This paper considers the robust control of a catenary robot composed of two quadrotors connected by an inextensible cable. The system is modeled on \(SE(3)\), with the cable treated as a geometric subsystem induced by the UAV configuration rather than as an independent dynamical element. The catenary shape determines configuration-dependent forces that couple the translational dynamics of the vehicles. We propose a geometric tracking controller for the relative configuration of the agents and analyze its robustness with respect to unstructured uncertainties in the catenary-induced forces. The main theoretical result establishes local input-to-state stability of the closed-loop tracking errors. In particular, we obtain asymptotic convergence in the nominal case and an explicit ultimate bound for the tracking errors under bounded catenary-force perturbations.

The dark photon plays an important role as a portal to dark matter and has been extensively studied on both experimental and theoretical frontiers. However, as no signals have been observed, the whereabouts of the dark photon remain a long-standing open question. With the proposal of a future $τ-c$ facility, this proceeding reviews and summarizes the current experimental status of the dark photon in the $τ-c$ energy region, which is expected to provide a reference for future searches. The experimental status indicates that the dark photon in the $τ-c$ energy region remains highly promising, highlighting the requirement for larger data samples or new methods to further investigate the benchmarks related to the observed cosmic dark matter.

This paper proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line segment to be clipped as line. The present algorithm treats the clipping boundary and the line segment to be clipped as line segment and using this strategy, it succeeds to avoid computation of false intersection points. A quadrilateral is constructed using the end points of a clipping boundary segment and the end points of the line segment to be clipped as its vertices. The concavity and convexity of the quadrilateral dictates whether a line segment actually intersects the clipping boundary. If the quadrilateral is found to be concave then the line segment is rejected, otherwise the point of intersection of the line segment with the clipping boundary is computed. Since a 'test & intersect' approach is used instead of a 'intersect & test', hence the proposed algorithm does not compute false intersection point thereby reducing the number of divisions required to obtain a clipped line segment. Only one routine can process line segments at any position. Improved performance is observed with respect to the Nicholl-Lee-Nicholl, Liang-Barsky, Cohen-Sutherland and Skala's algorithm through experiments with random line segments using a metric based on execution time.

The rapid growth of weather-dependent renewable generation increases price volatility and imbalance penalty risk in power markets, creating the need for advanced quantitative trading strategies. We develop a data-driven continuous-time stochastic optimal control framework for intraday electricity trading using stochastic differential equations with drift terms ensuring mean reversion to deterministic forecast trajectories. Production follows a Jacobi diffusion, while prices follow an asymmetric jump-diffusion to reflect the heavy-tailed behavior observed in intraday markets. The framework accounts for realistic market features by incorporating gate closure and energy-based imbalance settlement over the delivery window, where the path-dependent imbalance cost is handled by state augmentation to preserve the Markovian structure. The value function is characterized via the dynamic programming principle by a three-stage sequence of two linear Kolmogorov backward equations and a nonlinear Hamilton-Jacobi-Bellman partial integro-differential equation. To solve this problem efficiently, we propose a monotone IMEX finite-difference scheme with operator splitting, semi-implicit linearization, and a differential formulation for the jump operator. Numerical experiments based on German market data indicate that, under the provided forecasts, the computed strategy outperforms the TWAP benchmark and approaches the perfect-foresight benchmark. Sensitivity experiments further show how jump intensity, delivery-window length, and trading horizon affect the trading policy and the resulting profit-and-loss distribution.

Let $k\in\mathbb{N}$. Wigert's divisor function $d^{\left(\frac{1}{k}\right)}(j)$ counts the number of representations of $j$ of the form $m^k+mn$ with $m\geq1 , n\geq0$. Let $\mathcal{F}_k(s)$ denote the Dirichlet series of $d^{\left(\frac{1}{k}\right)}(j)$. While $\mathcal{F}_2(s)$ is essentially a well-known special case of the Euler-Zagier double zeta function, and hence well-studied, very little is known about $\mathcal{F}_k(s)$ for $k>2$. We offer three new representations for $\mathcal{F}_k(s)$ for $k\geq2$, one of which is an analogue of the Chowla-Selberg formula as well as of a formula of Atkinson. The meromorphicity of $\mathcal{F}_k(s)$ is also discussed. The special value $\mathcal{F}_3\left(\frac{3}{2}\right)$ is expressed in terms of an infinite series of Bessel functions and a generalized divisor function.

