The phase separation of purely-repulsive particles induced by self-propulsion is among the most well-studied non-equilibrium phase transitions. However, some notable features of this transition remain open questions, including the origin of bubbles within the dense phase in two dimensions. Various explanations have been proposed, ranging from a reversal of the Ostwald ripening process to topological defects at the borders of hexatic domains. We present particle-based simulations that disentangle the effect of hexatic domains on the bubble size and number distribution through the introduction of polydispersity. While hexatic order is found to be necessary for bubble formation, we also identify thermal translational noise is required for bubble generation. Intriguingly, the magnitude of the thermal noise needed for bubble formation can be remarkably small in comparison with the particle activity but cannot be identically zero. The cooperative motion evidenced within the dense phase of the thermal hexatic domains may may be necessary for bubble production.

Molecular dynamics (MD) simulations are powerful tools for elucidating the macroscopic physical properties of materials from microscopic atomic behaviors. However, the massive, high-dimensional datasets generated by MD simulations pose a significant challenge for analysis, necessitating efficient dimensionality reduction and feature extraction techniques. While existing methods such as principal component analysis and unsupervised learning have been utilized, issues regarding data efficiency and computational cost remain. In this study, we propose a statistical analysis framework focusing on the analysis of the particle data distributions through their covariance matrices, corresponding to the second-order moments of MD trajectory data. Discrepancies between system states are quantified using statistical distances between these covariance matrices. By applying dimensionality reduction to the resulting distance matrix, we extract lower-dimensional features that characterize the systems' dynamics. We validate the proposed method using Lennard-Jones (LJ) particle systems under different temperature conditions, as well as separate bulk systems of ice and liquid water. The results of LJ particles demonstrate an approximately linear correlation between the first principal component obtained through dimensionality reduction of the distance matrix and the diffusion coefficient. This suggests that global physical properties can be effectively inferred from local statistical information, such as covariance matrices, offering a data-efficient alternative for analyzing complex molecular systems. Furthermore, in the case of separate bulk systems of ice and liquid water, the method successfully distinguishes between the two phases, highlighting its potential for characterizing phase transitions and structural differences in molecular systems.

We study the exact decision problem for feedback capacity of finite-state channels (FSCs). Given an encoding $e$ of a binary-input binary-output rational unifilar FSC with specified rational initial distribution, and a rational threshold $q$, we ask whether the feedback capacity satisfies $C_{fb}(W_e, π_{1,e}) \ge q$. We prove that this exact threshold problem is undecidable, even when restricted to a severely constrained class of rational unifilar FSCs with bounded state space. The reduction is effective and preserves rationality of all channel parameters. As a structural consequence, the exact threshold predicate does not lie in the existential theory of the reals ($\exists\mathbb{R}$), and therefore cannot admit a universal reduction to finite systems of polynomial equalities and inequalities over the real numbers. In particular, there is no algorithm deciding all instances of the exact feedback-capacity threshold problem within this class. These results do not preclude approximation schemes or solvability for special subclasses; rather, they establish a fundamental limitation for exact feedback-capacity reasoning in general finite-state settings. At the metatheoretic level, the undecidability result entails corresponding Gödel-Tarski-Löb incompleteness phenomena for sufficiently expressive formal theories capable of representing the threshold predicate.

In dynamically varying optical wireless communication (OWC) links, conventional quadrature amplitude modulation (QAM) in optical orthogonal frequency-division multiplexing (OFDM) requires frequent channel estimation and equalization, incurring pilot overhead and processing latency. This paper proposes a virtual polarization modulation (VPM)-based direct-current-biased optical OFDM (DCO-OFDM) scheme that maps each data symbol onto the three-dimensional Stokes space and places its corresponding Jones vector across two adjacent OFDM subcarriers. Using a rotation-based analytical framework, closed-form symbol error rate (SER) expressions are derived for arbitrary spherical constellations, along with upper and lower bounds and high signal-to-noise ratio (SNR) approximations. The framework is further extended to practical OWC scenarios with frequency-selective channels and atmospheric turbulence. Monte Carlo (MC) simulations validate the theoretical results. The results show that under practical OWC impairments, VPM outperforms QAM with least-squares (LS) channel estimation and minimum mean square error (MMSE) equalization. At a target SER of $10^{-5}$, 16-VPM achieves SNR gains of approximately 7.5 dB and 4 dB over equalized 16-QAM and 8-QAM, respectively, in frequency-selective channels, and a 6 dB advantage over equalized 16-QAM under atmospheric turbulence. By eliminating the need for channel state information, the proposed VPM-based DCO-OFDM provides a robust and low-latency solution for dynamic OWC links.

