Papers

The introduction of Reconfigurable Intelligent Surfaces (RIS) technology marks a transformative era in modern communication systems, enhancing coverage and facilitating higher data transmission rates. While recent research has delved into the integration of RIS into satellite networks, a critical and practical gap persists concerning its implementation in the satellite-Very Small Aperture Terminal (VSAT) downlink, specifically amplifying contributions from the VSAT side. This paper addresses this gap by proposing a simple and engineering methodology to optimize RIS position and orientation, incorporating considerations for the antennas' radiation patterns and the system's topology to streamline optimization variables. The primary objective of this paper is to alleviate the double fading constraint in the reflect link without the need for active elements, achieved by leveraging the Fresnel zone of the RIS. The improvement power ratio depends on the frequency and the VSAT 's diameter. The results show that for a VSAT with diameter 1m the gain is up to 9dB at 2 GHz (S band) and up to 14dB at 4 GHz (C band). Additionally, the RIS channel equation is refined, encompassing the tropospheric attenuation and accounting for electromagnetic wave polarization.

The ISO GQL standard introduces a rich value-type system for property graphs, including scalar, temporal, byte-string, list, record, and dynamic union datatypes. The vocabulary presented here additionally covers a vector extension. At the same time, RDF-based knowledge graph systems identify literal datatypes by IRIs and interpret typed literals through value spaces, lexical spaces, and lexical-to-value mappings. This paper presents the GQL Datatypes RDF Vocabulary, a lightweight RDF vocabulary that represents selected GQL datatypes and the vector extension as RDF datatype IRIs and describes their hierarchy, aliases, and selected constraints using RDF, RDFS, OWL, and XML Schema Datatypes vocabulary terms. The vocabulary is intended to support interoperability between GQL-oriented property graph systems and RDF-based knowledge graph systems. We describe its namespace and datatype model, summarize its datatype coverage, and show how the accompanying generator and validator use the vocabulary. In the reference implementation, RDF literals retain GQL datatype IRIs; XSD mappings declared in the vocabulary support scalar validation, while lists, records, and vectors are encoded directly as JSON lexical forms of vocabulary-typed literals.

For polarized manifolds, we show that semistability for the quantized Mabuchi energy at one fixed finite parameter is equivalent to uniform K-stability and to unique existence of constant scalar curvature Kähler (cscK) metrics. We obtain sharp comparisons between quantized Mabuchi slopes at different parameters and with the ordinary Mabuchi slope. In the presence of automorphisms, we give an equivariant criterion using torus twists under the vanishing of the Futaki character. The estimates also hold for finite-energy geodesic rays in compact Kähler classes. On a fixed ruled surface with discrete automorphism group, we construct cscK polarizations with unbounded critical parameters. Their ratios to the $\alpha$-invariant are also unbounded.

Signal Temporal Logic (STL) specifies robot tasks with spatio-temporal requirements, and its robustness semantics allow planning by trajectory optimization. In practice, robots estimate their state from noisy measurements, and when the information gained from a measurement depends on the state, the robot can actively reduce its uncertainty by planning in the belief space. The resulting problem is, however, generally non-convex, for which gradient-based methods are neither complete nor globally optimal. In this paper, we consider Risk STL (RiSTL) planning in Gaussian belief space and show that an information-form parameterization of the belief, together with a convex relaxation of the belief dynamics, yields a mixed-integer convex program (MICP). We prove that the MICP is sound and complete, and that the relaxation preserves the globally optimal input trajectories. We validate the effectiveness of our method in numerical simulations.

Colloidal suspensions that are confined between two closely spaced plates and left to evaporate slowly form maze-like labyrinth patterns in the final stage of evaporation. The fingers in these patterns form bifurcations and occasionally loops, which we may quantify with a skeletonization method. We compare drying patterns formed with two different salt concentrations in the droplet which changes the screening length and therefore the effective colloid interactions. We find that the junctions generally follow Murray's law for optimal transport networks, and that the typical bifurcation angles peak around 53. Screened droplets additionally show more loopy networks, and is characterized by bands of transversal fingers before merging into a central non-fingering colloidal aggregate. Our observations suggest that colloid-colloid interactions can strongly influence the large-scale topology of the pattern while leaving the local geometry of the individual fingers unchanged.