Forecast reconciliation has become key to improving the accuracy and coherence of forecasts for linearly constrained multiple time series, such as hierarchical and grouped series. Yet, comprehensive software that jointly covers cross-sectional, temporal, and cross-temporal reconciliation has so far been lacking. The R packages FoReco and FoRecoML address this gap by offering a comprehensive and unified framework. The packages respectively implement classical and regression-based linear reconciliation approaches, and non-linear approaches based on machine learning for cross-sectional, temporal and cross-temporal frameworks. Designed for accessibility and flexibility, these packages provide sensible default options that allow new users to apply reconciliation methods with minimal effort, while still giving expert users full control to explore state-of-the-art extensions through customized settings. With this dual focus, FoReco and FoRecoML are versatile tools for practitioners and researchers working on forecast reconciliation.

Renewed public attention on the identity of Bitcoin's pseudonymous creator has sharpened focus on the Satoshi overhang, commonly framed as a tail risk for bitcoin. This paper argues that the mechanical downside of a disposition is bounded well below the existential-loss framing, and that the terminal states most consistent with sixteen years of holder behavior are nonbearish for bitcoin's effective supply. The approximately 1.148 million BTC Patoshi position is analyzed on two tracks. For a purely wealth-maximizing holder, a three-scenario quantitative analysis (Appendix A) shows that bitcoin's current market depth is sufficient to absorb a patient multi-year liquidation at a cumulative price impact in the mid-single-digit to mid-double-digit percent range relative to counterfactual, with the central scenario clustering near 10 percent. The paper maps a decision space rather than identifying a unique modal outcome, assuming a holder whose profile is consistent with the sixteen-year record. Preference sets consistent with the record, including ideological non-intervention, privacy above all, satisficing, and myth preservation, favor continued dormancy terminating in a cryptographically enforced nonrecovery or destruction arrangement; preference sets favoring adversarial or wealth-maximizing action are possible but less supported. Across the plausible region of the decision space, the bear case is bounded and the terminal states most consistent with observed behavior are neutral to slightly positive for bitcoin's effective supply.

We introduce a new logic, called \emph{cluster first-order logic}, a restricted fragment of first-order logic specifically designed to study order invariance. An order-invariant formula is one on a vocabulary that contains an order; however, whether a structure satisfies it or not is independent of the interpretation of the order. We show that while order-invariant cluster first-order logic can define properties outside the scope of plain first-order logic in general, its expressive power is included in that of first-order logic when it comes to classes of bounded degree. We establish this result by explicitly constructing linear orders such that similar structures remain similar when they are expanded with these orders. This similarity-preserving, local-to-global approach is technically involved and somewhat counterintuitive, since adding an order usually reveals distinctions that are otherwise hidden due to the locality of first-order logic. We believe that this work can be a stepping stone toward applying such techniques to plain first-order logic and toward settling the question of the expressive power of order-invariant plain first-order logic.

Template engines are indispensable components in modern software ecosystems, enabling the generation of structured documents and scripts across domains such as web development, Infrastructure as Code, and data engineering. However, the unique architectural characteristics of template engine-based applications (i.e., TE applications), including multi-language composition, opaque data flow, deferred validation, and complex integration, pose significant challenges for diagnosing and resolving bugs in TE applications. While prior research has primarily focused on template engine security, bugs in TE applications remain under-investigated. To bridge this gap, we present the first comprehensive study of TE application bugs. By analyzing 1,004 application bugs across 15 template engines in five programming languages, we identify the symptoms and root causes of TE application bugs and common patterns to fix them. Our findings reveal that Abnormal Rendering Result (e.g., unexpected or blank output) is the most prevalent symptom (48.61%), often manifesting as silent failures that are difficult to diagnose. We identify 17 root causes, with Syntax Misuse, Mismatched Data Context, and Incompatible Integration as the dominant categories. Furthermore, we find that while 67.92% of the bugs are fixed within the template, over 20% require modifications in the host-side logic to resolve data context issues. Based on these findings, we derive actionable implications for tool designers, practitioners, and researchers. To demonstrate the practical utility of our findings, we further develop two prototype tools for the Jinja engine to facilitate the development and debugging of TE applications.