User-centric recommendation has become essential for delivering personalized services, as it enables systems to adapt to users' evolving behaviors while respecting their long-term preferences and privacy constraints. Although federated learning offers a promising alternative to centralized training, existing approaches largely overlook user behavior dynamics, leading to temporal forgetting and weakened collaborative personalization. In this work, we propose FCUCR, a federated continual recommendation framework designed to support long-term personalization in a privacy-preserving manner. To address temporal forgetting, we introduce a time-aware self-distillation strategy that implicitly retains historical preferences during local model updates. To tackle collaborative personalization under heterogeneous user data, we design an inter-user prototype transfer mechanism that enriches each client's representation using knowledge from similar users while preserving individual decision logic. Extensive experiments on four public benchmarks demonstrate the superior effectiveness of our approach, along with strong compatibility and practical applicability. Code is available.

This paper deals with the mean first escape time of Brownian motion on asymptotically hyperbolic and gas giant surfaces. We show that for a boundary defining function $ρ$, the mean first escape time $u_ε(x)$ from the truncated Riemannian surface with an asymptotically hyperbolic metric $(M_ε,\bar{g}/ρ^2) = (\{x\in M:ρ(x)\geq ε\},\bar{g}/ρ^2) \subset (M,\bar{g}/ρ^2)$ satisfies the asymptotic expansion $u_ε(x) = -\log ε+ \mathcal{O}(1)$ as $ε\to 0 $. Furthermore, we show that in the case of a gas giant metric $g = \bar{g}/ρ^α$, where $α\in (0,2)$, the mean first escape time from the surface $(M_ε,\bar{g}/ρ^α)$ satisfies $u_ε(x) = \mathcal{O}(1)$ as $ε\to 0 $. Using techniques from the theory of polyhomogeneous conormal functions we explain this difference between in the mean first escape time on gas giant metric surfaces and asymptotically hyperbolic surfaces on the unit disc. Finally, we confirm these results using Monte Carlo simulations and finite difference methods on the disc.

Controlling the skyrmion Hall effect (SkHE) is pivotal for developing topological spintronics but typically relies on magnetic field reversal. Here, we demonstrate a general strategy for the purely electrical switching of the SkHE in two-dimensional altermagnets. Through symmetry and model analysis, we reveal that the intrinsic altermagnetic symmetry imposes sublattice-dependent anisotropic exchange and Dzyaloshinskii-Moriya interactions. These interactions induce a highly anisotropic SkHE, where the transverse velocity is strictly dictated by the current direction relative to the crystal axes. Crucially, we show that an external electric field can strongly modulate these interaction parameters by inversing the altermagnetic symmetry, allowing for the reversible inversion of the anisotropic SkHE. Using first-principles and atomistic spin model simulations, this mechanism is further demonstrated in monolayer CaMnSn. Our study establishes a unique strategy for realizing precise, electrically tunable skyrmion transport without magnetic fields.

The transition to open, distributed Multi-Agent Systems (MAS) promises scalable intelligence but introduces a non-trivial tension: maximizing global efficiency requires cooperative, resource-aware scheduling, yet autonomous agents may be self-interested and cannot be managed by a centralized controller. Prior approaches fall short in two key areas: they typically focus on single-query routing, neglecting long-term resource reuse (e.g., KV-caching) and the complexities of system-level many-to-many matching; furthermore, they rely on generic incentive mechanisms that ignore the distinct characteristics of LLM inference. To bridge this gap, we propose IEMAS (Incentive-Efficiency Mechanism for Multi-Agent Systems), a distributed framework that aligns economic incentives with system performance. IEMAS integrates a probabilistic predictive model to estimate Quality of Service (QoS) under uncertainty, which feeds into a VCG-based bipartite matching mechanism. This design guarantees truthful capability reporting and social optimality while explicitly leveraging KV cache-affinity to minimize computational redundancy. We implement IEMAS on top of vLLM and evaluate it via extensive simulations. Results demonstrate that our incentive-efficiency co-design reducing average service cost by 35% and end-to-end latency by up to 2.9 compared to baselines.

