Let $E$ be a flat Lorentzian space of signature $(2,1)$. A Margulis space-time is a noncompact complete flat Lorentzian $3$-manifold $E/Γ$, where the holonomy group $Γ$ is a free group of rank $g\geq 2$ acting freely and properly discontinuously by isometries. We consider the case where $Γ$ contains a parabolic element. We show that sufficiently small deformations of $Γ$ still act properly discontinuously on $E$ provided their linear parts are Fuchsian; moreover, the number of conjugacy classes of parabolic elements may increase or decrease under deformation. Our proof combines our previous compactification of $E/Γ$ relative to parabolic holonomy elements with a partial generalization of the work of Carrière. However, this result depends only on the parts on parabolic actions of our earlier work. We believe that the shortness of the proof of this openness result is of independent interest.

Opinionated chatbots are increasingly present on online platforms and have the potential to shape public discourse by influencing individuals' viewpoints before they engage in discussions. Despite their growing presence, the impact of interacting with opinionated chatbots on subsequent online interactions remains largely unexplored. This study investigated how exposure to different types of opinionated chatbots, specifically those expressing opposing, reinforcing, or balanced viewpoints, affected participants' subsequent online discussions. In a controlled experiment with 83 participants, we found that interacting with an opinionated chatbot that consistently opposed participants' arguments led to greater shifts in opinion, indicating enhanced openness to revising one's initial stance. Conversely, participants who interacted with a chatbot that consistently reinforced their views were more likely to adopt more agreeable communication styles in subsequent conversations with others. Furthermore, interactions with different types of opinionated chatbots resulted in varying levels of trust, as well as different perceptions of chatbots and human interlocutors. Our findings indicate that opinionated chatbots can influence both individuals' opinions on social topics and their communication behaviors in online environments. This presents a trade-off for future designers seeking to facilitate cognitive flexibility in changing opinions while maintaining positive user experiences and trust in the chatbots during public discourse. We discuss the implications for designing opinionated chatbots to promote more constructive and less polarized online

Every public LLM cost calculator we surveyed treats GPU utilization as a fixed input -- entered by the user, baked in as a preset, or silently assumed at 100% -- never measured against the operator's actual load. We show that this assumption is the dominant source of error: on identical H100 hardware, effective cost spans \$0.21 to \$15.25 per million output tokens, an underutilization penalty of 2.5-24x across low-to-moderate enterprise loads (1-10 rps) and up to 36.3x near idle -- driven by one operator-controlled variable, offered request rate lambda, which sets in-flight concurrency via Little's Law and which no open-source calculator exposes. Because calculators take utilization as a user-supplied input, any utilization-naive estimate understates true cost by exactly 1/U, systematically mispricing self-hosting -- most severely over-selling it for low-traffic workloads. We propose a measurement methodology that parameterizes the relationship as C_eff = f(H, M, Q, lambda, L), validate it with 42 benchmarks across dense, ultra-sparse MoE, and sparse MoE models, and release vllm-cost-meter, an open-source cost meter that attaches to a live vLLM server and reports real \$/M-tokens against the operator's own traffic. We further show that FP8 quantization benefits the MoE architectures we tested roughly 2.2-2.4x more than the dense model (+69 to +74% vs. +31% peak throughput; n=3, broader validation needed), and our data are consistent with active parameter count, not total model size, being a primary predictor of saturation economics. To rule out single-hardware confounding we repeat the core sweep on A100 80GB PCIe (56 runs): the load-driven spread reproduces at 7.0-11.4x, the active-parameters ordering survives at FP8, and the dense-FP8 advantage inverts on silicon without native FP8 tensor cores -- a hardware-conditional caveat the framework already accommodates.

