Principal Boundary on Riemannian Manifolds

We consider the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional ambient space, we aim to acquire a classification boundary for the classes with labels, using the intrinsic metric on the manifolds. Motivated by finding an optimal boundary between the two classes, we invent a novel approach -- the principal boundary. From the perspective of classification, the principal boundary is defined as an optimal curve that moves in between the principal flows traced out from two classes of data, and at any point on the boundary, it maximizes the margin between the two classes. We estimate the boundary in quality with its direction, supervised by the two principal flows. We show that the principal boundary yields the usual decision boundary found by the support vector machine in the sense that locally, the two boundaries coincide. Some optimality and convergence properties of the random principal boundary and its population counterpart are also shown. We illustrate how to find, use and interpret the principal boundary with an application in real data.Comment: 31 pages,10 figure

Superfluidity and effective mass of magnetoexcitons in topological insulator bilayers: Effect of inter-Landau-level Coulomb interaction

The effective mass and superfluidity-normal phase transition temperature of magnetoexcitons in topological insulator bilayers are theoretically investigated. The intra-Landau-level Coulomb interaction is treated perturbatively, from which the effective magnetoexciton mass is analytically discussed. The inclusion of inter-Landau-level Coulomb interaction by more exact numerical diagonalization of the Hamiltonian brings out important modifications to magnetoexciton properties, which are specially characterized by prominent reduction in the magnetoexciton effective mass and promotion in the superfluidity-normal phase transition temperature at a wide range of external parameters.Comment: 5.6 EPL pages, 4 figure

Coalitional Game Theoretic Approach for Cooperative Transmission in Vehicular Networks

Cooperative transmission in vehicular networks is studied by using coalitional game and pricing in this paper. There are several vehicles and roadside units (RSUs) in the networks. Each vehicle has a desire to transmit with a certain probability, which represents its data burtiness. The RSUs can enhance the vehicles' transmissions by cooperatively relaying the vehicles' data. We consider two kinds of cooperations: cooperation among the vehicles and cooperation between the vehicle and RSU. First, vehicles cooperate to avoid interfering transmissions by scheduling the transmissions of the vehicles in each coalition. Second, a RSU can join some coalition to cooperate the transmissions of the vehicles in that coalition. Moreover, due to the mobility of the vehicles, we introduce the notion of encounter between the vehicle and RSU to indicate the availability of the relay in space. To stimulate the RSU's cooperative relaying for the vehicles, the pricing mechanism is applied. A non-transferable utility (NTU) game is developed to analyze the behaviors of the vehicles and RSUs. The stability of the formulated game is studied. Finally, we present and discuss the numerical results for the 2-vehicle and 2-RSU scenario, and the numerical results verify the theoretical analysis.Comment: accepted by IEEE ICC'1

A Cross-layer Perspective on Energy Harvesting Aided Green Communications over Fading Channels

We consider the power allocation of the physical layer and the buffer delay of the upper application layer in energy harvesting green networks. The total power required for reliable transmission includes the transmission power and the circuit power. The harvested power (which is stored in a battery) and the grid power constitute the power resource. The uncertainty of data generated from the upper layer, the intermittence of the harvested energy, and the variation of the fading channel are taken into account and described as independent Markov processes. In each transmission, the transmitter decides the transmission rate as well as the allocated power from the battery, and the rest of the required power will be supplied by the power grid. The objective is to find an allocation sequence of transmission rate and battery power to minimize the long-term average buffer delay under the average grid power constraint. A stochastic optimization problem is formulated accordingly to find such transmission rate and battery power sequence. Furthermore, the optimization problem is reformulated as a constrained MDP problem whose policy is a two-dimensional vector with the transmission rate and the power allocation of the battery as its elements. We prove that the optimal policy of the constrained MDP can be obtained by solving the unconstrained MDP. Then we focus on the analysis of the unconstrained average-cost MDP. The structural properties of the average optimal policy are derived. Moreover, we discuss the relations between elements of the two-dimensional policy. Next, based on the theoretical analysis, the algorithm to find the constrained optimal policy is presented for the finite state space scenario. In addition, heuristic policies with low-complexity are given for the general state space. Finally, simulations are performed under these policies to demonstrate the effectiveness