Filtered approximate nearest neighbor (FANN) search must satisfy both vector similarity and structured predicates, yet evaluations remain brittle because real hybrid workloads are rarely shareable and existing benchmarks rely on ad-hoc synthetic or semi-real constructions. We argue that realism hinges on execution-driven query difficulty: failures in early filtering trigger over-fetching of additional candidates, shaping latency, throughput, and recall. Building on this insight, we propose $\alpha$-Hardness, a query-level hardness metric that models the conditional execution chain via the over-fetch factor and extends naturally to strategy-conditioned settings. Across diverse datasets and hybrid strategies, $\alpha$-Hardness exhibits strong monotonic alignment with empirical performance, while common proxies such as selectivity or attribute-vector correlation are frequently unstable or strategy-inconsistent. We further introduce HCBGen, a hardness-controlled benchmark generator that uses $\alpha$-Hardness as an explicit control signal to synthesize workloads under coarse bias modes or to match a target hardness profile. Our experiments show that widely used benchmarks occupy a narrow, relatively easy portion of the hardness spectrum, masking robustness gaps that emerge under harder queries. Finally, we demonstrate that matching hardness distributions enables privacy-preserving proxy workloads that closely reproduce performance trends, bridging research benchmarks and real evaluation.

We propose and analyze a generalized compartment model for hacker dynamics in cybersecurity systems. This model is an extension of a recently introduced framework, replacing the bilinear interaction term with a broad class of nonlinear incidence functions. This provides greater modeling flexibility and allows for the description of a wider range of cyber-propagation and information-spreading processes. First, we investigate the qualitative dynamics of the model. We establish the positivity and boundedness of solutions, derive the basic reproduction number, and characterize the existence of hacker-free and hacker-present equilibria. We obtain local and global asymptotic stability results, yielding a complete description of the global dynamics in terms of the basic reproduction number. Next, we develop a second-order, positivity-preserving, nonstandard finite difference (NSFD) scheme for numerical simulations. Unlike many existing NSFD approaches, which are typically first-order accurate, the proposed method achieves second-order convergence while preserving positivity for arbitrary step sizes. Furthermore, the proposed method reproduces the asymptotic stability properties of the continuous model, making it suitable for long-time simulations. Numerical experiments validate the theoretical results and demonstrate the superior accuracy and qualitative performance of the proposed scheme compared to several first-order methods.

We determine all possible intersection arrays of completely regular codes of covering radius one in the generalized Petersen graphs \(GP(n,k)\), where \(n\geq 3\) and \(1\leq k<n/2\). In the equivalent language of perfect colorings, this amounts to enumerating all quotient matrices of perfect \(2\)-colorings, up to interchanging the two colors. Since \(GP(n,k)\) is cubic, there are only six possible nontrivial quotient matrices. For each of them, we give necessary and sufficient arithmetic conditions on \(n\) and \(k\) for its existence. The feasible cases are realized by explicit periodic colorings. The nonexistence part is obtained by reducing the local coloring conditions to cyclic systems of linear equations and applying a Fourier argument on roots of unity. Together with the previously known cases \(GP(n,2)\) and \(GP(n,3)\), the results give a complete arithmetic classification of quotient matrices, and hence of covering-radius-one completely regular code parameters, in the generalized Petersen family.

The influence maximization problem aims to select a set of seed nodes that maximize the influence, i.e., the average number of influenced nodes, at the end of a spreading process. It has been widely studied with applications in viral marketing, public health campaigns, and social influence. In networks with pronounced community structure, existing approaches often yield an uneven distribution of influenced nodes across communities, which is unfair. Although the fair influence maximization (FIM) problem has been studied for pairwise networks, it remains largely unexplored for hyper graphs, which more accurately represent real-world systems involving group interactions. We introduce FIMH, a heuristic seed-selection algorithm for FIM on hyper graphs, under the Susceptible-Infected Contact Process (SICP) spreading model. FIMH iteratively estimates the contribution of each candidate node to influence and fairness and selects the node that best trades off these two objectives as an additional seed using a parameter-free utopia-distance criterion. Experiments on seven real-world hypergraphs demonstrate that FIMH achieves an influence comparable to that of state-of-the-art IM methods while significantly reducing influence disparity. Analysis of the topological properties of the selected seed nodes and their contributions to influence and fairness further supports the effectiveness of FIMH.

