We study three nonmonotone coupon-collector models through a stationary-entry viewpoint. In such models the all-present state is not absorbing, so completion is governed not by the disappearance of a monotone terminal cloud but by rare new entries into a target state, except in the reset-button model, where exact regeneration gives a separate reduction. We prove a finite stationary-entry theorem: a mixing estimate, a one-block clump-control estimate, and the stationary entry flux imply an exponential hitting law. For the reset-button collector, regeneration gives an exact probability-generating function in terms of the ordinary coupon-collector transform and recovers the known beta-function expectation, while also yielding rare-success exponential limits and negligible-reset Gumbel limits. For the clumsy collector with fixed loss probability $p$ and $q=1-p$, the stationary-entry flux is $p q^n$, and $p q^n T_n$ converges to $\operatorname{Exp}(1)$. Thus the fixed-loss standardized limit is exponential rather than Gumbel. For the post-loss careless collector, we compute the sharp stationary-entry flux $$ μ_n\sim (q;q)_\infty^{-1}\frac{n!}{n^n}q^{n(n+1)/2} $$ and prove $μ_nT_n\Rightarrow\operatorname{Exp}(1)$, with matching moment asymptotics. This shows that the careless scale is governed by a stationary high tail, or ordered lucky climb, rather than by the independent one-point marginal heuristic. We also analyze a combined clumsy-careless model, confirming stability of the high-tail entry mechanism.

This paper addresses the critical sensitivity issue of narrow-beam communication systems to physical misalignments and exploits the potential of Integrated Sensing and Communications (ISAC) technology to propose a sensor-free antenna tilt failure detection and estimation framework. The proposed methods utilize environmental static clutter as geometric anchors to monitor systematic gain shifts in clutter heat maps. The proposed methods are introduced for precise antenna tilt detection and estimation using the standard 5G NR frame structure and two different waveforms. Numerical results show the potential of the proposed framework to enable autonomous, self healing network maintenance without the need for external sensors.

The high penetration of voltage source converters in modern smart microgrids enhances operational flexibility while introducing complex cyber-physical vulnerabilities. Existing cyber-attack studies either require detailed knowledge of system topology and controller dynamics or depend on repeated online interactions, which may compromise practicality by generating operationally infeasible or limit-violating commands. This article investigates a dispatch command manipulation attack and develops an admittance-guided framework to identify the vulnerable inverter and the worst-case dispatch command that most severely degrades system stability. A compromised inverter is utilized to inject controlled harmonic perturbations for sparse admittance measurement, and a physics-informed neural network is then employed to reconstruct the operating-point-dependent admittance of target inverters over the feasible dispatch region. Based on the reconstructed admittance, a stability-margin-oriented optimization is formulated to locate the most vulnerable inverter and the corresponding worst-case dispatch command. Controller hardware-in-the-loop experiments on a five-inverter microgrid demonstrate that the identified command can drive the system into severe sub-synchronous oscillations while remaining within nominal dispatch bounds, highlighting the need for stability-aware command screening beyond static limit checking.

In this paper, we introduce the Laplacian and the signless Laplacian for the eccentricity matrix of a connected graph, referred to as the eccentricity Laplacian and the eccentricity signless Laplacian, respectively. We establish the equivalence among the eccentricity Laplacian, eccentricity signless Laplacian, and eccentricity spectrum for different classes of graphs. We provide spectral characterization of $\mathcal{E}$-bipartite graphs by the symmetry of $\mathcal{E}$-spectrum and the similarity of these Laplacian matrices.

Smooth maps $u\colon\mathbb B^3\to\mathbb S^2$ can be lifted to $\hat u\colon\mathbb B^3\to\mathbb S^3$ using the Hopf fibration $h\colon \mathbb S^3\to\mathbb S^2$ via the factorization $u=h\circ\hat u$. In this note we characterize the $W^{1,2}$-maps which have this lifting property in terms of exactness of the pullback form $u^*ω_{\mathbb S^2}$, and deduce a smooth approximation property preserving the constraint $u^*ω_{\mathbb S^2}=dη$.

