Hybridization of resonances is known to overcome inherent limitations of individual systems, enabling advanced functionalities and applications. Here we discuss hybrid plasmonic-Mie resonators that emerged recently as a promising direction in advancing nanophotonic structures by synergistically combining the strong near-field enhancement of plasmonic components with the low-loss, multipolar resonances of dielectric Mie elements. We review the recent progress in the field, encompassing the fundamental physical principles, structural design strategies, material platforms, computational optimization approaches, and representative device implementations. Our discussion starts by evaluating the complementary characteristics of plasmonic and Mie resonances followed by a description of the coupling between these resonances in order to boost light-matter interactions. Afterward, we explore the performance of efficient hybrid resonators for different application areas. Apart from the conventional metal-dielectric systems, we consider the recent class of epsilon-near-zero (ENZ) materials, which can provide unique advantages in terms of field localization, phase engineering, and energy flow management in the vicinity of zero-permittivity conditions, offering more flexibility in designing hybrid nano-optical devices. Lastly, we point out potential research avenues aiming to improve functional and efficient nanophotonic devices, especially those involving emerging topological material systems, such as Sb2Te3, Bi2Te3, Bi2Se3, combining plasmonic amplification, dielectric confinement, and spin-dependent optical behavior.

Many functional datasets are observed sparsely and irregularly. Ordering such data is challenging because only limited information is available from each observation, while the underlying trajectories remain infinite-dimensional. This paper develops a novel depth notion for sparse functional data, called the conditional regularized halfspace depth (CRHD). CRHD is defined as the infimum of conditional halfspace probabilities of the underlying trajectory given the observed sparse measurements, thereby enabling depth evaluation directly at sparse observations without requiring trajectory reconstruction. We study several basic theoretical properties of CRHD that clarify its behavior as a depth measure. The proposed depth is applicable even to extremely sparsely observed functional data, overcoming key limitations of existing sparse functional depths that often rely on reconstructed curves. In addition, CRHD induces meaningful rankings for complex functional data. Its numerical performance is demonstrated through rank-based tests, and its practical utility is illustrated using an infant growth dataset.

Let $G$ be a simple graph. We demonstrate a method for using $t$-admissible subgraphs of $G$ to determine the regularity of the $t$-th symbolic power of the cover ideal of $G$. As an application, we compute the regularity of powers of cover ideals of bipartite unicyclic graphs.

This paper studies quantile regression with an endogenous regressor and measurement error in the dependent variable. Standard quantile regression estimators ignoring these two elements can induce substantial bias. We adopt a control-function approach in a triangular system and show that the conditional quantile coefficient functions, together with all other distributional parameters, are nonparametrically identifiable. Building on this constructive identification result, we propose a two-step sieve ML estimator. The first step estimates the control function. The second step performs a sieve likelihood maximization that incorporates the generated control variable through copula weights. When the number of quantile grid knots grows at an appropriate speed, the estimator is consistent and asymptotically normal, permitting inference via bootstrap. Monte Carlo simulations demonstrate that the estimator markedly reduces bias relative to existing methods, confirming its effectiveness in settings with endogeneity and additive measurement error in the outcome.

We compute the pro-étale fundamental group of a connected Nagata J-2 scheme in terms of the étale fundamental groups of the normalizations of its irreducible components and a discrete free group. The result generalizes a formula of E. Lavanda for semi-stable curves and relies on a combination of proper descent techniques for étale morphisms and a combinatorial van Kampen construction for Noohi groups. As a by-product we characterize when a continuous representation of the pro-étale fundamental group factors through a discrete quotient.