We study the problem of online coloring for graphs with large odd girth. The best previously known algorithm uses $O(n^{1/2})$ colors, which was discovered by Kierstead in 1998. This algorithm works when the odd girth is 7 or more. In this paper, we provide the following: for every $\varepsilon > 0$, there exists a constant $g' \in \{3, 5, 7, \dots\}$ such that graphs with odd girth at least $g'$ can be deterministically colored online using $O(n^{\varepsilon})$ colors.

This paper proposes a bitwise over-parameterized neural network (ONN) decoder for polar-coded transmission and develops a tractable theoretical performance analysis framework. By modeling each synthesized message channel as an individual supervised regression task, the proposed decoder preserves the successive structure of polar decoding while enabling a communication-oriented integration of neural-network learning theory and polar-code reliability analysis. Under over-parameterization, we first characterize the empirical convergence behavior of each bitwise ONN and show that the training trajectory remains close to the random initialization. By expressing the empirical MSE convergence in the dB domain, the result further reveals a per-iteration training gain determined by the learning rate, the bit-channel Gram spectrum, and the training-set size. Upon this observation, we then derive a population mean squared error (MSE) bound via local generalization analysis and convert it into a bitwise decoding error bound through the posterior-margin structure of the bitwise maximum a posteriori (MAP) target. Under additive white Gaussian noise (AWGN) channels, a Gaussian approximation (GA)-based characterization of the low-margin probability is further established, which leads to explicit bounds for the bit error rate (BER) and block error rate (BLER). The analysis clarifies how the hidden-layer width affects optimization, generalization, and the final decoding performance, thereby providing theoretical guidance for network-scale selection. Numerical results validate the main theoretical findings and show that increasing the network width consistently improves both oracle-aided and sequential decoding performance.

On the flag variety $ \mathcal{F}l_s(E)$ associated to a vector bundle $E,$ , a sequence $s$ and a partition $a,$ there is a line bundle $\it Q^a_s$ on $ \mathcal{F}l_s(E).$ The aim of this paper is to prove the following conjecture: $Q^a_s $ on $ \mathcal{F}l_s(E)$ is big if only if $π_*(Q^a_s)=S_a(E)$ on X is big. The "if" part is proven here, the "only if" part is proven under the V-bigness hypothesis.

Incorporating molecular-scale effects in the description of contact line motion is essential for accurately capturing all sources of energy dissipation in wetting dynamics. This holds particularly true in the cases where contact line friction dominates, and hydrodynamics models struggle to achieve regularisation due to the negligible Navier slip. We perform Molecular Dynamics simulations of water/hexane biphasic systems in a two-phase Couette flow configuration. Wetting occurs over a silica-like surface with controllable wettability. The simulation results are reproduced by a Phase Field model (Cahn-Hilliard Navier-Stokes equations), which includes localised contact line slip and contact angle dynamics. The continuous equations are directly parametrized from Molecular Dynamics simulation results, under the numerical sharp interface limit. We demonstrate that the Phase Field model can quantitatively reproduce Molecular Dynamics through a systematic calibration protocol. Critically, we show that contact line friction is the primary physical parameter requiring empirical calibration based on Molecular Dynamics data. Once extracted by matching contact angle dynamics, quantitative agreement across multiple observables is obtained, including interface curvature, steady contact line displacement, and the structure of streamlines. All other model parameters are determined a posteriori, according to the calculation of independent observables and under numerical constraints. The results presented in this article indicate that Phase Field modelling can capture the net effect of molecular processes on the mobility of contact lines and that the careful calibration of contact line friction based on the reconstruction of contact angle dynamics and interface bending is key to fully reconcile continuous models with Molecular Dynamics.

