Nicholas of Cusa

Given the significance of Nicholas of Cusa’s ecclesiastical career, it is no surprise that a good deal of academic attention on Nicholas has focused on his role in the history of the church. Nevertheless, it would also be fair to say that a good deal of the attention that is focused on the life and thought of Nicholas of Cusa is the legacy of prior generations of scholars who saw in his theoretical work an opportunity to define the most salient features of transformations in the habits of thinking leading from the Middle Ages into the epoch of modernity. Thus, although contemporary scholars have not been able to achieve any clear consensus on the question of whether Nicholas belongs to the Middle Ages or to modernity, the field of Cusanus studies has become much more attentive to the possibility that the uniqueness and significance of Nicholas’s vision is a function of his ability to synthesize and redeploy a variety of strands in the Catholic intellectual tradition—strands that are as apt to involve practical matters of canon law and church reform as they are to hinge on a unique and richly developed mystical theology. Given the flourishing of the attention devoted to Nicholas in the late 20th and early 21st centuries, the choices about which texts to include in this article were difficult ones. The rationale for this article’s predominant focus on scholarship of the late 20th and early 21st centuries is that, insofar as the recent studies listed here enter into the debates that have been shaped by their predecessors, the sources mentioned here will point readers to the prior work in the field not acknowledged here

Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back

We present an $\tilde{O}(m^{10/7})=\tilde{O}(m^{1.43})$-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the long-standing $O(m \min(\sqrt{m},n^{2/3}))$ time bound due to Even and Tarjan [EvenT75]. By well-known reductions, this also establishes an $\tilde{O}(m^{10/7})$-time algorithm for the maximum-cardinality bipartite matching problem. That, in turn, gives an improvement over the celebrated celebrated $O(m \sqrt{n})$ time bound of Hopcroft and Karp [HK73] whenever the input graph is sufficiently sparse