On Degrees of Freedom of Projection Estimators with Applications to Multivariate Nonparametric Regression

In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as outputs of linearly constrained quadratic optimization procedures, namely, minimizers of the least squares criterion with linear constraints and/or quadratic penalties. As special cases of our results, we derive explicit expressions for the degrees of freedom in many nonparametric regression problems, e.g., bounded isotonic regression, multivariate (penalized) convex regression, and additive total variation regularization. Our theory also yields, as special cases, known results on the degrees of freedom of many well-studied estimators in the statistics literature, such as ridge regression, Lasso and generalized Lasso. Our results can be readily used to choose the tuning parameter(s) involved in the estimation procedure by minimizing the Stein's unbiased risk estimate. As a by-product of our analysis we derive an interesting connection between bounded isotonic regression and isotonic regression on a general partially ordered set, which is of independent interest.Comment: 72 pages, 7 figures, Journal of the American Statistical Association (Theory and Methods), 201

Development of Information Technology Auditing Teaching Modules: An Interdisciplinary Endeavor between Seidenberg and Lubin Faculty

The original goals of the project were to develop interdisciplinary Information Technology (IT) Auditing teaching modules, to be integrated into courses offered by both Business and Information Technology disciplines during Fall 2009 and Spring 2010. IT Auditing is an interdisciplinary field which requires understanding audit, control, technology and security concepts in accordance with audit standards, guidelines, and best practices. Thus, IT Auditing requires interdisciplinary knowledge across IT and Accounting/Auditing domains. With increasing use of IT in business processes, the demand for IT Auditors is increasing rapidly, offering a lucrative career path. Acquiring IT Audit related knowledge and skills will help our students improve their career opportunities by exploring this growing field. Based upon the curriculum content areas of the CISA Exam as well as the ISACA Model Curriculum, we proposed the following three interdisciplinary teaching modules for IT Auditing: 1) IT Auditing Frameworks & Business Continuity; 2) IT Lifecycle Management & Service Delivery; and 3) Protection of Information Assets. We had developed the three teaching modules. Each individual module can be covered in one to two weeks. The entire set of three IT Auditing modules can then be covered in 3-4 weeks of class time. For each of the individual modules, we had developed presentation slides, reading lists and online quizzes based on the CISA Exam. We had also identified an overarching case study to be used throughout the three individual modules for continuity reasons

Multiple Unpinned Dirac Points in Group-Va Single-layers with Phosphorene Structure

Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitute one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic $k$-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling, we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The spin-orbit coupling generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realize the unpinned Dirac points in strained phosphorene.Comment: 30 pages, 6 figure

Security and Privacy Issues in Wireless Mesh Networks: A Survey

This book chapter identifies various security threats in wireless mesh network (WMN). Keeping in mind the critical requirement of security and user privacy in WMNs, this chapter provides a comprehensive overview of various possible attacks on different layers of the communication protocol stack for WMNs and their corresponding defense mechanisms. First, it identifies the security vulnerabilities in the physical, link, network, transport, application layers. Furthermore, various possible attacks on the key management protocols, user authentication and access control protocols, and user privacy preservation protocols are presented. After enumerating various possible attacks, the chapter provides a detailed discussion on various existing security mechanisms and protocols to defend against and wherever possible prevent the possible attacks. Comparative analyses are also presented on the security schemes with regards to the cryptographic schemes used, key management strategies deployed, use of any trusted third party, computation and communication overhead involved etc. The chapter then presents a brief discussion on various trust management approaches for WMNs since trust and reputation-based schemes are increasingly becoming popular for enforcing security in wireless networks. A number of open problems in security and privacy issues for WMNs are subsequently discussed before the chapter is finally concluded.Comment: 62 pages, 12 figures, 6 tables. This chapter is an extension of the author's previous submission in arXiv submission: arXiv:1102.1226. There are some text overlaps with the previous submissio

Clinicopathological features and CCT2 and PDIA2 expression in gallbladder squamous/adenosquamous carcinoma and gallbladder adenocarcinoma

BACKGROUND: Gallbladder cancer (GBC) is a relatively uncommon carcinoma among gastrointestinal cancers and usually has a rather poor prognosis. The most common subtype of GBC is adenocarcinoma (AC), which accounts for about 90% of GBC. Squamous carcinoma/adenosquamous carcinoma (SC/ASC) are comparatively rare histopathological subtypes of GBC. The clinicopathological features and biological behaviors of SC/ASC have not been well-characterized. No molecular biomarkers are currently available for predicting the progression, metastasis, and prognosis of the SC/ASC subtype of GBC. METHODS: We examined the expression levels of CCT2 and PDIA3 by immunohistochemistry (IHC) staining in human GBC tissue samples collected from 46 patients with SC/ASC and evaluated the clinicopathological significance of both CCT2 and PDIA3 expression in the SC/ASC subtypes of GBC by Kaplan-Meier analysis and multivariate Cox regression analysis. For comparison, we included specimens from 80 AC patients in our study to investigate the specificity of CCT2 and PDIA3 expression in GBC subtypes. RESULTS: We found that the positive expression of CCT2 and PDIA3 was significantly associated with clinicopathological features of both SC/ASC and AC specimens, including high TNM stage and lymph node metastasis. Univariate analysis revealed that the two-year survival rate was significantly lower for patients with positive expression of CCT2 and PDIA3 than for those with negative expression. Multivariate analysis also indicated that the positive expression of CCT2 and PDIA3 was negatively correlated with poor postoperative patient survival and positively correlated with high mortality. CONCLUSIONS: Our study suggests that positive expression of CCT2 or PDIA3 is associated with tumor progression and the clinical behavior of gallbladder carcinoma. Therefore, CCT2 and PDIA3 could be potentially important diagnostic and prognostic biomarkers for both SC/ASC and AC subtypes of GBC

Enhanced DPPH radical scavenging activity and DNA protection effect of litchi pericarp extract by Aspergillus awamori bioconversion

BACKGROUND: Litchi (Litchi chinensis Sonn.) pericarp is a major byproduct which contains a significant amount of polyphenol. This study was designed to biotransformation litchi pericarp extract (LPE) by Aspergillus awamori to produce more bioactive compounds with stronger antioxidant activities. RESULTS: The study exhibited that the 2,2-diphenyl-1-picrylhydrazyl radical scavenging activities significantly (p < 0.05) increased from 15.53% to 18.23% in the water-extracted fraction and from 25.41% to 36.82% in the ethyl acetate-extracted fraction. Application of DNA cleavage assay further demonstrated the enhanced protection effect of the fermented phenolics on DNA damage. It is also noted that the water-extracted fraction of the fermented LPE possessed a much stronger capacity than the ethyl acetate-extracted fraction to prevent from damage of supercoiled DNA. Interestingly, it was found that some new compounds such as catechin and quercetin appeared after of A. awamori fermentation of LPE, which could account for the enhanced antioxidant activity. CONCLUSION: The DPPH radical scavenging activity and DNA protection effect of LPE were increased by Aspergillus awamori bioconversion while some compounds responsible for the enhanced antioxidant activity were identified. This study provided an effective way of utilizing fruit pericarp as a readily accessible source of the natural antioxidants in food industry and, thus, extended the application area such as fruit by-products