Kahler submanifolds and the Umehara algebra

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not

Optimization of Free Space Optical Wireless Network for Cellular Backhauling

With densification of nodes in cellular networks, free space optic (FSO) connections are becoming an appealing low cost and high rate alternative to copper and fiber as the backhaul solution for wireless communication systems. To ensure a reliable cellular backhaul, provisions for redundant, disjoint paths between the nodes must be made in the design phase. This paper aims at finding a cost-effective solution to upgrade the cellular backhaul with pre-deployed optical fibers using FSO links and mirror components. Since the quality of the FSO links depends on several factors, such as transmission distance, power, and weather conditions, we adopt an elaborate formulation to calculate link reliability. We present a novel integer linear programming model to approach optimal FSO backhaul design, guaranteeing $K$-disjoint paths connecting each node pair. Next, we derive a column generation method to a path-oriented mathematical formulation. Applying the method in a sequential manner enables high computational scalability. We use realistic scenarios to demonstrate our approaches efficiently provide optimal or near-optimal solutions, and thereby allow for accurately dealing with the trade-off between cost and reliability

Data Offloading in Load Coupled Networks: A Utility Maximization Framework

We provide a general framework for the problem of data offloading in a heterogeneous wireless network, where some demand of cellular users is served by a complementary network. The complementary network is either a small-cell network that shares the same resources as the cellular network, or a WiFi network that uses orthogonal resources. For a given demand served in a cellular network, the load, or the level of resource usage, of each cell depends in a non-linear manner on the load of other cells due to the mutual coupling of interference seen by one another. With load coupling, we optimize the demand to be served in the cellular or the complementary networks, so as to maximize a utility function. We consider three representative utility functions that balance, to varying degrees, the revenue from serving the users vs the user fairness. We establish conditions for which the optimization problem has a feasible solution and is convex, and hence tractable to numerical computations. Finally, we propose a strategy with theoretical justification to constrain the load to some maximum value, as required for practical implementation. Numerical studies are conducted for both under-loaded and over-loaded networks.Comment: 12 pages, accepted for publication in IEEE Transactions on Wireless Communication