Chiral crystals exhibit enantiomer-dependent transport phenomena that generate pure spin or orbital currents, while the handedness sensitivity of spin and orbital Hall conductivities (SHC/OHC) remains insufficiently understood. Using first-principles calculations, we demonstrate that trigonal selenium and tellurium -- prototypical chiral semiconductors -- exhibit opposite signs of the SHC/OHC tensor elements $σ_{yx}^{S_y}$ and $σ_{yx}^{L_y}$ between their left- and right-handed enantiomers. This behavior originates from the mirror operation relating the two structures, described by space groups $P3_221$ (left-handed) and $P3_121$ (right-handed). Although both enantiomers share identical band structures and four nonzero SHC/OHC tensor components, $σ_{yx}^{S_y}$ and $σ_{yx}^{L_y}$ reverse sign due to the antisymmetric transformation of the spin/orbital Berry curvature under the $M_{xy}$ mirror operation. More generally, for mirror-related enantiomorphic structures, selected SHC/OHC tensor components can exhibit symmetry-governed sign reversal. For trigonal Se and Te, the calculated signs of these components can be directly correlated with the left- and right-handed structures under the chosen coordinate convention. These results clarify the symmetry origin of handedness-dependent SHC/OHC and suggest a possible route for correlating measurable SHC/OHC signals with structural handedness in specific chiral materials.

The rigorous simulation of stratified turbulence remains challenging due to pronounced flow anisotropy, suppressed vertical transport, and high sensitivity to numerical dissipation. This study systematically evaluates the predictive capability of the lattice Boltzmann method (LBM) for a three-dimensional stratified Taylor--Green vortex. Within a double-distribution-function framework under the Boussinesq approximation, we examine the influence of stencil configurations, forcing formulations, and spatial resolutions up to $256^3$, with validation against spectral DNS benchmarks. The results demonstrate that the D3Q27$\times$19 configuration achieves an optimal balance between numerical accuracy and computational efficiency, accurately reproducing the temporal evolution of kinetic and potential energies as well as the characteristic double-peak dissipation structure. Grid-sensitivity analysis further reveals that potential energy and fine-scale turbulent structures are significantly more resolution-dependent than kinetic energy, requiring a minimum resolution of $256^3$ for quantitative convergence. Moreover, under strongly stratified conditions, the velocity-shift forcing schemes outperform discrete source-term approaches, reducing the overall error by approximately 45.54\%. Overall, this work provides practical guidelines for high-fidelity LBM simulations of stratified turbulence and highlights that the coordinated selection of stencil isotropy, spatial resolution, and force discretization is essential for accurately capturing energy cascade and mixing dynamics.

While Retrieval-Augmented Generation (RAG) is increasingly adopted to ground Large Language Models (LLMs) in software artifacts, the optimal configuration of its components remains an open question for software engineering (SE) tasks. The lack of systematic guidance forces practitioners into costly, ad-hoc experimentation. This paper presents a comprehensive, component-wise empirical study that dissects the RAG pipeline, evaluating over 21 distinct models and methods. Our study systematically isolates and evaluates 4 query processing techniques, 7 retrieval models spanning sparse, dense, and hybrid paradigms, 4 context refinement methods, and 6 distinct generators. We test these components on a suite of 3 core SE tasks: code generation, summarization, and repair. Our empirical findings reveal a crucial insight: the retriever-side components, particularly the choice of the retrieval algorithm, often exert a more significant influence on final system performance than the selection of the generator model. Strikingly, the classic lexical retriever BM25 demonstrates exceptionally robust performance across diverse tasks. Our analysis provides a practical, data-driven roadmap for researchers and practitioners, offering clear guidance on prioritizing optimization efforts when constructing effective RAG systems for software engineering contexts.

We study a geometric hitting-set problem in which the input consists of a set $P$ of weighted points and a family $S=H\cup V$ of axis-parallel segments in the plane. The goal is to select a minimum-weight subset of $P$ that hits every segment in $S$. Even restricted geometric hitting-set problems are known to be computationally hard, and for axis-parallel segments the standard decomposition into horizontal and vertical sub-instances yields only a simple factor-$2$ approximation. We present an LP-rounding algorithm that breaks the factor-2 barrier. For the weighted problem, we obtain a randomized $(1+2/e)$-approximation by combining systematic rounding on horizontal lines with an exact repair step on residual vertical sub-instances. In the unweighted case, a sharper analysis gives a $(1+1/(e-1))$-approximation. Finally, we consider the case where one of the sub-instances consists of lines instead of line segments, a problem considered by Fekete et al. (Geometric Hitting Set for Segments of Few Orientations, Theor. Comp. Sys., 62 (2) 2018),. In this case, we improve their result to obtain an approximation factor of $1+1/e$ and show that the problem is APX-hard. We also present algorithms for the generalization to $d$ orientations, as well as PTASes for bounded-complexity subclasses of the unweighted Hitting Set problem.