Resolving the instantaneous, position-dependent isotropic magnetic exchange coupling $J_{ij}$ across a dynamically deforming crystal lattice requires a computational approach that simultaneously handles structural forces and magnetic interactions at length scales inaccessible to first-principles methods. Here we introduce DSpinGNN, a bifurcated machine-learning architecture comprising an $E(3)$-equivariant graph neural network (E-GNN) for classical Langevin structural dynamics and a physics-informed $Δ$-MLP that maps instantaneous local Cr-I-Cr bond geometry to isotropic exchange couplings, with the Goodenough-Kanamori superexchange relationship embedded as an analytical inductive bias. Trained on 345 DFT+U configurations of monolayer CrI$_3$ and evaluated on a strictly withheld 61-configuration test set, DSpinGNN simultaneously achieves an energy MAE of $1.1$ meV/atom, a force MAE of $6.5$ meV/Å, and an exchange coupling MAE of $0.18$ meV ($R^2 = 0.91$). Deployed at 400$\times$ scale in a 3,200-atom supercell under a collinear Ising-constrained adiabatic approximation at $5$ K, the model maps the local exchange response to a propagating biaxial strain wave. Wave reflection at periodic boundaries generates transient constructive interference regions where local compressive strain exceeds the DFT-established FM-to-AFM threshold, producing spatially heterogeneous exchange coupling textures that damp as the wave dissipates. Quantitative analysis yields a domain wall width of $ξ= 1.7 \pm 0.3$~nm and a constructive-interference oscillation period of $τ= 0.27$~ps -- mesoscopic observables inaccessible to direct DFT and constituting testable predictions for cryogenic magnetic force microscopy. DSpinGNN provides a reproducible, transferable framework for mesoscale exchange mapping in strain-driven 2D magnetic materials.

Let $A$ be a finite-dimensional basic algebra over an algebraically closed field $K$, $T$ a finitely generated $τ$-tilting right $A$-module and $B={\rm End}_A T$. Denote by ${\rm Fac}T$ the subcategory of finitely generated right $A$-modules generated by $T$. We define the depth relative to $T$ and the delooping level relative to $T$ and show that the finitistic dimension of the opposite algebra of $B$ is bounded by the depth of $\textup{Fac}T$ relative to $T$ and the delooping level of $\textup{Fac}T$ relative to $T$. We give applications to the finitistic dimension conjecture. More precisely, we show that if $A$ is a minimal representation infinite algebra or an algebra of finite representation type, then the finitistic dimension of $B^{op}$ is finite.

The position operator plays a central role in condensed-matter observables such as velocity, orbital moment, and electric polarization. In solid-state physics, the evaluation of operators incorporating the position operator has not reached a consensus, as observed in the operator-level discrepancy between the local circulation of Wannier functions and the self-rotation of wave packets. Here, to achieve a consistent evaluation of such operators, we propose three rules for evaluating operators involving the position operator in the Bloch representation. The rules are devised to satisfy physical conditions: independence from the choice of unit cell, preservation of Hermitian conjugacy for the product of operators, and recovery of the correct intraband velocity. We further address the gauge dependence of the position operator and introduce a scheme termed gauge filtration, which systematically removes gauge-dependent contributions from the operators containing the position operator. This methodology ensures that the quantities obtained from the operator evaluation correspond to observable physical phenomena. By applying our framework, we reconcile the results concerning the self-rotation of the wave packet and the local circulation of the Wannier function. We expect our proposal to establish a consistent framework for evaluating operators involving the position operator.

We study Schrödinger operators with a one-center point interaction, formally defined by \begin{align*} -Δ_α=-Δ+α\,δ_0(\cdot), \end{align*} for $α\in\mathbb{R}$, and the associated heat equation \begin{align} \partial_t u=\tfrac{1}{2}Δ_α u,\quad u(0,x)=u_0(x)\in C_c^{\infty}(\mathbb{R}^3\setminus\{0\}).\label{eq:HEapp} \end{align} Here $Δ$ denotes the Laplacian (self-adjoint on $L^2(\mathbb{R}^3)$) and $δ_x$ the Dirac measure at $x$. The operator $-Δ_α$ can be realized either as a self-adjoint extension of $-Δ|_{C_0^{\infty}(\mathbb{R}^3\setminus\{0\})}$ in $L^2(\mathbb{R}^3)$, or as the norm-resolvent limit of $-Δ+λ_\varepsilon V(\cdot/\varepsilon)$ for suitable $λ_\varepsilon$ and $V:\mathbb{R}^3\to\mathbb{R}$. In this paper we construct, for each $t>0$ and $x\in\mathbb{R}^3\setminus\{0\}$, a probability law on path space and a normalizing function $G_t^α(x)$ giving the following probabilistic representation of the solution to the associated equation: \begin{align*} u(t,x)=G_t^α(x)\,\mathbb{E}\bigl[u_0\bigl(W^{t,x}(t)\bigr)\bigr], \end{align*} where $\{W^{t,x}(s):0\le s\le t\}$ is a continuous process depending on $(t,x,α)$. The result provides a Feynman--Kac type formula for the heat equation with a one-point interaction in three dimensions.

