We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind} issues, where agents must impute belief states and estimates of other agents to inform their own strategy. To avoid an infinite regress of higher-order beliefs amongst agents and obtain computationally implementable results, we focus on a linear quadratic Gaussian (LQG) model and consider strategies with limited internal state dimension. We present a novel iterative forward-backward algorithm to jointly compute belief states and equilibrium strategies and value functions for a finite-horizon problem. We also present a value iteration-like algorithm to jointly compute stationary belief states and equilibrium strategies for an average-cost infinite-horizon problem. An open-source implementation of the algorithms is provided, and we demonstrate the effectiveness of the proposed algorithms in numerical experiments.

Photonic quantum computing has gained significant interest in recent years due to its potential for scaling to large numbers of qubits. A critical requirement for fault-tolerant quantum computation is the reliable generation of non-Gaussian quantum states, typically achieved using Gaussian operations and photon-number-resolving detectors. However, the probabilistic nature of quantum measurement typically results in low success rates for state preparation. Conventionally, these circuits are optimized to herald a single specific target outcome, thereby disregarding the potential utility of alternative measurement patterns generated by the same physical setup. In this work, we propose and demonstrate a multi-outcome optimization strategy that increases the overall acceptance probability by allowing a single circuit to produce useful quantum states across several measurement patterns. To evaluate this approach, we apply the framework to the generation of Gottesman-Kitaev-Preskill core states, Schrodinger cat states, binomial codes, and cubic phase states using both two-mode and three-mode Gaussian circuits. We demonstrate that the success probability can be enhanced through two distinct mechanisms: first, by simultaneously targeting a diverse set of useful resource states, and second, by aggregating degenerate outcomes to maximize the production rate of a single target state.

Electron emission from hydrogen atoms induced by antiproton impact at intermediate energies is investigated using the one-centre Basis Generator Method within a semi-classical impact-parameter framework. The formulation employs a single-centre expansion of the time-dependent Schrödinger equation with a pseudostate basis consisting of hydrogenic orbitals acted upon by powers of a Yukawa-regularized potential, providing a compact and effective representation of the electronic continuum. Ionization probabilities are obtained by projecting the time-evolved wavefunction onto Coulomb continuum states, from which energy-differential cross sections (EDCS) are extracted. Exponential piecewise functions are constructed to interpolate between the pseudostate eigenenergies, yielding smooth EDCS profiles for each partial wave. The total EDCS, reconstructed by summing over all partial-wave contributions, exhibits good agreement with results from other pseudostate-based approaches.

General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For a cubic Yeoh model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives $u_{xxt}$ of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analyzed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition $c_1 < \abs{v} < c_2$, while tending to the larger material wave speed $c_1$ or $c_2$ for large times.

This paper presents the constrained Hybrid Metaheuristic (cHM) algorithm as a general framework for continuous optimisation. Unlike many existing metaheuristics that are tailored to specific function classes or problem domains, cHM is designed to operate across a broad spectrum of objective functions, including those with unknown, heterogeneous, or complex properties such as non-convexity, non-separability, and varying smoothness. We provide a formal description of the algorithm, highlighting its modular structure and two-phase operation, which facilitates dynamic adaptation to the problem's characteristics. A key feature of cHM is its ability to harness synergy between both candidate solutions and component metaheuristic strategies. This property allows the algorithm to apply the most appropriate search behaviour at each stage of the optimisation process, thereby improving convergence and robustness. Our extensive experimental evaluation on 28 benchmark functions demonstrates that cHM consistently matches or outperforms traditional metaheuristics in terms of solution quality and convergence speed. In addition, a practical application of the algorithm is demonstrated for a feature selection problem in the context of data classification. The results underscore its potential as a versatile and effective black-box optimiser suitable for both theoretical research and practical applications.

