efficient deployment with a focus on coverage over the North Atlantic, targeting maritime, aviation, and Arctic connectivity scenarios.

Multimodal representation learning has attracted increasing attention in AI, driven by the strong performance of large, pretrained multimodal foundation models such as Qwen, LLaVA, and CLIP. These models deliver impressive performance on a range of multimodal information retrieval (MIR) tasks, including web search, cross-modal retrieval, and recommender systems. Yet their massive parameter counts create major efficiency bottlenecks when adapting their representations for IR tasks during training, deployment, and inference. These limitations hinder the practical use of foundation models for representation learning in information retrieval. To address these issues, we propose organizing the EReL@MIR workshop at MM 2026, bringing together researchers from academia and industry to discuss emerging solutions, open challenges, and new efficiency metrics and benchmarks for multimodal IR representation learning in the foundation-model era. The workshop's official website is available at https://erel-mir.github.io/.

Here, a class of nonlinear moving boundary problems for a novel extension of a two-component mKdV system is shown to admit exact solution via application of a hybrid Ermakov-Ray-Reid / Painlevé II symmetry ansatz.The mKdV system has its genesis in a reduction of a coupled nonlinear NLS system incorporating deBroglie - Bohm potential terms.

Imaginary-time evolution by a local Hamiltonian cannot induce a phase transition in one dimension, but longer-range interactions may subvert such constraints. Starting from the ground state of the Kitaev Majorana chain, we modify the wave function by an imaginary-time evolution generated by a quadratic Hamiltonian with power-law couplings that enhance pairing correlations, typically of the form $1/r^α$, where $r$ is the distance between two sites. As the state remains Gaussian, entanglement and correlation functions can be computed analytically. We find that the decay exponent $α$ controls three distinct infrared regimes: for $α>1$, the deformation produces only smooth crossovers at finite deformation strength, while the topological regime is reached only asymptotically as the deformation strength tends to infinity. At $α=1$, the deformation induces an immediate flow to the topological phase: an infinitesimal deformation strength drives the system to a topological regime, and in a particular case, an emergent Kramers-Wannier symmetry enforces Ising-like scaling at long distances. For $α<1$, the deformed state shows the same critical-like behavior for all non-zero deformation strength. We observe that even with arbitrarily long-range interactions, these models do not display a sharp phase transition at non-zero deformation strength.

This paper investigates the privacy-preserving distributed Nash equilibrium seeking problem for aggregative games. A novel differential privacy mechanism is designed by incorporating stochastic event-triggering with stochastic quantization, which provides strong privacy protection by obfuscating the temporal patterns of information exchange among players and quantizing the transmitted information at triggering instants. Based on this mechanism, a differentially private distributed Nash equilibrium seeking algorithm with dual randomness is proposed. By embedding a decaying factor sequence into both the triggering condition and interaction terms among players, it is proved that the proposed algorithm can achieve rigorous $(0,δ)$-differential privacy at each iteration while maintaining provable convergence. Crucially, this privacy guarantee is sustained over infinite iterations for a sufficiently large quantization interval and a sufficiently small trigger threshold tuning coefficient. Moreover, the synergy between event-triggered communication and quantization significantly enhances communication efficiency. Simulation results verify the validity of the proposed approach.

All-to-All communication is a key performance bottleneck for distributed machine learning (ML) and high-performance computing (HPC) workloads, where dense traffic increasingly stresses scale-up interconnects. While these ML and HPC workloads have driven unprecedented infrastructure demand, optical reconfigurable networks (ORNs) offer a promising path forward. By adapting the physical topology to the active workload, they improve communication cost and bandwidth utilization. However, their benefit is critically contingent on whether the collective consists of structured phases that can be served by sparse and reusable topology states. In this paper, we revisit Bruck's All-to-All implementation and demonstrate the benefits of topology optimization in which both communication pattern and reconfiguration strategy are co-designed. We present ReTri, a bidirectional All-to-All schedule for ORNs. ReTri uses balanced ternary block propagation to complete All-to-All in $\lceil \log_3 n\rceil$ phases. The induced reconfiguration strategy from ReTri's pairwise bidirectional exchanges allow reconfiguration delays to be amortized across multiple phases. Preliminary simulations show that ReTri improves completion time by up to $10\times$ over static All-to-All, even for millisecond-scale reconfiguration delays, and improving reconfigurable Bruck by up to $2.1\times$.

