This paper examines how climate risk shapes the connectedness between fossil and clean energy markets. To do so, we use the quantile-on-quantile connectedness framework and extend it to the frequency domain to capture return and volatility spillovers across different market conditions and horizons. We further employ an autoregressive distributed lag (ARDL) model to assess the effects of physical and transition climate risks on the estimated connectedness structure. The results show that fossil and clean energy markets exhibit both comovement and asynchrony, although comovement is dominant overall. After decomposing connectedness into short-term and long-term components, we find that return spillovers are mainly driven by short-term dynamics, whereas volatility spillovers are mainly driven by long-term dynamics. In addition, climate risks significantly affect the connectedness structure between the two markets, and policy-related risk and global warming risk are particularly important in strengthening asynchronous features. These findings suggest that climate risk influences not only the strength of spillovers, but also the way fossil and clean energy markets interact under different market states.

This paper proposes a collaborative optimal scheduling strategy based on asymmetric Nash bargaining for the integrated electricity–heat–hydrogen multi-microgrid system, which can minimize the overall system operation cost while guaranteeing the dynamic fairness of multi-microgrids energy transactions with full consideration of wind–solar uncertainty. First, a scenario generation method based on temporally correlated Latin hypercube sampling and Wasserstein probability distance-based scenario reduction is adopted to construct representative wind–solar uncertainty scenarios, which effectively mitigates the operational risks arising from wind and solar power output fluctuations in the coordinated dispatch of multi-microgrids. Then, an asymmetric Nash bargaining-based cooperative game model for energy trading is established, with each microgrid’s optimal independent operation cost as the negotiation breakdown point. The alternating direction method of multipliers is used for a distributed solution to obtain the optimal scheme that balances total system cost and trading fairness. Simulation results verify that the proposed strategy can effectively suppress operation risks from renewable uncertainty, significantly cut total system cost by 36.85%, and fully ensure trading fairness among multi-microgrid entities, with favorable engineering application value.

Through a detailed study of nondestructive controlled quantum teleportation (NCQT) with two outputs in three-dimensional and high-dimensional Hilbert spaces, we propose an NCQT scheme that synchronously and probabilistically teleports N arbitrary unknown d-dimensional single-particle states from one sender to N different receivers under the supervision of a controller, by using a d-dimensional partially entangled (2N+1)-particle state as the quantum channel. The protocol succeeds if and only if all receivers recover their respective target states, and the optimal success probability of the N-output NCQT is determined by the minimum superposition coefficient of each product two-qudit state in the partially entangled channel. In our scheme, each receiver introduces an auxiliary qubit to assist in the local recovery test. When the auxiliary-qubit measurement outcome is |0⟩, the receiver can restore the target state; when the outcome is |1⟩, the corresponding unknown original state is retained by the sender. Accordingly, the N-output controlled teleportation process can be repeated as many times as additional quantum channels are available after a failed attempt. The results show that weakly entangled channels can still realize N-output controlled teleportation through sufficiently many repetitions, whereas strongly entangled channels require only a small number of repetitions to achieve the same goal.

The zero-inflated two-parameter Rayleigh (ZITR) distribution provides a flexible framework for modeling data with excess zeros and positive observations following a two-parameter Rayleigh distribution. It is particularly suitable for right-skewed data and has applications in areas such as road traffic mortality and survival analysis. This study develops and compares several methods for constructing confidence intervals for the difference and ratio of variances from two independent ZITR populations. The considered methods include Bayesian approaches based on Markov Chain Monte Carlo (MCMC) and highest posterior density (HPD) intervals, as well as the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), approximate normal (AN), percentile bootstrap (PB), and bootstrap with standard error (BS). The performance of these methods is evaluated via Monte Carlo simulations under various parameter settings and sample sizes, using coverage probability and expected interval length as performance criteria. The results indicate that the Bayesian HPD method generally performs well across a wide range of scenarios. A real-data application using road traffic mortality data from January 2025 in Chanthaburi and Narathiwat provinces is also presented, demonstrating the practical usefulness of the proposed approaches for comparing the variance structure between the two regions.

Unmanned Aerial Vehicles (UAVs) are complex nonlinear systems characterized by high dimensionality. They are prone to aerodynamic effects, structural dynamics, actuation constraints, and networked interactions, requiring advanced mathematical models and precise control. Their governing equations involve nonlinear rigid-body dynamics coupled with fluid and elasticity models, while modern architectures introduce redundancy that creates constrained mappings between generalized forces and actuator inputs. Coordinated UAV teams add another layer of mathematical structure through graph-based interaction models that determine consensus, formation keeping, and distributed stability. These characteristics give rise to several interconnected challenges. High-fidelity aerodynamic and aeroelastic solvers provide accurate results; however, these are computationally intensive, motivating the development of reduced-order models and data-driven approximations that preserve dominant physical behavior. Methods for quantifying uncertainty support robustness assessments by characterizing the effects of parametric variation and model form error. At the actuation level, control allocation problems rely on constrained linear algebra, convex optimization, and dynamic formulations to ensure feasible and stable realization of command forces and moments. In multi-agent systems, the spectral properties of adjacency and Laplacian matrices govern convergence and cooperative behavior. This article reviews the state of the art in these areas, highlights the mathematical foundations that relate them, and provides a coherent perspective on the methods that enable reliable modeling and control of modern UAV systems.

