Network expansion problems are a special class of multi-period network design in which arcs can be opened gradually different time periods but never closed. Motivated by practical applications, we focus on cases where demand between origin-destination pairs expands over discrete horizon. Arc opening decisions taken every period, and once an arc is it used throughout the remaining horizon to rou...

We present four new methods in addition to the standard methods of extrapolating the t-expansion series, and make a comprehensive comparison of these procedures by applying them to the t-series for three quantum systems. We have found that by writing the series as a ratio of decreasing exponentials it is possible to devise methods that are significantly more accurate than the standard methods f...

In reinforcement learning, the aim of the agent is to find a policy that maximizes its expected return. Policy gradient methods try to accomplish this goal by directly approximating the policy using a parametric function approximator; the expected return of the current policy is estimated and its parameters are updated by steepest ascent in the direction of the gradient of the expected return w...

Consider a finite irreducible Markov chain with invariant distribution π. We use the inner product induced by π and the associated heat operator to simplify and generalize some results related to graph partitioning and the small-set expansion problem. For example, Steurer showed a tight connection between the number of small eigenvalues of a graph’s Laplacian and the expansion of small sets in ...