Generative AI (GenAI) tools offer increasing opportunities for augmenting human cognitive tasks. Among these tasks, information seeking is being rapidly reshaped by GenAI tools, with potentially profound implications for learning and knowledge acquisition. To investigate these implications, we conducted a between-subjects field experiment in which participants pursued informal learning by seeking information through either ChatGPT or Google Search over a span of 8 days. Using a daily diary protocol, we gathered in-situ data on their information-seeking processes. Our findings show that participants in the ChatGPT group experienced diminished agency in their information-seeking processes, as they offloaded much of the information selection to AI, and consequently experienced greater meta-cognitive load arising from this reduced sense of control. We further highlight two sources of distortion in information access when using ChatGPT: biases in ChatGPT outputs, particularly towards providing solution-oriented artifacts over principled knowledge; and systematic shifts in users' information-seeking behaviors, whereby the conversational and socially-oriented interaction paradigm of current GenAI tools may inadvertently reduce exploration of the broader knowledge space. As a result, on average, participants in the ChatGPT group had worse learning outcomes than those using Google, especially for higher-order critical learning. Our work suggests inherent tensions between offloading information seeking to AI and meaningful learning, and provides broader implications for understanding AI's risks to human cognition.

WIMP scattering from 40Ar is investigated using a self-consistent Skyrme Hartree-Fock-Bogoliubov (HFB) approach. Nuclear form factors relevant to dark matter direct detection are calculated from the resulting one-body density matrix elements and compared with shell-model predictions. Good agreement is found for the spin-independent response, while significant differences are observed for the spin-orbit response due to variations in single-particle occupancies. The effects of particle-number projection are shown to be small for 40Ar. These results demonstrate the sensitivity of certain dark matter response channels to the underlying nuclear structure model and establish a framework for extending mean-field calculations to nuclei beyond the reach of large-scale shell-model studies.

Sybil attacks create an illusion of traffic congestion by utilizing fake identities, which undermines the reliable and safe operation of vehicular ad hoc networks (VANETs). Existing detection mechanisms struggle to effectively handle Sybil attacks as they are (i) susceptible to high false positive rates (FPR) due to the overlapping trajectories of both Sybil and legitimate vehicles, (ii) not practical for real-world deployment due to manual calibrations with ground data, (iii) ineffective for sparse distribution of roadside units (RSUs) and vehicles as they depend heavily on the presence of both, and (iv) inefficient due to computational overheads. This paper addresses these shortcomings and proposes a robust framework to tackle these issues. The proposed scheme reduces the FPR by utilizing GPS location data, enabling the construction of more accurate and distinguishable trajectories. Besides, it employs DBSCAN clustering to identify Sybil vehicles, facilitating unsupervised parameter selection. GPS data eliminates the dependency on RSUs and vehicles, making this scheme effective in both sparse and dense regions. Additionally, the proposed scheme is lightweight and consistent across vehicles with heterogeneous capacities. Experimental results demonstrate that the proposed scheme reduces the FPR by approximately 68% in dense regions and 70% in sparse areas. Furthermore, it lowers the false negative rate (FNR) by 67% in the sparse region and achieves a competitive detection rate compared to the existing methods in both dense and sparse regions. Additionally, the proposed scheme decreases the detection time by almost 80% in dense regions and 43% in sparse ones.

Power leaking directly from transmitting into receiving radio-frequency chains is a key challenge in the realization of monostatic sensing applications with multi-antenna communication front-ends, to which a promising solution is digitally precoding transmitted signals for improved leakage suppression. While digital transmit precodings perform well in theory, real-world deployments typically exhibit severely degraded leakage suppression. This work investigates quantization noise as a primary factor limiting the performance of such precoding schemes. A closed-form solution predicting the impact of quantization noise on the performance of arbitrary digital joint leakage estimation and leakage suppression precodings is derived, numerically analyzed, and validated in a hardware testbed.

We consider the homogenization of three dimensional viscous incompressible non-Newtonian flows satisfying certain general $r$-structure in perforated domains. We focus on the case of `small holes' by assuming the holes under consideration are of size $\varepsilon^α$ with $α>3$, where $\varepsilon$ is the perforation parameter used to measure the mutual distance between the holes. We show the limit equations remain unchanged in the homogenization limit under the constraint $ \frac{6(α- 1)}{4α-5}< r<3-\frac{3}α$, which seems optimal in the sense of Sobolev capacity of holes as explained in Remark 1.3. Quantitative convergence rates are further derived for both the velocity field and the pressure. To the best of our knowledge, both the qualitative and quantitative homogenization results are firstly given for non-Newtonian flows in the `small holes' case.

