We consider the problem of estimating overlapping community memberships. Existing provable algorithms for this problem either make strong assumptions about the population [33,16], or are too computationally expensive [3,15]. We work under the popular Mixed Membership Stochastic Blockmodel (MMSB) [2]. Using the inherent geometry of this model, we link the inference of overlapping communities to the problem of finding corners in a noisy rotated and scaled simplex, for which consistent algorithms exist [12]. We use this as a building block for our algorithm to infer the community memberships of each node. Furthermore, we prove that each node's soft membership vector converges to its population counterpart. To our knowledge, this is the first work to obtain rate of convergence for community membership vectors of each node, in contrast to previous work which obtain convergence results for memberships of all nodes as a whole. As a byproduct of our analysis, we derive sharp row-wise eigenvector deviation bounds, and provide a cleaning step that improves the performance significantly for sparse networks. We also propose both necessary and sufficient conditions for identifiability of the model, while existing methods typically present sufficient conditions. The empirical performance of our method is shown using simulated and real datasets scaling up to 100,000 nodes. Identifiability:We present both necessary and sufficient conditions for identifiability of the MMSB model in Section 2. Specifically, if each of the K communities has at least one "pure" node, then a full-rank B is sufficient for identifiability. Surprisingly, even a B of rank K − 1 can be sufficient, as long as no row of B is an affine combination of the other rows of B. On the other hand, if the entries of ρB are strictly between 0 and 1, then pure nodes are necessary for identifiability. Our sufficient condition is more general than that in [33]. To our knowledge, we are the first to report both necessary and sufficient conditions for identifiability under the MMSB model. Recovery algorithm:It is not hard to see that for the MMSB model, the population eigenvectors (i.e., eigenvectors of the matrix P) form a rotated and scaled simplex. We present an algorithm called SPACL, which re-purposes an existing algorithm [12] for detecting corners in a rotated and scaled simplex to find pure nodes, and then uses these to infer the parameters Θ and B. It also includes a novel preprocessing step that improves performance in sparse settings. The main compute-intensive parts of the algorithm are a) top-K eigen-decomposition of A, b) calculating k-nearest neighbors of a point for preprocessing. There are highly optimized algorithms and data structures for both of these steps [8,24,9].

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Hybrid electric vehicles (HEVs) combined with more than one power source offer additional flexibility to improve the fuel economy and to reduce pollutant emissions. The dynamic-programming-based supervisory controller (DPSC) presented here investigates the fuel economy improvement and emissions reduction potential and demonstrates the trade-off between fuel economy and the emission of nitrogen oxides (NO x) for a state-of-charge-sustaining parallel HEV. A weighted cost function consisting of fuel economy and emissions is proposed in this paper. Any possible engine-motor power pairs meeting with the power requirement is considered to minimize the weighted cost function over the given driving cycles through this dynamic program algorithm. The fuel-economy-only case, the NO x-only case, and the fuel-NO x case have been achieved by adjusting specific weighting factors, which demonstrates the flexibility and advantages of the DPSC. Compared with operating the engine in the NO x-only case, there is 17.4 per cent potential improvement in the fuel-economy-only case. The fuel-NO x case yields a 15.2 per cent reduction in NO x emission only at the cost of 5.5 per cent increase in fuel consumption compared with the fuel-economy-only case.

Energy optimization control for a parallel hybrid electric system with automated mechanical transmission (AMT) can be divided into two steps in this paper. First, the AMT shift is not optimized and the optimal torque distribution strategy is proposed to minimize the powertrain equivalent specific fuel consumption by considering the power conversion efficiency, which distributes the vehicle single torque request into separate torque requests for the internal combustion engine (ICE) and the electric motor (EM). The distribution results are expressed in a table format and can be found from the simple process of looking up the table using the vehicle torque request, the ICE speed, and the battery state of charge (SOC). Then, the AMT shift control is suggested to maximize the powertrain system efficiency and optimizes the speed as the basis for the above-mentioned torque distribution, in which the ICE efficiency, the EM efficiency, and the battery efficiency are all explicitly taken into account. The AMT optimal shift control law and the EM optimal torque are essentially look-up-table-based control according to the ICE power, the EM power, the vehicle velocity, and the battery SOC after offline calculations. Simulation results reveal that potential fuel economy improvement has been achieved by using the energy optimization control.

In this paper, the deactivation of diesel engines used in road vehicles was studied because it changes the progress of combustion, which might be advantageous to the economy of engines. Based on a one-dimensional simulation and an experimental study of a supercharged diesel engine which deactivates half the cylinders at light loads and idle, this paper presents results which show that, when the mean effective pressure of the engine is lower than 3.5 bar, cylinder deactivation decreases the brake specific fuel consumption by 0–17% and by 26% at idle if the intake valves and the exhaust valves are kept closed at the same time. However, the engine and the supercharger do not match well after deactivation and the mass of intake air decreased greatly, which also resulted in a large decrease in the nitrogen oxide emissions.