Topological Data Analysis (TDA) is an analysis method that aims to identify patterns and structures underlying complex data sets. TDA can be used to extract important information about the data, such as groupings and clusters. I'm going to describe an example of how to implement this method and explain why we chose the Julia language.
Systems of nonsmooth nonlinear equations of the form H(x) = 0 can often be solved by the semismooth Newton method. An adaptation of the classic Newton method, it yields fast local convergence with little cost per iteration, provided the B-differential of H has only nonsingular Jacobians at the solution. Such setting of nonsmooth H is encountered when complementarity problems are reformulated...
Seleroute.jl is an implementation of many state-of-the-art algorithms to compute optimum computer-network routing. These include oblivious routing to take into account the demand uncertainty into the routing or variants of fair routing. The possibilities of Julia have had a decisive impact on design decisions.
Energy storage systems have become a promising option to increase power system flexibility and harness larger shares of variable renewable energy. To get a full picture of their potential operation and benefits, a realistic representation of their characteristics is essential in power system models. Energy storage models require binary variables to correctly model reserves and to ensure that...