When $S$ is a finite set of positive integers, we can consider classical Subtraction Nim with $S$ as the set of removable numbers. Even when $S$ consists of three elements, many questions remain unanswered. For example, we do not have a period formula of the Nim value. In this paper, we generalize $S$ to be a finite set of positive real numbers. We found that in some regions, we can give concrete formulae for the period and the Nim value function. In particular when $S$ consists of three elements, we found sufficient conditions for the Nim value function to be purely periodic with the period which is equal to the sum of two of elements of $S$. To be more precise, let $S = {a,b,c}$ with $0 < a < b < c$, then for example when $a \leq b \leq 2a$ with $a+b \geq c$, the Nim value function is purely periodic with a period $a+c$. There are much more regions with precise period formulae. We have also some generalizations for the cases $|S| \geq 4$. Even when $S$ consists of integers, these results seem to be new.

Vector-quantized motion tokenizers provide a compact discrete interface for text-to-motion generation, but most motion-code priors treat code indices as unordered categorical labels. This view overlooks a key property of motion codes: they are decoder-bound prototypes of physical movement, and their learned codebooks can carry meaningful local kinematic geometry. We verify this property through codebook diagnostics. Distances between learned PartVQ group-specific codes align with local motion-prototype distances, shuffled controls remove this alignment, and replacing codes with progressively farther neighbors induces monotonically larger decoded motion changes. These results show that motion codebooks exhibit measurable, non-random, and decoder-causal geometry. Based on this observation, we propose \textbf{MoGeFlow}, a text-to-motion model that generates through motion codebook geometry. MoGeFlow represents each motion-code frame as a structured set of PartVQ group-specific code embeddings, learns a text-conditioned continuous flow over these frame states, and projects terminal states back to valid motion codes for frozen decoding. This preserves the compactness and validity of discrete tokenization while replacing categorical code prediction with geometry-aware codebook-space generation. Experiments set new state of the art in R-Precision on HumanML3D and KIT-ML, achieve the best HumanML3D MultiModal Distance and KIT-ML FID among generated methods, and obtain the best MotionMillion R@1, R@2, R@3, and FID under the benchmark protocol.

The appeal of adiabatic quantum computing lies in its intrinsic robustness against various technical imperfections, making it attractive for many quantum information applications. However, it faces a fundamental challenge: accelerating the adiabatic operations while preserving adiabaticity within the qubit coherence time. In this article, we propose an electromagnetically induced transparency-based adiabatic CNOT gate protocol which harnesses atomic hyperfine intermediate states (HISs) to speed up the adiabatic evolution. The HISs, naturally-existed in two-photon transitions, often need to be suppressed due to their significant decay errors. In contrast, this paper introduces a novel method that utilizes appropriately chosen HISs not only to enhance the adiabaticity in STAY pathway but also to accelerate the population transfer in TRANSFER pathway. Through pulse optimization, we achieve adiabatic gate fidelities exceeding 0.9991 within 0.3903 μs in realistic Cs atomic setups. To demonstrate the generality of protocol we further assess the impact of decays from multiple HIS and extend our model to arbitrary number of states, providing a practical route toward fast and robust adiabatic quantum gates in Rydberg-atom platforms.

Mangroves are increasingly promoted as nature-based solutions for coastal protection, yet many existing models neglect the vertical variation of vegetation biomass, leading to oversimplified representations of root-flow interactions. In this study, we introduce a generalised parametrisation of the mangrove vegetation profile that is applicable across multiple mangrove species and derive a wave attenuation model that explicitly accounts for the mangrove root characteristics. Based on this parametrisation, we propose a simplified mangrove representation that reproduces a prescribed drag force profile and is suitable for both computational fluid dynamics simulations and experimental fabrication. The hydrodynamic performance of the proposed model is evaluated using OpenFOAM simulations. Our results show that the wave attenuation effectiveness of mangroves is frequency-selective and species dependent. This nonlinear behaviour contrasts with classical vegetation models and reveals a previously unrecognized mechanism by which mangrove root characteristics govern coastal protection.

