We consider the nonlinear Schrodinger equation with cubic (focusing or defocusing) nonlinearity on the multidimensional torus. For special small initial data containing only five modes, we exhibit a countable set of time layers in which arbitrarily large modes are created. The proof relies on a reduction to multiphase weakly nonlinear geometric optics, and on the study of a particular two-dimensional discrete dynamical system.

Trusted Execution Environments (TEEs) provide hardware-based isolation to protect sensitive data and computations from potentially compromised operating systems (OS). However, TEE applications inevitably interact with the untrusted OS through SDK interfaces, and improper partitioning can introduce severe vulnerabilities such as data leakage and code injection. While prior work has proposed static analysis tools to detect such issues, automated repair remains largely unexplored. This problem is particularly challenging due to three TEE-specific factors: the lack of standardized secure development guidelines, the difficulty of extracting semantic information from low-level C code, and the absence of mature testing and validation methods. In this work, we present TEERepair, a framework for automatically repairing bad partitioning issues in TEE applications. Our approach tackles the above challenges by introducing a domain-specific language (DSL) to encode repair rules that express and capture common TEE security patterns, which are instantiated as patch templates with placeholders for context-specific variables. We then leverage large language models (LLMs) to reason about code semantics and synthesize context-aware patches, and further generate test clients to validate the repairs. We evaluate TEERepair on the TEE Partitioning Errors Benchmark (PartitioningE-Bench), achieving a significantly higher repair success rate of 87.6% compared to baselines. Furthermore, applying TEERepair to real-world TEE projects, we submitted 5 repair pull requests, 2 of which have been confirmed and merged by project maintainers.

Since the beam squint and near-field effects both inherently exist in upper-6 GHz (U6G) extremely large-scale multiple-input multiple-output (XL-MIMO) systems, wideband near-field channel estimation faces severe challenges, such as higher computational complexity, and higher pilot overhead particularly at hybrid architectures with fewer radio frequency (RF) chains. To precisely reduce the complexity and number of pilots, the parametric symmetry of wideband near-field channels is explored, such that the channel parameters, including angle, distance, and range, can be decoupled based on the delay variations observed by different antennas. Based on this, a distributed parametric symmetry-based (DPS) algorithm, applicable to U6G XL-MIMO, is proposed. The delays observed by different subarrays are estimated and extrapolated across the local processing units (LPUs) firstly, and then, the channel parameters are decoupled and estimated at the central processing unit (CPU), by only linearly combining the delays from different LPUs. The path gains are calculated at different LPUs, respectively, to reconstruct the channel with low complexity. Since the proposed algorithm does not rely on scanning the polar-domain dictionary, only a single pilot is required even with hybrid architectures. Furthermore, the computational complexity, multiple-path resolution, Cramer-Rao lower bound (CRLB) and lower bound (LB) of the estimates in hybrid architectures and the DPS algorithm, respectively, are analyzed, to evaluate the realizable potential of the proposed algorithm. The simulation results prove that the proposed algorithm has a higher estimation accuracy, while requiring less complexity and pilots.

We show how a broad class of two-component square-gradient models of wetting may be solved exactly for the surface tensions and density profile paths, and clarify how the presence or absence of critical point wetting, in binary and ternary mixtures, is related to universality and symmetry principles at critical end points. We begin by solving a model of fluid interfaces, first introduced by Koga and Widom, in ternary mixtures showing three phase coexistence. Numerical studies had revealed interesting wetting transitions, as well as curious geometrical properties of the profile paths in the density plane, and led these authors to conjecture expressions for the surface tensions. These conjectures were extended by Koga and Indekeu and predicted that partial wetting may persist up to the line of critical end points, i.e. critical point wetting was absent. Here, we obtain the exact density profiles and surface tensions for the Koga-Widom-Indekeu (KWI) model using complex analysis and drawing on the theory of algebraic curves. The exact solution determines the location and order of wetting transitions in the surface phase diagram, confirming that critical point wetting is absent. The model also displays the remarkable property that microscopic density profiles are mapped, by a conformal transform, onto the shape of a macroscopic drop near the contact line whose tensions satisfy the Neumann triangle. Two related models, which illustrate the role of the component isotropy, are also discussed. These models suggest that a universality principle governs wetting in fluid mixtures, resolving contradicting results from earlier studies: Critical point wetting is present if the order-parameter components of the mixture describe Ising-like criticality, but is absent if there is a local XY symmetry. Implications for wetting transitions in more microscopic models and in experiments are discussed.

