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3D networks with unmanned aerial vehicles (UAVs) are emerging as a cornerstone of next-generation communication infrastructure, offering flexibility and enhanced coverage in challenging environments. However, prior works predominantly focus on UAV-specific optimizations and high-throughput strategies, often overlooking the critical aspect of network reliability when incorporating these movable entities in the infrastructure. Resilience is paramount in such networks, as it ensures stable performance and connectivity in the face of dynamic conditions, such as mobile edges, transient ground devices, and significant signal interference from urban environments. To address this gap, this article proposes a topology-driven scheme from a holistic view of the 3D networks, leveraging comprehensive scene-based information to enable real-time network adaptability through topological (re)configuration. We decompose this reliability problem into three intertwined stages: topological resilience quantification, UAV self-positioning, and learning-based connectivity optimization. This framework ensures network resilience from a functional perspective, emphasizing the ability to consistently deliver high-quality performance while mitigating connectivity interruptions, essential for reliability of next-generation 3D communication infrastructure. Experimental results validate the effectiveness of our approach, demonstrating significant improvements over traditional methods in terms of bandwidth allocation to ground devices and load balancing among UAVs. Notably, our system excels in highly dynamic scenarios, where it adapts to network instability and connectivity failures on-demand, ensuring consistent and reliable communication performance. 

Abstract In this paper, we present a general wall‐crossing theory for K‐stability and K‐moduli of log Fano pairs whose boundary divisors can be nonproportional to the anticanonical divisor. Along the way, we prove that there are only finitely many K‐semistable domains associated to the fibers of a log‐bounded family of couples. Under the additional assumption of volume bounded from below, we show that K‐semistable domains are semialgebraic sets (although not necessarily polytopes). As a consequence, we obtain a finite semialgebraic chamber decomposition for wall crossing of K‐moduli spaces. In the case of one boundary divisor, this decomposition is an expected finite interval chamber decomposition. As an application of the theory, we prove a comparison theorem between geometric invariant theory (GIT)‐stability and K‐stability in nonproportional setting when the coefficient of the boundary is sufficiently small. 

Abstract We describe the K-moduli spaces of weighted hypersurfaces of degree$$2(n+3)$$in$$\mathbb {P}(1,2,n+2,n+3)$$. We show that the K-polystable limits of these weighted hypersurfaces are also weighted hypersurfaces of the same degree in the same weighted projective space. This is achieved by an explicit study of the wall crossing for K-moduli spaces$$M_w$$of certain log Fano pairs with coefficientwwhose double cover gives the weighted hypersurface. Moreover, we show that the wall crossing of$$M_w$$coincides with variation of GIT except at the last K-moduli wall which gives a divisorial contraction. Our K-moduli spaces provide new birational models for some natural loci in the moduli space of marked hyperelliptic curves.