Adversarial detection on evolving attributed graphs faces two challenges: fraud labels arrive late or not at all, and natural distributional drift erodes any trained decision boundary. Modern detectors can reach strong detection rates when labels are available and the distribution is stationary; sustaining that quality without labels and under drift is the open problem. We identify feature-context consistency – the alignment between a node's attributes and its aggregated neighborhood attributes – as a single structural signal that addresses both. We formalize it as the Context Boost (CB) score within a Restricted Boltzmann Machine framework (CB-RBM) and prove two complementary worst-case guarantees: a strict separation between the expected CB of legitimate and adversarial nodes, with gap growing linearly in model capacity, whenever the adversary's context stays far enough from legitimate neighborhood context; and a Wasserstein-Lipschitz bound on how far the CB distribution moves under natural drift. We validate on XBlock Ethereum phishing (~153K nodes) and Reddit banned-user detection (~11K nodes), with two further datasets in the appendix spanning diverse domains. With zero labels, CB-RBM achieves AUROC >= 0.96 on four adversarial attacks and keeps FPR close to its calibrated 5% target under drift – outperforming supervised GNNs (hundreds of labels), unsupervised graph-anomaly baselines, and a standard RBM whose FPR collapses to 89-100%. What typically requires separate mechanisms – label-free operation and drift stability – here follows from a single structural regularity of the data. Code: https://github.com/serval-uni-lu/CB-RBM.

We study normalized principal Steklov eigencouples on periodically perforated domains when both the bulk energy and the boundary normalization have general, possibly nonhomogeneous, Orlicz growth. The surface term on the hole boundaries carries the critical surface-to-volume scaling. For each fixed mass level, the constrained minima converge along the whole family, while selected minimizers, fluxes and Lagrange multipliers converge along subsequences to the corresponding objects of a homogenized problem. In the limit, the bulk operator is given by a convex cell problem, and the boundary term becomes a volume term weighted by the total surface density of the reference hole. The key tool is a strong approximation of the microscopic traces by cell averages, measured in the scaled surface modular.

We address the Cross-View Object Re-Identification (ReID) task, aiming to match identities across drastically different viewpoints. We focus on Single-View Aerial-Ground ReID (SV AG-ReID), where models train on one viewpoint and must generalize to another at inference. To bridge this viewpoint gap, related work employs generative models to synthesize novel views from source images as additional training data. We leverage recent advances in large-scale single-view 3D mesh reconstruction to lift source images into textured meshes and to render them from new viewpoints. However, this pipeline produces unreliable data in two distinct ways. First, the reconstruction may fail and produce geometrically incorrect meshes, resulting in severe corruption in rendered novel views. Second, even when the geometry is correct, the rendered novel views contain hallucinated textures in regions not visible in the source image. The reconstructed mesh carries a per-pixel partition between regions visible from the source view and regions that the reconstruction model had to hallucinate, available as a deterministic byproduct of rendering. We introduce this per-pixel visibility map and exploit it in a two-stage design. Cross-View Consistency Filtering (CVCF) discards geometrically incorrect meshes by ensuring multi-view consistency between source and novel views over visible patches. Visibility-Aware Attention Supervision (VAAS) leverages the visibility map to guide the model's attention toward reliable regions of the rendered view during training. Combined, these two components enable our method, 3D-VITAL, to better leverage the synthetic signal from single-view 3D mesh reconstruction. 3D-VITAL sets a new state-of-the-art on three SV AG-ReID benchmarks. Code and data will be released at https://github.com/TurtleSmoke/3D-VITAL.

Reinforcement learning (RL) post-training has emerged as the key paradigm for improving autoregressive video models. Emerging vision-language reward models further strengthen post-training with accurate rewards, but their long chain-of-thought inference substantially raises the associated costs, while the pursuit of long videos prolongs policy training. Despite these rising costs, existing video RL systems still adopt coarse-grained stage-centric execution, which stalls policy training until all reward evaluation finishes, replays every trajectory twice due to a further barrier within policy training, and induces load imbalance across GPUs. To address the challenges, we propose StageBreaker, a fine-grained data-dependency-driven scheduling framework, which schedules the true dataflow of an RL step rather than its stages. Specifically, StageBreaker overlaps policy training with reward evaluation by exploiting reward-separable policy training, and merges the two trajectory replays into one by leveraging loss-independent back-propagation. It further balances GPU load by scheduling computation at the finer granularity. Our evaluation results show that StageBreaker achieves a speedup of up to 1.41$\times$ over stage-centric execution.