We study relationships between dynamic programs by applying conjugacy methods from dynamical systems theory. When two dynamic programs are connected by an order isomorphism, we show that optimality properties transmit from one formulation to the other. We apply these results to Epstein--Zin preferences with time preference shocks, obtaining a sharp characterization of when optimality holds. We also show that multiplicative Kreps--Porteus preferences and risk-sensitive preferences are isomorphic, so that well-known results for the latter carry over to the former. Finally, we demonstrate how isomorphic transformations can improve the numerical accuracy of value function approximations, with gains of two orders of magnitude in a multisector real business cycle model.

Multimodal recommendation benefits from content signals, but the gain depends on how those signals interact with the ranking pipeline. We find that moderate cross-view agreement helps, while stronger agreement suppresses recommendation-specific variation. Spectral analysis shows a clear split: low-frequency components capture shared structure, and higher-frequency components preserve more discriminative signal. Based on this finding, we introduce a behavior-guided candidate calibration model that converts training-only co-user overlap into signed candidate evidence and applies it only to the shortlist produced by the multimodal backbone. The backbone keeps the representation space stable; behavior evidence acts only where ranking is decided. Results on Amazon Baby, Sports, and Electronics show consistent gains over strong multimodal baselines. Code is available at https://github.com/LIZESHENG13/bridge.

We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids. We also study the geometry of profinite monoids via the classifying topos construction, and show it identifies them as a full sub-2-category of the 2-category of topoi.

We establish a correspondence between two independent entropic probes -- the variation of Rényi mutual information (RMI) across the electroweak symmetry breaking (EWSB) transition and the stabilizer Rényi entropy (SRE) -- in tree-level $2\to 2$ elastic scatterings. After angular averaging, the RMI (helicity basis) and the SRE (fixed beam basis) exhibit identical dependence on $\sin^2θ_W$ within each neutral-current channel. We trace this correspondence to a common physical origin that it's the Yukawa mass insertion acts as a $-\mathrm{i}Y$ quantum gate in chirality space. Minimizing entropies across all processes yields $\sin^2θ_W$ values matching purely axial vector-like couplings in $Z$ boson exchanged channel.

This paper investigates the joint optimization of power allocation and antenna activation in sparse extremely large aperture array systems operating under power amplifier non-linearities. We first derive an analytical expression for the achievable spectral efficiency (SE) of point-to-point MIMO channels affected by non-linear distortions using the Bussgang decomposition. To address the combinatorial and non-convex nature of the energy-efficiency (EE) maximization problem, we employ an unsupervised deep neural network (DNN) that learns the non-linear mapping between the channel state information and the optimal EE operating point. The DNN jointly predicts distortion-aware power allocation, total transmit power scaling, and modular sub-array activation based on singular-value and geometric channel features. Numerical results demonstrate that the proposed DNN-based arrays achieve significant EE gains over the conventional sparse arrays.

We provide a complete description of the automorphism group $\Aut (W)$ of a Coxeter group $W$ admitting a star-shaped finite Coxeter diagram. We prove that each automorphism decomposes as a product of inner and diagram automorphisms, along with three additional types: transvections and two families of partial conjugations. Furthermore, we investigate the natural short exact sequence $1 \to \Inn (W) \to \Aut (W) \to \Out (W) \to 1$. Using Moussong's criteria for hyperbolicity, we show that these groups possess the $R_\infty$-property. Finally, we establish rigidity properties for these groups using known techniques and provide a solution to the isomorphism problem within the class of star-shaped Coxeter systems.

In this paper, we investigate the structure of the fine Mordell-Weil groups over the intermediate subextensions of a given $\mathbb{Z}_p$-extension $F_\infty$ of $F$.