In this article, I advance the idea that physics plays a central role in cell differentiation and makes fundamental contributions to morphogenesis, revealing the totipotent nature of the zygote. Totipotency is a persistent mechanical memory that preserves the biomechanical records of animal morphogenesis. I examine the mechanical and biophysical pathways underlying cell differentiation in embryonic development and cancer, treating them as closely related biological and mechanical processes. Drawing inspiration from evolutionary history, I also propose a biophysical mechanism for the emergence of the animal nervous system. By linking physical principles to cellular differentiation, this review positions mechanobiology as a pillar of innovation with high-impact clinical implications for diseases such as cancer.

Condensed-phase spectral line shapes encode the strength and timescale of interactions between molecules and their environments, yet these ideas are often difficult to introduce at the undergraduate level due to their reliance on formal theoretical treatments. We present a visualization-based approach that combines analytic results with numerical simulations to illustrate the physical origins of spectral line broadening in conjugated molecular systems. Using a time-dependent Hückel Hamiltonian, we derive closed-form expressions for coherent electronic motion in finite polyene chains and show how these results provide direct insight into the role of molecular orbital structure in light absorption. Environmental effects are introduced through stochastic fluctuations of the Hamiltonian matrix elements, allowing students to observe how system--environment interactions disrupt coherent motion and produce scattering-like features in electronic trajectories. Real-space animations and simulated absorption spectra provide an intuitive link between microscopic dynamics and measured line shapes. The MATLAB code provided with this work offers an accessible platform for integrating computation and visualization into undergraduate instruction while introducing key concepts in condensed-phase spectroscopy.

Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to study how coloring problems can be solved by groups of individuals on a graph, which has led to new insights into network structure, group dynamics, and individual human behavior. Despite this newfound utility, the exact nature of these distributed coloring problems is not well-understood, and established mathematical tools like the chromatic polynomial miss the unique challenges that arise in these social problem-solving situations with limited information. In this paper, we provide a new framework for understanding these distributed problems by defining a new kind of graph coloring with particular relevance to consensus formation on networks, in which all vertices are trying to agree on a common color. These strict gridlock colorings represent roadblocks to consensus where the group will not reach a uniform coloring using natural update processes. We describe a recurrence relation that provides an algorithm for counting these gridlocked colorings, which establishes a mathematical measure of how much a given graph hinders consensus in a group.

The aim of this work is to explicitly compute the K-theory of the category of matroids with respect to the covering family of Tutte coverings. In particular, we show that this is equivalent to the K-theory spectrum of the category of graphic matroids on looped forests, with the covering family generated by isomorphisms. Further, we show that this yields an equivalence of $C_2$-spectra.

We study Turnpike with uncertain measurements: reconstructing a one-dimensional point set from an unlabeled multiset of pairwise distances under bounded noise and rounding. We give a combinatorial characterization of realizability via a multi-matching that labels interval indices by distinct distance values while satisfying all triangle equalities. This yields an ILP based on the triangle equality whose constraint structure depends only on the two-partition set $\mathcal{P}_y=\{(r,s,t): y_r+y_s=y_t\}$ and a natural LP relaxation with $\{0,1\}$-coefficient constraints. Integral solutions certify realizability and output an explicit assignment matrix, enabling an assignment-first, regression-second pipeline for downstream coordinate estimation. Under bounded noise followed by rounding, we prove a deterministic separation condition under which $\mathcal{P}_y$ is recovered exactly, so the ILP/LP receives the same combinatorial input as in the noiseless case. Experiments illustrate integrality behavior and degradation outside the provable regime.

In Structural Health Monitoring (SHM), sensor measurements and derived features such as eigenfrequencies often exhibit systematic daily patterns and can therefore be naturally represented as functional data. Furthermore, these patterns are typically influenced by environmental factors, particularly temperature, which can substantially affect the observed system response. While most existing methods for removing environmental effects assume that confounding influences affect only the mean response, it has been shown that environmental and operational factors may also alter the covariance structure of the residual process. To address this limitation in a functional data monitoring framework, we incorporate so-called covariate-dependent functional principal component analysis (CD-FPCA), which allows eigenfunctions and eigenvalues of the residual process to vary smoothly with covariates such as temperature. The proposed methodology is illustrated using an extended version of the KW51 railway bridge eigenfrequency dataset. This case study suggests that accounting for covariate effects beyond the functional mean can improve the robustness of the monitoring procedure, in particular by reducing environmentally induced (false) alarms under challenging low-temperature conditions.

