The augmented marking complex of a surface

We build an augmentation of the Masur-Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, $\mathcal{AM}(S)$. Adapting work of Masur-Minsky, we prove that $\mathcal{AM}(S)$ is quasiisometric to Teichm\"uller space with the Teichm\"uller metric. A similar construction was independently discovered by Eskin-Masur-Rafi. We also completely integrate the Masur-Minsky hierarchy machinery to $\mathcal{AM}(S)$ to build flexible families of uniform quasigeodesics in Teichm\"uller space. As an application, we give a new proof of Rafi's distance formula for the Teichm\"uller metric.Comment: 30 pages; significantly rewritten to strengthen main construction

Convex cocompactness and stability in mapping class groups

We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show that the stable subgroups of mapping class groups are precisely the convex cocompact subgroups. This generalizes a well-known result of Behrstock and is related to questions asked by Farb-Mosher and Farb.Comment: 15 pages, 1 figur

Inverse Problems Related to the Wiener and Steiner-Wiener Indices

In a graph, the generalized distance between multiple vertices is the minimum number of edges in a connected subgraph that contains these vertices. When we consider such distances between all subsets of $k$ vertices and take the sum, it is called the Steiner $k$-Wiener index and has important applications in Chemical Graph Theory. In this thesis we consider the inverse problems related to the Steiner Wiener index, i.e. for what positive integers is there a graph with Steiner Wiener index of that value

Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth

In this paper, we study the existence of monotone equilibrium in first price auctions where bidders have a three-dimensional private type, i.e. their private values, degrees of risk aversion and initial wealth. Bidders' utility functions belong to the class of constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA). The bidders' types are independent across bidders, while a bidder's private value, initial wealth and degree of risk aversion are allowed to be correlated. We show that a monotone equilibrium always exists in a general setting allowing for asymmetric bidders. Moreover, with symmetric bidders, a symmetric monotone equilibrium strategy must exist. A bidder's equilibrium strategy increases with bidders' private values and degrees of risk aversion. When bidders have CRRA utility, equilibrium bids decrease with initial wealth; when bidders have CARA utility, equilibrium bids are invariant to initial wealth

Conservation of the glucan phosphatase laforin is linked to rates of molecular evolution and the glucan metabolism of the organism

<p>Abstract</p> <p>Background</p> <p>Lafora disease (LD) is a fatal autosomal recessive neurodegenerative disease. A hallmark of LD is cytoplasmic accumulation of insoluble glucans, called Lafora bodies (LBs). Mutations in the gene encoding the phosphatase laforin account for ~50% of LD cases, and this gene is conserved in all vertebrates. We recently demonstrated that laforin is the founding member of a unique class of phosphatases that dephosphorylate glucans.</p> <p>Results</p> <p>Herein, we identify laforin orthologs in a protist and two invertebrate genomes, and report that laforin is absent in the vast majority of protozoan genomes and it is lacking in all other invertebrate genomes sequenced to date. We biochemically characterized recombinant proteins from the sea anemone <it>Nematostella vectensis </it>and the amphioxus <it>Branchiostoma floridae </it>to demonstrate that they are laforin orthologs. We demonstrate that the laforin gene has a unique evolutionary lineage; it is conserved in all vertebrates, a subclass of protists that metabolize insoluble glucans resembling LBs, and two invertebrates. We analyzed the intron-exon boundaries of the laforin genes in each organism and determine, based on recently published reports describing rates of molecular evolution in <it>Branchiostoma </it>and <it>Nematostella</it>, that the conservation of laforin is linked to the molecular rate of evolution and the glucan metabolism of an organism.</p> <p>Conclusion</p> <p>Our results alter the existing view of glucan phosphorylation/dephosphorylation and strongly suggest that glucan phosphorylation is a multi-Kingdom regulatory mechanism, encompassing at least some invertebrates. These results establish boundaries concerning which organisms contain laforin. Laforin is conserved in all vertebrates, it has been lost in the vast majority of lower organisms, and yet it is an ancient gene that is conserved in a subset of protists and invertebrates that have undergone slower rates of molecular evolution and/or metabolize a carbohydrate similar to LBs. Thus, the laforin gene holds a unique place in evolutionary biology and has yielded insights into glucan metabolism and the molecular etiology of Lafora disease.</p

Glucan Phosphatase Variants for Starch Phosphorylation

Glucan phosphatase nucleotide or polypeptide variants of the presently-disclosed subject matter can alter the biophysical properties of starch in vitro or in planta, as well as the total starch biomass production in planta as compared to plants expressing wild-type glucan phosphatases. Plants producing the polypeptide variants of the presently-disclosed subject matter can have increased starch accumulation, increased starched biomass, and/or starch having desired biophysical properties. A method of the presently-disclosed subject matter for producing altered starch includes providing a plant that produces a glucan phosphatase polypeptide variant that comprises an amino acid mutation and collecting starch from the plant