On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Growing Income Inequality Threatens American Education

The first of two articles in consecutive months describes the origins and nature of growing income inequality, and some of its consequences for American children. It documents the increased family income inequality that's occurred over the past 40 years and shows that the increased income disparity has been more than matched by an expanding gap between the amounts of money that low- and high-income parents spend on enrichment activities for their children. It also shows that the growth in income inequality has been accompanied by increasing gaps in academic achievement. The article draws from the first part of the author's recent book, Restoring Opportunity: The Crisis of Inequality and the Challenge for American Education (Harvard Education Press and the Russell Sage Foundation, 2014). The second part to the series, also drawn from Restoring Opportunity, describes ideas based on proven policy approaches that will enable the country to make progress on the enormous task of restoring the educational opportunities that children from low-income families need if they are to lead productive and fulfilling lives. © 2014

The evolution of language: a comparative review

For many years the evolution of language has been seen as a disreputable topic, mired in fanciful "just so stories" about language origins. However, in the last decade a new synthesis of modern linguistics, cognitive neuroscience and neo-Darwinian evolutionary theory has begun to make important contributions to our understanding of the biology and evolution of language. I review some of this recent progress, focusing on the value of the comparative method, which uses data from animal species to draw inferences about language evolution. Discussing speech first, I show how data concerning a wide variety of species, from monkeys to birds, can increase our understanding of the anatomical and neural mechanisms underlying human spoken language, and how bird and whale song provide insights into the ultimate evolutionary function of language. I discuss the ‘‘descended larynx’ ’ of humans, a peculiar adaptation for speech that has received much attention in the past, which despite earlier claims is not uniquely human. Then I will turn to the neural mechanisms underlying spoken language, pointing out the difficulties animals apparently experience in perceiving hierarchical structure in sounds, and stressing the importance of vocal imitation in the evolution of a spoken language. Turning to ultimate function, I suggest that communication among kin (especially between parents and offspring) played a crucial but neglected role in driving language evolution. Finally, I briefly discuss phylogeny, discussing hypotheses that offer plausible routes to human language from a non-linguistic chimp-like ancestor. I conclude that comparative data from living animals will be key to developing a richer, more interdisciplinary understanding of our most distinctively human trait: language

The ecogenetic link between demography and evolution : can we bridge the gap between theory and data?

Calls to understand the links between ecology and evolution have been common for decades. Population dynamics, i.e. the demographic changes in populations, arise from life history decisions of individuals and thus are a product of selection, and selection, on the contrary, can be modified by such dynamical properties of the population as density and stability. It follows that generating predictions and testing them correctly requires considering this ecogenetic feedback loop whenever traits have demographic consequences, mediated via density dependence (or frequency dependence). This is not an easy challenge, and arguably theory has advanced at a greater pace than empirical research. However, theory would benefit from more interaction between related fields, as is evident in the many near-synonymous names that the ecogenetic loop has attracted. We also list encouraging examples where empiricists have shown feasible ways of addressing the question, ranging from advanced data analysis to experiments and comparative analyses of phylogenetic data

Size Doesn't Matter: Towards a More Inclusive Philosophy of Biology

notes: As the primary author, O’Malley drafted the paper, and gathered and analysed data (scientific papers and talks). Conceptual analysis was conducted by both authors.publication-status: Publishedtypes: ArticlePhilosophers of biology, along with everyone else, generally perceive life to fall into two broad categories, the microbes and macrobes, and then pay most of their attention to the latter. ‘Macrobe’ is the word we propose for larger life forms, and we use it as part of an argument for microbial equality. We suggest that taking more notice of microbes – the dominant life form on the planet, both now and throughout evolutionary history – will transform some of the philosophy of biology’s standard ideas on ontology, evolution, taxonomy and biodiversity. We set out a number of recent developments in microbiology – including biofilm formation, chemotaxis, quorum sensing and gene transfer – that highlight microbial capacities for cooperation and communication and break down conventional thinking that microbes are solely or primarily single-celled organisms. These insights also bring new perspectives to the levels of selection debate, as well as to discussions of the evolution and nature of multicellularity, and to neo-Darwinian understandings of evolutionary mechanisms. We show how these revisions lead to further complications for microbial classification and the philosophies of systematics and biodiversity. Incorporating microbial insights into the philosophy of biology will challenge many of its assumptions, but also give greater scope and depth to its investigations