Channel estimation for extremely large-scale uniform planar arrays (UPAs) requires exploiting near-field channel structure to reduce pilot overhead. With a specifically devised channel representation matrix, the near-field channel exhibits a 2D sparse structure, which a conventional 1D block partition might divide into multiple groups. This work develops a 2D block orthogonal matching pursuit (2D-BOMP) estimator that exploits this structure through rectangular coefficient grouping. We establish sufficient recovery conditions for noiseless and noisy measurements and compare the sufficient pilot-length requirements of 1D and 2D partitions. Numerical simulations demonstrate the estimation benefits of 2D-BOMP in estimating the near-field channels of large-scale UPAs, compared with the conventional 1D-BOMP as well as the polar-domain based OMP method.

Recruitment applications span diverse operations, from drafting job descriptions and interpreting queries to organizing profiles, assessing fit, and recommending candidates and jobs. Systematic LLM evaluation therefore requires task coverage that reflects this range of business needs. We introduce EHR-Bench, an open Chinese benchmark comprising twelve tasks across six capability families and five recruitment scenarios. The tasks cover generation, extraction, classification, retrieval, semantic similarity, and reciprocal ranking within one evaluation framework. An internal recruitment dataset guides task definitions, the occupation taxonomy and sampling targets, output requirements, and scoring protocols. Following these specifications, we construct 8,336 task instances from public materials and controlled augmentation, with source-aware expert review and documented provenance. We evaluate twelve LLMs through task-level, capability-level, and aggregate comparisons. Closely ranked models exhibit distinct task strengths, and performance varies across input sources, reference evidence, and candidate pools. Five shared models retain the same observed Overall ordering on a private operational reference, with variation in capability and task correspondence. EHR-Bench provides a reproducible foundation for systematic model assessment, task-specific model selection, and further research on LLMs for recruitment. The project repository is available at https://github.com/EhrBench/EHR-Bench.

False vacuum decay is conventionally described by a spherically symmetric bounce with a single negative fluctuation mode. This raises a fundamental question: can the single negative mode requirement itself enforce spherical symmetry, independently of action minimization? For a single real scalar field with a smooth potential in flat spacetime, we rigorously prove that every localized nonspherical saddle with zero initial velocity has at least three negative modes. Additional reflection symmetries further tighten these bounds, as illustrated in a sextic scalar model. Our findings exclude nonspherical bounce candidates with a single negative mode, providing a complementary spectral foundation for the spherical bounce description of false vacuum decay.

The majorization simplex $\mathcal{P}_n$ is the set of probability vectors of length $n$ whose entries are arranged in non-increasing order. Under the majorization order, $\mathcal{P}_n$ is a lattice, and it is the natural space for comparing distributions when the labels of the outcomes are not relevant. In this work, we study measures of dissimilarity (and, similarity) on $\mathcal{P}_n$. Our first set of results concerns the Rényi-entropy based distance $d_\alpha(p,q)=H_\alpha(p)+H_\alpha(q)-2H_\alpha(p\vee q)$ proposed by Yadav and Shkel (2026), which generalizes a metric of Cicalese, Gargano and Vaccaro (2013). We show that $d_\alpha$ is a metric on $\mathcal{P}_n$ for $\alpha\in[1,\infty)$, while for $\alpha\in[0,1)\cup\{\infty\}$, $d_\alpha$ is not a metric in general. Our main result in this part identifies the necessary and sufficient conditions for equality in the triangle inequality of $d_\alpha$ when $\alpha>1$, for which we identify the equality conditions for the supermodularity of the Rényi entropy $H_\alpha$. Our second set of results concerns the total variation distance and the Hellinger affinity (also called the Bhattacharyya coefficient) on $\mathcal{P}_n$. We obtain a number of bounds on these measures, along with some of their equality conditions. The resulting Hellinger affinity based upper bound on the total variation distance can be smaller than the bounds obtained from Pinsker's and the Bretagnolle–Huber inequalities.

