In this note, we extend the Vandermonde with Arnoldi method recently advocated by Brubeck et al. (2021) to dealing confluent matrix. To apply process, it is critical find a Krylov subspace which generates column space of A theorem established for such subspaces any order derivatives. This enables us compute derivatives high degree polynomials precision. It also makes many applications involving...

It is shown how to enhance any data structure in the pointer model to make it confluently persistent, with efficient query and update times and limited space overhead. Updates are performed in O(log n) amortized time, and following a pointer takes O(log c log n) time where c is the in-degree of a node in the data structure. In particular, this proves that confluent persistence can be achieved a...

This work is concerned with basic issues of the design of calculi and proof procedures for first-order connection methods and tableaux calculi. Proof procedures for these type of calculi developed so far suffer from not exploiting proof confluence, and very often unnecessarily rely on a heavily backtrack oriented control regime. As a new result, we present a variant of a connection calculus and...

A branchpoint of a compactum X is a point which is the vertex of a simple triod in X. A surjective map /: X -» Y is said to cover the branchpoints of Y if each branchpoint in Y is the image of some branchpoint in X. If every map in a class % of maps on a class of compacta & covers the branchpoints of its image, then it is said that the branchpoint covering property holds for ff on 0. According ...

IMPORTANCE With the increasing use of antiangiogenic agents in the treatment of high-grade gliomas, we are becoming increasingly aware of distinctive imaging findings seen in a subset of patients treated with these agents. Of particular interest is the development of regions of marked and persistent restricted diffusion. We describe a case with histopathologic validation, confirming that this r...