For every fixed $t\ge 1$, we prove a parity analogue of the mighty Erdős-Hajnal property for $t$-intersecting curves in the plane. Let $\mathcal B$ be a set of blue curves and $\mathcal G$ a set of green curves in the plane such that $\mathcal B\cup\mathcal G$ is a collection of $t$-intersecting curves in general position. We show that there exist subfamilies $\mathcal B'\subseteq\mathcal B$ and $\mathcal G'\subseteq\mathcal G$ such that $|\mathcal B'|\geq \varepsilon|\mathcal B|$ and $|\mathcal G'|\geq \varepsilon|\mathcal G|$, where $\varepsilon>0$ depends only on $t$, such that either every pair in $\mathcal B'\times\mathcal G'$ intersects an even number of times or every such pair intersects an odd number of times. For $t=1$, this recovers the theorem of Fox, Pach, and Suk for pseudo-segments. As an application, we show that every $n$-vertex topological graph with edges forming a $t$-intersecting family and with no $k$ edges that pairwise cross an odd number of times has at most $n(\log n)^{O_t(\log k)}$ edges.

On a charged interface, broken inversion symmetry permits a large field-linear Pockels response through $χ^{(2)}(ω;ω,0)$; at the water/ITO interface $|r_{13}|$ has been reported to reach the $10^{2}\,\mathrm{pm/V}$ order. The coexisting third-order DC Kerr term $χ^{(3)}(ω;ω,0,0)$ -- small in bulk water ($|χ^{(3)}_{\mathrm{bulk}}|\sim5.5\times10^{-21}\,\mathrm{m^2/V^2}$) -- had not been jointly parameterized with the Pockels term along the fundamental-frequency ($ω$) electro-optic path. Superimposing an AC modulation and a DC bias in 0.1\,M NaCl mixes the $χ^{(3)}$ contribution with the 1f response through the cross-term $2 s_{1133}\,E_{\mathrm{DC}}$, so that the water refractive-index modulation $Δn_{\mathrm{water}}$ varies linearly with $V_{\mathrm{WE}}$; a model-assisted linear fit then determines both terms from a single AC$+$DC sweep. At $V_{\mathrm{WE}}=0\,\mathrm{V}$ vs Ag/AgCl, $|r_{13}|=(1.18 \pm 0.06_{\mathrm{PZC}})\times10^{2}\,\mathrm{pm/V}$ and, under $η_{\mathrm{DC}}=1$, the thickness-normalized DC Kerr coefficient $|s_{1133}/d_{\mathrm{EDL}}|=33.0 \pm 5.6\,\mathrm{pm/V^{2}}$. Across physically reasonable $d_{\mathrm{EDL}}$ ($0.6$--$1.6\,\mathrm{nm}$), the interfacial DC Kerr susceptibility reaches $|χ^{(3),\mathrm{int}}_{1133}| \approx (2\text{--}5.5)\times10^{-20}\,\mathrm{m^2/V^2}$, several-fold above the visible-range bulk-water value. This response is a property of the specific interface, tunable through the choice of electrode, electrolyte, and solvent rather than intrinsic to bulk water. Amid renewed interest in the Kerr response of water (including recent THz-band optical Kerr studies), the method directly probes this DC Kerr term along the $ω$ path and complements SHG/SFG (the $2ω$ path).

Quantum cloud platforms are poised to deliver powerful computing capabilities, but users have no direct means to verify which physical device executes their workload. This lack of transparency enables hardware substitution attacks, where a malicious adversary could redirect a job to a substituted or inferior processor. We present a general authentication framework that addresses this problem by constructing multi-dimensional quantum fingerprints from raw measurement data. Without any curve fitting, we directly concatenate the raw statistics of complementary experiments into a high-dimensional feature vector that preserves subtle device-specific information. A Mahalanobis nearest-neighbor classifier achieves 100\% benign authentication accuracy on three superconducting processors over a three-week chronological split. The classifier naturally yields an authentication confidence $C_{\mathrm{claimed}}$ which reveals device-specific safety margins and motivates per-device alert thresholds. We assess the framework's robustness under two distinct scenarios. Under additive isotropic Gaussian noise, $C_{\mathrm{claimed}}$ decays predictably at a rate explained by inverse covariance traces, enabling an early warning mechanism. Against white-box adversarial perturbations, the same confidence threshold detects $L_2$ targeted attacks with near-perfect success and reveals device-dependent empirical thresholds for $L_\infty$ attacks, while untargeted and sparse attacks are ineffective. The proposed framework thus unifies fingerprint extraction, drift-resilient authentication, proactive health monitoring, and adversarial defense, offering a practical step toward trustworthy quantum cloud computing.