Let $p>1$ and $\Omega\subset\mathbb{R}^n$ be a bounded smooth domain. We study the following overdetermined problem for the p-Laplacian: \begin{equation*} \left\{ \begin{array}{ll} -\Delta_p u=f(x)&x\in\Omega,\\ u=0&x\in\partial\Omega,\\ \frac{\partial u}{\partial\nu}=g(x)&x\in\partial\Omega, \end{array} \right. \end{equation*} where $\nu$ is the inward unit normal to $\partial\Omega$ and both data may depend on position. A boundary-local version of the moving-plane argument is developed for the possibly degenerate p-Laplace operator. The advantage of this argument is that it avoids the analysis of the degenerate set of the p-Laplacian. Under some reasonable structural conditions, we prove that the solvability of the above mentioned problem forces the domain to be a ball, the source to be radial, and the Neumann datum to be a suitable constant. We also give an explicit formula for the solution. Further consequences include one directional domain symmetry, the conclusion that full rigidity follows from reflection information in any set of directions whose linear reflections generate a dense subgroup of the orthogonal group $O(n)$, and a constant mean curvature characterization.

Let $R$ be an integral domain and let $w$ denote the $w$-operation on $R$. A nonzero GV-torsion-free $R$-module $M$ is called $w$-secondary if, for every $r\in R$, either $M/rM$ is GV-torsion or $r^nM=0$ for some $n\in\N$. A $w$-module $M$ is said to admit a $w$-secondary representation if $M=(N_1+\cdots+N_n)_w$, where each $N_i$ is a $w$-secondary submodule of $M$. Such a representation is called minimal if the ideals $P_i=\sqrt{\Ann_R(N_i)}$ are pairwise distinct, and $M$ is called $w$-representable if it admits such a representation. If the sum can be chosen direct, then $M$ is called strongly $w$-representable. We characterize $w$-secondary modules and investigate their localization and $w$-closure properties. For a nonfield domain $R$, we prove that $R$ is $t$-almost Dedekind if and only if $\wdim R=1$ and every $w$-representable $w$-module is locally strongly $w$-representable: each of its nonzero localizations at maximal $w$-ideals is strongly representable. Global strong $w$-representability is retained when all the radical annihilators in the representation are nonzero.

We study the voter model with opinion graph, a generalization of the standard (pull) voter model that adds a notion of bounded confidence. In this process, we consider a finite set $A$ of $n$ agents. Each agent $u \in A$ has an opinion $x_u \in O$, where we model opinions as vertices in an undirected opinion graph $G = (O,E)$ with $|O|=q$. In each step, an agent $u$ interacts with another agent $v \in A$. In contrast to classical voting, $u$ adopts the opinion $x_v$ if and only if $x_v$ and $x_u$ are neighbors in $G$. The process is stable once all remaining opinions are an independent set in $G$. We analyze two variants of the process: the ordinary EdgeVOG process, which samples a pair of interacting agents uniformly at random from all possible pairs, and the productive EdgeVOG process, which samples only pairs with neighboring opinions in $G$. We show the following: - For every opinion graph and every initial configuration, ordinary EdgeVOG stabilizes within $O(n^2\log n)$ steps in expectation and with high probability. The expectation bound is asymptotically tight. For the productive EdgeVOG process, the expected stabilization time is exactly the initial number of compatible agent pairs, while $O(n^2\log n)$ steps suffice with high probability. - An opinion $i$ with initial support $s_i$ survives with probability at least $p_i:=s_i/(s_i+\sum_{j\in N(i)}s_j)$. Further, let $\mu = \sum_{i \in O} p_i$, then we show the probability that less than $(1-\delta)\mu$ opinions survive is at most $\exp(-\delta^2\mu/(2(\Delta^2+1)))$ for every $0\leq\delta\leq1$. -If $G$ has maximum degree $\Delta$ and every opinion initially has support at most $\hat{s}$, then no opinion ever acquires more than $\tilde{O}(\min\{n,\Delta^6\hat{s}\})$ agents with high probability. This yields near-linear stabilization bounds for productive EdgeVOG for a large class of configurations.

This paper delves into the intricate aspects of Reconfigurable Intelligent Surfaces (RIS) in the antenna design. It investigates the properties of the array factor of RIS, highlighting the significance of phase shifts in establishing of the reflect path. Additionally, the paper investigates spatial positions requiring identical phase shifts, nullification of the array factor, the count of total maxima, second maximum determination (amplitude of the second lobe), and the calculation of the 3dB bandwidth. They are very useful for RIS-assisted radio communication systems.

In skyrmion magnets, charge density waves induce higher-order exchange interactions that can select multi-Q ground states. Using resonant X-ray scattering and neutron diffraction, we measure temperature-dependent spin-charge coupling in GdRu2Si2. A minimal Landau model with one critical exponent and two ordering temperatures reproduces all six observed order parameters. Spin-density wave components of the multi-Q ground state drive charge ordering, but the onset of a magnetic helix suppresses it via destructive interference.

