Abstract. Consider a weighted and undirected graph, possibly with self-loops, and its corresponding Laplacian matrix, possibly augmented with additional diagonal elements correspon...
We show two new direct product results in two different models of communication complexity. Our first result is in the model of one-way public-coin model. Let f ⊆ X × Y × Z ...
We introduce the class of Rigid Tree Automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a res...
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and thei...
We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced — characteristics that are almost universal to modern datasets co...