High Dimensional Model Selection and Validation: A Comparison Study

Model selection is a challenging issue in high dimensional statistical analysis, and many approaches have been proposed in recent years. In this thesis, we compare the performance of three penalized logistic regression approaches (Ridge, Lasso, and Elastic Net) and three information criteria (AIC, BIC, and EBIC) on binary response variable in high dimensional situation through extensive simulation study. The models are built and selected on the training datasets, and their performance are evaluated through AUC on the validation datasets. We also display the comparison results on two real datasets (Arcene Data and University Retention Data). The performance differences among those approaches are discussed at the end

The Nelson-Seiberg theorem generalized with nonpolynomial superpotentials

The Nelson-Seiberg theorem relates R-symmetries to F-term supersymmetry breaking, and provides a guiding rule for new physics model building beyond the Standard Model. A revision of the theorem gives a necessary and sufficient condition to supersymmetry breaking in models with polynomial superpotentials. This work revisits the theorem to include models with nonpolynomial superpotentials. With a generic R-symmetric superpotential, a singularity at the origin of the field space implies both R-symmetry breaking and supersymmetry breaking. We give a generalized necessary and sufficient condition for supersymmetry breaking which applies to both perturbative and nonperturbative models.Comment: 10 pages, discussions on D-terms, runaway models and existence of vacua added, Advances in High Energy Physics accepted versio

The substructure and halo population of the Double Cluster hh and χ\chi Persei

In order to study the stellar population and possible substructures in the outskirts of Double Cluster $h$ and $\chi$ Persei, we investigate using the GAIA DR2 data a sky area of about 7.5 degrees in radius around the Double Cluster cores. We identify member stars using various criteria, including their kinematics (viz, proper motion), individual parallaxes, as well as photometric properties. A total of 2186 member stars in the parameter space were identified as members. Based on the spatial distribution of the member stars, we find an extended halo structure of $h$ and $\chi$ Persei, about 6 - 8 times larger than their core radii. We report the discovery of filamentary substructures extending to about 200 pc away from the Double Cluster. The tangential velocities of these distant substructures suggest that they are more likely to be the remnants of primordial structures, instead of a tidally disrupted stream from the cluster cores. Moreover, the internal kinematic analysis indicates that halo stars seems to be experiencing a dynamic stretching in the RA direction, while the impact of the core components is relatively negligible. This work also suggests that the physical scale and internal motions of young massive star clusters may be more complex than previously thought.Comment: 9 pagges, 9 figures, Accecpted to A&

Backpropagation-Based Cooperative Localization of Primary User for Avoiding Hidden-Node Problem in Cognitive Networks

Cognitive radio (CR) is a technology to implement opportunistic spectrum sharing to improve the spectrum utilization. However, there exists a hidden-node problem, which can be a big challenge to solve especially when the primary receiver is passive listening. We aim to provide a solution to the hidden-node problem for passive-listening receiver based on cooperation of multiple CRs. Specifically, we consider a cooperative GPS-enabled cognitive network. Once the existence of PU is detected, a localization algorithm will be employed to first estimate the path loss model for the environment based on backpropagation method and then to locate the position of PU. Finally, a disable region is identified taking into account the communication range of both the PU and the CR. The CRs within the disabled region are prohibited to transmit in order to avoid interfering with the primary receiver. Both analysis and simulation results are provided

Fast Detection Method in Cooperative Cognitive Radio Networks

Cognitive Radio (CR) technology improves the utilization of spectrum highly via opportunistic spectrum sharing, which requests fast detection as the spectrum utilization is dynamic. Taking into consideration the characteristic of wireless channels, we propose a fast detection scheme for a cooperative cognitive radio network, which consists of multiple CRs and a central control office. Specifically, each CR makes individual detection decision using the sequential probability ratio test combined with Neyman Pearson detection with respect to a specific observation window length. The proposed method upper bounds the detection delay. In addition, a weighted K out of N fusion rule is also proposed for the central control office to reach fast global decision based on the information collected from CRs, with more weights assigned for CRs with good channel conditions. Simulation results show that the proposed scheme can achieve fast detection while maintaining the detection accuracy