Domain walls in ferroic crystals are topological defects with a symmetry distinct from the domain interior, allowing them to display functionalities that are otherwise forbidden in the host material. Despite their unique properties, domain walls are strictly confined to two-dimensional interfaces, which hinders unveiling their true nature and limits their applicability. Here, we demonstrate reversible dimensionality control by expanding nanoscale domain walls into three-dimensional functional regions in polar epitaxial tungsten trioxide ($\text{WO}_3$). This domain-wall-to-domain interconversion is enabled by the conducting, non-polar domain walls adopting the parent-phase structure. An alternating electric field applied through a scanning probe tip induces localized heating, which expands this domain-wall phase into the adjacent polar domains. This approach enables reversible spatial control to switch between mutually exclusive properties of domains (polarity) and domain walls (conductivity), offering a new paradigm for reconfigurable oxide electronics.

Resampling is the standard remedy against weight degeneracy in particle filters, yet its effect on the spectrum of the particle second-moment matrix is poorly understood. We study a single resampling step for a d-dimensional ensemble of N particles with d/N -> c. For any unbiased scheme, the resampled empirical second-moment matrix dominates its pre-resampling counterpart in conditional convex order, while the conditional mean is preserved; the excess second spectral moment equals the Frobenius energy of the resampling perturbation. For multinomial resampling, the empirical count law converges to the mixed-Poisson law determined by the limiting weight law. For residual resampling, the count law is determined by the joint limit of floor-fraction pairs: we classify all residual limits of weight sequences converging to delta_1 in law as a one-parameter family between the deterministic identity and the full multinomial count law. Each count law feeds a common covariance-side spectral map, yielding exact consequences: a closed-form zero-eigenvalue mass, a rank-and-spectral-gap transition with a universal lower edge benchmark, computable regular edges, unbounded right support, and scheme-specific second-moment costs. The effective sample size determines one bulk statistic but cannot determine the limiting spectrum. Pre-registered numerical experiments confirm the theory at every level.

Spatial reasoning agents can inspect tool outputs and repair errors, but reusing these lessons requires preserving both the computation and the conditions that make it valid. We introduce EvoSpatial, a framework that learns from execution experience by updating a library of linked skills and tools. Skills describe procedures, geometric assumptions, and verification steps; tools implement the operations those procedures require. When solving a task, the agent retrieves relevant skills and synthesizes reusable computational functions if existing tools are insufficient. After each task, execution feedback and evidence checks guide skill revision and tool consolidation, without ground-truth answers or benchmark scores. Across 20 benchmarks, EvoSpatial averages 63.9, 4.0 percentage points above the average reported by SpatialClaw. The evolved library also improves held-out and cross-benchmark performance when updates are disabled, and trajectories generated with evolved skills improve supervised fine-tuning, even without external skills at evaluation. Keeping checked procedures on record, together with the tools that support them, lets an agent carry spatial reasoning experience from one task to the next.

The latent variable proximal point (LVPP) method solves optimization problems in function spaces with pointwise constraints by a sequence of smooth subproblems whose iterates are strictly feasible. We apply it to linear-quadratic elliptic optimal control problems. Control and observation are distributed but may be restricted to subdomains. We prove that the LVPP subproblems are well posed in appropriate function spaces, that the iteration converges for every sequence of proximity parameters with divergent sum, and that it delivers the Lagrange multiplier of the constraint as a by-product. We interpret the Newton step for the LVPP subproblem as a linear-quadratic optimal control problem with a spatially varying control cost, and we show that Newton's method converges locally quadratically. The Newton systems are solved by the minimal residual method with a block-diagonal preconditioner. We prove that the spectrum of the Newton operator with respect to the inner product defined by the preconditioner is bounded independently of the proximity parameter, the iterate, the mesh and the observation and control domains. The results are combined into a complete algorithm, and tested in numerical experiments.