User localization and beam management are tightly linked in extremely large-scale multiple-input multiple-output (XL-MIMO) systems, especially in dense low-altitude economy (LAE) scenarios. However, the near-field propagation in XL-MIMO introduces strong distance sensitivity and complex spatial coupling, which makes joint trajectory and beam prediction challenging. Meanwhile, large language models (LLMs) have attracted attention in physical-layer transmission for modeling long-range dependencies. In this paper, we propose NF-TrackLLM, a multi-modal semantic-aware framework for near-field unmanned aerial vehicles (UAVs) positioning and beam prediction in XL-MIMO systems. By incorporating visual and LiDAR sensing into a Sionna-based channel generation pipeline, environmental semantics and GPS are utilized to guide trajectory and beam prediction. Built upon the aligned multi-modal representation, a GPT-2-based spatiotemporal reasoning backbone, and a cascaded prediction strategy are employed, where future trajectories are first inferred and then used to guide beam prediction as geometric priors. Simulation results demonstrate that NF-TrackLLM achieves accurate beam prediction and reliable UAV trajectory tracking in dense urban low-altitude scenarios.

Grain boundaries (GBs) are ubiquitous defects in crystalline materials. However, they remain less explored in block copolymer ordered phases. Here, we develop a self-consistent field theory framework to investigate GB structure and energetics in double-gyroid (DG) diblock copolymer networks. The GB energy landscape is obtained as a function of GB orientation, which reveals multiple local minima representing distinct network-switching GBs. Remarkably, the global minimum is a previously unidentified asymmetric-tilt network-switching GB (ATNS), exhibiting a lower energy than the experimentally observed $(422)$ twin boundary (TB). Comparative analyses of representative low- (ATNS, $(422)$ TB) and high-energy twist ($(0\bar{1}\bar{1})$, $(100)$ TNSs) GBs reveal that, unlike enthalpy-dominated hard matter, GB stability in DG networks is predominantly entropy-driven. Twist-type GBs generate new nodes and disrupt nodal coplanarity, causing chain packing frustration and large entropy penalties. Conversely, the ATNS preserves favorable network connectivity and minimizes conformational constraints on polymer chains, making it the energetically preferred GB.

Quanta emitted by an open quantum system carry information about intrinsic parameters, enabling their estimation via continuous monitoring. In practice, however, only a fraction of the emitted quanta is detected, reducing the achievable sensitivity. Here, we consider few-level systems in which coherent couplings and dissipative processes compete, producing metastable dynamics characterized by emission intermittency or by the emergence of a dark state. We show that both phenomena can be beneficial for sensing but their relative performance depends strongly on the achievable detection efficiencies. Intermittent emission, marked by long alternating bright and dark periods, allows to achieve robustness with respect to inefficient detection and dephasing, whereas dark states yield significantly higher sensitivity at unit detection efficiency. Yet the latter are highly susceptible to losses. We quantify the impact of inefficient detection through the classical Fisher information of the emission record and benchmark it against the ultimate sensitivity encoded in the joint system-environment state. Finally, we demonstrate that maximum-likelihood estimators based on the observed emission record can effectively approach this sensitivity. We focus here on trapped-ion systems, however, the results extend to other quantum platforms in which similar emission dynamics can be observed.

We measured the hyperfine structure constants, $A(3s^2S_{1/2})$ and $A(3p^2P_{1/2})$, of the neutron-deficient isotope $^{21}\text{Na}$ using CLaSsy, a setup dedicated to collinear laser spectroscopy at RAON. The hyperfine structure constants of $^{21}\text{Na}$ were measured to be $103.6(10)_{\mathrm{stat}}(9)_{\mathrm{syst}}$ MHz for $A(3p^2P_{1/2})$ and $954.9(11)_{\mathrm{stat}}(25)_{\mathrm{syst}}$ MHz for $A(3s^2S_{1/2})$. A systematic comparison with the state-of-the-art ab-initio relativistic coupled cluster calculations shows the role of higher-order correlation effects such as triple excitations in $^{21}$Na. Furthermore, the measurement demonstrates a capability of the CLaSsy setup to conduct collinear laser spectroscopy experiments with a radioactive beam.