We construct stochastic thermodynamics of overdamped Langevin systems on nonrelaticvistic curved spaces with time-dependent metrics. The time dependence of the metric contributes to the energy balance by performing work on the kinetic energy, which is instantaneously dissipated as heat in the overdamped regime. This contribution makes our framework thermodynamically consistent so that entropy production satisfies the second law of thermodynamics. As a special case, when the metric evolves according to backward Ricci flow, the entropy balance exhibits a structure similar to Perelman's entropy functional. Our framework provides a way to quantify thermodynamic costs in dynamics on time-evolving spaces such as diffusion on membranes.

Lu proved that the set $$\mathcal{T}:=\{t\in\mathbb{Z}\setminus\{0\}:(q,\mathcal{D},tL)\text{ forms a Hadamard triple}\}$$ constitutes a spectral eigenvalue set for $\mu_{q,D}$, where $(q,\mathcal{D},L)$ is a Hadamard triple. And they prove for $s \in [0,\frac{\log \#\mathcal{D}}{\log q}]$, the corresponding spectra form a family of cardinality continuum. In this paper, we study Moran measures formed by random convolutions of finite Hadamard triples. Let $$\mu=\delta_{M_1^{-1}D_1}*\delta_{M_2^{-1}D_2}*\cdots, \qquad M_k=q_1q_2\cdots q_k,$$ where the factors are produced from finitely many triples $\{(N_j,B_j,L_j):1\le j\le m\}$, $(\omega_k)_{k=1}^{\infty}\in\{1,2,\ldots,m\}^{\mathbb N}$, and $n_k\in\mathbb N^+$, by setting $$ q_k=N_{\omega_k}^{n_k},\qquad D_k=B_{\omega_k},\qquad E_k=N_{\omega_k}^{n_k-1}L_{\omega_k}. $$ Assume a non-full-digit gap $$\rho:=\min_{1\le j\le m}\frac{N_j}{\#B_j}>1.$$ For the common Hadamard triple multiplier set $$\mathcal{T}_*:=\bigcap_{j=1}^m\{t\in\mathbb{Z}\setminus\{0\}:(N_j,B_j,tL_j)\text{ is a Hadamard triple}\},$$ Our main result is that, for every $$0\le s\le \kappa_\omega:=\limsup_{R\to\infty}\frac{\sum_{r=1}^R\log \#D_r}{\sum_{r=1}^R\log q_r},$$ there exist continuum many countable sets $\Lambda\subset\mathbb{Z}$ such that $t\Lambda$ is a spectrum of $\mu$ for every $t\in\mathcal{T}_*$ and $\dim_{Be}\Lambda=s$.

Magnetohydrodynamic waves redistribute energy in magnetic structures of the lower solar atmosphere, yet constraints on how wave power and dominant frequencies are organised above sunspots remain limited because most studies use only a few well-separated diagnostics. Here we present multiline wave signatures in a sunspot from near-UV spectroscopy with the Sunrise-III UV Spectropolarimeter and Imager (SUSI). We analyse a two-hour time series of repeated raster scans of a sunspot near disc centre in the 327-329 nm spectral window (> 100 lines). From these, we select 44 lines that radiative-transfer calculations suggest sample effective formation heights within the umbral core from deep photosphere toward the low chromosphere. For each line, we extract line-core intensity and line-of-sight velocity time series using a dedicated multi-line fitting routine and compute Morlet-wavelet power spectra. The refined global wavelet spectra show that most lines (in both intensity and velocity) are genuinely multi-frequency, with a dominant peak and substantial statistically significant power up to 12 mHz. Unsupervised clustering of the normalised spectra groups lines into families with similar spectral shapes and reveals a progression of dominant frequencies from ~2 to ~10 mHz across the ensemble, for both intensity and velocity (not necessarily in the same lines). This behaviour is not reproduced by a simple formation-height ranking, suggesting that uncertainties in the formation-height estimates and line-dependent diagnostic response together shape the ordering. These Sunrise-III/SUSI observations open a new regime for near-UV multi-line wave studies and provide the first systematic characterisation of frequency-structured sunspot wave behaviour in this spectral region.

