Neural networks have recently re-emerged as a powerful hypothesis class, yielding impressive classification accuracy in multiple domains. However, their training is a non-convex optimization problem which poses theoretical and practical challenges. Here we address this difficulty by turning to “improper” learning of neural nets. In other words, we learn a classifier that is not a neural net but...

Summary In this article, using the Mizar system [2], [3], we deal with Riemann’s improper integral on infinite interval [1]. As [4], referred to [6], which discusses integrals of finite values.

In this paper, we study a colouring problem motivated by a practical frequency assignment problem and up to our best knowledge new. In wireless networks, a node interferes with the other nodes the level of interference depending on numerous parameters: distance between the nodes, geographical topography, obstacles, etc. We model this with a weighted graph G where the weights on the edges repres...

We study the weighted improper coloring problem, a generalization of defective coloring. We present some hardness results and in particular we show that weighted improper coloring is not fixed-parameter tractable when parameterized by pathwidth. We generalize bounds for defective coloring to weighted improper coloring and give a bound for weighted improper coloring in terms of the sum of edge w...