If A is a symmetric algebra, then Hochschild homology of the dg enhancement of the singularity category of A agrees with singular Hochschild homology of A. For a basic finite dimensional k algebra A, the Cartan matrix of A is symmetric if and only if the k dual of the mixed complex of the dg enhancement of its singularity category is isomorphic to its shift by -1. We provide two counterexamples to show that neither result holds for general Frobenius algebras.

The rapid adoption of electric vehicles (EVs) can cause severe voltage drops and line current overloads in distribution networks, creating an urgent need for scalable expansion planning methods. This paper proposes a computationally efficient violation-informed spatio-temporal adaptive targeting (STAT) framework for EV-driven distribution system expansion planning. The framework first identifies potential voltage and current violations through a violation analysis model, and then mitigates them through a joint optimal expansion planning model that co-optimizes investment decisions for line reconductoring, shunt capacitors, and battery energy storage systems. To reduce computational burden, the proposed STAT-temporal criticality assessment (STAT-TCA) method extracts primitive stress events from annual operating data, derives an initial set of candidate planning horizons from signature-consistent segments, and selects a final transferable critical horizon set through cross-horizon validation based on optimization feasibility and cost. Meanwhile, the proposed STAT-adaptive spatial targeting (STAT-AST) method constructs device-specific spatial features for BESS and SC siting to retain compact yet high-impact candidate bus sets. Case studies on 33-bus and 240-bus distribution systems demonstrate that the proposed STAT framework can substantially reduce the temporal and spatial planning dimensions while preserving planning fidelity. Full-year validation further confirms that the resulting investment plans can eliminate EV-induced voltage and thermal violations while maintaining feasible BESS operations.

Let $λ_i(G)$ denote the $i$-th largest eigenvalue of adjacency matrix of a graph $G$. Gerschgorin's Theorem indicates $λ_1(G)$ belongs to the largest disk, i.e., $λ_1(G)\leΔ_1(G)$, where $Δ_i(G)$ is the $i$-th largest degree of $G$. We show that $λ_2(G)$ lies in the second largest disk. That is, in detail, $$λ_2(G)<Δ_2(G)-\frac{1}{n^2}.$$ A classical theorem proved by Hong [\textit{Linear Algebra Appl.} 1988] states that $λ_1(G)\le\sqrt{2m-n+1}$ for a connected graph $G$ with $n$ vertices and $m$ edges, where the equality holds if and only if $G$ is a star $S_n$ or a complete graph $K_n$. We give a refinement of Hong's theorem by showing $$λ_1(G)<\sqrt{2m-n}$$ for any connected graph $G\not\in\left\{S_n,S^1_{n-1},K_n,K^1_{n-1}\right\}$. Based on this improved upper bound of $λ_1(G)$, for a connected graph $G$ with $n$ vertices and $m$ edges, we are able to prove a sharp upper bound of $λ_2(G)$ that $$λ_2(G)\le\sqrt{m-\frac{n}{2}-\frac{1}{2}},$$ except $G$ is obtained from two disjoint $S_\frac{n}{2}$ by adding an edge between a pendant vertex of each star. Moreover, we provide a complete characterization to extremal graphs attaining the equality.

The coupling theory of quasinormal modes (QNMs) for a coupled system of generally lossy and dispersive optical nanoresonators has been established in a rigorous manner based on the first principle of Maxwell's equations [Phys. Rev. B 102, 045430 (2020)], and can achieve superior computational efficiency and physical intuitiveness compared with full-wave numerical methods if a small set of modes can achieve a high accuracy. The QNMs suffer from an exponential divergence of far field and can form a complete basis inside but not outside the resonator. In the QNM coupling theory (QCT), it is required that the QNMs of each resonator form a complete basis in expanding the scattered field both inside and outside the resonator, which can be achieved by using regularized QNMs (RQNMs). However, a strict numerical demonstration of the impact of the mode completeness of RQNMs on the accuracy of QCT by using a virtually complete basis of RQNMs is still absent. In this paper, we will provide such a numerical demonstration along with an improvement of the QCT and some theoretical demonstrations on a rigorous incorporation of RQNMs into the QCT. The RQNMs are obtained by introducing an equivalent surface current (ESC) encircling the resonator (called ESC-RQNMs) or the perfectly matched layer (PML) surrounding the computational domain (called PML-RQNMs). The numerical example is selected as two one-dimensional resonators of slabs in the extreme coupling case of direct contact, for which a virtually complete basis of RQNMs can be solved either analytically (for ESC-RQNMs) or numerically (for PML-RQNMs). The results show that by using a virtually complete basis of RQNMs, the QCT can achieve a high accuracy in predicting both the source-free eigenmodes and the source-excited scattered field of the coupled system, which is not true if using the incomplete basis of not-regularized QNMs (i.e., physical QNMs).