We study the extreme points of the convex set $\mathcal{C}(ρ_1,ρ_2)$ of bipartite quantum states with fixed marginals $ρ_1$ and $ρ_2$. We construct extreme points in $(d,\,d+m)$ dimension, of rank $d+m$, matching the highest possible value, for all $d\geq 3$, $m > \frac{d^2-2d-2}{2}$ (when $d=2$, $m\geq 1$). This proves the existence of extremal states with relatively large rank and also covers all the known examples. We further show that, in order to analyze the extreme points of $\mathcal{C}(ρ_1,ρ_2)$, it is sufficient to study the special case $\mathcal{C}(\mathcal{D}_1,\mathcal{D}_2)$, where the marginals are diagonal. Additionally, we observe that it is sufficient to consider $d_1\leq d_2$. Thus, our results show that apart from possibly a few finite cases, for each $d_1$, the maximal rank is achieved almost all times.

Preorder polytopes, defined from preorders on finite sets, are introduced and studied from a lattice point enumeration point of view. They naturally generalize arbor polytopes, recently introduced and studied by the second named author. Preorder polytopes are shown to be lattice polytopes which satisfy a certain duality relating their Ehrhart polynomials with the zeta polynomials of their posets of lattice points. A combinatorial interpretation of the normalized volume of a preorder polytope is proven, together with formulas for the Ehrhart polynomial and the $h^\ast$-polynomial, and a combinatorial interpretation of the latter is conjectured. Several conjectures and results on the lattice point enumeration of arbor polytopes are generalized to preorder polytopes, new conjectures are proposed and new interesting examples of preorder polytopes are studied.

This paper introduces a Gaussian process (GP)-based method for extended object estimation (EOE) in integrated sensing and communication (ISAC) scenarios, representing a promising approach to enhance environmental awareness beyond the conventional point-scatterer assumption. The suitability of the proposed GP-based method for EOE is investigated through a practical measurement setup compliant with the fifth-generation (5G) New Radio (NR) standard and employing bistatic sensing, with results evaluated for both mapping and simultaneous localization and mapping (SLAM ) cases at millimeter-wave (mmWave) frequencies. The findings reveal that the enhanced capabilities of communication networks, when combined with bistatic sensing and GP-based EOE, enable improved environmental awareness in future wireless systems. Importantly, the results demonstrate that, under practical conditions, GP effectively performs EOE in both mmWave mapping and SLAM scenarios.

Recent years have brought a dense sequence of experimental discoveries in heavy-flavor hadron spectroscopy. Heavy-flavor spectroscopy has entered a period in which new hadronic structures are no longer isolated surprises but recurring features across several flavor sectors, seen by multiple experiments in several decay environments. For systems with charm and bottom quarks, smaller widths and cleaner signatures expose regularities that would be harder to isolate in the light-quark sector. This contribution focuses on the classes of states that now define the modern ``exotic'' landscape: hidden-charm pentaquarks, charged charmonium-like structures, resonances in onia-onia systems, doubly-heavy tetraquarks, and open-flavor tetraquarks.

The relativistic mean field approach, within a theoretical framework known as the chiral confining model incorporating chiral symmetry breaking and quark confinement effects, is applied for the first time to finite nuclei. Model parameters are calibrated through a Bayesian approach using nuclear empirical properties and doubly magic nuclei. The model provides a satisfactory description of binding energies and charge radii for medium and heavy nuclei, while larger discrepancies are observed in light nuclei. This behavior is linked to the constrained form of the chiral potential, which reduces flexibility away from saturation density. Charge radii are reproduced with very good accuracy, although density profiles remain slightly more diffuse than experimental ones. The extension to open-shell nuclei with a separable Gogny pairing interaction reveals enhanced pairing correlations associated with the large Dirac effective mass, reduced spin-orbit splittings, and increased single-particle level density around the Fermi surface. Finally, departures from the linear sigma model potential motivated by the Nambu-Jona-Lasinio framework are explored. Allowing additional flexibility in the chiral potential improves the description of light nuclei and reduces the Dirac mass, which in turn suppresses the anomalous pairing. These results highlight the sensitivity of finite nuclei properties to the structure of the chiral potential and the associated single-particle spectrum.

