Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets

A Deep Learning Approach to Link Prediction in Dynamic Networks

Time varying problems usually have complex underlying structures represented as dynamic networks where entities and relationships appear and disappear over time. The problem of efficiently performing dynamic link inference is extremely challenging due to the dynamic nature in massive evolving networks especially when there exist sparse connectivities and nonlinear transitional patterns. In this...

From Operator Categories to Topological Operads

In this paper it is shown that an assortment of operads near to many topologists’ hearts enjoy (homotopy) universal properties of an expressly combinatorial nature. These include the operads An and En. The main idea that makes this possible is the new notion of an operator category, which controls the homotopy types of these operads in a strong sense.

Deep Learning a Quadrotor Dynamic Model for Multi-Step Prediction

In this work, we develop and assess models for a real quadrotor in a Multi-Step prediction problem, that is, predicting the system state over many future steps using only the input. We propose a hybrid model with two configurations by combining deep recurrent neural networks with a quadrotor motion model. The proposed models take only motor speeds as input and predict the system state over a pr...

A Machine Learning Approach to Modeling Dynamic Decision-Making in Strategic Interactions and Prediction Markets

Dynamic Pricing & Learning in Electricity Markets

We analyze the price-formation process in an infinite-horizon oligopoly model where hydroelectric generators engage in dynamic Bertrand competition. We provide a simple characterization of a Markov Perfect Equilibrium (MPE) in terms of “indifference” prices — i.e. prices that equate the gains from releasing or withholding water. Although the MPE solution represents an equilibrium consistent wit...