Layer-7 (L7) proxies are critical to modern cloud-native systems, yet their performance is increasingly bottlenecked by copying entire payloads across the kernel-user boundary. Existing approaches reduce this overhead but typically sacrifice compatibility with unmodified POSIX applications, introduce new APIs, or require specialized environments. We show that, under conventional OS abstractions, fully eliminating kernel-user copies while preserving standard socket semantics for unmodified proxies is fundamentally impossible. This leads to a practical insight: in common L7 workloads, proxies inspect only small metadata (e.g., HTTP headers) for routing, while forwarding the bulk payload unchanged. Based on this insight, we present Libra, an OS-level selective-copy framework that copies only metadata to the user space and retains the bulk payload in the kernel for forwarding, reducing data movement without breaking compatibility. Libra uses eBPF to identify protocol-specific metadata boundaries and coordinate selective copy and payload reuse across receive and transmit paths, all without modifying the socket API. Implemented in Linux and evaluated with unmodified Nginx and HAProxy, Libra improves plaintext throughput by up to 4.2x and reduces P99 tail latency by over 90%. With hardware-offloaded kTLS, it boosts encrypted throughput by 2.0x and cuts tail latency by 65%.

In recent years, radio detection of ultra-high-energy cosmic rays (UHECRs), with energies above $10^{18}$ eV, has become an established technique. The radio emissions can be simulated with high accuracy using Monte Carlo codes such as ZHAireS and CoREAS. These simulations are essential but are computationally intensive. In this work, we present a machine-learning-based emulator that reproduces radio signal simulations with high accuracy in milliseconds rather than hours. Primary particle properties can then be reconstructed by comparing measured signals to emulated traces using a Markov Chain Monte Carlo approach. Using ZHAireS simulations carried out over the GRANDProto300 experiment layout, the method achieves an 8.9\% resolution on electromagnetic energy and a 0.08° angular resolution, matching state-of-the-art reconstruction performance. Finally, we apply the method on real data, successfully reconstructing cosmic-ray candidates detected by the GP300 prototype.

Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitaev, and Zhang established the shape-Wilf-equivalence for individual claw-shaped POPs. In this paper, we extend their result by proving that certain families of claw-shaped POPs are shape-Wilf-equivalent and enumerate the number of permutations avoiding that set of claw-shaped POPs. Our approach is based on a new encoding process, which is entirely different from the method used in their work.

The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $α$ and a Hurst exponent $H$. We consider a nonstationary extension where the Hurst exponent is a function of time, and potentially random. The construction admits the standard linear fractional stable motion as tangent process, and we exactly determine its local Hölder exponent in terms of the pointwise values of the Hurst function. This is in contrast to other definitions of multifractional processes, where the Hurst function needs to have additional regularity in time.

The Amazon rainforest is considered one of the core tipping elements in the climate system with a potential tipping point from rainforest to savannah between 2 and 6 °C of global warming. However, ongoing deforestation constitutes an additional major threat to the Amazon rainforest that acts simultaneously to undermine the stability of the rainforest. Both effects could synergistically compound and lower the overall threshold in global warming and deforestation when tipping points may be crossed. Here, we quantify the safe operating space of the Amazon rainforest, which we define as the joint global warming and deforestation conditions where resilience of the system as a whole is preserved. Based on the underlying environmental data from a global climate model, we use a reduced complexity model and explicitly take into account the adaptive capacities of the forest as well as the atmospheric moisture recycling. We quantify that under current conditions of around 1.4 °C of global warming and around 17 % of deforestation, more than a third of the Amazon rainforest is at high risk of crossing critical thresholds. We therefore conclude that the Amazon rainforest may have already left its safe operating space. Furthermore, we find that the historic and projected deforestation pattern could be particularly detrimental. Our results support the need for ambitious climate action to hold the Paris climate target and also nature protection to end net deforestation.

