A common method for constructing a function from a finite set of moments is to solve a constrained minimization problem. The idea is to find, among all functions with the given ...
Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-p...
We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and no-regret learning. We first show that any c...
Background: The previous studies of genome-wide expression patterns show that a certain percentage of genes are cell cycle regulated. The expression data has been analyzed in a nu...
We consider the problem of finding a singularity of a differentiable vector field X defined on a complete Riemannian manifold. We prove a unified result for the existence and local...