Changing-look active galactic nuclei (CL AGNs) show large changes in luminosity and optical spectral state on time-scales of a few years, and provide a valuable probe of time-dependent accretion in the disc-BLR-torus system. We present a systematic statistical study of their optical variability in a well-defined Type-1 phase, using g- and r-band light curves from the Zwicky Transient Facility for 165 CL AGNs. A subsample of 34 objects also has NEOWISE W1 and W2 light curves, which we use to measure optical-mid-infrared time lags. We use structure functions and a damped random-walk model to characterize variability amplitudes and time-scales on rest-frame scales from tens to a few hundred days, and examine their dependence on black hole mass, luminosity, and Eddington ratio. In the Type-1 phase, the short-time-scale optical variability amplitude on about 30-day time-scales shows little dependence on black hole mass, luminosity, or Eddington ratio. By contrast, the longer-term amplitudes on 150-300 day time-scales, as well as the damped random-walk time-scales, increase slowly with black hole mass and luminosity, but still show no clear dependence on Eddington ratio. The sample shows a ubiquitous bluer-when-brighter trend and larger variability at shorter wavelengths, consistent with continuum variability from a multi-temperature accretion disc. For the NEOWISE subsample, the dust lag-luminosity relation inferred from the optical-mid-infrared lags is similar to that of normal Type-1 AGNs. Overall, CL AGNs in the Type-1 phase behave like normal Type-1 AGNs within the standard disc-BLR-dusty torus framework, but are more prone to large continuum reconfigurations on year-like time-scales.

In data lakes, information on the same subject is often fragmented across multiple tables. Table union search aims to find the top-k tables that can be unioned with a query table to extend it with more rows, without relying on metadata or ground-truth labels. Existing methods are mainly column-centric: they focus on modeling column unionability scores using column embeddings, which are then used throughout the search process for column matching, filtering, and aggregation. However, this overlooks holistic table-level semantics, which may result in suboptimal rankings and inefficiencies. We introduce TACTUS, a novel table-centric method for table union search. Unlike prior work that searches from columns to tables, we search in a table-first way and examine columns only in the final step. During offline processing, we directly generate table embeddings for holistic, table-level unionability scoring by designing table-level representation techniques, including positive table pair construction to simulate unionable tables, two-pronged negative table sampling to avoid latent positives and mine hard negatives to enhance representation quality, and attentive table encoding for effective embeddings. During online search, we first develop a table-centric adaptive candidate retrieval method that efficiently selects a compact, high-quality candidate pool by leveraging the distribution of table-level unionability scores induced by table embeddings. We then inspect columns only within this compact candidate set and design a dual-evidence reranking technique that integrates table-level and column-level scores to refine the final top-k results. Extensive experiments on real-world datasets show that TACTUS significantly improves result quality while being much faster than existing methods in both offline and online processing, often by an order of magnitude.

Current reconfigurable intelligent surface (RIS)-aided near-field (NF) localization methods assume the RIS position is known a priori, and it has limited their practical applicability. This paper applies a hybrid RIS (HRIS) at an unknown position to locate non-line-of-sight (NLOS) NF targets. To this end, we first propose a two-stage gridless localization framework for achieving HRIS self-localization, and then determine the positions of the NF targets. In the first stage, we use the NF Fresnel approximation to convert the signal model into a virtual far-field model through delay-based cross-correlation of centrally symmetric HRIS elements. Such a conversion will naturally extend the aperture of the virtual array. A single-snapshot decoupled atomic norm minimization (DANM) algorithm is then proposed to locate an NF target relative to the HRIS, which includes a two-dimensional (2-D) direction of arrival (DOA) estimation with automatic pairing, the multiple signal classification (MUSIC) method for range estimation, and a total least squares (TLS) method to eliminate the Fresnel approximation error. In the second stage, we leverage the unique capability of HRIS in simultaneous sensing and reflection to estimate the HRIS-to-base station (BS) direction vectors using atomic norm minimization (ANM), and derive the three-dimensional (3-D) HRIS position with two BSs via the least squares (LS)-based geometric triangulation. Furthermore, we propose a semidefinite relaxation (SDR)-based HRIS phase optimization method to enhance the received signal power at the BSs, thereby improving the HRIS localization accuracy, which, in turn, enhances NF target positionings. The Cramer-Rao bound (CRB) for the NF target parameters and the position error bound (PEB) for the HRIS coordinates are derived as performance benchmarks.