The full-field reconstruction of three-dimensional (3D) turbulent flows from sparse experimental measurements remains a significant challenge, particularly for flows exhibiting complex 3D flow separation. In this work, we address this challenge for the case of stall cells - spanwise coherent structures that form on the suction surface of wings at post-stall conditions. Planar particle image velocimetry (PIV) experiments are performed on a NACA 0012 wing at a chord-based Reynolds number of $Re_c \approx 450{,}000$ and angle of attack $α= 14^\circ$, acquiring two-component mean velocity data on four spanwise planes. The experimental data show clear spanwise variation in the extent of the separation and flow dynamics, consistent with the presence of stall cells. Three-dimensional variational (3DVar) data assimilation (DA) within the field inversion framework is then employed to reconstruct the full 3D mean flow field by augmenting these sparse planar measurements with the Spalart--Allmaras (SA) Reynolds-averaged Navier--Stokes (RANS) turbulence model. The performance of the reconstruction is assessed on planes not used in the assimilation. It is shown that a single plane of sparse experimental data is sufficient to recover the essential features of a stall cell, including counter-rotating vortices around focal points on the suction surface. The lowest reconstruction error is obtained when two planes of data that are close together but exhibit markedly different separation extents are used, and the complementary roles of the reference data placement and the computational boundary conditions in shaping the reconstructed stall cell structure are explained. These results demonstrate the capability of 3DVar DA to reconstruct the full 3D physics of stall cells from two-component velocity data acquired on select spanwise planes.

A double-transmon coupler (DTC) enables a fast, high-fidelity CZ gate between two highly detuned, fixed-frequency transmon qubits. Moreover, a recently proposed capacitively shunted DTC (CSDTC) realizes a small residual ZZ interaction over a wide flux-bias range around zero flux, eliminating the necessity of static flux biasing while maintaining high CZ-gate fidelity. However, CZ gates with the DTC and CSDTC require baseband flux pulses with large amplitudes, which are vulnerable to pulse distortion and decoherence due to large qubit-coupler hybridization. To address these issues, we experimentally demonstrate a parametrically driven iSWAP gate operated at zero flux bias between highly detuned, fixed-frequency transmon qubits coupled through a CSDTC. Using a simple flux-drive waveform without predistortion, we realize an average gate fidelity of 99.92(2)% at a total gate time of 112 ns. The observed high-fidelity performance is consistent with small qubit-coupler hybridization and small effective ZZ interaction during the gate. Our numerical simulations reproduce the experimentally observed iSWAP interaction rate and effective ZZ interaction, demonstrating the applicability of the theoretical model not only to spectral information but also to time-domain dynamics such as gate operations. These results boost further progress in the research of superconducting quantum computers.

Within an extended isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model, we study the protons, $K^+$ mesons and $Λ$ hyperons production in Au+Au collisions at $\sqrt{s_{\rm NN}}=3$ GeV. For the collision in 0-10% centrality, we study the transverse momentum spectra and rapidity dependent mean transverse momentum for protons. For the collision in 10-40% centrality, we study the directed and elliptic flows for protons and $K^+$ mesons. The results show that the momentum-dependent nuclear mean field with an incompressibility $K_0=230$ MeV can fit fairly the STAR experimental data, while the momentum-independent nuclear mean field with both $K_0=230$ MeV and $K_0=380$ MeV can only partially describe the experimental results. In addition, we also study the directed and elliptic flows for the associated $Λ$, observations reveal the same conclusions as for kaons. These findings indicate that the momentum dependence of nuclear mean field plays a significant role in understanding nuclear matter properties in heavy-ion collisions at $\sqrt{s_{\rm NN}}=3$ GeV.