We consider the optimization problem of minimizing a nonsmooth function characterized by a nonsmooth formulation of the descent lemma over a manifold. In the unconstrained case over a Euclidean space, this class of functions is called upper-$\mathcal{C}^2$. Using the recent notion of projectional subdifferentials, we show that their descent property carries over to submanifolds. We propose a nonmonotone subgradient method to solve these problems and prove stationarity of accumulation points of the generated sequence as well as convergence and rate-of-convergence results under the Kurdyka-Lojasiewicz property. We also perform numerical experiments and show how our approach can be applied to a certain type of difference of convex functions as well as clustering problems on manifolds.

In this paper, we investigate Polish semigroup topologies on the endomorphism monoids $\operatorname{End}(\mathbb{N},\leq)$ and $\operatorname{End}(\mathbb{Z},\leq)$. We introduce a new structural condition, property $\mathbb{XX}$, which yields automatic continuity of Borel measurable homomorphisms between certain topological semigroups. This provides a new method for analyzing Polish semigroup topologies on monoids with small groups of units. We show that for all monoids considered, the semigroup Zariski topology coincides with the pointwise topology and is therefore the coarsest Hausdorff semigroup topology. We prove that the submonoid $\operatorname{End}^{\infty}(\mathbb{N},\leq)$ of $\operatorname{End}(\mathbb{N},\leq)$ consisting of all endomorphisms with infinite image admits a unique Polish semigroup topology, namely the pointwise topology. On the other hand, despite possessing a finest Polish semigroup topology, the monoids $\operatorname{End}(\mathbb{N},\leq)$ and $\operatorname{End}(\mathbb{Z},\leq)$, admit infinitely many distinct Polish semigroup topologies. Also, we show that the monoid $\operatorname{End}(\mathbb{N},<)$ admits exactly $2^{\aleph_0}$ Polish semigroup topologies and no maximal second-countable semigroup topology.

We investigated the static and dynamic properties of a Rouse ring polymer modified by introducing an effective, spherically symmetric, attractive potential of entropic nature and a memory function describing the effect of dynamic entanglement. Renormalized Rouse formalism is used to approximate the time dependence of the memory matrix. The results obtained are in good agreement with existing experimental data and the results of computer simulations of ring polymer ring with , , where N_e is the number of Kuhn segments in linear polymer melts between neighboring entanglements and , the number of Kuhn segments. For large molecular weights, a refined self-consistent approximation is proposed to describe the time dependence of the memory function. It is shown that this approximation allows us to describe an exponential decrease in the self-diffusion coefficient with molecular weight of the rings, i.e., the effect of dynamic localization.

Single-cell-resolution spatial transcriptomics profiles gene expression at cellular locations in native tissues, yet accurate cell-type annotation remains challenging: imaging-based platforms are constrained by targeted gene panels, whereas sequencing-based platforms often suffer from sparse molecular capture and dropout. Reliable transfer of cell-type labels from single-cell RNA sequencing references is therefore critical for interpreting targeted and sparse spatial datasets. Here, we present SpCAST, a Kolmogorov--Arnold network-based framework for reference-guided spatial transcriptomics analysis. SpCAST captures nonlinear mappings between reference and spatial expression profiles and uses feature attribution to prioritize genes supporting cell-type predictions. Within a unified framework, SpCAST performs cell-type label transfer, spatial gene-expression reconstruction and marker-gene candidate prioritization. We benchmarked SpCAST on 53 datasets comprising 413,376 spatial cells across five technologies and diverse tissue contexts. SpCAST achieved competitive annotation performance with reduced runtime relative to representative existing methods. Case studies demonstrated that SpCAST supports cross-species label transfer and candidate assignment of originally unlabeled cells. It also reconstructs marker-gene expression patterns with improved spatial concordance and prioritizes cell-type-associated marker genes. Together, these results support SpCAST as an efficient and interpretable framework for extracting cell-type and gene-level information from targeted and sparse single-cell-resolution spatial transcriptomics data.

