Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new graph parameters: stack(G): the least integer t such that every configuration with t pebbles can be transformed, by a finite sequence of pebbling steps, into a configuration with all pebbles on a single vertex. clear(G): defined analogously, but requiring that from every configuration with t pebbles, all but one pebble can be removed. We prove that stack(G) is defined exactly for connected graphs, and that clear(G) is defined exactly for connected non-bipartite graphs. We also establish general upper bounds for these parameters; in particular, stack(G), clear(G) <= 2 |V(G)| 2^diam(G), where diam(G) denotes the diameter of G. Among our exact results are the equalities stack(K_n) = clear(K_n) = n + 1, stack(K_{m,n}) = 3 max{m,n} + 1, stack(P_n) = 2^n - 1. We also establish general lower bounds in terms of the independence number and odd closed walks. For cycles, the situation is more delicate. We prove the lower bounds stack(C_{2n}) >= 2^{n+1} - 1, clear(C_{2n+1}) >= 3 * 2^n - 2, and formulate the Almost Stacked Hypothesis, motivated by Sjostrand's cover pebbling theorem. Assuming this hypothesis, we obtain stack(C_{2n}) = 2^{n+1} - 1, clear(C_{2n+1}) = 3 * 2^n - 2. At present, we do not have a conjecture for the exact value of stack(C_{2n+1}). Finally, computational evidence leads us to a conjectural closed formula for the stacking number of a tree in terms of the distances and degrees of the vertices relative to a chosen root.

International student mobility plays a critical role in shaping future research careers, particularly in highly globalized fields such as astrophysics. The Leiden/ESA Astrophysics Program for Summer Students (LEAPS) offers a 10-week, fully funded research program at Leiden Observatory and the European Space Agency's ESTEC centre for undergraduate and master's students. Designed to foster early research involvement, LEAPS supports students from diverse academic and cultural backgrounds. Since its inception in 2013, LEAPS has hosted 194 students from over 40 countries. Data collected for 165 participants reveal that over 50% have progressed to Ph.D. studies, with some members of earlier cohorts already securing competitive international fellowships in astronomy. LEAPS participants have collectively contributed to at least 25 peer-reviewed publications and 13 international conference presentations. LEAPS has contributed successfully in preparing undergraduates for research careers in astrophysics through hands-on experience, mentorship, and scientific exposure. By addressing barriers related to financial means and promoting diversity, the program not only enhances individual career trajectories but also contributes to the broader goal of inclusive academic mobility. Continued efforts are needed to further increase global representation and assess long-term impacts on participants' scientific careers.

We propose a quantum-enhanced sensing scheme for the detection of wave-like dark matter and high-frequency gravitational waves using two-dimensional ion crystals in a Penning trap. The protocol employs spin-motion squeezed states to improve the signal-to-noise ratio and enable a super-Heisenberg scaling with respect to the number of ions over a broad parameter range. We analyze the sensitivity of the protocol to representative wave-like dark matter candidates, including the axion-like particle and the dark photon, as well as to high-frequency gravitational waves, taking into account the decoherence and dephasing of the ion spins. Our results indicate that two-dimensional ion crystals and this new protocol provide a promising platform for probing previously unexplored parameter space in searches for light dark matter and high-frequency gravitational waves.

We perform a global analysis of HERA total inclusive cross section and charm quark production data to extract the non-perturbative initial condition for the next-to-leading order Balitsky-Kovchegov (BK) equation. We extend our previous analyses to full next-to-leading order + next-to-leading logarithm (NLO+NLL) accuracy by combining the NLO DIS impact factors with the NLO BK equation that includes the resummation of large double and single logarithms. The developed Bayesian setup extracts the posterior that describes the distribution of the parameters that best fit the data. The posterior distribution allows for estimates of the theoretical uncertainty of the dipole amplitude and, hence, offers a streamlined method for propagating uncertainties in the BK initial condition in NLO CGC calculations.

