Concentration of the Stationary Distribution on General Random Directed Graphs

We consider a random model for directed graphs whereby an arc is placed from one vertex to another with a prescribed probability which may vary from arc to arc. Using perturbation bounds as well as Chernoff inequalities, we show that the stationary distribution of a Markov process on a random graph is concentrated near that of the "expected" process under mild conditions. These conditions involve the ratio between the minimum and maximum in- and out-degrees, the ratio of the minimum and maximum entry in the stationary distribution, and the smallest singu- lar value of the transition matrix. Lastly, we give examples of applications of our results to well-known models such as PageRank and G(n, p).Comment: 14 pages, 0 figure

A self-guided Internet-delivered intervention for adults with ADHD: a protocol for a randomized controlled trial

Background Attention-deficit/hyperactivity disorder (ADHD) in adulthood, with an estimated prevalence of 2–3%, is associated with several challenges in daily life functioning. The availability of evidence-based psychological interventions for adults with ADHD is still poor. Interventions delivered over the Internet on smartphones or personal computers may help to increase the availability of effective psychological interventions. The primary aim of this randomized controlled trial is to examine the efficacy of a self-guided Internet-delivered intervention on severity levels of ADHD symptomatology and quality of life. Methods We aim to include 118 participants with a self-reported ADHD diagnosis in a randomized controlled trial with two arms: 1) self-guided Internet-delivered intervention for coping with ADHD (N = 59); 2) self-guided online psychoeducation (control group, N = 59). After 3 months, the control group will be given access to the intervention. The primary clinical outcomes are inattention and quality of life. Secondary clinical outcomes are hyperactivity, stress and depression. Measures will be obtained at three time points: before (baseline), immediately after (8 weeks) and 3 months after the intervention. Uptake, usage, adherence and satisfaction will be explored. Discussion This RCT will provide valuable information on the clinical effectiveness of an Internet-delivered intervention for adults with ADHD. This study is, to our knowledge, one of the first randomized control trials that investigates the effects of a self-guided Internet-delivered psychological intervention in a fairly large group of adults with ADHD.publishedVersio