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The analysis of numerical sequential data, such as time series, is a frequent practice in both academic and industrial settings. Offline change detection segments the data retrospectively and is useful for uncovering events and systematic behaviors in data analysis tasks. It is applied in a variety of fields including finance, genomics and energy consumption. Furthermore, in the potential presence of change points, utilizing change detection prior to data modeling can help prevent building inappropriate models under the assumption of data homogeneity, and consequently supports improved prediction and statistical inference. In this thesis, we propose three methods that study the offline change point detection problem from different aspects and application domains. The first method is a nonparametric procedure that can provide computational speedups to simultaneously detect multiple change points. The second method models the relationship between the different channels of multivariate observations to detect change points and anomalies. The third method focuses on the specific biomedical domain of cell culture monitoring to detect the transition from cell growth to confluence. All proposed methods are evaluated through simulations and real-world data applications.

RNAs have gained significant attention in recent years because they can fold into well-defined secondary or tertiary structures. These three dimensional architectures provide interfaces for specific RNA-RNA or RNA-protein interactions that are essential for biological processes in a living system. These discoveries greatly increased interest in RNA as a potential drug target for the treatment of diseases. Two of the most studied RNA based regulatory systems are HIV-1 trans-activating response element (TAR)/Tat replication pathway and Rev response element (RRE)/Rev export pathway. To efficiently target TAR and RRE RNA, we designed and synthesized three generations of branched peptide libraries that resulted in medium sized molecules. The first generation of BPs were discovered from screening a one-bead one-compound library (4,096 compounds) against HIV-1 TAR RNA. One peptide FL4 displayed a binding affinity of 600 nM to TAR RNA, which is tighter than its native protein counterpart, Tat. Biophysical characterization of these BP demonstrated that "branches" in BPs impart multivalency, and they are cell permeable and non-toxic. The second generation peptides were discovered from an on-bead high-throughput screening of a 3.3.4 branched peptide boronic acids (BPBAs) library that bind selectively to the tertiary structure of RRE IIB. The library comprised of 46,656 unique sequences. We demonstrate that our highest affinity BPBA (BPBA1) selectively binds RRE IIB in the presence of competitor tRNAs as well as against six RRE IIB structural variants. Further, we show that the boronic acid moieties afford a novel binding mode towards RNA that is tunable; their Lewis acidity has critical effects on binding affinity. In addition, biophysical characterizations provide evidence that "branching" in these peptides is a key structural motif for multivalent interactions with the target RNA. Finally, RNA footprinting studies revealed that the BPBA1 binding site encompasses a large surface area that spans both the upper stem as well as the internal loop regions of RRE IIB. BPBA1 is cell permeable and non-toxic. In the next generation of branched peptides, a 3.3.4 branched peptide library composed of 4,096 unique sequences that featured boronic acid and acridine moieties was designed. We chose acridine as the amino acid side chain due to its potential for π-stacking interaction that provides high binding affinity to RNA target. The library was screened against HIV-1 RRE IIB RNA. Fifteen peptides were sequenced and four contained acridine alone and/or in conjunction with boronic acid moieties displayed dissociation constants lower than 100 nM. The ribonuclease protection assays of A7, a sequence that contains both boronic acid and acridine residues, showed a similar protection pattern compared to previous peptide BPBA1, suggesting that the 3.3.4 branched peptides shared similar structural elements and contacted comparable regions of the RRE IIB RNA. The results from this research indicated that "branching" in peptides imparts multivalent interactions to the RNA, and that functional groups such as boronic acid and acridine are key structural features for efficient binding and selectivity for the folded RNA target. We demonstrated that the branched peptides are cell permeable and non-toxic.