Low dimensional quantum materials have been extensively studied within the physics community, among which Co2+ is one of the most popular magnetic ions to be embedded into the structural motif. CoNb2O6 and CoTa2O6 both have adopted an effective spin-1/2 state, with the former attracting enduring interest while the latter being rarely investigated. This difference can be attributed to their distinct crystal structures, not only in crystal systems, but more important, how the CoO6 octahedra are connected. We successfully merge these two compounds together and map out the doping limits. We find out Ta and Nb dopants modify the properties of the parent compounds in subtle but different ways and construct a magnetic phase diagram of the Co(NbxTa1-x)2O6 (0 < x < 1) series. In addition, our results suggest that Ta-doping may pave a way to strengthen the lower-dimensional quantum phenomena in CoNb2O6 before its crystal structure starts to melt down.

We give a unified analytic account of correlation emergence and the Epps effect in two coupled limit order books. The model starts from a discrete random-walk description of order flow with creation, cancellation and diffusion. A pair-trader coupling between the books is introduced at the level of order creation. We clarify how the discrete model reduces to coupled reaction--diffusion equations with a moving reaction boundary defining the transaction price. Using a regularised local-response representation of the coupling, we derive approximate closed-form expressions for realised correlations as a function of aggregation time. Here the Epps effect is shown to arise from three distinct mechanisms: asynchronous event clocks (subordination), finite coupling response times, and their combination.

We present the propagation of massive Majorana neutrinos crossing an exact gravitational sandwich wave background. By employing a Takagi factorization to decouple the matrix field equations, We show that the localized pulse breaks the kinematic alignment of the mass eigenstates as they propagate through the wave zone, leaving a permanent residual phase shift across the transverse profile of the wavefront. The wave asymmetry couples directly to the Majorana spin tensor, forcing a transition from left-handed to right-handed configurations. Behind the wave tail, the residual drift parameters act to polarize the state's chirality, introducing a strong anisotropy across the transverse momentum plane. These results show that a passing gravitational wave leaves a modification on both the flavor and helicity of a neutrino beam, as a sign of the gravitational memory effect.

We investigate the decoherence of a quantum spatial superposition of a static particle in Schwarzschild and Reissner-Nordström black holes. By treating the particle as a localized classical source coupled to a quantum scalar field, we reformulate the decoherence process in the Danielson-Satishchandran-Wald (DSW) gedankenexperiment through coherent state generation and derive the local expression for the decoherence functional in terms of the Wightman function. In the long-time limit, the decoherence rate is shown to be characterized by the low-frequency behavior of the Wightman function. We then employ the asymptotic matching method to calculate the analytical expressions of the Wightman functions in the Boulware, Unruh, and Hartle-Hawking vacua. We show that the decoherence behavior depends on the quantum state of the environmental field. While the Boulware vacuum gives vanishing decoherence for a static superposition, the thermal effects associated with Hawking radiation in the Unruh and Hartle-Hawking vacua can induce nonvanishing decoherence.

In distributed quantum networks, interacting spin systems can mediate the generation of highly entangled links between distant nodes. We investigate the role of effective parity-time (PT)-symmetric non-Hermitian spin-1/2 bulks weakly coupled to two quantum links, obtained due to the environmental interactions affecting both the bulk and the links. Focusing on effective non-Hermitian nearest-neighbor (NN) Su-Schrieffer-Heeger (SSH) models, we analyze how non-Hermiticity influences the dynamical formation of long-distance entanglement (LDE). For a paradigmatic model consisting of a quantum XX bulk subjected to imaginary staggered magnetic fields, we analytically determine the exceptional points arising from the resulting bulk-mediated interactions between the links. Combining analytical and numerical methods, we demonstrate that an initially fully separable state can dynamically evolve into highly entangled link states near these exceptional points in the broken regime. Further, after optimizing over time and system parameters, near-unit time-averaged entanglement between the links emerges under weak imaginary magnetic fields and bulk-link couplings, which cannot be attained in the corresponding Hermitian systems. Moreover, the non-Hermitian dynamics exhibit a freezing of high entanglement in the vicinity of exceptional points, a feature absent in Hermitian counterparts. We also identify regimes of long-range interaction strengths that yield a higher time-averaged entanglement than the corresponding NN models. Furthermore, we establish that LDE persists in the stationary regime, highlighting the promise of engineered non-Hermitian dynamics for realizing robust and frozen entangled links in quantum networks.