The parity-violating asymmetry, accounting for the vector and axial-vector vertex plus self-energy correction as well as for vacuum polarization, is calculated nonperturbatively by solving the corresponding Dirac equation for the electronic scattering states. Investigating the nuclei $^{27}$Al, $^{48}$Ca and $^{208}$Pb at collision energies in the GeV region and at forward scattering angles matching the experimental geometries, it is found that the combined QED effects change the parity-violating asymmetry by less than one percent. The same is true for $^{12}$C and $^{208}$Pb at an energy of 150 MeV.

The emergence of the antiferromagnetic (AFM) Chern insulator (AFCI) phase in the Kane-Mele-Hubbard (KMH) model with a finite sublattice potential is investigated. The AFCI, characterized by AFM correlations coexisting with quantized Hall conductance, has long raised the question of whether it can exist in the KMH model that respects time-reversal symmetry (TRS). Using exact diagonalization, we analyze the excitation gap, anisotropic AFM correlations along the $z$ axis and in the $xy$ plane, and the fidelity susceptibility under twisted boundary conditions, all of which provide consistent evidence for the AFCI phase. In particular, our numerical evaluation on the (spin) Chern number reveals a breakdown of adiabatic continuity in the twist-angle space, indicating an instability toward TRS breaking driven by Hubbard-induced AFM perturbations. A modified computational scheme is further proposed, which yields a robust quantized Chern number $C=1$ within this phase.

This paper presents a novel control strategy for multi-agent shepherding of non-cohesive targets in obstacle-rich environments. Unlike previous approaches that assume cohesive flocking behavior, our method handles targets that interact only with nearby herders through repulsive forces and exhibit no inter-target coordination. Each herder employs a hybrid control policy that combines direct goal-oriented steering with obstacle-tangent maneuvering, enabling targets to circumnavigate obstacles while being guided toward a goal region. The herder dynamics integrate three key behaviors: return-to-goal motion when idle, target steering with adaptive directional control, and obstacle avoidance using both normal and tangential force components. Numerical simulations demonstrate superior performance compared to existing shepherding methods, achieving higher target confinement rates in cluttered environments. Experimental validation using TurtleBot4 herders and Osoyoo target robots in an indoor arena confirms the practical effectiveness of the proposed approach.

The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency.

Wave-domain processing is an emerging paradigm where signal processing operations are partially shifted from the digital to the electromagnetic (EM) domain. Leveraging reconfigurable EM devices, this approach aims to reduce complexity, energy consumption, and latency in next-generation wireless systems employing holographic MIMO. This paper establishes fundamental theorems on the controllability of generic reconfigurable EM devices, where wave processing is achieved through the dynamic configuration of passive scatterers. Specifically, we derive necessary and sufficient conditions for controllability as a function of geometry and mutual coupling between elements. Finally, we provide a detailed discussion and numerical results characterizing the interplay between the number of elements, physical size, degrees of freedom, and directivity.

Public awareness of AI ethics plays a crucial role in fostering the responsible and sustainable development of AI technology. However, finding effective ways to promote public understanding of the ethical risks of AI remains a challenge. Given the complexity of AI ethical issues and the cognitive limitations of the public, this review paper proposes a conceptual framework for inclusive learning analytics with embedded data comics. Data comics help transform complex and abstract AI ethics cases into compelling and relatable stories, fostering public empathy and introspection. More importantly, inclusive learning analytics targets not only people of different demographic attributes, but also different mindsets with inherent cognitive biases. By providing equal and easily accessible channels for AI ethics issues, we aim to encourage the public to reflect on AI ethics incidents from multiple perspectives and develop the habit of continuous learning to adapt to evolving AI technologies and ethical risks.

While the Dirac band structure of graphene has established it as a leading platform for ultrafast optoelectronics, its non-perturbative nonlinear response under intense excitation remains poorly understood. Here, we report ultrafast spectral modulation of nonlinear optical signals in graphene. By utilizing a robust suspended-graphene platform that allows for both wide-range electrostatic gating and high optical damage thresholds, we observe dramatic frequency shifts (up to 8 THz) in third-harmonic generation (THG) and sum-frequency generation (SFG) driven by pump-induced nonequilibrium carrier dynamics. The magnitude and even the direction of this spectral shift can be reversibly controlled by the Fermi level and excitation conditions. A quasiequilibrium theoretical framework based on hot-carrier dynamics quantitatively reproduces the measured spectral evolution, elucidating the critical interplay between carrier heating and the Fermi level. These findings establish a universal mechanism for carrier-mediated spectral control, providing a practical route toward high-speed, gatetunable nonlinear photonic architectures.

