Learning, Inference, and Unmixing of Weak, Structured Signals in Noise

In this thesis, we study two methods that can be used to learn, infer, and unmix weak, structured signals in noise: the Dynamic Mode Decomposition algorithm and the sparse Principal Component Analysis problem. Both problems take as input samples of a multivariate signal that is corrupted by noise, and produce a set of structured signals. We present performance guarantees for each algorithm and validate our findings with numerical simulations. First, we study the Dynamic Mode Decomposition (DMD) algorithm. We demonstrate that DMD can be used to solve the source separation problem. That is, we apply DMD to a data matrix whose rows are linearly independent, additive mixtures of latent time series. We show that when the latent time series are uncorrelated at a lag of one time-step then the recovered dynamic modes will approximate the columns of the mixing matrix. That is, DMD unmixes linearly mixed sources that have a particular correlation structure. We next broaden our analysis beyond the noise-free, fully observed data setting. We study the DMD algorithm with a truncated-SVD denoising step, and present recovery guarantees for both the noisy data and missing data settings. We also present some preliminary characterizations of DMD performed directly on noisy data. We end with some complementary perspectives on DMD, including an optimization-based formulation. Second, we study the sparse Principal Component Analysis (PCA) problem. We demonstrate that the sparse inference problem can be viewed in a variable selection framework and analyze the performance of various decision statistics. A major contribution of this work is the introduction of False Discovery Rate (FDR) control for the principal component estimation problem, made possible by the sparse structure. We derive lower bounds on the size of detectable coordinates of the principal component vectors, and utilize these lower bounds to derive lower bounds on the worst-case risk.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155061/1/prasadan_1.pd

Bone-marrow derived cells do not contribute to new beta-cells in the inflamed pancreas

The contribution of bone-marrow derived cells (BMCs) to a newly formed beta-cell population in adults is controversial. Previous studies have only used models of bone marrow transplantation from sex-mismatched donors (or other models of genetic labeling) into recipient animals that had undergone irradiation. This approach suffers from the significant shortcoming of the off-target effects of irradiation. Partial pancreatic duct ligation (PDL) is a mouse model of acute pancreatitis with a modest increase in beta-cell number. However, the possibility that recruited BMCs in the inflamed pancreas may convert into beta-cells has not been examined. Here, we used an irradiation-free model to track the fate of the BMCs from the donor mice. A ROSA-mTmG red fluorescent mouse was surgically joined to an INS1Cre knock-in mouse by parabiosis to establish a mixed circulation. PDL was then performed in the INS1Cre mice 2 weeks after parabiosis, which was one week after establishment of the stable blood chimera. The contribution of red cells from ROSA-mTmG mice to beta-cells in INS1Cre mouse was evaluated based on red fluorescence, while cell fusion was evaluated by the presence of green fluorescence in beta-cells. We did not detect any red or green insulin+ cells in the INS1Cre mice, suggesting that there was no contribution of BMCs to the newly formed beta-cells, either by direct differentiation, or by cell fusion. Thus, the contribution of BMCs to beta-cells in the inflamed pancreas should be minimal, if any

Time Series Source Separation using Dynamic Mode Decomposition

The dynamic mode decomposition (DMD) extracted dynamic modes are the non-orthogonal eigenvectors of the matrix that best approximates the one-step temporal evolution of the multivariate samples. In the context of dynamic system analysis, the extracted dynamic modes are a generalization of global stability modes. We apply DMD to a data matrix whose rows are linearly independent, additive mixtures of latent time series. We show that when the latent time series are uncorrelated at a lag of one time-step then, in the large sample limit, the recovered dynamic modes will approximate, up to a columnwise normalization, the columns of the mixing matrix. Thus, DMD is a time series blind source separation algorithm in disguise, but is different from closely related second order algorithms such as SOBI and AMUSE. All can unmix mixed ergodic Gaussian time series in a way that ICA fundamentally cannot. We use our insights on single lag DMD to develop a higher-lag extension, analyze the finite sample performance with and without randomly missing data, and identify settings where the higher lag variant can outperform the conventional single lag variant. We validate our results with numerical simulations, and highlight how DMD can be used in change point detection

Riboflavin carrier protein from carp (C. carpio) eggs: comparison with avian riboflavin carrier protein

A protein exhibiting immunological cross-reactivity with the chicken egg-white riboflavin carrier protein was detected by radioimmunoassay in the eggs and serum of the fresh water fish Cyprinus carpio and subsequently purified to homogeneity by use of affinity chromatography. Fish riboflavin carrier protein resembled chicken riboflavin carrier protein with respect to most of its physicochemical characteristics. The major epitopes of chicken riboflavin carrier protein were shown to be conserved in the fish protein as probed with monoclonal antibodies to the avian vitamin carrier

Phylogenetic position of Pleurogenoides species (Plagiorchiida: Pleurogenidae) from the duodenum of Indian skipper frog, Euphlyctis cyanophlyctis (Amphibia: Dicroglossidae) inhabiting the Western Ghats, India

Two species of digenetic trematodes of the genus Pleurogenoides viz., P. cyanophlyctiShinad & Prasadan (2018a) and P. euphlyctiShinad & Prasadan (2018b) have been described from India. Information regarding the molecular data of various species of the genus Pleurogenoides Travassos, 1921 is virtually lacking. This study addresses the application of molecular markers to validate the phylogenetic position of P. cyanophlycti and P. euphlycti. In the present study, two species P. cyanophlycti and P. euphlycti were collected between January 2016 to October 2017, infecting the freshwater frogs inhabiting the Western Ghats, India. In the present study, the two species were identifi ed morphologically and by PCR amplification of the 28S ribosomal RNA gene. Phylogenetic tree results clearly demonstrate that both P. cyanophlycti and P. euphlycti belongs to the family Pleurogenidae Looss, 1899. Based on these results, we presented and discussed the phylogenetic relationships of P. cyanophlycti and P. euphlycti within family Pleurogenidae from India. Phylogenetic analyses showed that P. cyanophlycti and P. euphlycti cluster according to their vertebrate host and revealed an important congruence between the phylogenetic trees of Pleurogenoides and of their vertebrate hosts. P. cyanophlycti and P. euphlycti clearly constitute a separate, sister branch with other species of the genera, Pleurogenoides, Pleurogenes (=Candidotrema), Prosotocus and Brandesia. The present study firstly provides important information about the molecular study and phylogenetic analysis of P. cyanophlycti and P. euphlycti. This study will also serve as a baseline for Pleurogenoides species identifi cation for further studies