Informational Divergence Approximations to Product Distributions

The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verd\'{u} on resolvability. The result also extends to cases where the source distribution is unknown but the entropy is known

Light Field Denoising via Anisotropic Parallax Analysis in a CNN Framework

Light field (LF) cameras provide perspective information of scenes by taking directional measurements of the focusing light rays. The raw outputs are usually dark with additive camera noise, which impedes subsequent processing and applications. We propose a novel LF denoising framework based on anisotropic parallax analysis (APA). Two convolutional neural networks are jointly designed for the task: first, the structural parallax synthesis network predicts the parallax details for the entire LF based on a set of anisotropic parallax features. These novel features can efficiently capture the high frequency perspective components of a LF from noisy observations. Second, the view-dependent detail compensation network restores non-Lambertian variation to each LF view by involving view-specific spatial energies. Extensive experiments show that the proposed APA LF denoiser provides a much better denoising performance than state-of-the-art methods in terms of visual quality and in preservation of parallax details

Robust parameter estimation and pivotal inference under heterogeneous and nonstationary processes

Robust parameter estimation and pivotal inference is crucial for credible statistical conclusions. This thesis addresses these issues in three contexts: long-memory parameter estimation robust to low frequency nonstationary contamination, long-memory properties of financial time series, and inference on structural changes in a joint segmented trend with heterogeneous noise. Chapter 1 considers robust estimation of the long-memory parameter allowing for a wide collection of contamination processes, in particular low frequency nonstationary processes such as random level shifts. We propose a robust modified local-Whittle estimator and show it has the usual asymptotic distribution. We also provide modifications to further account for short-memory dynamics and additive noise. The proposed estimator provides substantial efficiency gains compared to existing methods in the presence of contaminations, without sacrificing efficiency when these are absent. Chapter 2 applies the modified local-Whittle estimator to various volatilities series for stock indices and exchange rates to robustly estimate the long-memory parameter. Our findings suggest that all series are a combination of long and short-memory processes and random level shifts, with the magnitude of each component varying across series. Our results contrast with the view that long-memory is the dominant feature. Chapter 3 is concerned with pivotal inference about structural changes in a joint segmented trend with heterogeneous noise. We provide tests for changes in the slope and the variance of the noise valid when both may be present, each allowed to occur at different dates. We suggest procedures for four testing problems

Identification and Characterization of the Lysobactin Biosynthetic GeneCluster and Its Unusual Termination Module

Nonribosomal peptides (NRPs) constitute a class of structurally and functionally diverse natural products, which are synthesized by nonribosomal peptide synthetases (NRPSs). NRPs exhibit a wide range of bioactivities, including antimicrobial, antifungal, antiviral, immunosuppressive and antitumor properties. Numerous of these compounds have been discovered via screening of microbial extracts. In recent years, increasing knowledge of the biosynthesis of natural products and development of new sequencing techniques lead to the identification of gene clusters, which are putatively involved in the biosynthesis of nonribosomal peptides. Based on the sequencing result of the genome of Lysobacter sp. ATCC 53042 and the former work from Bernhard et al.[1] on the gene fragment involved in the biosynthesis of lysobactin, the entire biosynthetic gene cluster of lysobactin was identified and characterized. The cluster encodes two multimodular nonribosomal peptide synthetases (LybA and LybB). Due to the correlation of the number of modules found within the lysobactin gene cluster and the primary sequence of lysobactin, the biosynthesis of lysobactin follows the colinearity principle. Investigation of the adenylation domain substrate specificities confirmed the direct association between the synthetases and lysobactin biosynthesis. Furthermore, an unusual tandem thioesterase domain architecture (PCP-TE1-TE2) of the LybB termination module was identified. Biochemical characterization of the individual thioesterases in vitro proved that the first thioesterase is responsible for the cyclization and the release of the final product, while the second thioesterase showed a type II TE activity, which is responsible for the regeneration of the mis-primed peptide carrier protein during the biosynthesis of lysobactin. Together with the observation of the proteolytic degradation during the heterologous production of LybB-PCP-TE1-TE2 giving rise of LybB-PCP-TE1, we have proposed that the LybB is also cleaved to generate lone-standing LybB-TE2 prior to lysobactin synthesis in the native strain. The resulting lone-standing TE2 serves as external type II TE to regenerate mis-primed peptide carrier protein via hydrolytic cleavage of the PCP-bound noncognate substrates. Additionally, the sequence of the genome of Lysobacter sp. ATCC 53042 was bioinformatically analyzed. The analysis result delivered further potential NRPS and PKS-NRPS hybrid gene clusters. Based on the proposed substrate specificities of the adenylation domains, the chemical structures of the products were proposed. However, further experiments are needed to confirm the production of these compounds