The origin of half of the rapid neutron-capture nucleosynthesis (r-process) elements in the Universe remains an open question. Binary neutron star (BNS) mergers have been shown to face difficulties in reproducing the observed r-process enrichment in Milky Way disk stars. However, their r-process enrichment efficiency may evolve with redshift beyond the star formation history, potentially due to evolution in the merger rate or the average r-process yield in the early Universe. In this paper, we explore the possibility that BNS mergers with an evolving enrichment efficiency could serve as the sole r-process production channel. By jointly comparing gravitational-wave observations from LIGO--Virgo--KAGRA, short gamma-ray bursts, Galactic neutron star populations, and stellar abundance measurements in Milky Way disk stars, we find that scenarios with additional evolution are strongly preferred over non-evolving scenarios, with Bayes factors exceeding $10^{20}$. We quantify the required evolution in both the merger rate and yield, and directly compare them with observations and theoretical predictions. We find that the evolved scenarios are in tension with short gamma-ray burst observations and predictions from multiple population synthesis models, while remaining consistent with current stochastic gravitational-wave background constraints. Our results provide a quantitative framework for evaluating whether BNS mergers with evolving enrichment efficiency can account for the observed r-process enrichment history of Milky Way disk stars.

We give a negative answer to a question of Ciliberto, Knutsen, Lesieutre, Lozovanu, Miranda, Mustopa, and Testa on effective divisors of positive self-intersection on smooth projective surfaces. The main result of this paper is obtained by generative AI, particularly Chatgpt 5.5 pro and the Rethlas system.

This paper studies the stochastic optimal control of jump-diffusion processes and the associated fully nonlinear backward stochastic Hamilton--Jacobi--Bellman (BSHJB) equations. We establish the dynamic programming principle (DPP) via backward semigroups to characterize the value function. To handle non-local integro-differential operators and polynomial growth, we introduce a stochastic viscosity solution framework based on semimartingale test functions and global tangency conditions. Existence is proved using the measurable selection theorem and the generalized Itô--Kunita formula. Finally, under a super-parabolicity condition, we establish a weak comparison principle and prove global uniqueness via localized bounding envelopes and backward induction.

Understanding the role of the environment in galaxy evolution is key to revealing the physical processes that regulate galaxy growth. We study the star formation activity of \pab\ emitters (PBEs) in the Spiderweb protocluster at $z=2.16$ using \textit{James Webb Space Telescope}/NIRCam narrow-band imaging. To investigate the environmental dependence of star formation, we derive star formation rates (SFRs) from the \pab\ emission line and compare SFRs in the Spiderweb protocluster with those in the field. Our main finding is that low-mass PBEs ($M_\star < 10^9\,M_\odot$) in the Spiderweb protocluster exhibit an enhancement in star formation compared to their field counterparts. This excess persists even without applying dust-attenuation corrections, indicating that enhanced star formation in the protocluster is robust regardless of whether a dust correction is applied. In contrast, intermediate- and high-mass PBEs ($M_\star > 10^9\,M_\odot$) show no significant deviation from the field, revealing a strong mass dependence in the environmental effects on star formation. No clear spatial concentration toward the cluster core of starbursting low-mass galaxies within the protocluster is seen, suggesting that their enhancement is not restricted to the cluster core. We suggest that starbursts in low-mass galaxies are facilitated by environmental processes such as galaxy mergers/interactions, and/or efficient gas supply. While the enhancement at the low-mass end is consistent with trends reported for other protoclusters at similar redshifts, the behaviour of star formation at intermediate masses ($10^{9} < M_\star/M_\odot < 10^{10}$) is not uniform across protoclusters. Our \pab-based results in the Spiderweb protocluster indicate that star-formation enhancement at cosmic noon depends on both mass and the dynamical state of the protocluster.

We compute the exact log-asymptotics of the persistence probability, and determine the entropic repulsion profile conditioned on persistence, for general $d$-dimensional stationary Gaussian fields with spectral singularity at the origin of order $α\in [0,d)$. Under mild regularity conditions these are shown to be universal, depending only on $α$ and $d$, and to have explicit formulations in terms of the capacity and equilibrium potential of the $α$-Riesz kernel. This generalises a result of Bolthausen, Deuschel and Zeitouni on the Gaussian free field to a wide class of Gaussian fields with spectral singularity.