Learning interaction structures from spatiotemporal event data is a key statistical problem in fields such as neuroscience, epidemiology, and seismology. We study this problem for Hawkes processes on a continuous spatial domain, where events may trigger future events at different locations. Following the framework developed in “Spatiotemporal Hawkes processes with a graphon-induced connectivity structure” by Baars, Laeven, and Mandjes (2026), we model the spatial interaction mechanism using an underlying graphon that characterizes how the intensities' excitation strength varies across locations. By expanding the baseline intensity, temporal excitation kernel and graphon in orthogonal bases, we represent the problem as a high-dimensional parametric inference problem. We propose a sparse penalized least-squares estimator that recovers the effective interaction structure while controlling model complexity. Our analysis establishes non-asymptotic error bounds in a high-dimensional regime where the number of parameters may grow with the observation horizon, without requiring the conditional intensity to be almost surely bounded. We further establish sparsistency results, showing that the latent interaction network can be consistently recovered. Simulation studies demonstrate the good finite sample performance of the proposed method and an application to large-scale neuronal spike data, comprising 1.81 million events, showcases its practical effectiveness.

Recent work [Kundu, Damle, Phys. Rev. X 15, 011018 (2025)] has demonstrated that a class of $S=1$ kagome lattice antiferromagnets with competing anisotropies can exhibit unusual low-temperature behavior that is best described in terms of the statistical mechanics of an interesting interpolation between the fully-packed dimer model and the fully-packed loop model on the bipartite honeycomb lattice. On this and other bipartite lattices in two and three dimension, such fully-packed dimer-loop models generically have two distinct power-law correlated Coulomb phases, both of which admit a low-energy description in terms of a fluctuating divergence-free polarization vector field [Phys. Rev. X 15, 011018 (2025); arXiv:2510.11607]. The transition between these phases corresponds to a confinement transition for the $Z_2$ part of the corresponding $U(1)$ flux [Phys. Rev. X 15, 011018 (2025); arXiv:2510.11607]. Here we demonstrate that a variant of such a topological confinement transition can also exist in dimer-loop models on non-bipartite lattices such as the kagome and triangular lattices although the low-energy description does not feature any conserved $U(1)$ flux. In these non-bipartite dimer-loop models, both phases are short-range correlated liquids, and the topological distinction between them is in terms of a $Z_2$-valued winding number instead of the flux of a divergence-free polarization field. In spite of this key difference, this transition appears to be in the same Ising universality class as the analogous transition of the bipartite dimer-loop models. These kagome and triangular lattice dimer-loop models correspond respectively to the low-energy limit of a class of $S=1$ antiferromagnets with competing anisotropies on the ruby lattice comprising a corner-sharing arrangement of fully-frustrated squares and a lattice of corner-sharing fully-frustrated hexagons.

We study the recovery of the hidden vertex correspondence between two correlated dense random geometric graphs. Each graph is generated from $n$ latent unit vectors in $\mathbb R^d$; the vectors $u_i^A$ and $u_i^B$ of corresponding vertices satisfy $\langle u_i^A,u_i^B\rangle=\rho$, and the vertex labels of the second graph are permuted by an unknown permutation $\pi$. For every fixed correlation $\rho\in(0,1]$ and every edge density bounded away from zero and one, we give a randomized polynomial time algorithm that recovers $\pi$ exactly with probability tending to one whenever $d\ge(\log n)^L$, where $L$ depends only on the correlation and the density bounds. The algorithm assigns to each vertex a signature formed by counting decorated paths with a constant number of seeds. The number of such seeded templates grows exponentially with the path length, with an arbitrarily large constant base, so the resulting statistics amplify an arbitrarily small constant correlation. We control the dependencies created by the latent geometry in two ways: when $d$ is larger than $n/(\log n)^{L_0}$ for a suitable constant $L_0$, by comparing local moments with those of correlated Erdős–Rényi graphs; for smaller $d$, by spectral estimation of the latent geometry combined with a harmonic correction. We also provide low-degree evidence for a tradeoff between the correlation and the computational cost.

Topological chiral superconductivity has been extensively studied from the perspective of electronic structures in momentum space, while its emergence from real-space processes in strongly interacting systems remains largely unexplored. Here, we study a doped charge-transfer insulator in a strongly repulsive spinless-fermion model with three sublattices and $2\pi$ flux per unit cell. Combining perturbative analysis, exact diagonalization, and density matrix renormalization group simulations, we establish a topological superconducting ground state with $p+ip$ symmetry. In the large charge-transfer gap limit, chiral charge-transfer excitations generate a correlated-hopping process that provides a microscopic mechanism for electron pairing and its chiral structure. The chiral superconductivity persists into the smaller-gap regime, where chiral excitonic two-particle bound state can emerge. Our results establish a concrete real-space route to topological chiral superconductivity upon doping strongly interacting charge-transfer insulators with orbital magnetism.

