Spectral matrix methods for partitioning power grids: Applications to the Italian and Floridian high-voltage networks

Intentional islanding is used to limit cascading power failures by isolating highly connected "islands" with local generating capacity. To efficiently isolate an island, one should break as few power lines as possible. This is a graph partitioning problem, and here we give preliminary results on islanding of the Italian and Floridian high-voltage grids by spectral matrix methods.Comment: 4 pages, 2 figures

Single Molecule Studies of ssDNA Dynamics Near a DNA (p/t) Junction and Their Role in Protein Nucleic Acid Interactions of the T4 Bacteriophage.

Thermally induced conformational fluctuations of deoxyribonucleic acid (DNA) play an important role in the regulation of DNA replication, recombination and repair, which depends on the ability of protein machinery to recognize and bind to selected conformations of DNA lattices. Obtaining information about the nature of these functionally relevant DNA conformations, in addition to the time scales of their inter-conversion, is critical to understanding the detailed molecular mechanisms of protein-DNA interactions. An important component to DNA replication in all organisms is the single-stranded (ss) DNA binding protein (ssb), which binds to ssDNA, protecting and priming it for interaction with other proteins. We used the T4 Bacteriophage as a model organism to study the process of DNA replication, with a focus on the T4 ssb, gene-product32. I investigated fundamental questions: 1. How does the molecular structure of ssDNA affect its conformational fluctuations? 2. How do gp32 proteins assemble onto ssDNA to form functional microscopic machines? And, 3. How is the gp32 assembly mechanism affected by ssDNA polarity and length? To answer these questions, I used a combination of spectroscopic techniques including sub-millisecond single-molecule Förster Resonance Energy Transfer (FRET) measurements. We analyzed our data by performing numerical optimizations of a transport master equation to simulate multi-order time correlation functions (TCFs) and the equilibrium distribution of conformational macrostates. We discovered that the pathway for gp32 dimer assembly onto short oligonucleotides near ss—double-stranded (ds) DNA junctions proceeds through a transiently bound monomer, which does not slide along ssDNA. I developed methods to analyze the single-molecule signal at sub-millisecond resolution, which led to new insights into the nature of ssDNA fluctuations as well as the gp32 dimer assembly mechanism. I found that the ssDNA backbone fluctuates between various conformational states on a sub-millisecond timescale, only some of which are available for binding by gp32. By examining different lengths and polarities of ssDNA p/t constructs, I show that gp32 dimer sliding occurs on the timescale of a millisecond and that it is sensitive to the polarity of the ssDNA to which it is bound. This dissertation includes both previously published and unpublished co-authored materials