Virtual double categories provide an effective framework for formal category theory. Recent work has investigated the question of higher morphisms between virtual double categories, following on from work on higher morphisms between double categories, and building up to Arkor's recent conjecture on exponentiable virtual double categories--those virtual double categories, morphisms out of which can themselves be enriched to a whole virtual double category. In this paper we resolve Arkor's conjecture by providing a number of equivalent characterizations of the exponentiable virtual double categories in terms of existence of decompositions of cells. We also show that virtual double categories of cospans are always exponentiable, as are the virtual double categories arising from pseudo double categories or from exponentiable multicategories, as studied by Pisani. We give conditions under which the virtual double category of virtual double functors admits composites, following work of Paré for the non-virtual case. We base our work on a general approach to exponentiability for categories of models of limit sketches, which we apply to give new treatments of exponentiability for semicategories, categories, multicategories, and their functors.

We answer a question of Kollár and Kovács by constructing a flat projective morphism to a smooth curve whose fibers are Cohen--Macaulay and reduced, whose generic fiber is smooth, and for which the first cohomology of the structure sheaf of the fibers is not constant. The main result of this paper is obtained by generative AI, particularly Chatgpt 5.5 pro and the Rethlas system.

Pentagonal gold bipyramids with dimensions of 75x25 nm and a longitudinal plasmon resonance (PR) at 753 nm are synthesized. For comparison, gold nanorods with a diameter of 20 nm, lengths ranging from 95 to 50 nm, and longitudinal PR from 945 to 644 nm were synthesized by chemical etching. The samples were characterized by UV-vis spectroscopy and transmission electron microscopy (TEM). It is shown that the absorption spectral quality factor of the bipyramids is significantly higher than that of the nanorods. To compare the nanoparticles as platforms for surface-enhanced Raman scattering (SERS), their surface was functionalized with thiolated nitrobenzene molecules (NBT). It is demonstrated that the SERS enhancement factor for the bipyramids is approximately three times higher than that for the nanorods. The red shift of the bipyramids' PR after functionalization with NBT molecules is also about three times greater than for nanorods with the same PR. This agrees with the theoretical estimate of the bipyramids' PR shift being more sensitive to variations in the refractive index of the external medium or the dielectric shell thickness than that of gold nanospheres and nanorods. The high efficiency of the bipyramids as thermosensitizers for converting laser radiation into heat in photothermal therapy is experimentally and theoretically demonstrated. Effective photothermal killing of E. coli was shown upon irradiation with a laser at the plasmon resonance wavelength using nanobipyramids or nanorods.

We show that there are sets of $n$ points in the plane with $n$ arbitrarily large that contain more than $n^{1.014}$ pairs of points separated by a distance exactly $1$. This improves on very recent work of a team at OpenAI, who proved the same result with an inexplicit exponent greater than $1$, drastically improving on the best previous lower bound and disproving a conjecture of Erdős. The method is number-theoretic, relying on constructing algebraic number fields of large degree and small discriminant with many primes of small norm via a Golod-Shafarevich criterion argument.

Triple junctions, line defects formed by the intersection of different grain boundaries, exist within all polycrystalline materials. While it has long been recognized that triple junctions could play an important role in microstructural evolution, there remains much uncertainty regarding their properties. Triple junctions are line defects capable of carrying dislocation content. However, no general method for calculating this content has been established. In this work, we derive the necessary equations to calculate the intrinsic dislocation content of a triple junction whose trichromatic pattern forms a coincidence site lattice. We further show that this approach can be easily applied to facet junctions, and in principle, any type of grain boundary junction for which a coincidence site lattice can be defined. We apply this formalism to atomistic simulations of tungsten to compute the Burgers vectors of a facet junction and a triple junction formed during twin grain nucleation and growth from a free surface. By tracking the evolution of the triple junction's Burgers vector and its core structure, we reveal the sequence of individual line defect reactions responsible for triple-junction-mediated twin growth.

