The problem of weakly-private information retrieval, is a variant of private information

retrieval, where the user wants to retrieve 1 out of K messages from a distributed storage

system with N servers that stores all K messages, and is willing to leak some information

of the identity of the desired message. In this work, we study the problem of weakly-private

information retrieval. A novel information leakage metric is proposed, and the capacity for

the setting of N = 2 servers, and arbitrary number of messages K is characterized. In

particular, in the capacity achieving scheme, designing the distribution of the non-uniformly

distributed noise Z turns out to be the key to achieve the capacity.

Originating from the construction of the asymptotic-capacity achieving scheme for X-secure T-private information retrieval (XSTPIR), the technique of cross-subspace alignment (CSA) emerges as the natural solution to secure and private information retrieval, secure distributed matrix multiplication, and coded distributed batch computation. Characterized by a Cauchy-Vandermonde structure that facilitates interference alignment along Vandermonde terms, while the desired signals remain resolvable along the Cauchy terms, the idea of CSA is shown to be the essential ingredient in the optimal/asymptotically optimal/state-of-art approaches that minimize the download and/or communication cost of these independently introduced but closely related problems.

In this dissertation we will first introduce the idea of CSA to the applications of XSTPIR, XSTPIR with graph-based replicated storage (GXSTPIR) and XSTPIR with MDS coded storage (MDS-XSTPIR). The CSA solution to XSTPIR exploits the Cauchy-Vandermonde structured answer strings that align interference symbols guaranteeing T-privacy and X-security to achieve the asymptotic capacity. The achievability scheme for GXSTPIR reveals a non-trivial generalization of CSA that takes the advantage of a special structure inspired by dual Generalized Reed Solomon (GRS) codes to allow interference alignment for arbitrary storage patterns. For MDS-XSTPIR, we propose a novel scheme based on confluent Cauchy-Vandermonde storage structure and a strategy of successive decoding with interference cancellation. Next, by characterizing a connection between a form of XSTPIR problem known as multi-message XSTPIR and the problem of secure distributed matrix multiplication (SDMM), we characterize a series of capacity regions of SDMM, as well as several of its variants. The idea of CSA serves as an essential component of the construction of several achievability schemes. Given the insights from all these results, next, we construct CSA/GCSA codes based on (confluent) Cauchy-Vandermonde structures for coded distributed batch computation (CDBC) that unify, generalize and improve upon the state-of-art codes for distributed computing such as LCC codes for multivariate polynomial evaluations and EP codes for matrix multiplication. Finally, we study the problem of X-secure T-private federated submodel learning (XSTPFSL), which is a non-trivial generalization of the XSTPIR problem where private writes are needed. The proposed ACSA-RW scheme achieves the desired private read and write functionality with elastic dropout resilience, takes the advantage of the synergistic gain from the joint design of private read and write for low communication costs, and sheds light on a striking symmetry between upload and download costs. Intuitively, private read and write functionalities, as well as their synergistic gain, rely on secure distributed matrix multiplication so that the idea of CSA emerges as the core of the solution.

Schistosomiasis is a neglected tropical disease (NTD) caused by flatworm parasites belonging to the genus Schistosoma. The disease infects over 200 million people in developing countries where access to clean water is limited. Treatment of schistosomiasis relies on just one drug, praziquantel (PZQ). This drug is only partially effective and resistance is a concern. Together, these encourage the search for new drugs and new drug targets. The proteasome is an essential proteolytic enzyme complex in the cell being responsible for protein turnover. It is a validated drug target for treatment of certain cancers and a promising target for a number of parasitic infections, including Schistosoma. My lab has been using RNA-sequencing (RNA-Seq) to profile the transcriptomic changes after exposure of Schistosoma mansoni to the proteasome inhibitor, bortezomib (BTZ). As part of the aims of my project, I provide an initial characterization of the top 300 gene transcripts that were upregulated after treatment of S. mansoni with 1 µM BTZ after 12 and/or 24 h in vitro. Among these, I identify and discuss heat shock proteins and proteasome subunits that were upregulated at both time points, as well as proteins particular to each time point. Next, using primers that I helped design and then test for efficiency for nine selected genes of interest, I validated the RNA-Seq data via quantitative reverse polymerase chain reaction (qPCR). Lastly, I utilized the Basic Local Alignment Search Tool (BLAST) at the National Center for Biotechnology Information’s (NCBI) website to understand whether particular genes of interest are expressed in other developmental stages of the parasite. The resulting data and analysis offer an initial insight into the transcriptomic response of the S. mansoni after exposure to a proteasome inhibitor with the goal of identifying new drug targets.