In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...
Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...
Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...
Genome duplication, transcription, and translation are among many crucial cellular processes that need to be performed with high fidelity. However, those extremely low error rates cannot be explained with simple equilibrium thermodynamic considerations. Th ...
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...
The arms race between viruses and their hosts shaped the evolutionary history and the genome composition of both parties. Restriction factors are the first-line antiviral effectors encoded by the host genomes and are often conserved through evolution to pr ...
Human papillomavirus (HPV) infections are the primary drivers of cervical cancers, and often HPV DNA gets integrated into the host genome. Although the oncogenic impact of HPV encoded genes is relatively well known, the cis-regulatory effect of integrated ...
DNA-binding proteins physically interact with the DNA and directly affect genomic functions. The eukaryotic genome is compacted into chromatin, limiting the DNA access to nuclear factors. In this Ph.D. thesis, I explored the dynamic mechanisms, that allow ...