Scalar-tensor-vector gravity, also known as modified gravity (MOG), has emerged as an alternative to General Relativity (GR). It aims to explain astrophysical phenomena without invoking dark matter. The S-stars orbiting the supermassive black hole at the Galactic centre provide a unique opportunity to test the predictions of MOG because the orbital measurements are highly precise. We investigate the perturbations in the orbits of S-stars under MOG, focusing on the effects on orbital elements, observables such as right ascension, declination, and radial velocity, and the potential degeneracy with dark matter scenarios. We numerically integrated the first post-Newtonian equations of motion for S-stars within the MOG framework, considering contributions from the space-time geometry and the fifth force. We analysed the time evolution of orbital elements and projected the orbits onto the plane of the sky to assess deviations from GR. Furthermore, we compared the MOG-induced effects with those expected from a dark matter distribution. We found that MOG significantly alters the orbital precession, particularly for higher values of the MOG parameter $α$. For sufficiently large $α$ or long observational baselines, the deviations in the observables can reach amplitudes comparable to current observational precision. Furthermore, we demonstrate that MOG effects can mimic those of a dark matter distribution, particularly in the argument of pericentre, and we reveal an unexplored connection between MOG and GR with electromagnetism. The effects of MOG on stellar orbits are distinct from those predicted by GR and can be tested with precise astrometric and spectroscopic measurements of the S-stars. However, a potential degeneracy with dark matter signatures necessitates careful interpretation of observational data.

The kagome superconductor family AV3Sb5 (A=Cs, Rb, K) provides a rich platform for exploring diverse electronic symmetry breaking phenomena, including superconductivity and various forms of density wave orders. Although these compounds share the identical lattice structure in the normal state, they exhibit distinct forms of symmetry breaking upon entering the charge density wave (CDW) phase, and the microscopic origin of which remain elusive. Here, we investigate the lattice and charge degrees of freedom in AV3Sb5 using angle-resolved polarized Raman spectroscopy. Our comprehensive polarization-resolved measurements reveal that the lifting of the twofold-degeneracy of the E2g phonon mode in the CDW phase-previously reported only in CsV3Sb5 with a 3 GHz splitting-also appears ubiquitously in the other two compounds. In contrast, the collective CDW excitations exhibit markedly different polarization dependences depending on the alkali-metal species. These distinct behaviors in the lattice and charge channels provide crucial insight into the enigmatic material-dependent symmetry breaking phenomena that appear in the CDW phase. Furthermore, our experiments, together with first-principles calculations and an effective Hamiltonian model, shed light on the nature of the charge order structure in AV3Sb5 kagome superconductors.

We study design-unbiased estimation of the finite-population total $\sum_{i=1}^N y_i$ when each outcome satisfies known bounds $y_i\in[a_i,b_i]$. For any sampling design with inclusion probabilities $π_i>0$, we prove a sharp lower bound on the worst-case squared error over the rectangular parameter space. This bound is attained if and only if the unit inclusion indicators are pairwise independent, in which case the minimax estimator is the midpoint-differenced Horvitz-Thompson estimator $\sum_{i=1}^N m_i+\sum_{i\in S}(y_i-m_i)/π_i$, with $m_i=(a_i+b_i)/{2}$. We then solve the joint design-and-estimation problem under the constraint $\sum_i π_i\le n$. We find that a minimax strategy samples units independently with probabilities $π_i^\ast=\min(1,c (b_i-a_i))$ where $c>0$ is chosen so that $\sum_i π_i^\ast=n$, and uses the midpoint-differenced estimator. This extends Gabler (1990)'s linear minimax result to the full class of design-unbiased estimators. We also show that the estimator is admissible among unbiased estimators and affine equivariant.