Spacetime is foamy due to quantum fluctuations. Various gedanken experiments show that distances fluctuate by amounts consistent with the holographic principle, hence the name "holographic quantum foam" (HQF). One important prediction of HQF is that necessarily there exists a dark sector in the universe. The resulting cosmology is found (at least qualitatively) to be consistent with observations. Interestingly the quanta of the dark sector are found not to obey the familiar (fermionic or bosonic) statistics, but the exotic statistics known as infinite statistics (or quantum Boltzmann statistics). The most important challenge now is to check if HQF is consistent with experiments/observations. One way is to look for observational evidence of blurred distant point-sources due to physics at the Planck scale. For over two decades it has been debated whether those tiny inherent uncertainties in time and path-length can accumulate in transiting electromagnetic wavefronts from quasars and Gamma-Ray Bursts (GRBs). But a recent event is special: GRB221009A was extremely bright and energetic. That allowed follow-up across the whole spectrum from the optical/near-infrared through to X-rays, and including the highest-ever-recorded energy gamma-rays; all consistent with blurring by HQF. Those data, and a calculation of the HQF-widened point-spread function (PSF) for real telescopes viewing a GRB are presented.

We model, simulate, and analyze the intramolecular modes of liquid H2O and D2O to elucidate how energy excitation, relaxation, and vibrational dephasing interplay through anharmonic mode-mode coupling. Our analysis employs two-dimensional (2D) correlation spectra, a representative observable in nonlinear infrared vibrational spectroscopy. Accurate reproduction of these 2D spectral profiles requires not only a precise dynamical description of intramolecular vibrations but also an appropriate treatment of thermal environmental effects arising from strong interactions with surrounding molecules, which act as thermal baths. Capturing the essential features of the 2D spectra further demands a non-Markovian, non-perturbative, and nonlinear description of the interactions between intramolecular modes and their baths. To this end, we adopt a hierarchical equations of motion (HEOM) framework to compute the 2D spectra. By comparing the resulting spectra of H2O and D2O, we explore the underlying mechanisms governing their complex energy and phase relaxation dynamics.

We introduce sbml4md, a newly developed algorithm implemented as a software package to extract parameters of multimode anharmonic Brownian (MAB) models from molecular dynamics (MD) trajectories for simulating nonlinear vibrational spectra of intramolecular modes of molecular liquids. By leveraging machine learning (ML) techniques to capture vibrational anharmonicity, intermolecular couplings, and bath correlation functions for each mode, sbml4md obviates empirical fitting and enables the modeling of environments with spatial and temporal heterogeneity. This work provides a set of parameters specifically tailored for the Hierarchical Equations of Motion (HEOM) framework, enabling numerically "exact" simulations of nonlinear vibrational spectra. Building upon our previous implementation for intramolecular vibrational modes [Park, Jo, and Tanimura, J. Chem. Phys. 163, 214104 (2025)], the present code enhances optimization efficiency by explicitly accounting for intermolecular vibrational contributions. This extension enables sbml4md to broaden the applicability of HEOM-based dynamical modeling by seamlessly integrating classical MD approaches, thereby providing a flexible and scalable framework for simulating both linear and nonlinear spectra under realistic conditions with minimal empirical input. The accompanying ML code, written in Python, is provided as supporting material.