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality: heterogeneous-agent economies, overlapping-generations models with aggregate risk, continuous-time models with occasionally binding constraints, climate-economy models, and macro-finance environments with many assets and frictions generate state and parameter spaces that strain classical tensor-product grid methods. The exposition is organized around four complementary methodologies. Deep Equilibrium Nets embed discrete-time equilibrium conditions into neural-network loss functions. Physics-Informed Neural Networks approximate continuous-time Hamilton--Jacobi--Bellman, Kolmogorov forward, and related partial differential equations. Deep surrogate models provide fast, differentiable approximations to expensive structural models, while Gaussian processes add a probabilistic layer that quantifies approximation uncertainty; together they support estimation, sensitivity analysis, and constrained policy design. Gaussian-process-based dynamic programming, combined with active learning and dimension reduction, extends value-function iteration to very large continuous state spaces. Applications span representative-agent and international real business cycle models, overlapping-generations and heterogeneous-agent economies, continuous-time macro-finance, structural estimation by simulated method of moments, and climate economics under uncertainty. Companion notebooks in TensorFlow and PyTorch invite hands-on experimentation. These notes are a deliberately subjective and inevitably incomplete snapshot of a rapidly evolving field, aimed at equipping PhD students and researchers to engage with this frontier hands-on.

Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where temporal dependence alters the stochastic behavior of sample covariance estimators. This paper studies sparse covariance matrix estimation for high-dimensional time series under weak dependence. We propose a thresholding procedure that incorporates long-run variance into the construction of entry-specific thresholds, thereby adapting to temporal dependence. Under suitable regularity conditions, we show that the proposed estimator is consistent under the spectral norm and attains the optimal convergence rate over a class of sparse covariance matrices. We further establish support recovery consistency for identifying the nonzero entries of the covariance matrix. In addition, we show that universal and adaptive thresholding methods developed for independent data may fail to recover the support consistently in the presence of autocorrelation. Simulation studies demonstrate that the proposed method compares favorably with existing thresholding estimators in terms of both estimation accuracy and support recovery. Applications to gene expression data and stock return data further illustrate its practical usefulness.

We introduce a geometric framework for constructing superintegrable systems from Poisson centralizers (commutants) in the Lie-Poisson algebra $S(\mathfrak{g})$ of a complex semisimple Lie algebra. Starting from a chain of reductive subgroups, we study the corresponding invariant Poisson subalgebras and their Poisson centers, and formulate superintegrability in terms of a \emph{Poisson projection chain} of affine Poisson varieties. For a maximal torus $T\subset G$, we prove that the inclusions $S(\mathfrak{g})^G\subset S(\mathfrak{g})^T\subset S(\mathfrak{g})$ determine a superintegrable chain and identify the associated quotient maps $\mathfrak{g}\xrightarrow{χ_T}\mathfrak{g}//T\xrightarrowρ\mathfrak{g}//G$. The rank (transcendence degree) computations yield the expected dimension split between commuting Hamiltonians and first integrals, and we describe the corresponding symplectic leaves in the intermediate space. Several examples illustrate how the centralizer generators organize into explicit superintegrable Poisson chains.

We study a model in which shocks propagate along a path chosen by agents embedded in a network. When a shock hits an agent, the affected agent cancels one of her outgoing edges. This cancellation cascades sequentially along a chosen path until reaching a terminal agent, resulting in a systemic cost equal to the sum of individual cancellation losses. A liability rule determines agent payments for realized losses, and we seek to implement efficient path selection in the induced sequential-move game. Our main axiomatic result characterizes a family of rules, which set each agent's liability to be proportional to the system's total realized losses with agent weights depending only on the network structure. We propose a way to set such weights based on a simple path-based procedure that assigns equal importance to all non-sink agents along each path and then aggregates these contributions across paths. These weights coincide with the Shapley value of an associated "path-counting" cooperative game and can be computed in polynomial time. A simulation study illustrates the mechanics of our approach.