As Numerical Weather Prediction (NWP) models approach hectometric resolution, they increasingly enter a regime where urban heterogeneity is only partially resolved and the assumptions underlying conventional urban canopy models (UCMs) become questionable. To address this scale gap, we apply a multi-scale coarse-graining framework (van Reeuwijk and Huang 2025, Boundary-Layer Meteorology) to building-resolving Large-Eddy Simulations (LES) of the University of Bristol campus. Two related morphologies are considered: an original layout with large open-space contrasts and a modified configuration with these regions infilled. By systematically filtering the LES fields, we quantify how flow heterogeneity evolves with resolution and identify a characteristic urban length scale at which resolved and unresolved variability are comparable. This scale is strongly morphology-dependent, with values of about 256 m for the original layout and 64 m for the modified case, showing that neighbourhood-scale organisation can remain important at resolutions relevant to next-generation NWP. We then perform an a priori assessment of distributed drag and turbulent-stress parameterisations. Parameterisations derived from idealised geometries perform reasonably well only at sufficiently coarse resolutions, where horizontal transport is negligible and the flow appears approximately homogeneous. At finer resolutions, their fidelity degrades rapidly because of increasing heterogeneity and filter-to-filter variability in morphology, with stronger limitations in realistic layouts than in idealised cuboid arrays. Overall, the results show that the applicability of urban parameterisations depends critically on the relationship between model resolution and a morphology-dependent heterogeneity scale, providing a systematic route for developing scale-aware UCMs for high-resolution NWP.

In this article, we investigate the optical, thermodynamic, and scattering properties of a ModMax black hole surrounded by a cloud of strings within the framework of Einstein-bumblebee gravity. We then analyze in detail the thermodynamic properties of this black hole, including the Hawking temperature, entropy, and other relevant thermodynamic quantities, and examine the outcomes. Furthermore, we study the greybody factors (GFs) associated with the emission of various perturbative fields propagating in this black hole background. In particular, we consider spin-0 scalar fields, spin-1 electromagnetic fields, and spin-2 graviton fields, and evaluate the corresponding absorption probabilities and energy emission rates. Our analysis demonstrates how the optical features, thermodynamics and GFs depend on the underlying parameters of the system, such as the Lorentz symmetry violation parameter, the cloud of strings parameter, the ModMax parameter, the electric charge, and the black hole mass, thereby providing a comprehensive understanding of the physical effects of these parameters on the radiation and scattering processes around the black hole.

We show that every dense subgroup of a connected Lie group G contains a dense subgroup generated by 2d elements, where d=dim(G). We also give a detailed proof for the quantitive characterization of a contracting projective transformation in terms of the ratio between the two leading terms in its Cartan decomposition.

Background: Often when undertaking meta-analyses of time-to-event (TTE) outcomes, especially in a Health Technology Assessment context, a hazard ratio (HR) scale is used. However, issues arise when there is evidence of non-proportional hazards in some of the studies included. A number of methods have been advocated, but their use has been limited by either their complexity and/or the ease with which their results can be used in HTA. An alternative approach is to assume a treatment-log(time) interaction within a Cox proportional hazards model for each study, and to then undertake a bivariate meta-analysis of the resulting treatment and interaction coefficients, so that an overall time-varying HR (TVHR) can be obtained. Methods: A TVHR approach was applied to a meta-analysis of chemotherapy compared to Standard of Care for advanced recurrent gastric cancer, and in which Progression-Free Survival (PFS) was an outcome. The approach was also applied to a network meta-analysis (NMA) evaluating overall survival (OS) in advanced BRAF-mutated melanoma. Results: Five trials in the advanced gastric cancer meta-analysis displayed evidence of non-proportional hazards for PFS. Using a TVHR model produced HRs ranging from 0.83 (CrI:0.75-0.91) at 0.5 years to 0.99 (CrI:0.79-1.23) at 3.5 years. Three studies showed evidence of non-proportional hazards in the advanced BRAF-mutated melanoma NMA for OS. Using a TVHR model, nivolumab plus ipilimumab demonstrated consistent superiority from month 7 onwards, with a HR improving from 0.37 (CrI:0.26-0.51) at one year to 0.24 (CrI:0.12-0.45) at five years. Conclusions: A TVHR approach to the meta-analysis or NMA of TTE outcomes when the proportional hazards assumption appears not to hold, produces an intuitive solution which can be readily used in HTA.