The growing adoption of electric vehicles (EVs) is increasing peak demand in distribution systems, which can threaten grid stability and reduce operational efficiency. Dynamic electricity pricing is a promising means of mitigating these peaks by shifting flexible demand. However, most existing approaches rely on detailed user-level consumption data and behavioral models, which are often difficult to obtain in practice and may raise privacy concerns. This paper proposes an Online Feedback Optimization (OFO) algorithm for day-ahead price design with limited data, where only aggregate loads are observed. OFO updates prices iteratively using aggregate load measurements, enabling effective peak reduction without access to individual user data. The formulation also includes a term that penalizes deviations in total electricity cost relative to a reference tariff. Although relying only on aggregate load measurements, the OFO price updates efficiently converge to the optimal price. In finite-horizon simulations, OFO achieves peak reduction close to that of the Stackelberg benchmark with full model information. Meanwhile, its computational effort is substantially lower. Additional tests under multiple initial conditions and delayed charging-window mismatch further confirm the robustness of the proposed method. Overall, these results show that OFO is a scalable and computationally efficient approach for peak-demand management in distribution systems with limited observability.

We develop a spectral cut-off construction of real-time oscillatory integrals associated with non-autonomous Hamiltonian evolution equations. Let \(H_0\) be a positive self-adjoint reference operator on a Hilbert space \(\Hilb\), and let \(P_N=\mathbf 1_{[0,N]}(H_0)\) be its spectral projections. For a time-dependent family of generally unbounded Hamiltonians \(H(t)\), we consider the finite-dimensional cut-off Hamiltonians \[ H_N(t)=P_NH(t)P_N . \] The corresponding propagators are represented by time-sliced finite dimensional oscillatory integrals. Under suitable \(H_0\)-relative regularity and stability assumptions, we prove convergence of these cut-off oscillatory amplitudes to the strong solution of the original Hamiltonian evolution equation \[ \ii \partial_t u(t)=H(t)u(t). \] In the periodic case, the same construction yields finite-dimensional effective Hamiltonians and provides a natural bridge with the Floquet--Magnus expansion for unbounded operators. We also discuss how spectral cut-offs may later be used to define renormalized traces of real-time amplitudes.

Explicit incorporation of magnetic degrees of freedom in machine-learning interatomic potentials (magnetic MLIPs) plays a crucial role in the correct description of magnetic materials and their properties. An important ingredient for fitting of magnetic MLIPs is spin-polarized density functional theory (DFT) calculations with non-equilibrium magnetic moments, i.e. DFT calculations with constraints on magnetic moments. In this study, we present a workflow for active learning of magnetic Moment Tensor Potential (mMTP) during molecular dynamics (MD) simulations. Magnetic MTP and its active learning algorithm were implemented in the open-source spin-MLIP code, DFT soft-constrained spin-polarized calculations were performed with the VASP code, and MD simulations were conducted in the open-source LAMMPS code. We test our workflow on the Fe-Pd crystal. The dependencies of magnetization and density of states (DOSs) on the volume of a supercell (or, pressure) are in good agreement with those calculated with DFT. Furthermore, the calculated DOSs correspond to the experimental ones.

Forcing was first introduced by Paul J. Cohen in his work on the independence of the Continuum Hypothesis. Other formulations of forcing appeared using Model Theory, Boolean-valued Models, and Topos Theory. There is a folkloric claim that these three approaches are equivalent, at least at the level of their mathematical content. In this work, we present some results not found in the literature toward establishing connections between these versions of forcing.

Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $τ$. In this paper we extend the quantum-mechanical framework introduced in [1] to a relativistic scalar quantum field theory in Minkowski space-time. The construction is based on the analytic continuation of fields and action from $\mathbb{R}$ to $\mathbb{C}$ together with constraints that select stable intrinsic-time trajectories and, at the same time, define convergent integration cycles for the corresponding microcanonical functional. We show that, in the continuum limit, the microcanonical generating functional reproduces the Feynman generating functional. For the free scalar field in $1+1$ dimensions we derive the constrained equations of motion, implement the resulting dynamics numerically, and verify real-time two-point correlators, equal-time commutator relations, and Dyson--Schwinger equations including the expected contact terms.