Mode-pairing quantum key distribution (MP-QKD) protocol achieves performance beyond the repeaterless rate-transmittance bound and exhibits excellent practicality by avoiding the requirement for difficult global phase locking. However, the source side of MP-QKD still relies on the assumption of continuous phase randomization, an experimentally infeasible requirement in practice. Therefore, the practical security of the protocol cannot be fully guaranteed. In this work, we propose a discrete-phase-randomized mode-pairing quantum key distribution (DPR-MP-QKD) protocol and analyze the basis-dependence of the source side. Then, we introduce a concrete discrete version of the decoy state method that ensures the security of the DPR-MP-QKD protocol. Finally, simulation results indicate that as the number of discrete phases increases, the key rate performance of DPR-MP-QKD progressively approaches that of the continuous case, with convergence achieved at approximately 14 discrete phases. Moreover, our approach drastically lowers the demand for randomness. While conventional continuous phase randomization demands an unlimited supply of random bits, we show that merely a few bits (e.g., 4) are adequate.

We propose Walsh-Hadamard Transform Division Multiplexing (WHTDM), a multicarrier waveform that replaces the conventional IFFT/FFT pair in OFDM with a real-valued, unitary Walsh-Hadamard transform (WHT). WHTDM inherits the CP-OFDM transceiver structure while eliminating all complex multiplications from the transform stage, yielding a transmitter with zero real multipliers in the core modulation block. For detection under doubly-selective channels, we adopt a cross-domain memory approximate message passing (CD-MAMP) equalizer that operates on the banded structure of the equivalent WHT-domain channel matrix. Simulation results under the 3GPP TDL-C channel model at 28 GHz demonstrate that WHTDM with CD-MAMP significantly outperforms conventional OFDM 1-tap MMSE at high mobility, achieving over an order of magnitude lower BER at 120 km/h. Among the compared CD-MAMP-equalized new waveforms, WHTDM achieves the best BER performance while maintaining a transmitter complexity 2.5 $\times$ lower than OFDM and completely eliminating complex multipliers from the transform stage, making it well-suited for low-power IoT terminals.

Digital backpropagation (DBP) is one of the most effective techniques for compensating nonlinear distortions in coherent optical fiber communication systems. However, its practical application to wideband transmission remains limited by high computational complexity caused by large channel memory and the requirement for fine spatial discretization. In this work, we propose a subband-based learned digital backpropagation (SbL-DBP) framework for wideband optical transmission systems. The received signal is decomposed into multiple subbands, enabling independent frequency-domain compensation of the chromatic dispersion with reduced effective channel memory and lower computational complexity. Nonlinear intra- and inter-subband interactions are addressed in the time domain using a trainable multi-input multi-output filtering structure. The parameters of the proposed framework are jointly optimized using end-to-end gradient-based learning. In addition, sparsification techniques are employed to remove insignificant coefficients and further reduce computational complexity. Numerical simulations of an 11$\times$40~Gbaud WDM RRC-16QAM 20$\times$100 km transmission system demonstrate that the proposed method provides a superior performance--complexity trade-off compared to conventional DBP and enhanced DBP. In the low- and medium-complexity regimes, SbL-DBP provides higher signal-to-noise ratio gains while requiring fewer propagation steps.

Motivated by recent work on consistent fluid couplings in $f(R, T)$ gravity, we study cosmology in the nontrivial model $f(R, T) = R + σR T$ using the Brown variational principle for a barotropic perfect fluid. For a flat FLRW universe, we cast the field equations into Einstein-like form and obtain explicit expressions for the effective energy density, pressure and equation of state (EOS) parameter. This allows us to rewrite the null, weak, strong and dominant energy conditions as simple polynomial inequalities. We show that radiation reproduces standard relativistic cosmology, whereas for dust and $σ>0$ the effective fluid acquires negative pressure and can drive accelerated expansion. In this dust case, there exists a finite window in the Hubble parameter during which the strong energy condition is violated, but the null, weak, and dominant energy conditions remain satisfied. Conversely, whenever the strong energy condition is imposed, the other conditions are automatically fulfilled. The additional viability requirement $1 + σT > 0$ further restricts the allowed Hubble range and yields an upper bound on $σ$ that still leaves a non-empty accelerating regime. Our analysis provides a transparent energy-condition study of a consistent $R\, T$ coupling in $f(R, T)$ cosmology, based on qualitative techniques.