The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant computational challenge. Accurately resolving the thin boundary layers of finite-size objects while tracking massive numbers of small particles within a large turbulent domain is often prohibitively expensive on uniform grids. To address this, we present a parallel scalable computational framework that couples the lattice Boltzmann method with the immersed boundary method on a dynamically adaptive octree grid. A key algorithm is developed for the efficient parallel host-cell searching, which significantly accelerates the tracking of Lagrangian points on distributed unstructured grids. The accuracy and robustness of the code are rigorously validated against canonical benchmarks, including the flow induced by an oscillating cylinder and the sedimentation of a sphere. The framework is applied to the multiscale problem of bubble-particle collisions. In quiescent flow, the simulations accurately capture the hydrodynamic interception mechanism, reproducing the theoretical collision efficiency scaling law proportional to the square of the particle-to-bubble size ratio. Furthermore, the framework is applied to the simulation of fully resolved bubbles interacting with inertial point particles in homogeneous isotropic turbulence.

Post-Newtonian (PN) theory provides the analytic foundation for modeling the early inspiral of binary black holes. However, as an asymptotic series, successive PN orders do not necessarily improve agreement with the full nonlinear dynamics. While this has been explored in the extreme-mass-ratio limit, comparable-mass systems most relevant to current observations have not been benchmarked as systematically at high PN order. We study the convergence of the PN series for non-spinning and quasi-circular systems by comparing the PN energy flux at future null infinity to a long, high-accuracy numerical relativity (NR) simulation. To enable a gauge-consistent comparison, we place both descriptions in the same BMS frame and calibrate the intrinsic PN parameters by fitting to the NR waveform in the early inspiral. We find that for orbital velocities $v\lesssim0.45$, higher PN orders continue to reduce the PN--NR flux discrepancy, with (incomplete) 6PN providing the best agreement among the orders considered. The improvement with PN order is non-monotonic with local extrema around 2.5PN and 4PN. This implies that the optimal truncation order of the PN series cannot be identified from the first local minimum in the energy flux residuals, contrary to suggestions in earlier work. As $v$ approaches $\sim 0.5$ near the innermost circular orbit, higher PN orders no longer improve the agreement between NR and PN, indicating a loss of convergence. These results motivate continued high-order PN calculations and clarify the NR accuracy needed to validate them.

In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential stability are established, highlighting the interplay between the principal eigenvalue of the governing operator, the drift coefficient, and the noise intensity. The relationship between these two notions of stability is also clarified. Applications to several stochastic partial differential equations are presented. In addition, a fully discrete spectral Galerkin method together with the implicit Euler--Maruyama scheme is shown to preserve these stability properties at the discrete level. Finally, numerical simulations are provided to confirm the theoretical results.

Classical kernel density estimation usually derives the AMISE and optimal bandwidth from a pointwise Taylor expansion, which requires twice continuous differentiability. This assumption is stronger than necessary and excludes natural densities arising from threshold models, regime changes, and robust mixture models, where the first derivative may be Lipschitz while the curvature is kinked, discontinuous, or only weakly defined. We show that the classical AMISE theory remains valid under the weaker condition $f\in C^{1,1}(\mathbb{R})$. The pointwise $C^2$ Taylor expansion is replaced by an integral Taylor representation based on the weak second derivative, so that $R(f'')$ is interpreted as a weak-curvature functional. Under $f\in C^{1,1}(\mathbb{R})$ and $f''\in L^2(\mathbb{R})$, we recover the classical AMISE formula, the $n^{-1/5}$ optimal bandwidth, and Epanechnikov kernel optimality without assuming a continuous classical second derivative. We also propose a generalized-curvature plug-in bandwidth selector, prove its first-order AMISE equivalence under ratio-consistent curvature estimation, and establish consistency of a leave-one-out U-statistic curvature estimator. A multivariate extension using weak Hessians recovers the scalar-bandwidth rate $n^{-4/(d+4)}$.

