Homological finiteness conditions for groups, monoids and algebras

Recently Alonso and Hermiller introduced a homological finiteness condition\break $bi{-}FP_n$ (here called {\it weak} $bi{-}FP_n$) for monoid rings, and Kobayashi and Otto introduced a different property, also called $bi{-}FP_n$ (we adhere to their terminology). From these and other papers we know that: $bi{-}FP_n \Rightarrow$ left and right $FP_n \Rightarrow$ weak $bi{-}FP_n$; the first implication is not reversible in general; the second implication is reversible for group rings. We show that the second implication is reversible in general, even for arbitrary associative algebras (Theorem 1'), and we show that the first implication {\it is} reversible for group rings (Theorem 2). We also show that the all four properties are equivalent for connected graded algebras (Theorem 4). A result on retractions (Theorem 3') is proved, and some questions are raised.Comment: 10 page

Effects of methylphenidate on cognition and behaviour in children with neurofibromatosis type 1:a study protocol for a randomised placebo-controlled crossover trial

INTRODUCTION: Dopamine dysregulation has been identified as a key modulator of behavioural impairment in neurofibromatosis type 1 (NF1) and a potential therapeutic target. Preclinical research demonstrates reduced dopamine in the brains of genetically engineered NF1 mouse strains is associated with reduced spatial-learning and attentional dysfunction. Methylphenidate, a stimulant medication that increases dopaminergic and noradrenergic neurotransmission, rescued the behavioural and dopamine abnormalities. Although preliminary clinical trials have demonstrated that methylphenidate is effective in treating attention deficit hyperactivity disorder (ADHD) symptoms in children with NF1, its therapeutic effect on cognitive performance is unclear. The primary aim of this clinical trial is to assess the efficacy of methylphenidate for reducing attention deficits, spatial working memory impairments and ADHD symptoms in children with NF1.METHODS AND ANALYSIS: A randomised, double-blind, placebo-controlled trial of methylphenidate with a two period crossover design. Thirty-six participants with NF1 aged 7-16 years will be randomised to one of two treatment sequences: 6 weeks of methylphenidate followed by 6 weeks of placebo or; 6 weeks of placebo followed by 6 weeks of methylphenidate. Neurocognitive and behavioural outcomes as well as neuroimaging measures will be completed at baseline and repeated at the end of each treatment condition (week 6, week 12). Primary outcome measures are omission errors on the Conners Continuous Performance Test-II (attention), between-search errors on the Spatial Working Memory task from the Cambridge Neuropsychological Test Automated Battery (spatial working memory) and the Inattentive and Hyperactivity/Impulsivity Symptom Scales on the Conners 3-Parent. Secondary outcomes will examine the effect of methylphenidate on executive functions, attention, visuospatial skills, behaviour, fine-motor skills, language, social skills and quality of life.ETHICS AND DISSEMINATION: This trial has hospital ethics approval and the results will be disseminated through peer-reviewed publications and international conferences.TRIAL REGISTRATION NUMBER: ACTRN12611000765921.</p

Occupancy Modeling, Maximum Contig Size Probabilities and Designing Metagenomics Experiments

Mathematical aspects of coverage and gaps in genome assembly have received substantial attention by bioinformaticians. Typical problems under consideration suppose that reads can be experimentally obtained from a single genome and that the number of reads will be set to cover a large percentage of that genome at a desired depth. In metagenomics experiments genomes from multiple species are simultaneously analyzed and obtaining large numbers of reads per genome is unlikely. We propose the probability of obtaining at least one contig of a desired minimum size from each novel genome in the pool without restriction based on depth of coverage as a metric for metagenomic experimental design. We derive an approximation to the distribution of maximum contig size for single genome assemblies using relatively few reads. This approximation is verified in simulation studies and applied to a number of different metagenomic experimental design problems, ranging in difficulty from detecting a single novel genome in a pool of known species to detecting each of a random number of novel genomes collectively sized and with abundances corresponding to given distributions in a single pool