Chatterjee's rank correlation is a directed measure of association designed to detect whether one variable can be predicted as a function of another. While the original coefficient is naturally defined for real-valued data, circular data poses additional difficulty. Applying the usual construction requires cutting each circle at an arbitrary point and treating it as a line. Different choices of cut points can lead to different finite-sample values, even though the underlying circular relationship is unchanged. This paper proposes a circular version of Chatterjee's coefficient that removes this arbitrary choice. The population construction averages over response cuts in circular rank space, and the finite-sample construction averages over sample cut gaps and reduces to a simple statistic based only on cyclic ranks. The resulting coefficient is intrinsic to the circular ordering of the data, remains directed, and retains the key interpretation of Chatterjee's original coefficient. Under non-atomic circular marginals, it is zero exactly under independence and one exactly when the circular response is a measurable function of the circular predictor. We prove consistency and derive its distribution-free null behavior under independence. Simulations show that the proposed coefficient is especially useful for detecting multi-winding circular relationships, such as cases where the response goes around the circle twice or four times as the predictor goes around once, where standard circular correlations can be nearly blind.

We study the distribution of closed geodesics in short intervals on random hyperbolic surfaces of large genus, and compare it with the classical problem of primes in short intervals. Viewing the surface $M$ as a random point in moduli space equipped with the Weil--Petersson measure, we investigate the random variable $Ψ_M(x;H)$ counting closed geodesics with norms in the interval $[X, X+H]$, weighted by primitive length, where $H=o(X)$. This is analogous to the Chebyshev function in prime number theory. Our main result establishes that in the large genus limit, \[ \lim_{g\to \infty}\mathrm{Var}(Ψ_M(X;H)) \sim 2\,H \log X, \] when $X\to \infty$, $H=o(X)$. Goldston and Montgomery related the variance for primes in short intervals to the form factor associated with zeros of the Riemann zeta function, and conjectured that it is asymptotic to \[ H\log(X/H). \] We show that for automorphic L-functions of degree $d>1$, the early-time GUE form factor already follows from the Riemann Hypothesis, thereby recovering the variance $H\log X$ in the very short interval regime predicted by Bui, Keating and Smith. In the geometric setting, the appearance of $\log X$ reflects the much higher spectral density of Laplace eigenvalues relative to zeros of finite-degree $L$-functions, while the additional factor of $2$ is explained by the expected GOE statistics for the Laplace spectrum of generic hyperbolic surfaces.

Trusted Execution Environments (TEEs) provide hardware-enforced isolation that protects sensitive code and data from untrusted software. Despite their strong security guarantees, analyzing TEE applications remains challenging due to the high cost and complexity of configuring complete TEE build and runtime environments, as well as the limited observability imposed by hardware isolation. This paper presents SymTEE, a novel large language model (LLM)-assisted symbolic execution framework for detecting missing input validation issues in TEE applications without requiring real TEE setups. SymTEE begins by leveraging Abstract Syntax Tree (AST) analysis to extract TEE code slices that may lack sufficient input validation, and then employs an LLM (GPT-5 in our case) to automatically convert the extracted slices into KLEE-compatible harness programs containing lightweight mock execution environments for symbolic analysis. Evaluations on 26 vulnerabilities (11 real-world and 15 synthetic) show that SymTEE achieves 100% precision and 92.3% recall in detecting missing input validation vulnerabilities while incurring an average analysis cost of only $0.05. These results demonstrate the effectiveness and practicality of SymTEE's pioneering paradigm of LLM-assisted symbolic execution, where LLMs autonomously generate mock environments to enable automated security analysis without complex setup, providing a more accessible and scalable framework for trusted computing systems.

Living cells and tissues can generate complex patterns of electric fields and fluid flows which can play important role in physiology. Both, fields and flows are rooted in ion transport across biological interfaces: cell membranes and epithelial cell layers. Here we develop a unified electrohydraulic framework that combines electric fields, osmotic pressures, and fluid flows, emphasising their couplings. We consider an active, permeable interface that drives electrohydraulic fields in the surrounding bulk. We show that spatially heterogeneous ion transport acts as a distributed current source, generating long-range electric fields, osmotic gradients, and fluid flows. Using this framework, we show that patterns of ion pumping at cell and tissue boundaries can simultaneously produce large-scale electric fields and fluid flows due to electrohydraulic coupling. A key insight is that an external electric field and an internal dipolar pumping pattern can be physically equivalent and can generate the same pattern of ion current and fluid flows. The induced dipolar osmotic pressure can drive self-propulsion through bulk osmotic coupling, with a mobility determined by interfacial permeability and system size, a mechanism distinct from classical electrophoresis or electro-osmosis. We further show that for strong fields a new effect emerges. Nonlinear coupling can lead to isotropic swelling of a hollow ball of cells. This can explain recent experiments on epithelial organoids. Finally, we show that feedback between ion transport and resulting electric fields can drive spontaneous symmetry breaking, generating dipolar or multipolar fields and patterns. Our work highlights the importance of electrohydraulic coupling in the emergence in currents and fields in the biological systems.

