An asymptotic existence result on compressed sensing matrices

For any rational number $h$ and all sufficiently large $n$ we give a deterministic construction for an $n\times \lfloor hn\rfloor$ compressed sensing matrix with $(\ell_1,t)$-recoverability where $t=O(\sqrt{n})$. Our method uses pairwise balanced designs and complex Hadamard matrices in the construction of $\epsilon$-equiangular frames, which we introduce as a generalisation of equiangular tight frames. The method is general and produces good compressed sensing matrices from any appropriately chosen pairwise balanced design. The $(\ell_1,t)$-recoverability performance is specified as a simple function of the parameters of the design. To obtain our asymptotic existence result we prove new results on the existence of pairwise balanced designs in which the numbers of blocks of each size are specified.Comment: 15 pages, no figures. Minor improvements and updates in February 201

Empowering statistical methods for cellular and molecular biologists.

We provide guidelines for using statistical methods to analyze the types of experiments reported in cellular and molecular biology journals such as Molecular Biology of the Cell. Our aim is to help experimentalists use these methods skillfully, avoid mistakes, and extract the maximum amount of information from their laboratory work. We focus on comparing the average values of control and experimental samples. A Supplemental Tutorial provides examples of how to analyze experimental data using R software

Statistical practices of educational researchers: An analysis of their ANOVA, MANOVA, and ANCOVA analyses

Articles published in several prominent educational journals were examined to investigate the use of data-analysis tools by researchers in four research paradigms: between-subjects univariate designs, between-subjects multivariate designs, repeated measures designs, and covariance designs. In addition to examining specific details pertaining to the research design (e.g., sample size, group size equality/inequality) and methods employed for data analysis, we also catalogued whether: (a) validity assumptions were examined, (b) effect size indices were reported, (c) sample sizes were selected based on power considerations, and (d) appropriate textbooks and/or articles were cited to communicate the nature of the analyses that were performed. Our analyses imply that researchers rarely verify that validity assumptions are satisfied and accordingly typically use analyses that are nonrobust to assumption violations. In addition, researchers rarely report effect size statistics, nor do they routinely perform power analyses to determine sample size requirements. We offer many recommendations to rectify these shortcomings.Social Sciences and Humanities Research Counci

Post-copulatory opportunities for sperm competition and cryptic female choice provide no offspring fitness benefits in externally fertilizing salmon

There is increasing evidence that females can somehow improve their offspring fitness by mating with multiple males, but we understand little about the exact stage(s) at which such benefits are gained. Here, we measure whether offspring fitness is influenced by mechanisms operating solely between sperm and egg. Using externally-fertilising and polyandrous Atlantic salmon (Salmo salar), we employed split-clutch and split-ejaculate in vitro fertilisation experiments to generate offspring using designs that either denied or applied opportunities for sperm competition and cryptic female choice. Following fertilisations, we measured 140 days of offspring fitness after hatch, through growth and survival in hatchery and near-natural conditions. Despite an average composite mortality of 61%, offspring fitness at every life stage was near-identical between groups fertilised under the absence versus presence of opportunities for sperm competition and cryptic female choice. Of the 21,551 and 21,771 eggs from 24 females fertilised under monandrous versus polyandrous conditions, 68% versus 67.8% survived to the 100-day juvenile stage; sub-samples showed similar hatching success (73.1% versus 74.3%), had similar survival over 40 days in near-natural streams (57.3% versus 56.2%), and grew at similar rates throughout. We therefore found no evidence that gamete-specific interactions allow offspring fitness benefits when polyandrous fertilisation conditions provide opportunities for sperm competition and cryptic female choice

The weight of emotions in decision-making: how fearful and happy facial stimuli modulate action readiness of goal-directed actions

Modern theories of behavioral control converge with the idea that goal-directed/voluntary behaviors are intimately tied to the evaluation of resources. Of key relevance in the decision-making processes that underlie action selection are those stimuli that bear emotional content. However, even though it is acknowledged that emotional information affects behavioral control, the exact way in which emotions impact on action planning is largely unknown. To clarify this issue, I gave an emotional version of a go/no-go task to healthy participants, in which they had to perform the same arm reaching movement when pictures of fearful or happy faces were presented, and to withhold it when pictures of faces with neutral expressions were presented. This task allows for the investigation of the effects of emotional stimuli when they are task-relevant without conflating movement planning with target detection and task switching. It was found that both the reaction times (RTs) and the percentages of errors increased when the go-signal was the image of a fearful looking face, as opposed to when the go-signal was a happy looking face. Importantly, to control for the role of the features of the stimuli, I ran a control task in which the same pictures were shown; however, participants had to move/withhold the commanded movement according to gender, disregarding the emotional valence. In this context, the differences between RTs and error percentages between the fearful and happy faces disappeared. On the one hand, these results suggest that fearful facial stimuli are likely to capture and hold attention more strongly than faces that express happiness, which could serve to increase vigilance for detecting a potential threat in an observer's environment. On the other hand, they also suggest that the influence of fearful facial stimuli is not automatic, but it depends on the task requirements