Large Language Models (LLMs) have enabled collaborative Multi-Agent (MA) systems, where interacting agents improve performance through diverse reasoning and iterative refinement. However, these systems remain vulnerable to error propagation, where early-stage information degrades downstream reasoning. To address this, we conduct a systematic analysis of inter-agent communication to identify which information drives MA performance. We find that the absence of reasoning and verification in inter-agent communication significantly degrades performance. Based on these insights, we propose Category-Aware Recovery Augmentation (technique), which enforces the presence of critical information during communication. recovers up to 86.2% of failed cases. Our results highlight the key role of information quality in effective MA collaboration. Our code is available at https://anonymous.4open.science/r/cara_mas

The Invisible Internet Project (I2P) provides strong anonymity through garlic routing and distributed network architecture, making it attractive for legitimate privacy needs. Nevertheless, the same properties can be exploited by malicious actors to steal sensitive information from corporate networks without detection. Current network security measures often fail to detect I2P traffic, and existing literature has focused primarily on protocol-level traffic identification without addressing behavioral threat assessment. This paper proposes a two-stage machine-learning model for I2P traffic analysis using the SafeSurf Darknet 2025 dataset comprising 184,548 network flows. Phase 1 achieved 99.96% accuracy in distinguishing I2P traffic from normal network traffic using a Random Forest classifier, with only 2 false positives among 32,318 normal flows. Phase 2 performed behavioral analysis on traffic identified as I2P, classifying it as either exfiltration or legitimate activity, achieving 91.11% accuracy using XGBoost. The system demonstrates that tree-based ensemble methods substantially outperform deep neural networks and support vector machines for this task. Feature importance analysis indicates that the most discriminative features are packet timing and flow duration. These findings establish that accurate I2P traffic detection and threat prioritization are achievable in operational network environments, enabling security teams to focus resources on high-risk events rather than monitoring all encrypted traffic.

We study a two-level system coupled to two quantized electromagnetic modes within the Jaynes-Cummings framework. While the single-mode model is exactly solvable due to its conserved excitation number, yielding finite-dimensional invariant subspaces, the two-mode model extension presents a fundamental challenge: although the total excitation number remains conserved, each invariant subspace is infinite-dimensional, preventing a closed-form analytical solution. Our scheme separates the dynamics into a dominant, exactly solvable semiclassical component, the atom interacting with the mean fields of both modes, and treats the remaining quantum fluctuations through a sequence of unitary transformations that preserve essential quantum features. We validate our approach through direct comparison with numerical solutions, focusing on the non-resonant regime where multiple detunings give rise to rich interference effects and multi-timescale dynamics inaccessible to standard approximations. The method accurately reproduces atomic inversion, field observables, and fidelity over relevant timescales, while remaining computationally efficient.

Background: Days Alive and at Home (DAH) over a pre-defined follow-up period is a novel post-intervention composite outcome that combines data from at least three components: (i) initial length of hospital stay, (ii) length of total readmissions or other post-discharge care and (iii) mortality. Missing values bring unique challenges to the analysis of trials with the DAH outcome as the three components may have different rates of missingness caused by distinct missing data mechanisms. Current approaches define DAH as missing if any of the components are missing, and proceed with complete cases or Multiple Imputation (MI) of the composite. Methods: Through a simulation study motivated by the NOTACS trial, we compare several methods of handling missing data, including complete case analysis, MI of the composite, and MI of the components when the primary analysis is a Mann-Whitney-Wilcoxon test. Results: MI on the component level has good properties in terms of type I error control and power. We caution against the use of MI on the composite level with Predictive Mean Matching, which can lead to type I error inflation. Conclusions: Given the complex distributional characteristics of DAH, naive approaches such as defining missingness on the composite level and directly imputing the composite with Predictive Mean Matching, can lead to type I error inflation. Imputing on the component level is recommended, suggested future work included imputation approaches that are compatible with more complex definitions of DAH, as well as recommendations for sensitivity analyses to the Missing at Random assumption.