Minimax rank estimation for subspace tracking

Rank estimation is a classical model order selection problem that arises in a variety of important statistical signal and array processing systems, yet is addressed relatively infrequently in the extant literature. Here we present sample covariance asymptotics stemming from random matrix theory, and bring them to bear on the problem of optimal rank estimation in the context of the standard array observation model with additive white Gaussian noise. The most significant of these results demonstrates the existence of a phase transition threshold, below which eigenvalues and associated eigenvectors of the sample covariance fail to provide any information on population eigenvalues. We then develop a decision-theoretic rank estimation framework that leads to a simple ordered selection rule based on thresholding; in contrast to competing approaches, however, it admits asymptotic minimax optimality and is free of tuning parameters. We analyze the asymptotic performance of our rank selection procedure and conclude with a brief simulation study demonstrating its practical efficacy in the context of subspace tracking.Comment: 10 pages, 4 figures; final versio

Profile Likelihood Biclustering

Biclustering, the process of simultaneously clustering the rows and columns of a data matrix, is a popular and effective tool for finding structure in a high-dimensional dataset. Many biclustering procedures appear to work well in practice, but most do not have associated consistency guarantees. To address this shortcoming, we propose a new biclustering procedure based on profile likelihood. The procedure applies to a broad range of data modalities, including binary, count, and continuous observations. We prove that the procedure recovers the true row and column classes when the dimensions of the data matrix tend to infinity, even if the functional form of the data distribution is misspecified. The procedure requires computing a combinatorial search, which can be expensive in practice. Rather than performing this search directly, we propose a new heuristic optimization procedure based on the Kernighan-Lin heuristic, which has nice computational properties and performs well in simulations. We demonstrate our procedure with applications to congressional voting records, and microarray analysis.Comment: 40 pages, 11 figures; R package in development at https://github.com/patperry/biclustp

Fingerprint fuzzy vault: Security analysis and a new scheme

A fingerprint fuzzy vault uses a fingerprint A to lock a strong secret k and only a close fingerprint from the same finger can be used to unlock k. An attacker who has stolen the vault will not be able to get useful information about A or k.%0d%0a In this research, we shall study the security of a major fingerprint fuzzy vault developed by Nandakumar et al. through investigating the security implication of helper data, which are stored in the fuzzy vault for fingerprint alignment. We will show that helper data leak information about fingerprints and thus compromise the security claim on the fingerprint fuzzy vault scheme. Next, we will propose a new fingerprint fuzzy vault scheme, which is based on traditional representation of fingerprints in minutia points and does not need helper data for alignment

MECHANISTIC INVESTIGATIONS OF THE TRANS EXCISION-SPLICING AND TRANS INSERTION-SPLICING REACTION

Group I intron-derived ribozymes are catalytic RNAs that have been engineered to catalyze a variety of different reactions, in addition to the native self-splicing reaction. One such ribozyme, derived from a group I intron of Pneumocystis carinii, can modify RNA transcripts through either the excision or insertion of RNA sequences. These reactions are mediated through the trans excision-splicing (TES) or trans insertionsplicing (TIS) reaction pathways. To increase our current understanding of these reactions, as well as their general applicability, a mechanistic and kinetic framework for the TES reaction was established. Furthermore, additional ribozymes were investigated for their ability to catalyze the TES reaction. Lastly, the development of the TIS reaction into a viable strategy for the manipulation of RNA transcripts was investigated. The TES reaction proceeds through two reaction steps: substrate cleavage followed by exon ligation. Mechanistic studies revealed that substrate cleavage is catalyzed by the 3’ terminal guanosine of the Pneumocystis ribozyme. Moreover, kinetic studies suggest that a conformational change exists between the individual reaction steps. Intron-derived ribozymes from Tetrahymena thermophila and Candida albicans were also investigated for their propensity to catalyze the TES reaction. The results showed that each ribozyme could catalyze the TES reaction; however, Pneumocystis carinii is the most effective using the model constructs. Investigations of the TIS reaction focused on developing a new strategy for the insertion of modified oligonucleotides into an RNA substrate. These studies used oligonucleotides with modifications to the sugar, base, and backbone positions. Each of the modified oligonucleotides was shown to be an effective TIS substrate. These results demonstrate that TIS is a viable strategy for the incorporation of modified oligonucleotides, of varying composition, into an intended RNA target. The results from these studies show that group I introns are highly adaptable for catalyzing non-native reactions, including the TES and TIS reactions. Furthermore, group I introns are capable of catalyzing these unique reactions through distinct reaction pathways. Overall, these results demonstrate that group I introns are multi-faceted catalysts