On Inferences from Completed Data

Matrix completion has become an extremely important technique as data scientists are routinely faced with large, incomplete datasets on which they wish to perform statistical inferences. We investigate how error introduced via matrix completion affects statistical inference. Furthermore, we prove recovery error bounds which depend upon the matrix recovery error for several common statistical inferences. We consider matrix recovery via nuclear norm minimization and a variant, $\ell_1$-regularized nuclear norm minimization for data with a structured sampling pattern. Finally, we run a series of numerical experiments on synthetic data and real patient surveys from MyLymeData, which illustrate the relationship between inference recovery error and matrix recovery error. These results indicate that exact matrix recovery is often not necessary to achieve small inference recovery error

Acid red 88 dye doped polyaniline framed by soft template method: A potential candidate for dye-sensitized solar cells

The metal-like band structure and the tripping transfer of electrons between bipolarons and polarons found in polyaniline make it for elevated scientific validity. Through a soft template in situ oriented oxidative polymerization, self-assembled nano tubular structures of Acid red (AR88) dye-doped Polyaniline in the presence of hydrochloric acid medium (AR88/PAni/HCl) were prepared and characterized well using different analytical tools. The AR88 (5x10-4 M) doped PAni prepared in the presence of 1 M HCl shows higher conductivity (2.2679 Scm−1) and seized its eminent electrical properties. The presence of sulfonic acid group-containing AR88 provides a better environment to give higher conductivity than the PAni-HCl. Due to its better optical transparency, the as-synthesized samples were used for photovoltaic applications. The AR88/PAni/HCl was used as a photosensitizer in dye-sensitized solar cells which shows photoconversion efficiency of around 1.58 %

Statistical energy minimization theory for systems of drop-carrier particles.

Drop-carrier particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution without using costly microfluidic equipment and techniques. DCPs are useful for automated and high-throughput biological assays and reactions, as well as single-cell analyses. Surface energy minimization provides a theoretical prediction for the volume distribution in pairwise droplet splitting, showing good agreement with macroscale experiments. We develop a probabilistic pairwise interaction model for a system of such DCPs exchanging fluid volume to minimize surface energy. This leads to a theory for the number of pairwise interactions of DCPs needed to reach a uniform volume distribution. Heterogeneous mixtures of DCPs with different sized particles require fewer interactions to reach a minimum energy distribution for the system. We optimize the DCP geometry for minimal required target solution and uniformity in droplet volume