The beta distribution is the default choice of likelihood in many regression problems with a $[0,1]$-bounded support response despite its sensitivity to outliers, inability to accommodate exact zero observations, and a lack of closed-form conjugate priors. We address these shortcomings by introducing the triply-randomized negative binomial beta distribution, denoted $\mathrm{TNBbeta}(p,\,q,\,\varepsilon)$, parameterized by a median $p$, concentration parameter $q$, and boundary parameter $\varepsilon$ which permits positive density at $0$ and $1$. The TNBbeta arises by randomizing the parameters of a standard beta distribution with three dependent negative binomial random variables, each of whose complete conditional distribution we show is itself negative binomial. Moreover, connecting $p$ and $q$ to Gaussian latent variables with logit link functions yields closed-form updates via Pólya-gamma augmentation. Together, these properties yield simple auxiliary-variable Gibbs samplers for regression models of bounded-support data, which often outperform standard beta regression approaches in terms of effective sample size per second and held-out prediction, especially in the presence of outliers. In a case study of forest canopy cover, we demonstrate that this framework can easily incorporate spatial structure and exact zero observations. Overall, this work substantially expands the class of Bayesian models for $[0,1]$-bounded support data that can be fit efficiently.

In this paper, we demonstrate the effects on the second largest eigenvalue $λ_2(G)$ of a connected graph $G$ after edge addition or deletion. In 1989, Chung, Graham and Wilson showed $\max\{|λ_2|,|λ_n|\}>Ω(n)$ for dense $K_{r+1}$-free graphs of order $n$, giving spectral comprehension of existence of large clique or independent set, respect to Ramsey theory. Applying the results of effects on $λ_2$ after edge operations, we determine the maximum value of $λ_2$ among all $K_{r+1}$-free connected graphs with given order, and completely characterize the extremal graphs. Moreover, for arbitrary given graph $F$, we investigates the maximum second largest $λ_2(G)$ among $F$-free connected graphs of order $n$. Let $ρ^*(n,F)$ be the maximum spectral radius of $F$-free graphs on $n\ge n_F$ vertices, and $G^*(n,F)$ be a graph with its spectral radius $ρ\big(G^*(n,F)\big)=ρ^*(n,F)$. We prove that, for an $F$-free connected graph $G$ of order $n\ge f(n_F)$, \\(1) if $n$ is odd, then $$λ_2(G)\leρ^*\left(\frac{n-1}{2},F\right)$$ with equality if and only if $G\in \mathcal{I}\big(G^*(\frac{n-1}{2},F),G^*(\frac{n-1}{2},F)\big)$; and\\ (2) if $n$ is even, and $F$ does not contain cut edges, then the graph $G^†$ with the maximum second largest eigenvalue satisfies $$λ_2(G^†)=ρ^*\left(\frac{n}{2},F\right)-o(1)$$ and $G^†\in \mathcal{E}\big(H_1,H_2\big)$, where $H_1$ and $H_2$ are $F$-saturated graphs on $\frac{n}{2}$ vertices. In particular, other than a complete graph $K_{r+1}$, when $F$ is a book graph $B_{k+1}$ or an odd cycle $C_{2k+1}$, we are able to determine the maximum second largest eigenvalue for $F$-free connected graphs of given order, and completely characterize the extremal graphs.

The Frequency Range 3 (FR3) band is attracting increasing attention due to limited lower-frequency spectrum and growing mobile communication demand. This study experimentally investigates channel characteristics in Urban Macro (UMa) scenarios at 8 GHz and 15 GHz using a large-scale MIMO platform with time-division multiplexing (TDM). Key parameters, including root mean square (RMS) delay spread (DS) and angular spread (AS), were extracted and compared with 3rd Generation Partnership Project (3GPP) TR 38.901. Results reveal clear frequency-dependent behaviors: RMS delay spread remains nearly constant under line of sight (LOS) but decreases from 8 GHz to 15 GHz in non-line of sight (NLOS), indicating reduced multipath dispersion at higher frequencies. Both azimuthal spreads (including ASA and ASD) and elevation spreads (including ESA and ESD) exhibit a corresponding decrease with increasing frequency, demonstrating a consistent trend towards more directional propagation across all angular domains. Capacity analysis indicates that the 15 GHz channel slightly outperforms 8 GHz in both LOS and NLOS scenarios due to more concentrated multipath energy and larger dominant singular values. Higher frequencies exhibit greater directionality, whereas lower frequencies provide broader multipath distributions and more stable performance, offering valuable guidance for multi-band MIMO modeling and 6G system design.