A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in $\mathbb{R}^\infty$ and related approximation properties are investigated using the popular $L_{\infty}$ norm and $L_2$ norms. A computationally efficient sieve maximum likelihood (sML) estimation is then developed to nonparametrically estimate the unknown isotropic covaraince function valid in $\mathbb{R}^\infty$. Consistency of the proposed sieve ML estimator is established under increasing domain regime. The proposed methodology is compared numerically with couple of existing nonparametric as well as with commonly used parametric methods. Numerical results based on simulated data show that our approach outperforms the parametric methods in reducing bias due to model misspecification and also the nonparametric methods in terms of having significantly lower values of expected $L_{\infty}$ and $L_2$ norms. Application to precipitation data is illustrated to showcase a real case study. Additional technical details and numerical illustrations are also made available.

AI-mediated Communication (AIMC) systems increasingly aim to protect minority voices by anonymizing or proxying their input, but anonymity and authenticity are not the same construct. This position paper draws on an ongoing empirical study comparing two LLM-powered minority support strategies in hierarchical group decision-making. We found that relaying minority input anonymously through AI increased participation but significantly reduced psychological safety and satisfaction, while generating only autonomous counterarguments improved satisfaction and reduced marginalization. These counterintuitive findings reveal three provocations for AIMC design in hierarchical contexts: the inherent trade-offs among anonymity, authenticity, agency, and accountability; the risk that power asymmetry reverses intended effects; and the need for AI to facilitate group reflection rather than substitute for human responsibility. These findings and provocations are offered as a contribution to the Restoring Human Authenticity in AI-Mediated Communication workshop.

We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory, we first formalize the problem of strategically robust linear quadratic dynamic games. We show that these can be rewritten as simple transformations of linear quadratic games in which each player chooses a controller in a fictitious game in which they are faced with an adversary who is penalized for deviating from the other players' policies. This formulation naturally induces a novel notion of dynamic equilibrium, which we call a strategically robust dynamic equilibrium. We establish existence and uniqueness of such equilibria and furthermore show that the equilibrium policies are Markovian, linear, and can be efficiently computed via coupled backward Riccati equations. Through numerical simulations, including experiments in a network game, we illustrate the benefits of strategic robustness in designing robust and resilient decentralized control schemes. Our experiments also expose a "free-lunch" phenomenon in games in which robustness does not incur a corresponding loss in performance but can yield improvements in players' utilities and social welfare.

This paper addresses a Stackelberg stochastic linear-quadratic (LQ) differential game under closed-loop information, a problem inherently time-inconsistent. Existing approaches rely on solving two coupled Hamilton-Jacobi-Bellman (HJB) equations derived via time discretization and a limiting argument, whose convergence remains an open problem. We propose an alternative framework based on closed-loop equilibrium strategies. We reformulate the leader's problem as a forward-backward optimal control problem involving a coupled system of forward SDEs and backward Riccati equations. Due to the presence of controlled Riccati equations, the leader's problem becomes essentially nonlinear. Using a variational method, we characterize the leader's closed-loop equilibrium strategy and derive the associated equilibrium Riccati equation (ERE). A key conceptual distinction is that the follower adopts a globally optimal strategy against any admissible control of the leader, whereas in previous literature the follower's strategy was only locally optimal along the leader's specific equilibrium path. This makes the follower's strategy more robust and the leader's commitment more credible. In our LQ setting, the resulting ERE coincides exactly with the coupled HJB system from the literature, showing the leader's strategy is equivalent to the feedback Stackelberg solution. Thus, our framework provides not only an alternative derivation but also a rigorous justification of the limiting argument. We establish a priori estimates for the ERE, covering 1D and high-dimensional cases, ensuring global well-posedness for any finite horizon. This significantly extends existing results which require a sufficiently short time horizon or control-independent diffusion. An application to an asset management problem with numerical simulations illustrates the theoretical results.