To evaluate the performance of audio signal processing algorithms and to train data-driven algorithms, e.g., as applied in hearing instruments, either simulated or recorded data can be used. While large batches of simulated data can be generated using mathematical models, recorded data provide a more adequate representation of real-life scenarios. Therefore, in this paper, the Hearing Instrument Dataset in Various Acoustical Scenarios (HIDVAS) is introduced. This dataset consists of both impulse responses and audio recordings using eight external loudspeakers, two external microphones, and a dummy head. On this dummy head behind-the-ear (BTE) hearing instrument shells with two microphones per shell are mounted, and in the dummy head's ears receiver-in-canal (RIC) hearing instrument loudspeakers are inserted. The dummy head also contains microphones located at its eardrum. The impulse responses have been computed from a swept-sine recording for each microphone-loudspeaker pair, and the audio recordings have been obtained by playing back audio (male and female speech, speech shaped noise, singing voice, stringed instrument, wind instrument, and percussion instrument) through each individual loudspeaker and recording simultaneously using all microphones. These recordings have been repeated for four hearing instrument domes (open, semi-open, closed, and no-RIC) in three reverberation conditions in one room (T30 = 0.09 s, T30 = 0.47 s, and T30 = 0.73 s), and in one reverberation condition in a different room (T30 = 1.48 s). The usage of the dataset as a `hearing instrument in a box' is exemplified with three example use cases.

A scalar potential landscape is one of the most useful ways to understand the stability and transition of a dynamical system. For non-gradient dynamics, however, the construction of a global Lyapunov-type scalar for nonlinear flows with recurrent structures remains a major obstacle. We introduce the generalized Lyapunov function, a scalar function that is non-increasing along deterministic trajectories, as a unifying notion of nonequilibrium potential. Ordinary Lyapunov functions, Freidlin--Wentzell quasi-potentials, and Ao-type potentials are recovered as special representatives. We then propose a data-free physics-informed neural-network framework in which the Lyapunov inequality and a weak divergence-scale compatibility condition are directly embedded into the loss function. The method is tested on linear systems, the Hopf normal form, the van der Pol oscillator, and a three-dimensional Hopf-link flow with two linked limit cycles. The learned landscapes agree with available analytical benchmarks and reveal the invariant sets as low-potential or constant-potential structures, providing a practical route to potential-landscape construction for nonlinear non-gradient systems.

Holography offers unique advantages for delivering perceptual realism while preserving compact form factors in VR/AR. Its perceptual quality, however, hinges on encoding rich wavefronts of photorealistic scenes into interference patterns and then incoherently multiplexing the resulting wave fields for perception. Existing CGH paradigms decouple radiance estimation from wave propagation by pre-rendering radiance on discretized scene sectors. This separation between radiometric and wave-optical computation inherently limits the range of focus cues and visual effects that can be faithfully reproduced, including depth- and view-continuity, and physically based material behaviors such as glossy or mirror-like reflection and refraction. We present a physically accurate yet computationally efficient wave optics rendering framework leveraging path tracing to encode full 3D visual cues into phase holograms. Specifically, we employ a Monte Carlo method to solve both the rendering equation and the Rayleigh--Sommerfeld integral simultaneously. Our algorithm is fully compatible with modern graphics techniques and can generate multiple time-multiplexed random holograms with minimal additional time cost via Path Reuse. By employing a fast approximation with an ambient radiance cache, we realize an order of magnitude convergence speed improvement. The resulting coherent wave fields that inherently encode comprehensive visual effects are converted into phase-only holograms under complex-amplitude supervision. Through extensive simulations and experimental validations on a spatial light modulator-based display prototype, we demonstrate faithful holographic reconstructions of natural 3D cues and complex materials, including realistic defocus blur, view-dependent effects, as well as appearance highlights and reflections.