Transition-related financial markets are increasingly exposed to abrupt repricing episodes, elevated volatility, and heterogeneous macro-financial shocks. Under such conditions, conventional Gaussian-linear forecasting frameworks may provide an incomplete representation of the dependence structure linking fossil-energy, renewable-energy, technology, and utility-sector assets. This paper investigates whether transition-related financial returns exhibit residual non-linear predictability after controlling for heavy-tailed multivariate linear dynamics. To address this question, we develop a hybrid forecasting framework combining Student-t Vector Autoregressions with nonlinear recurrent residual learning architectures. The empirical analysis considers six major exchange-traded funds representing broad equity markets and key transition-sensitive sectors. The results reveal substantial departures from Gaussian-linear behavior, including excess kurtosis, volatility clustering, and remaining nonlinear dependence after econometric filtering. Out-of-sample forecasting experiments show that the proposed framework consistently improves predictive accuracy relative to conventional VAR models, standalone machine-learning methods, and alternative hybrid specifications. The forecasting gains become more pronounced during periods of macro-financial stress, particularly during the COVID-19 crisis and the Ukraine-related energy shock. Overall, the findings suggest that transition-related financial systems exhibit regime-sensitive and heavy-tailed predictive dynamics that are insufficiently captured by standard Gaussian-linear models alone.

Magnetization is thermodynamically defined as the derivative of the grand potential with respect to a uniform magnetic field. However, a uniform magnetic field makes the kinetic momentum operators noncommuting and Landau-quantizes the electron motion. This changes the zero-field momentum-space to Landau-levels and raises a fundamental question: how can the thermodynamic response to a uniform field be reproduced by a linear-response calculation carried out in the momentum space of the zero-field problem? We address this question analytically in a quantum Hall ferromagnet that allows the orbital magnetization $M$ to be computed in a closed form. We first compute $M$ from the local Hartree--Fock projector response to a periodic magnetic field with zero net flux. We then compute $M$ from the derivative of the grand potential with respect to a uniform magnetic field along the Středa line. The two approaches give the same result, even though the first keeps the Hilbert space fixed while the second changes the Landau-level degeneracy. Their agreement suggests that we should view orbital magnetization as the energy associated with the spectral flow that gives rise to the Středa formula. Our work provides a tutorial introduction to orbital magnetization and its relation to the Středa formula.

The thinning-based integer-valued autoregressive moving-average (INARMA) models are popular for count time series. Recently, types of INARMA models have also been developed for count random fields, i.e., for spatial count data located on a regular two-dimensional grid. This article provides a comprehensive survey on existing INARMA random fields, covering approaches with different thinning operators, first- and higher-order models, as well as unilateral and multilateral model structures.

We develop a self-consistent spectral quadrature (sc-SQ) framework for the calculation of many-body Green functions. The method approximates the Källén--Lehmann spectral measure by Gauss--Christoffel (GC) quadrature, yielding a rational Green function representation with guaranteed spectral positivity that exactly reproduces the first $2N$ spectral moments at pole order $N$. A key component is an SVD-based rank-selection criterion on the Hankel matrix, which identifies the numerically resolvable pole rank $N^*$ from the singular-value gap and acts as a precision-guided diagnostic of correlation complexity. The scheme is made self-consistent by requiring that the spectral function used to evaluate expectation values coincides with the spectral function generated by the quadrature reconstruction. This defines a fixed-point hierarchy that connects systematically to established approximations, including Hartree--Fock and Hubbard-I, and incorporates non-perturbative features such as multi-peak spectral structure. We benchmark the approach for the Anderson impurity model against numerical renormalization group (NRG) results and apply it within dynamical mean-field theory for the Hubbard model on the Bethe lattice. The method captures the three-peak Anderson impurity spectrum and the suppression of quasiparticle weight in the half-filled Hubbard model on the Bethe lattice, including Mott-gap formation on the insulating branch for $N\geqslant 5$, in qualitative agreement with NRG references.