We present a direct derivation of Arai's effective Hamiltonian in non-relativistic quantum electrodynamics without relying on the scaling limit. Our result applies to a broader class of potentials, including the Rollnik class and confining potentials such as the harmonic potential.

This paper addresses decentralized control of large-scale heterogeneous multi-agent systems subject to bounded external disturbances and limited communication, with the objective of satisfying cooperative Signal Temporal Logic (STL) specifications. The considered specifications involve spatiotemporal tasks that require collaboration among multiple agents, including agents beyond direct communication neighborhoods. To address the communication constraints, a $k$-hop Prescribed Performance State Observer ($k$-hop PPSO) is designed to enable each agent to estimate the states of agents up to $k$ communication hops away using only information from $1$-hop neighbors, while guaranteeing predefined performance bounds on the estimation errors. The estimation error bounds are explicitly incorporated into a reformulation of the spatial robustness of the STL specifications, yielding robustness measures that account for worst-case estimation uncertainty. Based on the modified robustness, a decentralized continuous-time feedback control law is designed to guarantee satisfaction of the STL specifications in the presence of bounded disturbances and estimation errors. The proposed framework provides formal correctness guarantees using only local information and limited communication. Numerical simulations illustrate the theoretical results.

Sparse-attention decoders rely on exact Top-K selection to choose the most important key-value entries for each query token. In long-context LLM serving, this Top-K stage runs once per decode query and becomes a meaningful latency bottleneck even when the indexer and attention kernels are already highly optimized. We present \textbf{Guess-Verify-Refine (GVR)}, a data-aware exact Top-K algorithm for sparse-attention decoding on NVIDIA Blackwell. GVR exploits temporal correlation across consecutive decode steps: it uses the previous step's Top-K as a prediction signal, computes pre-indexed statistics, narrows to a valid threshold by secant-style counting in 1-2 global passes, verifies candidates with a ballot-free collector, and finishes exact selection in shared memory. We connect this behavior to the Toeplitz / RoPE structure of DeepSeek Sparse Attention (DSA) indexer scores and validate the design on real DeepSeek-V3.2 workloads integrated into TensorRT-LLM. GVR achieves an average \textbf{1.88x} single-operator speedup over the production radix-select kernel, with up to \textbf{2.42x} per layer per step, while preserving bit-exact Top-K outputs. In controlled TEP8 min-latency deployment, it improves end-to-end TPOT by up to \textbf{7.52%} at 100K context, with larger gains at longer contexts and smaller but still positive gains under speculative decoding. While implemented and validated in the current TensorRT-LLM DSA stack on Blackwell, the same principle may extend to sparse-attention decoders whose decode-phase Top-K exhibits temporal stability.

We construct an $SU(5)$ Grand Unified Theory on domain walls in the five-dimensional space-time. In this setup, we introduce an adjoint scalar field and a singlet that together form a set of five domain-wall solutions, realizing a dynamical brane-world. The same scalar fields also localize chiral fermion zero modes around the walls via the Jackiw-Rebbi mechanism, break $SU(5)$ down to the Standard Model gauge group via geometric Higgs mechanism and simultaneously trap gauge fields through a field-dependent gauge kinetic term. Furthermore, they enable localization of the Higgs field, providing a novel solution to the doublet-triplet splitting problem. As a result, all essential ingredients of the model are realized by a single adjoint scalar field and a singlet, making the construction very economical. We propose two realizations of the Higgs sector, derive the four-dimensional effective theory, and demonstrate that the Standard Model Yukawa couplings at the weak scale can be reproduced from the five-dimensional Yukawa couplings by the renormalization group analysis with a suitable choice of parameters.

In this paper, we have studied the hyponormality and invertibility of the operator of type $wT_φ+T_ψ$ where $w$ is any non-zero complex number and $T_φ, T_ψ $ are Toeplitz operators. We have also studied hyponormality when the symbol of Toeplitz operator is a linear functional.