As a general and robust alternative to traditional mean regression models, quantile regression avoids the assumption of normally distributed errors, making it a versatile choice when modeling outcomes such as cognitive scores that typically have skewed distributions. Motivated by an application to Alzheimer's disease data where the aim is to explore how brain-behavior associations change over time, we propose a novel Bayesian tensor quantile regression for high-dimensional longitudinal imaging data. The proposed approach distinguishes between effects that are consistent across visits and patterns unique to each visit, contributing to the overall longitudinal trajectory. A low-rank decomposition is employed on the tensor coefficients which reduces dimensionality and preserves spatial configurations of the imaging voxels. We incorporate multiway shrinkage priors to model the visit-invariant tensor coefficients and variable selection priors on the tensor margins of the visit-specific effects. For posterior inference, we develop a computationally efficient Markov chain Monte Carlo sampling algorithm. Simulation studies reveal significant improvements in parameter estimation, feature selection, and prediction performance when compared with existing approaches. In the analysis of the Alzheimer's disease data, the flexibility of our modeling approach brings new insights as it provides a fuller picture of the relationship between the imaging voxels and the quantile distributions of the cognitive scores.

Modern cyber-physical systems are complex, and requirements are often written in Signal Temporal Logic (STL). Writing the right STL is difficult in practice; engineers benefit from concrete executions that illustrate what a specification actually admits. Trace synthesis addresses this need, but a single witness rarely suffices to understand intent or explore edge cases - diverse satisfying behaviors are far more informative. We introduce diversified trace synthesis: the automatic generation of sets of behaviorally diverse traces that satisfy a given STL formula. Building on a MILP encoding of STL and system model, we formalize three complementary diversification objectives - Boolean distance, random Boolean distance, and value distance - all captured by an objective function and solved iteratively. We implement these ideas in STLts-Div, a lightweight Python tool that integrates with Gurobi.

Retrieval-Augmented Generation (RAG) systems introduce a critical vulnerability: contextual leakage, where adversaries exploit instruction-following to exfiltrate Personally Identifiable Information (PII) via adaptive extraction. Current defenses force a rigid trade-off between semantic utility and latency. We present SEAL-Tag, a privacy-preserving runtime environment that resolves this via a Verify-then-Route paradigm. SEAL-Tag introduces the SEAL-Probe protocol, transforming auditing into a structured tool-use operation where the model generates a verifiable PII-Evidence Table (PET) alongside its draft. To adjudicate this evidence, we employ a Probabilistic Circuit (PC) that enforces verifiable logical constraints for robust decision-making. To overcome the privacy "Cold Start" problem, we introduce the S0--S6 Anchored Synthesis Pipeline, generating high-fidelity, provenanced RAG interactions. We pair this with a Two-Stage Curriculum that first optimizes for entity detection before aligning the model to the rigorous audit protocol. Our evaluation demonstrates that SEAL-Tag establishes a new Pareto frontier, reducing adaptive leakage by over 8$\times$ while matching the utility and speed of unsafe baselines.

Let $G, G_1,\dots,G_N$ be independent copies of a standard gaussian random vector in $\mathbb{R}^d$ and denote by $Γ= \sum_{i=1}^N \langle G_i,\cdot\rangle e_i$ the standard gaussian ensemble. We show that, for any set $A\subset S^{d-1}$, with exponentially high probability, \[ \sup_{x\in A} \frac{1}{N}\sum_{i=1}^N \big| (Γx)^\sharp_i - q_i\big| \le c \frac{ \mathbb{E} \sup_{x\in A} \langle G,x\rangle + \log^2N }{\sqrt N }. \] Here each $q_i$ is the $\frac{i}{N+1}$-quantile of the standard normal distribution and $(Γx)^\sharp $ denotes the monotone increasing rearrangement of the vector $Γx$. The estimate is sharp up to a possible logarithmic factor and significantly extends previously known bounds. Moreover, we show that similar estimates hold in much greater generality: after replacing the gaussian quantiles by the appropriate ones, the same phenomenon persists for a broad class of random vectors.

These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight some recent tools and developments. The text is largely structured through exercises that lead readers to the desired conclusions, so it serves as a guided introduction to the basics of Poisson geometry.

We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guarantee the correctness of the monodromy action produced by the algorithm, and builds on previous ``homotopy graph" frameworks. We conduct extensive experiments with an implementation of this algorithm, which we have used to certify properties of several notable Galois/monodromy groups which arise in several examples drawn from pure and applied mathematics.

In a recent preprint, Mike Cummings showed that the smooth components of suitably parametrized Springer fibers are in bijection with contracted, fully reduced Plücker degree-two $\mathfrak{sl}_r$-webs of standard type and that are forests. He showed these are enumerated by sequence A116731 in the OEIS, which is equinumerous with permutations avoiding the patterns {321,2143,3124}. Cummings posed the problem of strengthening this enumerative result by finding a bijection between these webs and a collection of pattern-avoiding permutations. Here we solve this problem, although notably not with the collection of patterns that Cummings had proposed. Rather, we give a bijection between this class of webs and permutations avoiding the patterns {132,4321,3214}.