We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the π-calculus as formulas. We provide correctness criterion, sequentialization procedure, and a proof translation algorithm. We show that proof nets provide a canonical representation of sequent calculus derivations modulo rule permutations.

Rydberg atomic quantum receivers have been seen as novel radio frequency measurements and the high sensitivity to a large range of frequencies makes it attractive for communications reception. However, their performance can be significantly degraded by hardware-induced noise, particularly the noise from laser, which impacts the overall system noise floor and exhibits correlation. To address this challenge, this paper proposes a weight hybrid (WH) architecture for Rydberg-atomic sensors, a novel four-channel combining scheme designed for atomic sensors operating in correlated noise environments. By jointly processing dual signal channels and dual noise reference channels, the WH architecture effectively mitigates noise contributions from lasers and other hardware components. All channels are optimally combined via maximum likelihood estimation within an expectation maximization framework, enabling robust signal extraction under correlated noise. Moreover, the proposed WH architecture is universal and can be readily extended to other types of Rydberg receivers to achieve consistent performance improvements.

The standard Hamiltonian of a coupled electron-phonon system is based on second-order perturbation theory. The EPI contribution in the standard Hamiltonian consists of two terms, the EPI contribution to the band-structure energy and the partial-Fan-Migdal (FM)-occupied contribution. Within the non-adiabatic approximation, we derive a new expression for the partial-FM-occ contribution and show that it has the structure of a higher-order term, and not a second-order term. Along similar lines, we derive new expressions for the computation of the partial-FM-occ term. The new expressions for the partial-FM-occ term must be preferred over the standard expressions, in theoretical and computational studies, because they incorporate the complete physics underlying this term. Unlike the EPI contribution to individual eigenstates, the EPI contribution to the total energy must be computed in the non-adiabatic approximation for all materials, Infra-red (IR) active and IR-inactive. We report the computation of the standard Hamiltonian, for the first time, for Carbon polymorphs (diamond and hexagonal lonsdaleite) by including the EPI contribution to the total energy. This is the most accurate ab initio total energy reported till date. The present work also opens the way to compute the ab initio free-energy more accurately at finite temperatures by including the EPI contribution.

High-pressure research is a productive route to new structures and emergent properties. However, crucial high-pressure structural information remains highly fragmented across individual publications and heterogeneous computational repositories. This fragmentation creates a major bottleneck for data-driven materials design. To bridge this gap, we introduce the High-Pressure Crystal Structure Database (HPCSD), a traceable, pressure-resolved repository that integrates experimental and theoretical high-pressure structures. HPCSD is constructed from two complementary data streams: elemental high-pressure phases and a searchable configuration space of stable and metastable phases generated via CALYPSO crystal structure prediction. To ensure rigorous comparability, all retained structures underwent re-optimization under a unified density functional theory (DFT) framework , with continuous enthalpy curves systematically generated specifically for the elemental phases across their stability fields. The initial release encompasses 77,346 consistently evaluated structural entries spanning 89 elements. An analysis reveals that pressure-induced polymorphism is ubiquitous and exhibits pronounced family-dependent trends. Structural diversity is strongly influenced by an element's electronic adaptability , with the greatest structural complexity emerging at intermediate rather than highest pressures. By providing standardized, reusable, and rigorously evaluated high-pressure structural data, HPCSD establishes a robust infrastructure to accelerate experimental phase identification, facilitate cross-study thermodynamic comparisons, and support the development of machine-learning interatomic potentials and generative models for high-pressure systems.

We prove the analog of the Morel-Voevodsky localization theorem over complex analytic stacks, which is used in arXiv:2511.09371 to establish a 6-functor formalism of complex analytic motivic homotopy theory and produce an analytification map that is compatible with the six operations. Along the way, we establish general techniques for proving this theorem over other geometric settings, which also apply, for example, to the settings of algebraic stacks and differentiable stacks.

