We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves by means of a simple rule. While word series have appeared before in the literature, extended word series are introduced in this paper. We exemplify the use ...

Introduction: Children with attention-deficit/hyperactivity disorder (ADHD) have some impairment in emotional relationship which can be due to problems in emotional processing. The present study investigated neural correlates of early stages of emotional face processing in this group compared with typically developing children using the Gamma Band Activity (GBA). Methods: A total of 19 childre...

This talk reviews some recent results on the NLL resummed smallx gluon splitting function, as determined including renormalisation-group improvements. It also discusses the observation that the LO, NLO, NNLO, etc. hierarchy for the gluon splitting function breaks down not when αs ln 1/x ∼ 1 but rather for αs ln 2 1/x ∼ 1. It is well-known that the resummation of leading-logarithms of x (LLx) [1...

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these Primal–Dual splitting methods....

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples: