This dissertation presents two research topics. The first topic focuses on the tagging of jets to hadronically decaying top quarks and W bosons in the ATLAS detector. Two jet tagging algorithm optimization studies are described. The second topic focuses on the search for vector-like top quarks (T), which are predicted by beyond the Standard Model theories that aim to solve the Hierarchy Problem, using a dataset of proton-proton collisions with a center of mass energy of √s = 13 TeV collected with the ATLAS detector. Two search analyses that probe different production mechanisms of the T are performed towards this goal.The first jet tagging algorithm study focuses on the optimization of two deep neural network (DNN) top taggers and a three-variable W tagger, all of which use information from the substructure of jets. The tagging signal efficiency is extracted for each tagger both in Standard Model (SM) Monte Carlo (MC) simulations and in the data that was collected by the ATLAS detector in 2015-2017. The performance of the taggers in MC is calibrated to that of the data with the derivation of tagging signal efficiency scale factors. Additionally, uncertainties are derived for this measurement, which take into account effects from the MC modeling of the SM processes considered and the reconstruction and calibration of the different physics objects used in this measurement.The second jet tagging algorithm study consists of a topological data analysis (TDA) of jets that analyzes their simplicial homology. A framework that applies a persistent homology analysis and the Mapper algorithm to jets is devised. The information obtained from this framework is applied in the design of a DNN and convolutional graph neural network (GNN) top tagging algorithms. Optimization studies were performed in which these two taggers achieved a comparable performance to the substructure-based DNN top taggers.Two search analyses for a T are performed, one targeting the single production mechanism of a T and the other targeting the pair production mechanism of TT ̄. Both analyses focus on the decay topologies T → Ht and T → Zt in final states that include a single electron or muon. A search strategy is devised for each analysis that takes advantage of several experimental features that are unique to each production mechanism. The tagging of jets to hadronically decaying top quarks and W, Z, and Higgs bosons is a cornerstone of the search strategies. A statistical analysis is performed for both searches to test for the presence of potential T production events in the data. No significant excesses over the SM prediction are observed in both searches, and 95% CL upper limits are set on the T and TT ̄ production cross sections. These limits are interpreted as exclusion limits on the T mass and other theory parameters that vary depending on the signal benchmark considered.
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