Strong hyperbolicity is a coarse notion of negative curvature, stronger than Gromov hyperbolicity, that includes all CAT(-k) metrics for k positive and allows the use of dynamical techniques available in negative curvature, such as thermodynamical formalism. We prove that the subset of geodesic currents whose dual pseudometric is strongly hyperbolic is dense in the space of geodesic currents. The proof combines an elementary finite-cover argument with a characterization of strong hyperbolicity in terms of boundary data for pseudometrics dual to geodesic currents. In contrast, we show that currents arising from non-positively curved metrics on the surface are not dense. As a consequence, we construct infinitely many pairwise non-roughly-isometric invariant strongly hyperbolic geodesic metrics on the universal cover of the surface which are not CAT(0). Finally, we establish correlation counting results for the associated length spectra.

Solid-state Spatial Light Modulators (SLMs) are fundamentally limited in their ability to achieve high spatial complexity and high temporal bandwidth simultaneously. High-speed, low-energy modulation requires sub-wavelength active mode volumes, and sophisticated spatial wavefront engineering necessitates an ultra-fine pixel pitch. While small pixels can simultaneously solve both, in conventional architectures, the dense 2D electrical routing required for such pixels creates an insurmountable physical bottleneck. This results in a compromise between the SLM refresh rate, number of pixels and the field of view. Here, we demonstrate a hybrid architecture that overcomes this limit by spatially decoupling the electrical modulation plane from the optical output plane. By integrating a metasurface doublet with a photonic integrated circuit (PIC)-based optical phased array (OPA), we achieve independent 2D electrical control over each phase-element while simultaneously realizing a three-fold reduction in effective pixel pitch. This decoupling allows us to maintain the small active volume required for high-speed operation, while circumventing the routing constraints of dense spatial array of emitters. We utilize this platform to demonstrate tunable varifocal lensing, 2D beam steering, and 2D holography. Our work provides a scalable foundation for next-generation solid-state SLMs that simultaneously offer high speed, low power consumption, and large field of view.

This paper presents a novel method for measuring the Poynting vector characteristics of monochromatic electromagnetic waves. We outline a specific design for such a meter and provide experimental data to validate the approach. For testing purposes, we utilized vortex beams with both linear and circular polarization.

Relational data stored in RDBMS is foundational to many real-world applications across domains such as e-commerce, finance, and sociality. While deep neural networks (DNNs) have achieved strong performance on tabular data with a single table, extending these models to relational databases is challenging due to the normalized multi-table structure and complex inter-table relationships. Existing approaches often rely strictly on schema-defined graphs, which overlook implicit semantic signals embedded in tuple attributes and suffer from rigid connectivity. In this work, we propose Retrieval-Augmented Modeling (RAM), a novel framework that combines graph structure with attribute semantics for relational data analytics. RAM treats tuple attributes as tokens and uses random walks to construct contextual documents, enabling the use of information retrieval techniques to estimate semantic relevance between tuples. Building on these documents, we introduce two retrieval-based augmentations: ATRA, which leverages intra-table relevance for contrastive learning, and ETRA, which links semantically related tuples across tables to enhance graph connectivity. Then, we propose a layer-wise model architecture tailored for relational data, which involves attribute embedding, feature integration, and graph aggregation layers to enable expressive and flexible representation learning. Extensive experiments on five real-world relational databases demonstrate that RAM consistently outperforms existing baselines in diverse prediction tasks, establishing a state-of-the-art for relational data analytics.

Change-point detection in dynamic networks has received much attention due to its broad applications in social networks and biological systems. Kernel-based methods have shown strong potential for this problem. However, their performance can depend sensitively on the choice of kernel, and selecting an appropriate kernel is challenging when the underlying change pattern is unknown. Motivated by this challenge, we propose KAP-CPD, a new kernel-based testing framework for change-point detection in dynamic networks. KAP-CPD aggregates information from multiple kernels, allowing it to adapt to diverse change patterns. The proposed method does not assume specific underlying network distribution, and achieves strong empirical power across a wide range of network change scenarios. To improve scalability, we further develop a fast analytic testing procedure, KAPf-CPD, that substantially reduces computation time for long network sequences compared with permutation-based alternatives and current state-of-the-art methods. We evaluate our proposed framework through extensive simulations and real-world data on email communication networks and brain functional connectivity networks.