Stacked intelligent metasurfaces (SIMs) and fluid antenna systems (FAS) are emerging technologies for wave-domain and spatial signal manipulation, respectively.This letter proposes a novel joint SIM-FAS communication model in which transmission and reception are performed by a SIM and an FAS, respectively. Using the block-diagonal matrix approximation (BDMA), a closed-form expression for the outage probability is derived, and the SIM phase shifts are optimized to minimize outage. Numerical results validate the analytical accuracy and demonstrate substantial performance gains over conventional benchmark schemes.

We give negative answers to both parts of a question of Mauri and Moraga on log Calabi-Yau pairs whose boundary decomposes into big divisors. The main result of this paper is obtained by generative AI, particularly Chatgpt 5.5 pro and the Rethlas system.

In this paper, we provide complete characterizations for the spectrum, essential spectrum, and point spectrum of the generators of weighted composition $C_0$-semigroups induced by hyperbolic semiflows on Bergman spaces. We give an explicit example showing that the spectral properties can be influenced by the behavior of the semigroup near non-fixed self-contact points.

We show that the cohomology of the structure sheaf of smooth and proper schemes over a complete non-archimedean field $K$ of characteristic zero, can be refined to an $\mathbf{A}^1$-invariant cohomology theory of smooth (not necessarily proper) schemes over $K$ with values in $\mathcal{O}_K$-lattices, and the same holds for $K$ of positive characteristic in dimensions at most $3$. As one application, we obtain that the automorphism group of the function field of a proper smooth variety $X$ of dimension at most 3 over a field of positive characteristic acts quasi-unipotently on the cohomology of the structure sheaf of $X$. The construction of the lattices relies on a variant of the tame cohomology of Hübner--Schmidt with coefficients in a twisted version of the tame structure sheaf and uses results from rigid analytic geometry on the cohomology of twisted integral rigid structure sheaves due to Bartenwerfer and van der Put.

This paper addresses the challenge of obtaining strong optimality guarantees in constrained nonsmooth nonconvex optimization under mild regularity conditions, namely local Lipschitz continuity and existence and continuity of directional derivatives. While standard methods typically ensure weak stationarity notions, achieving directional (d-)stationarity remains nontrivial. We show that a random direction exploration step is sufficient to attain d-stationarity. The proposed approach augments any base optimization method with a single exploration step that samples a direction and step size and accepts the candidate based on a function value comparison. The resulting scheme guarantees that all accumulation points are d-stationary almost surely, independently of the behavior of the underlying method. Moreover, it preserves convergence rates of the base method, as established for DCA and prox-linear-type schemes. The theoretical results are complemented by numerical experiments illustrating the effect and guarantees of the exploration step.

Flexure of Antarctic ice shelves under excitation from long ocean waves induces mechanical ice shelf stresses that amplify fractures and, hence, contribute to calving events. Here, a solution method is developed for a hydroelastic mathematical model of wave-induced ice shelf flexure, based on the conventional theory of a Kirchoff-Love plate floating on shallow water under linearised conditions, but allowing wave forcing of ice shelves with variations in both horizontal dimensions, and where the ice shelves are of arbitrary shape, including non-uniform thickness. The method uses finite elements specifically designed for the high-order hydroelastic system, and a Dirichlet-to-Neumann map to bound the computational domain in the open ocean. Following verification, the method is used to conduct novel studies on how the ice-shelf deflection is affected by the ice shelf shape, the incident wave direction and the proportion of the shelf that is grounded. The efficiency of the method allows the studies to be conducted over a broad frequency range, such that resonant responses are identified.