Constructing and curating high-quality code datasets requires significant resources, making them valuable intellectual property. Unfortunately, these datasets currently face severe risks of unauthorized use. Although digital watermarking offers a post hoc mechanism for copyright authentication, existing methods are predominantly based on the co-occurrence pattern, which is not robust and is susceptible to watermark detection and removal attacks. In this paper, we propose PuzzleMark, a robust watermarking method for code datasets. To reduce the risk of watermark exposure, PuzzleMark introduces a carrier selection strategy that leverages code complexity to evaluate the suitability of code snippets as watermark carriers, and selects those with high suitability for watermarking. To enhance the robustness of the watermark, PuzzleMark proposes a novel concatenation pattern to replace the traditional co-occurrence pattern, and implements two watermarking strategies through variable name concatenation. PuzzleMark adaptively embeds watermarks based on the inherent characteristics of the code, making it more stealthy while maintaining design simplicity. For watermark verification, PuzzleMark employs Fisher's exact test to verify suspicious models under a black-box setting. Experimental results demonstrate that PuzzleMark achieves a 100% verification success rate and a 0% false positive rate, with negligible impact on model performance. Both our human study and our evaluation using four state-of-the-art watermark detection methods show that PuzzleMark exhibits strong imperceptibility, with an average suspicious rate $\leq$ 0.24 and an average recall $\leq$ 30.41%, respectively. As a practical digital watermarking method, PuzzleMark provides strong protection for the intellectual property of code datasets and offers new insights for future research.

Arabidopsis roots show oscillatory growth patterns on homogeneous agar surfaces, whereas other plants, such as maize, do not. Although several explanations have been proposed, a simple and general model that makes testable predictions across species has been lacking. Roots sense gravity and correct their growth direction towards the vertical. Motivated by recent evidence for a time delay in this gravitropic correction, we develop a minimal nonlinear model based on the delay hypothesis that predicts whether a root oscillates or grows vertically downwards. The model identifies a fourfold relation between the delay and time period, robust across different response functions. Analysing images of Arabidopsis, we find that the mode of the oscillatory arc length is not significantly different between inclined and vertical growth conditions. The quantitative agreement between the experimentally measured oscillatory arc length and the arc length estimated from estimated root growth speed and response delay supports this fourfold delay-period rule for delay-driven root oscillations. The simplicity of our model allows for a direct comparison with data from diverse plant species.

LoRa has become a widely adopted wireless modulation scheme in LPWANs due to its low cost, long range, and minimal transmission power. However, collisions between frames of the same spreading factor -- common in dense LoRa deployments -- prevent conventional LoRa receivers from detecting and correctly decoding frames. Recent work has introduced methods to improve recovery, yet their detection stage degrades sharply under low signal-to-noise ratio (SNR) and high collision rates. In this work, we introduce LZn, a low-complexity synchronization scheme driven by a spectral intersection operation. Our method enables robust frame synchronization even under multiple packet overlaps or extremely low SNR conditions. We evaluate LZn on simulations and three independent, real-world LoRa datasets. LZn improves detection sensitivity by up to 10dB and increases detection probability by up to 1.54x. In real-world datasets, LZn improves decoding by 3.46x in the most challenging single-user scenario and up to 1.22x in collision scenarios compared to the second best collision-tolerant scheme (TnB). These results demonstrate that LZn substantially improves the frame recovery of LoRa receivers, while remaining compatible with real-time requirements.

This article develops a Hamilton--Jacobi theory for non-conservative classical field theories, with particular emphasis on dissipative systems, in the framework of co-oriented k-contact geometry. We introduce evolution k-contact k-vector fields, extending the contact evolution formalism to field theories, and analyse the corresponding Hamilton--De Donder--Weyl equations. Moreover, we develop two distinct families of Hamilton--Jacobi theories: a z-independent approach, based on the reconstruction of the dynamics from an integrable k-vector field defined on the base manifold of $(\bigoplus^kT^*Q)\times\mathbb{R}^k\to Q$, and a z-dependent approach, where the integrable k-vector field is defined on the base manifold of $(\bigoplus^kT^*Q)\times\mathbb{R}^k\to Q\times\mathbb{R}^k$. We develop in detail the important case of Hamiltonian functions with affine dependence on the dissipative variables, show how quadratic dependence on these variables can be used structurally to enlarge the range of applications, and recover the ordinary contact Hamilton--Jacobi theory as the particular case k=1, while removing some technical assumptions appearing in previous formulations. Our theory is illustrated through several representative examples, including the telegrapher/Klein--Gordon equation, a dissipative Hunter--Saxton equation, a simple dissipative non-regular first-order field model, and a relativistic thermodynamic model.

