This paper studies least-squares ReLU neural network method for solving the linear advection-reaction problem with discontinuous solution. The is a discretization of an equivalent formulation in set functions activation function. capable approximating interface underlying automatically through free hyper-planes and, hence, outperforms mesh-based numerical methods terms number degrees freedom. N...

We show that the maximum number of convex polygons in a triangulation of n points in the plane is O(1.5029). This improves an earlier bound of O(1.6181) established by van Kreveld, Löffler, and Pach (2012) and almost matches the current best lower bound of Ω(1.5028) due to the same authors. Given a planar straight-line graph G with n vertices, we also show how to compute efficiently the number ...

For any planar straight line graph (Pslg), there is a vertexface assignment such that every vertex is assigned to at most two incident faces, and every face is assigned to all its reflex vertices and one more incident vertex. The existence of such an assignment implies, in turn, that any Pslg can be augmented to a connected Pslg such that the degree of every vertex increases by at most two.

The key to successful long-term peritoneal dialysis (PD) is permanent and safe access to peritoneal cavity. The two most commonly used Tenckoff catheters for PD are the straight and coiled catheters. The present study was undertaken to assess the catheter survival, catheter associated infections, and all cause mortality and to compare the straight with coiled catheters in PD. During April 1997-...

With rising trading volumes in domestic and cross-border security transactions, risks faced by global financial firms and markets are increasing. To manage settlement risks and maintain competitiveness in global financial markets, the U.S. Security and Exchange Commission (SEC) has decided to shorten the settlement cycle of security transactions from the current T+3 to T+1. As a result, key pla...