Unmanned Aerial Vehicles (UAVs) have emerged as powerful tools for real-time data collection across Points of Interest (PoIs) in critical domains such as environmental monitoring, disaster response, and intelligent transportation systems. In this paper, we tackle the challenging problem of UAV trajectory planning to minimize Age of Information (AoI)—a key metric that captures data freshness—within networks modeled as graphs. By establishing fundamental lower bounds on achievable AoI under any routing policy, we reveal that these bounds become tight specifically when the graph contains a Hamiltonian cycle, while proving the general AoI minimization problem is NP-hard. To overcome this complexity barrier, we introduce two innovative approximation algorithms: HPA, which achieves a 4 3 -approximation ratio for Hamiltonian paths, and TSA, which guarantees a 2-approximation ratio for general connected graphs. For disconnected graphs, we propose algorithms to construct the connected graphs by adding additional nodes, and then apply HPA and TSA on the connected graphs. Numerical studies further show that these algorithms outperform both conventional heuristic and deep reinforcement learning approaches and maintain robust performance across diverse graph granularities, confirming their real-world applicability and effectiveness.

Data streams collected from multiple sources are rarely independent. Values evolve over time and influence one another across sequences. These correlations improve prediction in healthcare, finance, and smart-city control yet violate the record-independence assumption built into most Differential Privacy (DP) mechanisms. To restore rigorous privacy guarantees without sacrificing utility, we introduce Correlated-Sequence Differential Privacy (CSDP), a framework specifically designed for preserving privacy in correlated sequential data. CSDP addresses two linked challenges: quantifying the extra information an attacker gains from joint temporal and cross-sequence links, and adding just enough noise to hide that information while keeping the data useful. We model multivariate streams as a Coupling Markov Chain, yielding the derived loose leakage bound expressed with a few spectral terms and revealing a counterintuitive result: stronger coupling can actually decrease worst-case leakage by dispersing perturbations across sequences. Guided by these bounds, we build the Freshness-Regulated Adaptive Noise (FRAN) mechanism—combining data aging, correlation-aware sensitivity scaling, and Laplace noise—that runs in linear time. Tests on two-sequence datasets show that CSDP improves the privacy-utility trade-off by approximately 50% over existing correlated-DP methods and by two orders of magnitude compared to the standard DP approach.

We investigate an unmanned aerial vehicle (UAV) trajectory planning problem for minimizing the Age of Information (AoI) over a sensor network defined on a square grid graph. Despite that the AoI-minimal trajectory planning problem is NP-hard, we derive the fundamental limit of minimum network AoI achieved among all feasible UAV trajectories. We show that such a lower bound is only achievable for graphs with a Hamiltonian Cycle (HC). Based on this finding, we develop an HPA algorithm for graphs with at least one Hamiltonian Path (HP). It achieves a time-average network AoI no more than of that of the optimal trajectory. For more general graphs, we propose a tree-searching algorithm (TSA) which achieves a time-average network AoI at most twice that of the optimal trajectory with a polynomial-time complexity. Numerical results show that the average performance of TSA could be much better than the theoretical bound, and both two algorithms significantly outperform the baseline scheme.

We consider a priority queueing system where a single processor serves k classes of packets that are generated randomly following Poisson processes. Our objective is to compute the expected Peak Age of Information (PAoI) under various scenarios. In particular, we consider two situations where the buffer size at each queue is one and infinite, and in the infinite buffer size case we consider First Come First Serve (FCFS) and Last Come First Serve (LCFS) as service disciplines. For the system with buffer size one at each queue, we derive PAoI exactly for the case of exponential service time and bounds (which are excellent approximations) for the case of general service time, with small k. For the system with infinite buffer size, we provide closed-form expressions of PAoI for both FCFS and LCFS where service time is general and k could be large. Using those results we investigated the effect of ordering of priorities and service disciplines for the various scenarios. We perform extensive numerical studies to validate our results and develop insights.insights.

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.

The relationships between artificial neural networks and graph theory are considered in detail. The applications of artificial neural networks to many difficult problems of graph theory, especially NP-complete problems, and the applications of graph theory to artificial neural networks are discussed. For example graph theory is used to study the pattern classification problem on the discrete type feedforward neural networks, and the stability analysis of feedback artificial neural networks etc.