We discuss the peculiarities of scattering in a three-proton system induced by the presence of an entangled proton-proton Bell-like state in the initial configuration. We formulate the problem using the standard spin formalism of nuclear physics in order to follow in detail the reaction pathways leading to the teleportation of a quantum-mechanical state within this system. By performing numerical simulations of the system and calculations based on a realistic nucleon-nucleon potential, we evaluate the relevant spin observables and search for a simple, experimentally feasible signal that could provide clear evidence of quantum teleportation. For the case in which proton 2, belonging to the entangled proton pair 23, interacts with hydrogen target 1, thereby triggering the teleportation process, we find clear evidence of teleportation through measurements of the final polarization of proton 3', even for small values of the polarization of target proton 1. The dominant component of this polarization is transferred almost entirely from target proton 1 to proton 3 in the angular region characterized by strong entanglement. For an unpolarized target proton 1, quantum teleportation is no longer possible. The only unambiguous signature of the residual quantum correlations would be provided by measurements of the spin correlations within the strongly entangled final-state proton pair 1'2'. Indirect evidence may also be obtained from measurements of the polarization of proton 2' in the final state, although the corresponding effectis relatively weak.

In this work, by construct an asymptotic coupling by reflection, we first explore the uniform-in-time estimate on probability distance for two measure-valued processes induced by a McKean-Vlasov SDE with common noise and an interacting particle system, where the drift terms are dissipative merely in the long distance. As direct applications of this estimate, we establish the uniform-in-time error estimates for the numerical solutions derived via backward/tamed/adaptive Euler-Maruyama methods. Moreover, as another direct application, the uniform-in-time conditional propagation of chaos is quantified.

We study existential Presburger arithmetic extended with divisibility predicates (EPAD). Its satisfiability problem has long been known to be NP-hard, and has often been expected to lie in NP. We prove that it is PP-hard, ruling out this expectation unless NP=PP. This also implies \PP-hardness of satisfiability for positive Boolean combinations of word equations and length constraints. The lower bound is compatible with a strong form of Lipshitz-style simplification. We define a polynomial-time recognizable fragment, called \MergeAbs, in which the usual finite-quotient replacement of divisibility atoms can be repeated until no divisibility atom remains. Nevertheless, EPAD satisfiability is already PP-hard on this fully simplifiable fragment. The reduction starts from a threshold coefficient problem for a class of arithmetic circuits using only addition and shifts. The same systems used in the reduction also expose a limitation of normalization. A polynomial-size scaling family, indexed by $j$, forces an endpoint relation $v=(2^{2^j}+1)u$, and the natural finite-quotient simplification records it as one equation with coprime coefficients whose largest coefficient has bit-size $\Theta(2^j)$.

We investigate thermal dilepton production from a quark-gluon plasma (QGP) with finite baryon chemical potential ($\mu_{\text{B}}$) in central Pb-Pb collisions at $\sqrt{s_{\text{NN}}}=5.02~\text{TeV}$. Recent studies suggest that sizable baryon densities can be achieved at forward rapidity even at LHC energies. We incorporate finite $\mu_{\text{B}}$ into a (3+1)-dimensional hydrodynamic framework and find that $\mu_{\text{B}}$ exceeds 500 MeV around $\eta_\text{s} = 6$ during the medium evolution. Using this framework, we calculate thermal dilepton spectra over a wide rapidity range and evaluate the impact of finite $\mu_{\text{B}}$ on dilepton production. A suppression of 3-4% is observed in the forward-rapidity region $5.2 < y < 7.2$ due to the reduced quark-antiquark abundance at finite baryon density. We further examine the effective temperature extracted from dilepton mass spectra in the intermediate-mass region $1.2 < M_{\ell \ell} < 2.6~\text{GeV}$. The effective temperature remains strongly correlated with the underlying hydrodynamic temperature and retains sensitivity to the early high-temperature stage of the QGP evolution. These results demonstrate that forward-rapidity dileptons remain effective thermometers while providing sensitivity to finite baryon density at the LHC.