Fluid antenna systems (FASs) are emerging as a reconfigurable-aperture technology that expands physical-layer design beyond fixed, rigid antenna geometries. While the \emph{fading diversity} of FASs -- which exploits spatial channel fluctuations for signal enhancement and interference avoidance -- has been widely studied, the \emph{geometry diversity} created by reconfigurable port placement remains far less understood, particularly for planar architectures under finite-aperture constraints. This paper develops a systematic analytical framework for finite-aperture planar fluid antenna arrays (FAAs). First, we derive a closed-form characterization of the minimum inter-port distance under uniform random placement over a rectangular aperture and show that it follows a Rayleigh law. Its mean scales as $\mathcal{O}(M^{-1})$, in sharp contrast to the $\mathcal{O}(M^{-2})$ behavior in the linear case in which $M$ represents the number of candidate ports, revealing a fundamentally more favorable packing geometry in two dimensions. Secondly, we establish a universal Cramér-Rao bound (CRB) for joint elevation-azimuth estimation, governed by a $2\times 2$ \emph{geometric inertia matrix} whose determinant and eigenstructure fully capture the role of port placement in estimation precision. We further prove that both the trace and determinant of this matrix are invariant to the azimuth look direction. Third, we uncover an intrinsic \emph{precision--ambiguity trade-off}: maximizing the geometric determinant to minimize the CRB drives ports toward the aperture boundary, but simultaneously increases sidelobe-induced spatial ambiguity.

Epilepsy is a neurological disorder characterized by recurrent seizures affecting more than 70 million people worldwide. Often, an individual with epilepsy is more likely to experience subsequent seizures following an initial seizure, a process we call seizure clustering. Motivated by seizure diary data collected over three years from 407 individuals newly diagnosed with focal epilepsy in the Human Epilepsy Project (HEP), we propose a Bayesian mixed Hawkes process model that addresses seizure clustering and heterogeneity between individuals. In the Hawkes process, the intensity is accelerated each time an event occurs, through the composition of background and excitation intensity functions. The proposed model incorporates a Weibull baseline intensity to model a trend in background seizure rates over time, while the excitation process accounts for seizure clustering within individuals. We model heterogeneity among individuals by including covariates and random effects in both the background and excitation intensities. In the HEP study, the average time between primary and secondary seizures within an individual is 1.57 (95\% CrI: 1.43, 1.70) days, with an average of 2.20 (1.96, 2.47) seizures per cluster. We demonstrate that omitting random effects in the presence of heterogeneity leads to underestimation of the background intensity and overestimation of excitation rates.

In a companion paper arXiv:2510.27676, we introduced a non-perturbative classical renormalisation group (RG) flow equation as a novel method for treating strongly interacting problems in general relativity, with a prominent application to the two-body problem. While we demonstrated that it reproduces perturbation theory, via the Post-Minkowskian (PM) expansion, and its computational efficiency in reproducing the 1PN Post-Newtonian action, its derivation was heuristic. In this work, we place this flow equation on a firm formal foundation. In particular, we demonstrate that a Legendre transform maps the classical analogue of the Polchinski equation precisely to our classical RG equation. This establishes a duality between equivalent, exact RG equations for the gravitational effective action. The result, combined with the successful applications in arXiv:2510.27676, solidifies the classical RG framework as a powerful and rigorous new approach to the general relativistic two-body problem and gravitational wave physics.

We study theoretically the lasing synchronization of the two arrays of lasers with the complex mode dispersion, separated by a spectrally detuned barrier. We demonstrate that for lasing at the Dirac point, the synchronization persists for an order of magnitude higher barriers than in the arrays with a usual parabolic dispersion or a purely dissipative coupling. We interpret this effect as the Klein tunneling of the laser coherence through the barrier. Our numerical findings are supported by an analysis of the delocalization of the linearized eigenmodes of the arrays, which enhances the synchronization.