Two-dimensional colloidal nanoplatelets (NPLs) with atomically defined thickness exhibit unique physical properties, yet understanding their formation mechanism and assembly remains essential for tuning their collective behavior. We report an optimized synthesis of triangular cerium-based NPLs with narrow size and shape distributions via thermal decomposition of cerium trifluoroacetate. Combining X-ray diffraction, XPS, and high-resolution STEM, we show that the expected CeF3 NPL structure undergoes partial oxidation, yielding an oxyfluoride composition CeOxFy. Beyond their composition, we investigate how these oleic acid-capped NPLs organize in solution and at interfaces. The choice of solvent governs both the solution-phase organization and the resulting superstructures formed upon evaporation at the liquid--air interface. In solvents that promote face-to-face stacking in solution, evaporation produces films organized into columnar assemblies tens of micrometers long, with the NPL planes oriented perpendicular to the interface. In contrast, solvents in which NPLs remain individually dispersed yield extended hexagonally ordered superlattices with edge-to-edge stacking spanning several micrometers, where the NPLs lie parallel to the interface in an edge-to-edge arrangement. These results highlight that solvent-mediated interactions and pre-existing organization in solution are decisive factors in determining the outcome of evaporative self-assembly of colloidal nanocrystals.

We determine certain Banach-Mazur distances involving $\ell_p$-direct sums of finite-dimensional real normed spaces and related cone constructions of convex bodies. Using a recent characterization of the optimal Banach-Mazur position with respect to the Euclidean ball, we derive a closed formula for the distance from $X_1 \oplus_p \cdots \oplus_p X_k$ to Euclidean space in terms of the distances of the spaces $X_i$ to Euclidean space. For $p = 1$ we show that if $d_{BM}(X,\ell_1^n) \leq 3$, then $d_{BM}(X \oplus_1 \ell_1^m, \ell_1^{n+m}) = d_{BM}(X,\ell_1^n)$. Interpreting $\ell_1$-sums geometrically as double cones motivates a study of single cones over arbitrary convex bases, for which we establish an analogous result with the simplex replacing $\ell_1$. We further show that in dimension $3$ the distance between single cones with symmetric bases equals the distance between the bases, and that the same equality holds for double cones over planar symmetric bases in arbitrary dimension, under an additional assumption on the distance of the bases to $\ell_1^2$. As consequences, we obtain an explicit isometric embedding of the $2$-dimensional symmetric Banach-Mazur compactum into the $3$-dimensional (non-symmetric) compactum and lift a recent construction of arbitrarily large equilateral sets in the $2$-dimensional symmetric compactum to all higher dimensions.

Resonant drive in tokamaks is routinely quantified using a variety of different metrics that target different aspects of a resonant response to an external perturbation. Two of the most direct metrics, $Δ_{mn}$ and $b_{pen}$, are widely used but their relative behavior was previously uncharacterized. This work examines how these metrics representing the shielding current and penetrated field relate in resistive perturbed tokamak equilibria using asymptotically matched solutions with a resistive MHD inner layer model in GPEC. $b_{pen}$ scales with Lundquist number as $S^{-2/3}$ until saturation at low $S$, and $Δ_{mn}$ remains consistent with its ideal definition but is affected by global kink structure. Both metrics are shown to yield closely similar dominant coupling modes within the same resistive model. However, the resistive physics shifts this dominant mode spectrum to lower poloidal mode numbers $m$ in a low-rotation ITER equilibrium. This alteration is predicted to be observable in experiment in the form of optimal relative phasings of resonant magnetic perturbation coils.