The rapid digitalization of the Sudanese financial sector has precipitated a surge in Mobile Banking Applications (MBAs); however, this growth has frequently outpaced rigorous security auditing. This study provides a comprehensive technical audit of the four most widely used Sudanese MBAs( Bankak, Fawry, Okash, and Sahil )collectively serving a user base of over 1.6 million. Utilizing Static Application Security Testing (SAST) via the Mobile Security Framework (MobSF) and Quixxi, the applications were evaluated against the OWASP Mobile Application Security Verification Standard (MASVS). Findings were mapped to Common Weakness Enumeration (CWE) identifiers to identify systemic vulnerabilities. Analysis revealed critical disparities in security posture. Bankak, the market leader, exhibited the highest risk profile (12 vulnerabilities), including a critical absence of SSL certificate pinning and unsafe TrustManager implementations, rendering it highly susceptible to Man-in-the-Middle (MitM) attacks. While Fawry demonstrated relative maturity (7 vulnerabilities), a universal failure was observed across all four applications regarding secure random number generation (CWE-330), potentially compromising session token integrity. Additionally, Bankak and Okash were found to utilize deprecated cryptographic algorithms (MD5/SHA-1). Notably, all applications successfully disabled ADB backups, yet 100% retained verbose debugging symbols in production APKs, significantly lowering the barrier for reverse engineering. This research addresses a critical gap in the national fintech ecosystem by providing actionable technical recommendations for developers and a strategic roadmap for implementing "security-by-design" principles across the sector.

Fuzz drivers are essential components of greybox fuzzing, as they encapsulate target interfaces, define test spaces, and largely determine fuzzing effectiveness. Existing fuzz drivers typically rely on crash-based oracles for security testing, overlooking library functionality and limiting bug detection capability. In this paper, we present the first study on metamorphic-based fuzz oracle enhancement (MFOE), which augments existing fuzz drivers with metamorphic-based oracles derived from metamorphic relations (MRs). Since constructing and integrating such oracles requires substantial domain knowledge, automating MFOE is challenging. To address this challenge, we propose MetaFOE, an LLM-based framework that automatically generates and integrates metamorphic-based oracles. We evaluate MetaFOE on OSS-Fuzz drivers using three modern LLMs and five prompt strategies. MetaFOE generates 3,475 MRs, of which 77.3% are applicable, and implements 12,351 meta drivers, with 6,228 being valid. After three hours of fuzzing, the valid meta drivers improve edge coverage by an average of 18.7% and trigger 1,528 unique crashes. Our results demonstrate both the effectiveness of metamorphic-based oracle enhancement and the feasibility of using LLMs to automate MFOE, providing valuable insights for advancing greybox fuzzing.

We study a system qubit repeatedly interacting with the same environmental qubit, with a reservoir acting on the environment between collisions via a completely positive, trace-preserving map. We show that complete suppression of system--environment correlations uniquely requires a full environmental reset, recovering a semi group dynamics with a time-independent Gorini--Kossakowski--Sudarshan--Lindblad generator, whereas a partial reset yields a continuous transition between Markovian and non-Markovian regimes governed by a single dimensionless relaxation parameter. For a resonant excitation-exchange interaction, we obtain exact closed-form expressions for the Bloch-vector dynamics for both a generalized depolarizing channel and a generalized amplitude-damping channel acting as the reservoir-induced map. Using the Breuer--Laine--Piilo measure and a Choi-matrix CP-divisibility witness, we identify three distinct dynamical regimes across the parameter space: CP-divisible Markovian dynamics, CP-indivisible but P-divisible dynamics, and non-P-divisible non-Markovian dynamics. The boundaries between these regimes, and the structural differences between uniform and anisotropic environmental relaxation, are characterized numerically.

The classical Corrádi-Hajnal theorem states that for any multiple $n$ of $3$, if $G$ is a graph with $n$ vertices and $\delta(G) \geq 2n/3$, then $G$ can be partitioned into $n/3$ vertex-disjoint copies of the triangle [\emph{Acta Math. Acad. Sci. Hung.}, 14:423-439, 1964]. Balogh, Molla and Sharifzadeh obtained a smaller lower bound by adding the independence number condition [\emph{Random Struct. Algorithms}, 49:669-693, 2016]. In this paper, we study perfect tilings in digraphs subject to conditions on the independence number and the degree. The independence number, $\alpha(D)$, of $D$ is the maximum integer $k$ such that $D$ has an independent set of cardinality $k$. We show that if $D$ is an $n$-vertex digraph with $\alpha(D)\leq o(1)n$ and $\delta(D) \geq (1+o(1))n$, then $D$ has a perfect $T_3$-tiling, where $T_3$ denotes a transitive triangle. This minimum degree condition is asymptotically best possible. Moreover, our result implies the theorem of Balogh, Molla, and Sharifzadeh concerning perfect triangle tilings.