The coefficients $A_n(α,β,ω)$ in the Maclaurin expansion $(1+ωz)^α(1-z)^{-β}=\sum_{n=0}^{\infty} A_n(α,β,ω)z^n$ are considered for $|ω|=1$ and $α,β\in(0,1]$. D. A. Brannan conjectured in a 1973 paper that $|A_n(α,β,ω)|\le A_n(α,β,1)$ for every positive odd integer $n$. The present author recently established the conjecture outside a small neighbourhood of $ω=-1$. The remaining range is treated here by combining compound Laplace integral representations with two types of local approximation: a Meijer $G$ function approximation for $n|\arg(-ω)|$ bounded, and a modified Watson approximation for the complementary range. The resulting lower bounds reduce the problem to numerical positivity checks for explicit functions on compact parameter sets. These computations verify the inequality for all $α,β\in(0,1]$ and all odd integers $n\ge5$, and hence, together with Brannan's result for $n=3$, complete the proof of his conjecture.

Low-Altitude Wireless Networks (LAWNs), composed of Unmanned Aerial Vehicles (UAVs) and other aerial platforms, provide integrated perception, communication, and computation services in low-altitude airspace. However, deploying large generative models in this domain faces three major challenges: 1) Limited embodied action mapping; 2) Inadequate physical environment modeling; 3) Insufficient closed-loop optimization. To address these challenges, this study proposes an Embodied Agentic UAV framework. Centered on a Vision-Language-Action (VLA) model as the execution core, the framework establishes an end-to-end embodied decision-making pipeline from multimodal environmental perception to continuous control generation. In addition, a World Model (WM) is introduced to capture the coupling between UAV actions and environmental state evolution, thereby supporting environment prediction, policy verification, and dynamic optimization. Furthermore, memory and reflection mechanisms are incorporated to form an adaptive closed-loop optimization paradigm of decision, execution, evaluation, and update, thereby enhancing the system's autonomous decision-making capability and continual evolution ability in complex dynamic environments. Experimental results validate its effectiveness in enabling robust, predictive, and sustainable autonomous control in LAWNs.

Euclidean lattice correlators determine spectral functions only through a smoothing integral transform, so a nominal uncertainty band on a reconstructed spectrum need not have a coverage interpretation for a physical summary. We formulate this as a target-wise adequacy test for reported spectral uncertainties. For a chosen summary \(T[ρ]\), the reported interval is tested on Euclidean-admissible mock correlators with known truth using empirical coverage, simulation-based calibration ranks, physical diagnostics, and stress tests. The test is conditional, but it is a useful falsification tool: passing it does not prove that a reconstruction is the QCD truth, while failing it shows that the reported uncertainty law is not adequate for the chosen functional under the stated mock extension. In a generic benchmark, peak locations are substantially better calibrated than peak heights or low-frequency weights, reflecting different degrees of functional identifiability under the Euclidean kernel. We then apply the same logic to a finite-temperature shear correlator. A family of BG-style reconstructions is compatible with the Euclidean data at \(χ^2/N_τ\simeq 1.3\). Within the scanned grid and stated observable-matched mock extension, a \(W_{\rm low}\)-calibrated representative can be identified, whereas pointwise peak-height intervals are not certified for the tested BG-style uncertainty law. Thus Euclidean compatibility is a necessary consistency check, but not a sufficient adequacy criterion for spectral uncertainty claims.

A nontopological soliton of the Q-ball type in a Chern-Simons-Higgs gauge model is studied using both analytical and numerical methods. The general non-self-dual case is considered. It is shown that the soliton solution is an extremum of the energy functional at a fixed Noether charge. A differential relation between the energy, Noether charge, and the boundary value of the gauge potential of the soliton is derived. A linear relation between the components of the soliton energy is obtained. The parametric domain of existence of the soliton solution is determined. It is established that the soliton properties depend significantly on the form of the self-interaction potential of the scalar field. In particular, the energy and charge of the soliton can take arbitrarily large values only if the self-interaction potential has two degenerate zero minima.