The non-resonant divertor (NRD) offers a promising exhaust solution for stellarators, combining topological simplicity with resilience to magnetic field perturbations. To experimentally validate the robustness of non-resonant divertors in a quasi-axisymmetric (QA) configuration, we introduce STAR_Lite, a new stellarator experiment at Hampton University. This paper details the design and analysis of the first STAR_Lite coil configuration, STAR_Lite-A. The two field-period configuration manifests an NRD through X-points with zero rotational transform, at the top and bottom of the device. The divertor legs extruding from the X-points are topologically similar to the poloidal divertors of tokamaks. To expand the experimental range, STAR_Lite-A is optimized for experimental flexibility, producing a wide range of distinct QA configurations by only varying the currents in the modular coils. The NRDs not only persist across these configurations, but numerical strike-line simulations confirm that heat exhaust remains resilient to changes in coil currents, with plasma following the divertor legs and creating a toroidal, discontinuous, strike pattern. We further examine the resilience of the NRD to magnetic perturbations caused by manufacturing errors in the modular coils. We find that quasisymmetry and the existence of X-points is well-preserved under these magnetic field changes, but the rotational transform may vary substantially and displacements of the divertor X-points may lead to one X-point having a dominant effect on edge transport. Overall, our analysis indicates a compact, modular design can likely generate a resilient NRD structure while satisfying the practical constraints of a university-scale experiment.

We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories equipped with a twisted cylinder twist, a structure closely related to the twisted reflection equation and quantum symmetric pairs. Under mild assumptions, we establish an order-preserving bijection between submodules of a module category $\mathcal{M}$ and submodules of the path-algebra module $\mathcal{M}(1,-)$. We show that this correspondence is compatible with idempotent completion and analyze its behavior under decategorification to the split Grothendieck group, giving criteria for classification in terms of indecomposable objects. As an application, we study the disoriented skein category as a module category over the oriented skein category, describe its indecomposable objects, and obtain a complete classification of its submodules.

Cavitation in soft elastomers and adhesives is often viewed as an elastic instability, commonly tied to the study of incompressible solids. It is the first step prior to fibrillation and ultimate failure in adhesives. Building on the work of Lamont et al. (2025), elastomeric materials are treated as a crosslinked van der Waals fluid. The van der Waals contribution, capturing excluded volume and cohesive forces, is non-(poly)convex, readily providing an intrinsic analytical criterion for cavity nucleation. This work introduces a gradient-enhanced continuum framework that examines the emergence of cavity formation from the perspective of a cohesive instability and corresponding phase transition without requiring a pre-existing defect. The corresponding thermodynamically consistent derivation includes the introduction of a relevant material length scale as well as viscous dissipation associated with polymer chain disentanglement during the cohesive instability. This work does not study the impending damage that the material undergoes during the cohesive instability and transition from a dense to a rare phase. Interestingly, it is shown that for both strain stiffening and strain softening models (in terms of their shear response), an instability reminiscent of what is expected in the case of cavitation is recapitulated. Simulations reproduce key experimental trends, including the aspect ratio-driven transition from a few large to many small cavities depending on the thickness of an adhesive layer. The framework offers a robust, physically grounded basis for the cohesive instability that drives cavity nucleation, enabling future integration with damage, fracture, and dissipation models to capture the complete cavitation, fibrillation, and failure process.

We present Active Learning for Accelerated Bayesian Inference (\texttt{alabi}): an open-source Python package for performing Bayesian inference with computationally expensive models. Given a forward model and observational data to construct a likelihood and priors, \texttt{alabi}\ uses a Gaussian Process (GP) surrogate model trained to predict posterior probability as a function of input parameters, and employs active learning to iteratively improve GP predictive performance in high-likelihood regions where the GP is most uncertain. \texttt{alabi}\ provides a uniform interface for using Markov chain Monte Carlo (MCMC) with different packages, including the affine-invariant sampler \texttt{emcee}, and nested samplers \texttt{dynesty}, \texttt{multinest}, and \texttt{ultranest}. This approach facilitates accurate estimation of the desired posterior distribution, while reducing the number of computationally expensive model evaluations required by factors of thousands. We demonstrate the performance of \texttt{alabi}\ on a variety of test cases, including where inference is challenging due to complex posterior structure or high dimensionality. We show that \texttt{alabi}\ offers a substantial improvement for likelihood functions with evaluation times $\gtrsim 1$\,s, speeding up MCMC computations by a factor of $10-1000\times$ when tested on problems with up to 64 dimensions.

