Community Detection by L0L_0-penalized Graph Laplacian

Community detection in network analysis aims at partitioning nodes in a network into $K$ disjoint communities. Most currently available algorithms assume that $K$ is known, but choosing a correct $K$ is generally very difficult for real networks. In addition, many real networks contain outlier nodes not belonging to any community, but currently very few algorithm can handle networks with outliers. In this paper, we propose a novel model free tightness criterion and an efficient algorithm to maximize this criterion for community detection. This tightness criterion is closely related with the graph Laplacian with $L_0$ penalty. Unlike most community detection methods, our method does not require a known $K$ and can properly detect communities in networks with outliers. Both theoretical and numerical properties of the method are analyzed. The theoretical result guarantees that, under the degree corrected stochastic block model, even for networks with outliers, the maximizer of the tightness criterion can extract communities with small misclassification rates even when the number of communities grows to infinity as the network size grows. Simulation study shows that the proposed method can recover true communities more accurately than other methods. Applications to a college football data and a yeast protein-protein interaction data also reveal that the proposed method performs significantly better.Comment: 40 pages, 15 Postscript figure

The Multiple Reconstruction out of Crisis: Masculinities in Bellow’s Novellas

Saul Bellow’s novels mainly focus on social lives of contemporary urban American men. Taking his four novellas covering the second half of the 20th century as an example, this paper aims to reveal in change of social structure and cultural contexts how masculinity is in crisis extrinsically or intrinsically, and how social factors such as work and marriage assist in fashioning it. Through positive dialogues with social changes and cultural turn, Bellow deconstructs the masculinity as well as establishes a new democratic gender order and harmonious gender relations to reconstruct multiple masculinities

Optimal Event-Driven Multi-Agent Persistent Monitoring of a Finite Set of Targets

We consider the problem of controlling the movement of multiple cooperating agents so as to minimize an uncertainty metric associated with a finite number of targets. In a one-dimensional mission space, we adopt an optimal control framework and show that the solution is reduced to a simpler parametric optimization problem: determining a sequence of locations where each agent may dwell for a finite amount of time and then switch direction. This amounts to a hybrid system which we analyze using Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven gradient-based algorithm which is also robust with respect to the uncertainty model used. The resulting controller depends on observing the events required to excite the gradient-based algorithm, which cannot be guaranteed. We solve this problem by proposing a new metric for the objective function which creates a potential field guaranteeing that gradient values are non-zero. This approach is compared to an alternative graph-based task scheduling algorithm for determining an optimal sequence of target visits. Simulation examples are included to demonstrate the proposed methods.Comment: 12 pages full version, IEEE Conference on Decision and Control, 201

Contributing to the Individual Income Tax Reform Debate in China: Is Family Based Filing of Individual Income Tax Returns a Feasible Solution to the Social Problems Arising from the Increasing Family Income Inequality in China?

China’s new wave of Individual Income Tax Reform is currently hotly debated. The Finance Minister, Lou Jiwei was reported to say that the relevant government departments in China – the State Council, the Ministry of Finance, and the State Administration of Finance had worked out a reform plan together in 2015. One goal of this plan is to move China’s scheduler individual income tax to a global structure, and to put in place policies that contribute to income redistribution that takes into consideration family related expenditure, such as looking after the elderly and childcare.A review of the literature shows that Chinese scholars and commentators suggest that China could learn directly from the US, adopt their global income tax system and allow family based filing of individual income tax returns. The literature does not provide reasons for this suggestion.This paper performs a feasibility study to assess whether China could adopt the suggestions proposed by the prevailing literature. The study is performed based on a “revenue neutrality” analysis that compares projected revenue from existing policies, and that collectable if China allows family based individual income tax filing.Results from a pilot study reports that the projected revenue from allowing family based individual income tax filing would be at a level that is closer to 40% of revenue collectable if China does not allow family based individual income tax filing. This result suggests that policy makers in China need to take careful considerations of costings before proceeding with thereform

Vacuum induced transparency and photon number resolved Autler-Townes splitting in a three-level system

We study the absorption spectrum of a probe field by a {\Lambda}-type three-level system, which is coupled to a quantized control field through the two upper energy levels. The probe field is applied to the ground and the second excited states. When the quantized control field is in vacuum, we derive a threshold condition to discern vacuum induced transparency (VIT) and vacuum induced Autler- Townes splitting (ATS). We also find that the parameter change from VIT to vacuum induced ATS is very similar to that from broken PT symmetry to PT symmetry. Moreover, we find the photon number resolved spectrum in the parameter regime of vacuum induced ATS when the mean photon number of the quantized control field is changed from zero (vacuum) to a finite number. However, there is no photon number resolved spectrum in the parameter regime of VIT even that the quantized control field contains the finite number of photons. Finally, we further discuss possible experimental realization