The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as Mg ,w for a particular genus g and a wei...

The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present a geometric construction of the Bergman fan, and we discuss its relationship with the simplicial complex of nested sets in the lattice of flats. The Bergman complex is triangulated by the nested se...

Data envelopment analysis (DEA) is a mathematical programming - based technique to evaluate the performance of homogeneous group decision-making units (DMUs) with multiple inputs and outputs. One DEA applications involves aggregating input resources reallocating them create efficient DMUs.The present study employs centralized resource allocation (CRA) approach develop model for creating new DMU...

The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present a geometric construction of the Bergman fan, and we discuss its relationship with the simplicial complex of nested sets in the lattice of flats. The Bergman complex is triangulated by the nested se...

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [1, 2]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [3] in practice. We also introduce a ...

Figure 1: A line arrangement in the plane The study of configurations of lines in the plane or planes in space has a relatively short history. Some say the field arose from the cheese cutting problem: what is the maximum number of pieces one can produce from a fixed number of cuts? Others say that it arose through the history of braid groups: the pure braid group on n strands turns out to be th...