A growing number of Internet of Things (IoT) devices are used across consumer, medical, and industrial domains. They interact with their environment through sensors and actuators and connect to networks such as the Internet. Because sensors may collect sensitive data and actuators can trigger physical actions, security, privacy, and safety are major challenges. Threat modelling can help identify risks, but established IT-focused methods transfer to the IoT only to a limited extent. In this paper, a new modelling technique specifically for IoT devices called Cyber-Physical Data Flow Diagram (CPDFD) is proposed that also allows modelling of hardware with the aim to support manufacturers in identifying threats and developing countermeasures. The technique was examined through an experimental study and a survey with interviews. The results suggest that numerous other attack scenarios can be found through the modelling technique, improving the identification of threats to IoT devices.

Enhancing seismic fragility and risk assessment of nuclear power plants relies on accurate prediction of reactor building responses to seismic hazards, which can be further improved through dynamic analysis of high-fidelity finite element (FE) models. However, FE models often exhibit non-negligible discrepancies from actual structures due to various sources of uncertainty, necessitating FE model updating with rigorous quantification of associated uncertainties. This paper presents a GPU-accelerated latent space--based Bayesian framework for FE model updating of building structures. In the proposed framework, high-dimensional structural response data (e.g., time histories or frequency response functions) are projected into a low-dimensional latent space using a multimodal variational autoencoder (MVAE), thereby enabling efficient and tractable likelihood evaluation without explicit modeling in the original observation space. Once trained, the surrogate enables amortized inference, allowing posterior sampling to be performed without additional simulator evaluations. We specifically employ a sequential Monte Carlo (SMC) sampler, whose population-based formulation allows parallel evaluation of the approximate likelihood on GPUs, resulting in computational efficiency and robustness against multimodal and complex posterior distributions. The proposed framework is validated through both numerical benchmarking and experimental data from a shaking table test of a reinforced concrete building structure. The results demonstrate that the method accurately estimates structural parameters with well-quantified uncertainties, while achieving fast and efficient inference through GPU-based parallelization, and enabling robust inference even in the presence of sparse observations that induce multimodal and highly complex posterior distributions.

This paper proposes a resource-aware allocation model for layered intrusion detection in het erogeneous networks. Monitoring traffic at higher protocol layers improves the ability to detect sophisticated attacks, but it also increases computational and storage costs. The problem is formu lated as an integer linear program that assigns a single monitoring depth, ranging from Ethernet to the application layer, to each device, while accounting for device importance, attack probability, layer-dependent detection rates, and per-layer monitoring costs. The model further enforces a global resource budget, a minimum monitoring level for critical devices, and maximum-feasibility limits for constrained devices such as simple IoT sensors. The formulation is solved with the SCIP optimization framework on a small heterogeneous network of six devices, and the resulting allocation illustrates how the model concentrates monitoring effort on important and high-risk devices while respecting feasibility and budget constraints.

Understanding quantum system dynamics driven by nonclassical light pulses is challenging, particularly for general light states with large photon numbers. Here we introduce an efficient framework that makes this task tractable. By introducing a pulse-shaped P-representation, the exact quantum evolution is decomposed into a mixture of many independent quasi-classical branches, each governed by a standard master equation with a classical pulse which can be solved efficiently. As an illustration, for a two-level system interacting with an exponential pulse, we first find out the exact analytical solutions to the Bloch equations in each quasi-classical branch, and then by taking proper P-function average over all branches, the full system dynamics driven by nonclassical light pulses is analytically obtained. For the one-photon and two-photon cases, our method well reproduces the previous exact results either analytically or numerically. Crucially, our approach scales efficiently to more complex light states (Fock, thermal, squeezed vacuum states) with large photon numbers ($N\sim 100$). We further provide a clear physical interpretation how the system dynamics is influenced through the high-order optical coherence of the nonclassical pulses. This work provides a unified and computationally efficient route and a useful starting point to explore more complex quantum dynamics driven by nonclassical light in quantum optics and quantum information processing.