We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces with weighted $L^2$ spaces on the dual cone and reveals their intrinsic Fourier structure. This representation leads naturally to a Hardy--Sobolev decomposition theorem for boundary Sobolev spaces on $\mathbb{R}^d$. Building on these structural results, we derive explicit reproducing kernels and characterize Carleson measures for the Hilbertian Hardy--Sobolev spaces. As a preliminary operator-theoretic application, we also derive basic consequences for multipliers and weighted composition operators on these spaces.

Juggling patterns can be mathematically modeled as closed walks within directed state graphs. In this paper, we present a unified framework of unbounded juggling patterns and its variations (including multiplex, colored, and passing) primarily through the formalism of the juggling state. By extending this state-based approach and utilizing combinatorial tools such as set partitions and filled Ferrers diagrams, we find and prove a new lower bound on the number of $b$-ball prime patterns with period $n$. Further, we determine exact counts for 2-ball multiplex, 1-ball passing, and 2-ball colored juggling patterns, as well as a lower bound for 2-ball passing. We also provide an extensive analysis of the asymptotic growth rates for these pattern counts. Finally, we formalize the infinite state graph, $G_\infty$, and utilize flip-reverse involutions to establish bijections between classes of prime patterns, exploring how fixing a specific state influences the enumeration of prime walks.

It has been shown that the channel state information (CSI) of a Wi-Fi system can be exploited to localize Wi-Fi devices or track trajectory of a moving target. In the existing literature, both sensing tasks are treated separately and some prior information is usually requested, including the signal fingerprints, the locations of some anchor devices in the Wi-Fi system, and etc. In the proposed WiSLAT method, however, it is shown that both sensing tasks can assist each other, such that the request on prior system information can be eliminated. Particularly, in a Wi-Fi system with an access point (AP) and at least three stations, where the locations of the stations are unknown, the WiSLAT is designed to detect the Doppler frequencies of the downlink CSI at the stations, such that their locations and the trajectory of the target with respect to the AP can be inferred. The joint detection can be conducted by searching the optimal stations' locations and target's trajectory, such that their corresponding Doppler frequencies fit the observed ones best. Due to the tremendous non-convex search space, a low-complexity sub-optimal algorithm integrating alternate optimization, extended Kalman filter and density-based clustering is proposed in WiSLAT. Experiments conducted in indoor environments demonstrate the effectiveness of WiSLAT, achieving a median trajectory-tracking error of 0.68 m.

Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably noninvertible and dipole symmetries--have become powerful organizing principles for exotic quantum phases, yet their implications for mixed states remain less explored. In this work, we bridge these directions through a gauging correspondence between mixed-state phases with generalized symmetries and mixed-state phases with ordinary group symmetries, recasting the classification of noninvertible and dipole ASPT phases into familiar classifications of symmetry breaking and ASPT phases with dual symmetries. Using this approach, we classify and construct a subclass of ASPT phases with non-invertible and dipole symmetries in $(1+1)d$, including phases that are intrinsic to mixed states, and characterize them via string order parameters and protected edge modes.

The use of antiferromagnets in magnetoelectronic devices as counterparts of ferromagnets is a new, rapidly developing trend in spintronics that leverages antiferromagnetic (AFM) magnons for transmitting of spin currents. Van der Waals (vdW) antiferromagnets are particularly attractive in this respect as they possess tunable magnetic properties and can be easily integrated into spintronic devices. In this work we use electron spin resonance (ESR) spectroscopy to assess the potential of the vdW AFM compound CuCrP$_{2}$S$_{6}$ for magnonic applications by exploring the magnetic field ($H$) dependence of the spectrum of magnon excitations below its AFM ordering temperature $T_{\rm N} \approx 30$ K and the correlated spin dynamics above $T_{\rm N}$. ESR reveals prominent ferromagnetic (FM) spin correlations that persist far above $T_{\rm N}$ suggesting an intrinsically two-dimensional character of the spin dynamics in CuCrP$_{2}$S$_{6}$. Most interestingly, at $T < T_{\rm N}$, CuCrP$_{2}$S$_{6}$ features two non-degenerate, i.e., distinct in energy AFM magnon modes at $H = 0$ which can be tuned to the FM type of collective spin excitations with increasing $H$. These remarkable properties are favorable for the induction and control of unidirectional spin current in CuCrP$_{2}$S$_{6}$ and suggest it as a new functional material for magnetoelectronics.