Financial time series forecasting remains a persistent challenge due to the non-stationary nature, inherent noise, and multi-scale temporal dependencies present in market data. This paper presents MSTFNet, a multi-scale temporal fusion network that combines dilated causal convolutions with a frequency-enhanced sparse attention mechanism for improved financial prediction. The proposed architecture consists of three core components: a multi-scale dilated causal convolution module that extracts temporal patterns across different time horizons through parallel convolutional branches with varying dilation rates, a frequency-enhanced sparse attention mechanism that leverages Fast Fourier Transform to identify dominant periodic components and modulate attention weights accordingly, and an adaptive scale fusion gate that learns to dynamically combine representations from multiple temporal scales. Extensive experiments conducted on three public financial datasets (S&P 500, CSI 300, and NASDAQ Composite) spanning the period from January 2015 to December 2024 show two key results. First, consistent with near-efficient markets, the random-walk benchmark (y^t+1=yt) outperforms all the data-driven models on level-error metrics (MAE, RMSE, MAPE, and R2), establishing the martingale as the binding lower bound on point-prediction error. Second, MSTFNet achieves the highest directional accuracy (DA) across all three indices—56.3% on the S&P 500 versus 50.0% for the martingale—representing a 6.3 percentage-point improvement that generates positive pre-cost returns in a trading strategy backtest. Among the eight data-driven baselines (LSTM, GRU, TCN, Transformer, Autoformer, FEDformer, PatchTST, and iTransformer), MSTFNet also achieves the lowest MAE, reducing it by 13.6% relative to the strongest data-driven baseline (iTransformer) on the S&P 500. These results confirm that integrating multi-scale temporal modeling with frequency-domain guidance extracts a real, if modest, directional signal from financial time series.

We study functions satisfying the composition law F(xy)+F(x/y)=P(F(x),F(y)) with a symmetric polynomial combiner P. We prove that symmetry together with a quadratic degree bound on P forces a composition law of d’Alembert type. We establish a degree mismatch exclusion criterion showing that symmetric polynomial combiners with degP(u,v)≥3 do not admit nonconstant continuous solutions, provided the leading term does not cancel (Theorem 1). For continuous nonconstant functions F:R>0→R with F(1)=0 satisfying the composition law with a symmetric polynomial P of degree at most two, the combiner is necessarily of the form P(u,v)=2u+2v+cuv, c∈R (Theorem 3). The equation reduces in logarithmic coordinates to the classical d’Alembert functional equation. For c≠0, one obtains hyperbolic or trigonometric branches, while c=0 yields the squared-logarithm family. Under the cost-function assumptions F≥0 and convexity, only the hyperbolic branch with c>0 remains. A unit log-curvature calibration selects the canonical value c=2, which yields the canonical reciprocal cost F(x)=12(x+x−1)−1. For c≠0, the result extends to R>0n: every solution depends only on a single linear combination of coordinate logarithms; for c=0, the solution is a general quadratic form ∑i,jaijlnxilnxj. In either case, nontrivial coordinate-wise separable costs are excluded.

In urban traffic systems, traditional signal control can no longer meet the increasing traffic demand, and local congestion is severe during peak hours. Fixed detector data is characterized by high deployment density, full sample detection and restorable vehicle paths, providing new data support for coordinated signal control. We propose an optimization method for regional coordinated control, with the Changsha road network as the study area. Firstly, based on License Plate Recognition (LPR) data, the road network is divided into sub-networks and combined with the boundary control for regional coordinated control. Then, the critical path is taken as the control object, and the phase coordination rate is introduced as the optimization objective. The particle swarm optimization algorithm improved by the logistic chaotic map is used as the global searcher, and sequential quadratic programming is adopted as the local searcher to solve the optimization strategy for the objective function. Finally, a simulated road network is constructed in VISSIM 6.0 simulation software to verify the effectiveness of the strategy. The results show that the optimization strategy reduces intersection delay and saturation by 20.3% and 19.3% in the critical path coverage area. Road travel time and the average number of vehicle stops are reduced by 21% and 22.1%. This indicates that the regional coordinated control based on the improved particle swarm algorithm can better alleviate the peak hour traffic congestion.

The rapid expansion of the Internet of Vehicles (IoV) necessitates high-capacity backhaul connectivity, yet the deployment of such networks under strict hardware and power constraints poses significant computational challenges for network optimization. To address this challenge, this paper investigates a joint transmit–receive beamforming optimization problem for narrowband wireless backhaul in IoV networks under constant-modulus constraints. Unlike ideal digital architectures, we focus on cost-effective analog phase shifters, which introduce strictly non-convex constant-modulus constraints, rendering the optimization problem mathematically intractable for standard solvers. Since the resulting problem is highly non-convex, we develop two structured numerical methods: an iterative alternating optimization (AO) method and a joint optimization (JO) method, where AO employs auxiliary WMMSE-guided alternating updates together with constant-modulus projection, while JO jointly updates both beamformers over the constant-modulus feasible set. We compare their achievable sum-rate performance with that of a CDO-based benchmark and analyze their dominant computational costs through representative Big-O complexity expressions. Furthermore, we examine the effect of SVD-based and random feasible initializations on empirical convergence behavior, runtime, and final achievable performance. Simulation results demonstrate that the proposed computational methods significantly improve achievable sum-rate performance compared with the CDO benchmark. Moreover, SVD-based initialization provides a more structured starting point and generally leads to better convergence behavior and lower runtime than random feasible initialization. The empirical timing results further show that AO exhibits faster empirical convergence and requires lower runtime, whereas JO achieves better final sum-rate performance after more iterations.

The three main IBE schemes, i.e., Boneh–Franklin, Cocks and Boneh–Gentry–Hamburg present both strengths and weaknesses. In this paper, we introduce a more efficient variant of BGH (while preserving receiver’s anonymity) based on the work of Jhanwar and Barua. More precisely, we provide the reader with a scheme with reduced complexities for encryption and decryption algorithms and present a new perspective on the initial set of solutions.