The observation of strong and tunable spin-orbit interaction (SOI) in surface conducting diamond opens up a new avenue for building diamond-based spintronics. Herein we provide a comprehensive method to analyze the magnetotransport behavior of surface conducting hydrogen-terminated diamond (H-diamond) Hall bar devices and Al/Al2O3/V2O5/H-diamond MOSFETs, respectively. By adopting a significantly improved theoretical magneto transport model, the reduced magnetoconductance can be accurately explained both within and outside the quantum diffusive regime. The model is valid for all doping strategies of surface conducting diamond tested. From this analysis, we find that the orbital magnetoresistance, a classical effect distinct from the SOI, dominates the magnetotransport in surface conducting diamond at high magnetic fields. Furthermore, local hole mobilities as high as 1000 ~ 3000 cm2/Vs have been observed in this work, indicating the possibility of diamond-based electronics with ultra-high hole mobilities at cryogenic temperatures.

This note provides a lightweight tutorial on using Eigen, a C++ template library for linear algebra, to implement statistical and machine learning algorithms. The emphasis is practical rather than methodological: we show how common matrix operations, decomposition-based solvers, and vectorized updates can be written in readable C++ and then connected to Python through pybind11. Two examples are used throughout the tutorial: kernel ridge regression and matrix factorization with stochastic gradient descent. The examples are intentionally small enough to be studied as code, but they contain many operations that appear in larger research software projects, including kernel matrix construction, regularized linear system solving, row-wise updates, and NumPy--Eigen data conversion. The goal is to provide a reproducible starting point for researchers who want to move from mathematical formulas to efficient C++ implementations while retaining a convenient Python workflow.

We provide a general theoretical derivation of the phase sensitivity achieved by SU(1,1) interferometers under homodyne detection. The general expressions obtained accommodate arbitrary input states and include internal and external losses. In this systematic review, both full SU(1,1) interferometers with two parametric amplifiers and the truncated interferometers with only one parametric amplifier are examined. We investigate scenarios involving both single-output ports and joint homodyne detection, and consider parametric amplifiers with equal gains or with a boosted gain second amplifier. Our analytical formulation provides physical insight and understanding of the improvements in the sensitivity, which are shown to originate from noise reduction and/or signal amplification, depending on the configurations and practical implementations. Surprisingly, the configuration with single-output mode detection and parametric amplifiers with equal gains exhibits the highest robustness to very high internal losses. We finally apply this framework to a ubiquitous $|α,0\rangle$ input two-mode coherent probe state. This approach permits the comparison of different strategies and the optimization of the interferometer performance in the presence of losses. In particular, we determine which amplification and detection configurations provide the best performance, depending on the level of losses. This exemplifies how this general analytical approach provides a powerful tool to design quantum-enhanced interferometers and achieve optimal sensitivity with selected probe states and homodyne detection.

In modern industrial systems, machinery frequently operates under dynamic environments with continuously varying loads and speeds. Consequently, deep learning-based fault diagnosis models often suffer from severe performance degradation under unseen operating conditions due to complex data distribution shifts. Since existing methods predominantly rely on static offline training, they lack the capability to dynamically adapt to these continuous variations. To address this issue, an integrated framework combining offline domain generalization (DG) and online test-time adaptation (OTTA) is proposed. Initially, a model with preliminary generalization capability is obtained offline by extracting domain-invariant features via adversarial learning. During the online phase, a dual-memory replay mechanism is developed. By selectively storing high-confidence online pseudo-labeled samples and replaying them with historical offline data, the model facilitates adaptation to changing data distributions and helps reduce forgetting of previously learned knowledge Experiments on a real-world motor dataset show that the proposed approach achieves competitive performance under the considered unseen operating conditions.

Security analysts routinely query system logs to detect threats and investigate incidents, but each log source uses its own semi-structured format: logs are cheap to produce, but expensive to use. The standard approach, building per-source parsers to normalize logs into structured schemas, is powerful but requires continuous engineering effort for each new format. Querying raw logs directly with tools like grep avoids this cost, but requires analysts to know each source's message variants and cannot express the multi-line temporal queries that security investigations demand. We present Sieve, a system that generates executable query code from natural-language security questions by grounding a large language model with lightweight, automatically extracted log-format context, requiring only one LLM call per query followed by deterministic execution. Evaluating 133 security queries across 5 log types, we find that Sieve achieves over a 3x reduction in error rate on complex temporal and cross-event queries compared to manual analyst scripting, with the largest gains on the multi-line correlation tasks most critical to active investigations. Our results and benchmark provide evidence that LLM-generated code can bridge the gap between the expressiveness of structured log querying and the immediacy of working directly with raw files.