This paper investigates the nonlinear asymptotic stability and optimal decay rates of entropy waves for the Landau equation with physically realistic Coulomb interactions under general perturbations. We consider the infinite channel domain $\mathbb{R} \times \mathbb{T}^2$ in three dimensions, which possesses both one-dimensional and high-dimensional characteristics, thereby posing two primary analytical challenges: (i) for the one-dimensional Landau equation with Coulomb potentials, the absence of a spectral gap in the linearized operator has obstructed the derivation of wave pattern stability results with explicit time decay rates; (ii) in the study of contact discontinuities, the multidimensional case fundamentally differs from the one-dimensional setting due to lack of a key structural condition. We develop effective analytical approaches to treat those difficulties. To overcome the weak dissipation caused by the spectral gap deficiency, we implement a time-velocity interpolation technique to enhance dissipation and simultaneously construct coupled diffusion waves to compensate for the loss of time decay. To address the missing structural condition in higher dimensions, a novel transformation is introduced to recover the two-sided structural condition within the perturbation system. By developing a derivative-level transformation and a refined energy framework, we restore the necessary structural condition for derivatives, establish the optimal decay of the solution, and prove the stretched exponential decay of its non-zero modes. In contrast to previous methods that rely on artificial viscosity or the Navier--Stokes approximation, our approach directly leverages the intrinsic physical dissipation of the equation and its coupling with the microscopic kinetic component, ensuring broader applicability.

Large language model (LLM) agents increasingly extend their capabilities at runtime by loading Agent Skills, which pair natural-language specifications ( this http URL ) with executable scripts and resources. Because a skill's behavior relies on both natural-language instructions and executable code, assessing its safety requires cross-modal reasoning, creating a new language-and-code attack surface. Attackers can present a benign workflow in this http URL while embedding implicit directives that steer the agent to exfiltrate sensitive files, even if the scripts appear harmless. This attack surface remains understudied; prior work treats skills merely as prompt-injection vectors or static code artifacts, leaving attacks emerging from cross-modal interactions largely unmeasured. In our evaluation, open-source and commercial skill scanners detect only 2%-8% and 9%-17% of such attacks, respectively. To address this gap, we introduce SkillMutator, the first benchmark for install-time detection of language-and-code cross-modal attacks on Agent Skills. It emulates an adversarial mutation process across 13 attack categories, iteratively refining malicious skills using scanner feedback to make injected behaviors indistinguishable from legitimate workflows. We further propose a four-phase reasoning-trajectory distillation framework to distill frontier-teacher traces into smaller open-weight models. This produces a locally deployable scanner avoiding third-party data exposure and excessive API costs. On the strongest SkillMutator subset (n=76), our distilled model (Qwen2.5-Coder-7B-Instruct) improves detection from 17.1% to 88.2%, surpassing GPT-4o-mini (23.7%) and GPT-5.4-mini (79.0%), and reaching frontier-level GPT-5.4 (86.8%). These results show practical defense against cross-modal attacks is feasible without relying on costly frontier models.

Warped galactic discs are common, yet their detection remains challenging, as the outskirts of galaxies are typically faint. Advances in deep imaging surveys improve the detectability of such features, while machine learning enables efficient analysis of large datasets. Using the Pan-STARRS EGIPS catalogue, we develop a deep learning framework by fine-tuning the Zoobot convNext-nano model on 1000 edge-on galaxy FITS images to distinguish warped and non-warped edge-on galaxies with 83\% accuracy. The trained model is then applied to a larger sample, identifying 2088 warped and 1398 non-warped galaxies with a high prediction probability threshold ($\geq 0.85$). Additionally, we use the model to predict on 3226 edge-on galaxies from the Euclid Q1 survey, demonstrating the model's ability to generalise across datasets with differing resolutions. To analyse the model predictions, we employ LayerCAM to identify the regions of galaxy images that contribute to the classification. We find that warped galaxies differ primarily in their structural properties, exhibiting lower axis ratios and higher asymmetry. Warped galaxies were found to be bluer, with younger stellar populations and enhanced star formation. These results highlight the effectiveness of deep learning methods in identifying subtle morphological features, such as warps, and demonstrate their potential for studying structural properties of galaxies in current and upcoming large imaging surveys.