We demonstrate a suspended thin-film aluminum nitride (AlN) microbolometer for narrowband very long-wave infrared detection. The device uses a 100-nm-thick AlN membrane suspended above a Pt back reflector by a 1-um air gap. Resonant absorption is set by the AlN transverse optical phonon near 15.4 um and is strengthened by suspension above the reflector. A periodic perforation pattern reduces membrane thermal mass and enhances absorption without further thinning the film. DC resistance measurements under tunable infrared illumination verify bolometric operation, and the measured spectral response follows the absorption profile expected from spectroscopic measurement of passive devices. Narrowband response is observed in the 14--18 um range, with peak responsivity of 920.8 ppm/mW at 15.48 um. This platform can enable compact wavelength-selective thermal detectors for multispectral imaging, on-chip infrared spectroscopy, and chemical sensing.

We present a comprehensive first-principles investigation of a hypothetical cubic Pm-3m phase of the ternary hydride NaAlH3, focusing on its lattice dynamics, electronic structure, and electron-phonon-mediated superconducting properties at ambient pressure. Using density functional theory and the Migdal-Eliashberg formalism, we find an exceptionally strong electron-phonon coupling ($λ=2.23$), resulting in a superconducting critical temperature of up to 73.7 K for a Coulomb pseudopotential $μ^* = 0.1$. Phonon dispersion calculations, complemented by ab initio molecular dynamics simulations, indicate dynamic and thermal stability within the adopted theoretical framework. The electronic structure exhibits a metallic character with substantial contributions from Al- and Na-derived states at the Fermi level. The resulting superconducting gap ratio ($2Δ(0)/k_B T_c \approx 4.8$) and specific heat jump ($ΔC/γT_c \approx 2.2$) significantly exceed BCS weak-coupling predictions, highlighting the strong-coupling nature of superconductivity in this hypothetical phase.

We consider off-diagonal asymptotic series for integral kernels of functions of Laplace-type operators on curved backgrounds. These expansions are obtained by applying integral transforms to the DeWitt series for the heat kernel of the corresponding operator and thus represent a DeWitt-type series in the heat kernel coefficients with the coefficients of this expansion (which we call basis kernels) being some hypergeometric-type functions of the Synge world function. Basis kernels of a certain class of operator functions were found previously in terms of $N$-fold Mellin-Barnes integrals. In this paper we study series representations of the corresponding Mellin-Barnes integrals in both non-resonant and resonant cases and suggest a physical interpretation for the emerging series, which is related to the UV and IR properties of operator functions.

Entanglement is a key resource for many quantum applications. Understanding fundamental properties of entangled states is an important step towards their practical exploitation. We characterize entanglement in the context of Gaussian and non-Gaussian processes and identify entangled states that cannot be produced by any Gaussian evolution acting on separable states. This distinction exposes intrinsic limitations of Gaussian operations and highlights the role of non-Gaussian operations as an important resource. We apply this framework to develop a certification method that connects entanglement theory with quantum non-Gaussianity - an advanced quantum feature that is essential for several quantum applications. Our approach tailors the certification to experimentally relevant states that can be produced in current quantum optics experiments. We demonstrate this certification for recognizing the genuine non-Gaussian entanglement of various entangled Fock states and hybrid entangled states.

The widespread availability of large-scale code datasets has accelerated the development of code large language models (CodeLLMs), raising concerns about unauthorized dataset usage. Dataset poisoning offers a proactive defense by reducing the utility of such unauthorized training. However, existing poisoning methods often require full dataset poisoning and introduce transformations that break code compilability. In this paper, we introduce FunPoison, a functionality-preserving poisoning approach that injects short, compilable weak-use fragments into executed code paths. FunPoison leverages reusable statement-level templates with automatic repair and conservative safety checking to ensure side-effect freedom, while a type-aware synthesis module suppresses static analysis warnings and enhances stealth. Extensive experiments show that FunPoison achieves effective poisoning by contaminating only 10% of the dataset, while maintaining 100% compilability and functional correctness, and remains robust against various advanced code sanitization techniques.

In this paper, we study numerical invariants associated with a homogeneous submodule of the Hardy module over the bidisk. We focus on the submodule generated by the polynomial $(z-w)^2$ and obtain explicit formulas for the corresponding invariants. As an application, we verify the monotonicity property in this concrete setting. Our results provide a detailed example illustrating the behavior of these invariants beyond the linear case.