Magnon-polaritons provide a room-temperature platform for investigating nonlinear cavity quantum electrodynamics in the microwave domain, but experimentally observing controlled transitions among distinct nonlinear attractors remains challenging in conventional passive systems, where strong external driving is usually required. Here we report the observation of attractor transitions in an active magnon-polariton formed by a self-oscillating microwave cavity coupled to a yttrium iron garne (YIG) sphere. The feedback loop supplies an internal microwave drive, while Kerr frequency pulling and Suhl-mediated magnon-magnon scattering produce an enhanced effective nonlinearity. Stability analysis using experimentally calibrated parameters reveals a rich fixed-point (FP) landscape with multiple unstable-FP phases and a triple-point region. By tuning gain across these phases, we observe the first experimental evidence of explosive growth of bistability, followed by transitions to multifrequency limit cycles, comb-like/fractal spectra, and broadband chaotic dynamics at microwatt powers. Near a critical point, magnetic-field-triggered switching between nonlinear emission states produces spectral shifts up to 162 times the bare gyromagnetic response. By enabling low-power attractor transitions and attractor-switching-amplified spectral response, active magnon-polaritons open opportunities for nonlinear microwave signal generation, high-precision sensing, and neuromorphic computing.

Large Language Model (LLM) watermarking is crucial for establishing the provenance of machine-generated text, but most existing methods rely on a centralized trust model. This model forces users to reveal potentially sensitive text to a provider for detection and offers no way to verify the integrity of the result. While asymmetric schemes have been proposed to address these issues, they are either impractical for short texts or lack formal guarantees linking watermark insertion and detection. We propose VOW, a new protocol that achieves both privacy-preserving and cryptographically verifiable watermark detection with high efficiency. Our approach formulates detection as a secure two-party computation problem, instantiating the watermark's core logic with a Verifiable Oblivious Pseudorandom Function (VOPRF). This allows the user and provider to perform detection without the user's text being revealed, while the provider's result is verifiable. Our comprehensive evaluation shows that VOW is practical for short texts and provides a crucial reassessment of watermark robustness against modern paraphrasing attacks.

In this paper, we aim at estimating the quarticity of continuous Itô semimartingales. Instead of using some classical estimators, we introduce a more intuitive one and establish a central limit theorem (CLT) for it, with a convergence rate of $1/\sqrt{Δ_n}$ in the sense of stable convergence. Moreover, we compare the asymptotic variance of this estimator with that of other existing estimators.

In multi-core quantum computing architectures, waveguide-mediated interconnects are essential for facilitating fast, high-fidelity quantum state transfer between qubits located in different chips. However, optimizing these systems typically relies on computationally expensive numerical simulations that offer limited physical insight. In this work, we derive exact analytical expressions for the state transfer dynamics of a two-qubit system coupled via a waveguide, modeled through a Jaynes-Cummings Hamiltonian and the Lindblad master equation. We apply the Monte Carlo wave-function method and obtain a closed-form solution for qubit occupation probabilities that accounts for both detuning and dissipative losses. Our analytical framework provides a significant computational speedup compared to standard numerical solvers, enabling large-scale parameter sweeps while maintaining high precision in both fidelity and latency predictions. Furthermore, the model reveals and explains systematic low-fidelity regions arising from destructive interference between internal oscillations and detuning-induced envelopes, which are phenomena that are difficult to characterize through numerical means alone. Finally, we propose a simplified latency model and an efficiency-based function to enable rapid identification of optimal operating points. This analytical approach provides a robust foundation for the design and optimization of interconnects in multi-core quantum processors.

We develop a harmonic gauge on the space of Riemannian metrics and study its role in the variational and flow-theoretic structure of geometric analysis. We prove that the harmonic gauge eliminates divergence-type terms in the first variation of the Hilbert-Einstein functional and induces a natural elliptic structure for the second variation. As a consequence, positivity of the curvature operator of the second kind implies spectral stability of the functional. This establishes a conceptual link between gauge fixing, elliptic operator theory, and geometric rigidity, and provides a variational counterpart to the Ricci-DeTurck mechanism.