Changing-look active galactic nuclei (CL-AGN) exhibit spectroscopic and photometric changes on timescales of months to years, making them powerful laboratories for studying accretion variability onto supermassive black holes. Motivated by the growing relevance of large spectro-photometric time-domain surveys, especially the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST), we compiled a master catalog of known CL-AGN from the literature and evaluated its spatial overlap with the Rubin survey footprint. Using a geometric cross-match based on sky coordinates, we identify 79 sources located in high-cadence regions of the main survey footprint (Wide-Fast-Deep, or WFD), including 5 particularly favorable targets lying within the Deep Drilling Fields (DDFs) of COSMOS and XMM-LSS. These sources represent especially promising candidates for future variability studies in the Rubin era. This Research Note presents a first proof of concept for connecting known CL-AGN with Rubin observing fields, while the full catalog and a more comprehensive analysis will be presented in a forthcoming paper.

In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3); Conjecture 3 implies Conjecture 1 and seems simple itself. However, both conjectures remain unproven in the general case. In the present paper, some special cases are proved, Conjecture 4 is formulated in the same spirit, and some of its special cases are proved. In addition, Conjecture 1 is reduced to a matrix inequality (Conjecture 5); this inequality is, in turn, also proved in a special case.

In this paper, we examine the distribution of radio signal propagation within the city of Poznan (Poland) to determine optimal locations for deploying Reconfigurable Intelligent Surfaces (RIS). The study focuses on designing a 5G/6G Radio Access Network (RAN), incorporating eight Base Stations (BSs) that utilize either Single Input Single Output (SISO), or Multiple Input Multiple Output (MIMO) antenna technologies, depending on the network cell configuration. Through detailed simulations and analyses, we explore various propagation scenarios in both Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) conditions, considering the complex urban landscape characterized by high-rise buildings. The results demonstrate the potential of using RISs in mobile networks to enhance radio signal quality in urban environments through strategic placements. Our findings suggest that RISs can significantly mitigate Path Loss (PL) and improve signal coverage in challenging urban environments, particularly in areas where traditional base station deployment alone would be insufficient. Furthermore, the study highlights the role of RISs in reducing the need for additional base stations, thereby optimizing network costs and infrastructure while maintaining high-quality service delivery. The insights gained from this research provide valuable guidelines for network planners and engineers seeking to implement RIS technology in future 5G and beyond networks, ensuring more efficient and robust urban communication systems.

Random Feature Models (RFMs) have become a powerful tool for approximating multivariate functions and solving partial differential equations efficiently. Sparse Random Feature Expansions (SRFE) improve traditional RFMs by incorporating sparsity, making it particularly effective in data-scarce settings. In this work, we integrate active learning with sparse random feature approximations to improve sampling efficiency. Specifically, we incorporate the Christoffel function to guide an adaptive sampling process, dynamically selecting informative sample points based on their contribution to the function space. This approach optimizes the distribution of sample points by leveraging the Christoffel function associated with an iteratively-chosen basis obtained by the sparse recovery solver. We conduct numerical experiments comparing adaptive and nonadaptive sampling strategies with the SRFE framework and examine their accuracy for various function approximation tasks. Overall, our results demonstrate the advantages of adaptive sampling in maintaining high accuracy while reducing sample complexity for SRFE, highlighting its potential for scientific computing tasks where data is expensive to acquire.

High-energy astrophysical events, particularly Gamma Ray Bursts (GRBs), have been proposed as significant contributors to mass extinction events on Earth-like planets in most of the galaxy, internal to our radius in it. This paper examines the extent to which GRBs may reset the evolutionary progress of complex life through repeated extinction-level disruptions. While resilient extremophiles may survive even the most intense GRBs, more complex surface-dwelling organisms are vulnerable to indirect atmospheric effects, primarily UV exposure following ozone depletion. By identifying evolutionary milestones and estimating how frequently GRBs would need to occur to prevent recovery between such milestones, this work proposes that GRBs could act as evolutionary filters, limiting the emergence of advanced life, but only much closer to the galactic center. We consider the implications for searches of various biosignatures versus technosignatures.