Autonomous agents powered by Large Language Models (LLMs) acquire external functionalities through third-party skills available in open marketplaces. Adopting these integrations broadens the potential attack surface, prompting a need for systematic security evaluation. Current auditing mechanisms are effective at identifying explicit code payloads and predefined threat contents through security scanning. These detection mechanisms are bypassed if malicious behaviors lack direct injection and are instead synthesized dynamically at runtime through the agent's inherent generative capabilities. Exploring this blind spot, we introduce Semantic Compliance Hijacking (SCH), a payload-less supply chain attack targeting autonomous coding environments. The SCH approach translates malicious goals into unstructured natural language instructions formatted as necessary compliance rules, leading the agent to generate and execute unauthorized code. To assess the real-world viability of this attack, we developed an automated pipeline to evaluate its effectiveness across a test matrix comprising three mainstream agent frameworks and three distinct foundation models using contextualized scenarios. The findings demonstrate the pervasive nature of this threat, with SCH achieving peak success rates of up to 77.67% for confidentiality breaches and 67.33% for Remote Code Execution (RCE) under the most vulnerable configurations. Furthermore, the introduction of Multi-Skill Automated Optimization (MS-AO) further boosted attack efficacy. By omitting recognizable Abstract Syntax Tree (AST) signatures and explicit harmful intents, the manipulated skill files maintained a 0.00% detection rate, evading current scanning tools. This research highlights an underexplored attack surface within agent supply chains, pointing to a necessary transition from signature-based detection models toward semantic intent validation.

We study finite-element and deep feedforward neural network (DNN for short) expressivity rate bounds for solution sets of a model linear, second order singularly perturbed, elliptic two-point boundary value problem, in Sobolev norms on a bounded interval $(-1,1)$, with explicit dependence on the singular perturbation parameter $\e\in (0,1]$. Emphasis is on low Sobolev regularity of the data, i.e., source term $f$ and reaction coefficient $b$. A proof of $\e$-explicit solution regularity based on exponentially weighted energy-norm bounds is developed, and \emph{$\e$-robust, algebraic expression rate bounds} in Sobolev norms for $\mathbb{P}_1$ Finite-Elements on exponential and Shishkin type meshes is proved. Expression rates for shallow (fixed depth) $\ReLU$-NNs are shown which are robust w.r. to $\e$ and explicit in terms of the NN size. Robust NN expression rate bounds are further studied for deep feedforward DNNs with ReLU and tanh-activations. As in \cite{OSX24_1085}, tanh- and sigmoid-activated sub-NNs allow to include exponential boundary layer functions exactly into the NN feature space, leading to reduced NN sizes. Recent bitstring encoding techniques for deep NNs with ReLU activations afford, still under low data regularity $f,b \in H^1(I)$ \emph{twice the (robust) convergence rate of $\mathbb{P}_1$ Finite-Elements} achievable with ``eXp'' or Shishkin meshes.

Let $\mathcal{L}_k = -Δ_k + V$ be a Schrödinger operator associated with the Dunkl Laplacian $Δ_k$, where $V$ is the non-negative potential function belonging to the reverse Hölder class $RH_k^q(\mathbb{R}^n)$ with $q> \max\{1, \frac{n+2γ}{2}\}$. Here, $2γ$ denotes the degree of homogeneity of the weight function $w_k$, which is determined by the normalized root system and the non-negative multiplicity function $k$. In this paper, we investigate the dual space of the Hardy space $H_{\Tilde{\mathcal{L}}_k}^1$ associated with the Dunkl-Schrödinger operator. The dual space $BMO(\mathcal{L}_k)$ is a subspace of the $BMO_k$ space, which is the Dunkl analogue of the classical $BMO(\mathcal{L})$ space. We provide a characterization for the $BMO(\mathcal{L}_k)$ space. The duality result is obtained via the atomic decomposition of $H_{\Tilde{\mathcal{L}}_k}^1$, where the cancellation condition of atoms depends on the critical radius function associated with the potential $V$. Finally, we establish the boundedness of the uncentered maximal function on the space $BMO(\mathcal{L}_k)$.