With the rapid proliferation of non-geostationary orbit (NGSO) mega-constellations, beam hopping (BH) has become indispensable for resource scheduling in multi-satellite, multi-coverage scenarios. By dynamically adjusting spot beam power and pointing within each time slot, BH enables highly efficient spectrum utilization. A principal engineering challenge is the real-time generation of beam hopping time plans (BHTP). Traditional algorithms, such as the round-robin strategy, distribute beams evenly across all service cells in a round-robin fashion. However, real traffic follows a long-tail distribution; the most active 10% of hotspot cells generate more than 50% of the aggregate demand, making uniform allocation inadequate. To address this issue, existing frameworks adopt a genetic algorithm (GA), whose throughput is approximately 80.7% higher than the traditional baseline. Operational satellite footprints encompass more than 1,000 service cells. The GA requires 67.8 s to generate a BHTP for 1,127 cells. With a 550 km LEO satellite providing only a 300 s visibility window, multiple online recomputations are impractical. State-of-the-art algorithms, such as multi-agent deep reinforcement learning (MADRL), fail to converge once the cell count exceeds 200. To overcome these challenges, we propose a novel BH scheduling algorithm Aidos. The algorithm integrates traffic-aware random-key encoding into a multi-objective metaheuristic search, and then applies a sliding-window Beta resampling strategy during adaptive distribution evolution, to improve both the search efficiency and the solution quality of the BHTP. Experiments demonstrate that Aidos improves throughput by 79.2% and reduces latency by 99.45%. Its average computation time is 9.3 s, enabling online replanning within a 300 s satellite overpass window.

We prove that many virtual properties are closed under taking graph products, including: virtually RFRS, virtually (compact) special, virtually CAT(0) cube, and virtually normally poly-free. Our proof uses Januszkiewicz and Świątkowski's strong commensurability theorem for graph products, for which we provide an elementary proof.

The rapid expansion of non-geostationary orbit (NGSO) satellites alongside existing geostationary orbit (GSO) systems has intensified spectrum congestion and inter-system interference, placing stringent demands on real-time interference management to sustain reliable coexistence in next-generation communication networks. While existing machine learning (ML)-based reconstruction models have made strides, they remain constrained to an area under the curve (AUC) of 0.83 due to fixed thresholds, causing unacceptable false alarm rates that undermine critical link reliability. Additionally, their decoupled training paradigm neglects cross-domain dependencies, limiting time and frequency-domain AUCs to 0.83 and 0.71, respectively. To address these limitations, this paper introduces a semi-supervised satellite interference detection framework named Agon, employing a novel two-stage hybrid learning paradigm. Agon integrates masked autoencoder (MAE) pre-training of a dual attention transformer (DAT) with multi-task fine-tuning to optimize a direct binary classifier, effectively eliminating unstable thresholds. Furthermore, it incorporates high-order statistics (HOS)-augmented attention and wavelet regularization to bolster noise robustness and structural fidelity. Extensive validation on public NGSO-GSO dataset and a high-fidelity NGSO-NGSO dataset demonstrates that Agon achieves state-of-the-art (SOTA) detection performance, with a 25.3% improvement in AUC. Moreover, the multi-task learning (MTL) framework facilitates accurate modulation classification with accuracies exceeding 90%, while simultaneously maintaining optimal detection performance across diverse scenarios characterized by varying off-axis angles and interference-to-noise ratios (INRs).

Learning in biological multilayer neuronal networks offers insights that extend beyond the classical weighted-sum neuron model commonly used in artificial neural networks. This article presents an accessible guide to a mechanistic neuronal network model that more accurately captures aspects of biological computation while enabling a simple yet powerful mechanism for learning in multilayer neural networks. The proposed approach supports efficient online streamed learning and provides a practical alternative to backpropagation. We demonstrate its potential in an image classification task, achieving competitive classification performance. The approach's simplicity, biological grounding, and broad applicability highlight a promising path toward algorithms that unify mechanistic neuron models and machine learning.