Local geometry of random geodesics on negatively curved surfaces

It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation -- for instance, the fraction of triangles -- approach those of the limiting Poisson line process.Comment: This version extends the results of the previous version to surfaces with possibly variable negative curvatur

CDASOCS

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 148-150).Planners of military air and space operations in a battlefield environment seek to allocate resources against targets in a way that best achieves the objectives of the commander. In future conflicts, the presence of new types of assets, such as tactical space-based sensors and Operationally Responsive Spacelift (ORS) assets, will add complexity to air and space operations decisions. In order to best achieve objectives, planners of different types of assets will likely need to work collaboratively when formulating tasking for their resources. The purpose of this research is to investigate the challenges of air and space collaboration and to quantify its potential benefit. We model a future threat scenario involving a rogue nation with Weapons of Mass Destruction (WMD) capability and a significant air defense force. We consider three separately-controlled resource groups - aircraft, satellites, and ORS assets - to combat the target threat. In addition, we formulate a top-level coordination controller, whose job it is to effect collaborative decision-making among resource groups. Using a combination of pre-existing software and new algorithms, we develop the Coordinated Dynamic Air and Space Operations Control System (CDASOCS), which simulates controller-generated plans in a battlefield environment recurring over multiple planning periods. New algorithms are presented for both the top-level coordination controller and the ORS controller. The benefits of resource coordination in CDASOCS are demonstrated in three main experiments along with several parameter variation tests.by Matthew Christian Wroten.S.M

Targeted de novo phasing and long-range assembly by template mutagenesis

Short-read sequencers provide highly accurate reads at very low cost. Unfortunately, short reads are often inadequate for important applications such as assembly in complex regions or phasing across distant heterozygous sites. In this study, we describe novel bench protocols and algorithms to obtain haplotype-phased sequence assemblies with ultra-low error for regions 10 kb and longer using short reads only. We accomplish this by imprinting each template strand from a target region with a dense and unique mutation pattern. The mutation process randomly and independently converts ∼50% of cytosines to uracils. Sequencing libraries are made from both mutated and unmutated templates. Using de Bruijn graphs and paired-end read information, we assemble each mutated template and use the unmutated library to correct the mutated bases. Templates are partitioned into two or more haplotypes, and the final haplotypes are assembled and corrected for residual template mutations and PCR errors. With sufficient template coverage, the final assemblies have per-base error rates below 10-9. We demonstrate this method on a four-member nuclear family, correctly assembling and phasing three genomic intervals, including the highly polymorphic HLA-B gene