Spatial transcriptomics (ST) profiles gene expression across a tissue section while preserving the spatial coordinates. Because current ST technologies typically profile two-dimensional tissue slices, integrating and aligning slices from different regions of the same three-dimensional tissue or from samples under different conditions enables analyses that reveal 3D organization and condition-associated spatial patterns. Two major challenges remain. First, interpretable and flexible control over spatial distortion is needed because rigid transformations can be overly restrictive, whereas highly deformable mappings may arbitrarily distort spatial proximity. Second, biologically plausible matching is also needed, especially when the slices overlap partially. Here, we introduce RAFT-UP, a tool for robust ST alignment that provides explicit control over spatial distance preservation through a fused supervised Gromov-Wasserstein (FsGW) optimal transport framework. FsGW combines expression and spatial information, incorporates spot-wise constraints to discourage biologically implausible matches, and enforces a pairwise distance-consistency constraint that prevents mapping two pairs of spots when their spatial distances differ beyond a specified tolerance. We demonstrate that RAFT-UP accurately aligns slices from different regions of the same tissue and slices from different samples. Benchmarking shows that RAFT-UP improves spatial distance preservation while achieving spot label matching accuracy comparable to state-of-the-art methods. Finally, we demonstrate RAFT-UP on two spatially constrained downstream applications, including spatiotemporal mapping of developing mouse midbrain and comparative cross-slice analysis of cell-cell communication. RAFT-UP is available as open-source software.

Large Language Model (LLM) agents increasingly act through external tools, making their safety contingent on tool-call workflows rather than text generation alone. While recent benchmarks evaluate agents across diverse environments and risk categories, a fundamental question remains unanswered: how complete are existing test suites, and what unsafe interaction patterns persist even after an agent passes the benchmark? We propose SafeAudit, a meta-audit framework that addresses this gap through two contributions. First, an LLM-based enumerator that systematically generates test cases by enumerating valid tool-call workflows and diverse user scenarios. Second, we introduce rule-resistance, a non-semantic, quantitative metric that distills compact safety rules from existing benchmarks and identifies unsafe interaction patterns that remain uncovered under those rules. Across 3 benchmarks and 12 environments, SafeAudit uncovers more than 20% residual unsafe behaviors that existing benchmarks fail to expose, with coverage growing monotonically as the testing budget increases. Our results highlight significant completeness gaps in current safety evaluation and motivate meta-auditing as a necessary complement to benchmark-based agent safety testing.

We find that partisan misère quotients can have any finite cardinality other than 3, answering a question of Allen. This contrasts with impartial misère quotients, which must have even cardinality.

We study multi-digit correlations in Benford sequences b^n for integer bases 2 <= b <= 1000, measuring dependence via conditional mutual information (CMI). A resonance ratio derived from the continued fraction expansion of log_10(b) classifies bases into convergent and persistent regimes (Theorem 3.13): among 996 bases surveyed, 84 (8.4%) exhibit persistent correlations at sample depth N = 10,000, and extended computation to N = 200,000 confirms 53 (5.3%) as genuinely persistent. We prove that CMI deviation is bounded by the distribution error (Theorem 3.4); exhaustive computation across 2,988 test cases confirms that the effective scaling is quadratic, yielding a two-sided rate beta = 2 for bounded-type bases (conditional on a computationally verified Hessian positivity condition). The observed effective exponent across 774 convergent bases is beta_eff = 1.72 +/- 0.19, consistent with finite-sample corrections to the asymptotic rate. We conjecture that the persistence rate converges to 1/12, a prediction grounded in the Gauss-Kuzmin distribution of partial quotients. For persistent bases, the convergence threshold N_epsilon exceeds 10^6 at standard precision, rendering the asymptotic limit observationally irrelevant within our computational scope.