We compute the Poisson cohomology of the linear Poisson structure dual to the n-dimensional "book" Lie algebra, defined by [e_0,e_i]=e_i, [e_i,e_j]=0, for i,j=1,...,n-1.

It is a simple fact that a group has a trivial automorphism group if and only if it is of order $1$ or $2$. We prove that the same holds for certain families of skew braces, and given any odd prime $p$, we construct a skew brace of order $2p^3$ that has a trivial automorphism group.

The surface phonon Hall viscosity (PHV)-an acoustic analog of axion electrodynamics-emerges from the strain response of magnetic topological insulators and gives rise to novel acoustic phenomena. In this work, we propose a previously unexplored effect: a phonon polarization-filter mechanism induced by the surface PHV, which generates an interface phonon mode with its frequency below the bulk mode frequency. This interface mode possesses a specific circular polarization and therefore acts as a polarization filter, confining only phonons with the matching polarization at the interface. Magnetic topological insulators can thus selectively transmit one type of circularly polarized phonon mode, enabling the manipulation of phonon polarization and angular momentum. In addition, we further develop a generalized scattering framework to study the effect of an injected acoustic wave from a trivial insulator to a magnetic topological insulator with both normal and oblique incidence, and discuss the phenomena of surface acoustic Faraday rotation and longitudinal-transverse mode conversion. Our results establish surface Hall viscosity as a powerful mechanism for engineering axial phonon states and open new avenues for topological phononic devices based on phonon angular momentum.

Quantum emitters near the surface of silver nanoparticles undergo Rabi oscillations in electronic population dynamics due to strong coupling with near-field multipole modes that are not radiative. Low-frequency nanoparticle dipole modes are radiative but do not couple strong enough to quantum emitters. These features limit the observation of strong coupling. Using macroscopic quantum electrodynamics theory within a Lorentzian pseudo-mode approximation for the non-Markovian interaction kernel, we demonstrate that by coating spherical silver nanoparticles with a thin molecular J-aggregate layer, the resulting core-shell plexciton resonance restructures the local electromagnetic vacuum at dipole-mode frequencies to enable Rabi oscillations for quantum emitters that otherwise would only undergo exponential population decay. Specifically, we show for quantum dot emitters in the near field of silver nanospheres of 20 nm radius, that weak-to-strong coupling crossovers can be induced using 2 nm J-aggregate shells. Our work demonstrates the potential of molecular aggregates to enable deep sub-wavelength structuring of the vacuum field for the observation of coherent quantum dynamics in optical nanocavities.

In this paper, we establish the asymptotic linear stability of a class of Coriolis-driven columnar vortices for the 3-D axisymmetric Euler equations. This result represents a critical step toward proving the nonlinear asymptotic stability of such vortices. The key and widely applicable strategy is to construct a distorted Fourier basis, which is achieved by solving a two-parameter $(c, ξ)$-dependent Schrödinger equation associated with the linearized operator of the system. To capture the precise asymptotic behavior of the solution, we decompose the $c-ξ$ plane into distinct regions, with the partitioning guided by the leading-order profiles of the Schrödinger equation across different parameter regimes.

Attacks can exploit zero-day or one-day vulnerabilities that are not publicly disclosed. To detect these vulnerabilities, security researchers monitor development activities in open-source repositories to identify unreported security patches. The sheer volume of commits makes this task infeasible to accomplish manually. Consequently, security patch detectors commonly trained and evaluated on security patches linked from vulnerability reports in the National Vulnerability Database (NVD). In this study, we assess the effectiveness of these detectors when applied in-the-wild. Our results show that models trained on NVD-derived data show substantially decreased performance, with decreases in F1-score of up to 90\% when tested on in-the-wild security patches, rendering them impractical for real-world use. An analysis comparing security patches identified in-the-wild and commits linked from NVD reveals that they can be easily distinguished from each other. Security patches associated with NVD have different distribution of commit messages, vulnerability types, and composition of changes. These differences suggest that NVD may be unsuitable as the \textit{sole} source of data for training models to detect security patches. We find that constructing a dataset that combines security patches from NVD data with a small subset of manually identified security patches can improve model robustness.

Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects of biological systems. In this case, an appropriate simple model represents a universality class. The extraction of universal properties is supported by evolutionary robustness and the reduction of dimensionality in high-dimensional states. Integrating the data-driven omics approach with the universality approach is an important step in systems biology.