Absolutely maximally entangled states of four six-level systems, AME$(4,6)$, are the quantum solutions of Euler's problem of the thirty-six officers. Until recently all reported solutions were complex, and it was conjectured that no real orthogonal 2-unitary matrix of order $36$ exists. We give real AME$(4,6)$ states with $60$ non-zero coefficients in $\{\pm1,\sqrt2\}/\sqrt{72}$. Of their thirty-six officers, $12$ are classical, as some must be whenever fewer than $72$ coefficients are non-zero. They lie in the $-1$ eigenspace of an order-$4$ local symmetry, and on their support the AME conditions become linear. We derive two closed-form families of AME$(4,6)$ states that meet at one of these states: a $10$-parameter family that is supported on $72$ basis states, and an $11$-parameter family on $60$ basis states. At each of its two ends the first family loses $12$ coefficients, and the AME states on the remaining $60$ basis states form an $11$-parameter family: the second family at one end, and an analogous family at the other. These two $60$-term families contain $4096$ real AME states up to diagonal local unitaries, $1024$ of which are limits of the first family. They fall into exactly $20$ classes under local unitaries and permutations of the parties, and we certify their separation with interval arithmetic.

Assuming that $\mathcal{P}(\omega)$ is tightly $\sigma$-filtered, we prove that $C(\omega^*)$ fails the ball fixed point property. This axiom holds under the continuum hypothesis and in the $\aleph_2$-Cohen model. The proof shows that the Stone space of the countable–cocountable algebra $\operatorname{Cc}(\omega_1)$ is a continuous retract of $\omega^*$ and uses the equivalence between tight $\sigma$-filteredness of $\operatorname{Cc}(\omega_1)$ and of $\mathcal{P}(\omega)$. We also prove that the quotient of a tightly $\sigma$-filtered Boolean algebra $B$ with the countable separation property by an $\aleph_1$-generated $P$-ideal is a Boolean retract of $B$.

The multivariate linear mixed model combined with restricted maximum likelihood estimation of (co)variance components and solving the mixed model equations is widely used for the analysis of plant breeding data. Several algorithms for restricted maximum likelihood estimation have been proposed, with the average information algorithm being widely used for its computational efficiency, quadratic rate of convergence, and ability to handle large amounts of parameters. A key reason for the scalability of linear mixed models is the exploitation of sparse matrix techniques. Recently, decreasing costs of high-throughput data collection have led to high-dimensional sets of features characterizing genotypes and environments. A convenient way of using these features is through the use of kernel-based covariance structures. However, while convenient, these kernels typically have dense inverses meaning optimizations based on sparse matrix techniques are not always applicable. For these settings, the introduction of general-purpose computing on graphics processing units brought significant computational advantages for dense linear algebra operations. We present a hybrid GPU/CPU implementation of the average information restricted maximum likelihood algorithm. We eliminate sparse equations using supernodal Cholesky factorization and rely on CUDA GPU acceleration to solve the resulting reduced dense system. We show the significant computational advantages of this approach for fully dense problems, as well as problems with a mix of dense and sparse equations.

In the complex Hilbert space $L_2(\mathbb{R}_+)$ on the half-line $\mathbb{R}_+ = [0, \infty)$, we investigate non-symmetric Schrödinger operators \[ Su = -u'' + qu, \qquad u(0) = 0, \] with complex-valued, highly singular distributional potentials \[ q = s + Q' \in H_{\mathrm{loc}}^{-1}(\mathbb{R}_+), \qquad s \in L_{1,\mathrm{loc}}(\mathbb{R}_+), \quad Q \in L_{2,\mathrm{loc}}(\mathbb{R}_+), \] where the derivative $Q'$ is understood in the sense of Schwartz distributions. A rigorous operator-theoretic setting is established within the framework of Shin–Zettl quasi-derivatives. We prove that every accretive operator $S$ of this class is automatically $m$-accretive in $L_2(\mathbb{R}_+)$ and $C$-self-adjoint with respect to the complex conjugation involution $C : u \mapsto \bar{u}$. In particular, no additional boundary conditions at infinity are needed, meaning that a Weyl limit-point type situation always prevails for accretive realizations. Constructive local conditions on the coefficients $s$ and $Q$ are found under which the generated strongly continuous semigroup $\{e^{-tS}\}_{t \ge 0}$ is contractive or holomorphic in a sector of the complex plane.