A nilpotent IP polynomial multiple recurrence theorem

We generalize the IP-polynomial Szemer\'edi theorem due to Bergelson and McCutcheon and the nilpotent Szemer\'edi theorem due to Leibman. Important tools in our proof include a generalization of Leibman's result that polynomial mappings into a nilpotent group form a group and a multiparameter version of the nilpotent Hales-Jewett theorem due to Bergelson and Leibman.Comment: v4: switch to TeXlive 2016 and biblate

What do Babies hear? Analyses of Child- and Adult-Directed Speech

Child-directed speech is argued to facilitate language development, and is found cross-linguistically and cross-culturally to varying degrees. However, previous research has generally focused on short samples of child-caregiver interaction, often in the lab or with experimenters present. We test the generalizability of this phenomenon with an initial descriptive analysis of the speech heard by young children in a large, unique collection of naturalistic, daylong home recordings. Trained annotators coded automatically-detected adult speech 'utterances' from 61 homes across 4 North American cities, gathered from children (age 2-24 months) wearing audio recorders during a typical day. Coders marked the speaker gender (male/female) and intended addressee (child/adult), yielding 10,886 addressee and gender tags from 2,523 minutes of audio (cf. HB-CHAAC Interspeech ComParE challenge; Schuller et al., in press). Automated speaker-diarization (LENA) incorrectly gender-tagged 30% of male adult utterances, compared to manually-coded consensus. Furthermore, we find effects of SES and gender on child-directed and overall speech, increasing child-directed speech with child age, and interactions of speaker gender, child gender, and child age: female caretakers increased their child-directed speech more with age than male caretakers did, but only for male infants. Implications for language acquisition and existing classification algorithms are discussed

Population genetics of the highly polymorphic RPP8 gene family

Plant nucleotide-binding domain and leucine-rich repeat containing (NLR) genes provide some of the most extreme examples of polymorphism in eukaryotic genomes, rivalling even the vertebrate major histocompatibility complex. Surprisingly, this is also true in Arabidopsis thaliana, a predominantly selfing species with low heterozygosity. Here, we investigate how gene duplication and intergenic exchange contribute to this extraordinary variation. RPP8 is a three-locus system that is configured chromosomally as either a direct-repeat tandem duplication or as a single copy locus, plus a locus 2 Mb distant. We sequenced 48 RPP8 alleles from 37 accessions of A. thaliana and 12 RPP8 alleles from Arabidopsis lyrata to investigate the patterns of interlocus shared variation. The tandem duplicates display fixed differences and share less variation with each other than either shares with the distant paralog. A high level of shared polymorphism among alleles at one of the tandem duplicates, the single-copy locus and the distal locus, must involve both classical crossing over and intergenic gene conversion. Despite these polymorphism-enhancing mechanisms, the observed nucleotide diversity could not be replicated under neutral forward-in-time simulations. Only by adding balancing selection to the simulations do they approach the level of polymorphism observed at RPP8. In this NLR gene triad, genetic architecture, gene function and selection all combine to generate diversity

Vocal development in a large‐scale crosslinguistic corpus

This study evaluates whether early vocalizations develop in similar ways in children across diverse cultural contexts. We analyze data from daylong audio recordings of 49 children (1–36 months) from five different language/cultural backgrounds. Citizen scientists annotated these recordings to determine if child vocalizations contained canonical transitions or not (e.g., “ba” vs. “ee”). Results revealed that the proportion of clips reported to contain canonical transitions increased with age. Furthermore, this proportion exceeded 0.15 by around 7 months, replicating and extending previous findings on canonical vocalization development but using data from the natural environments of a culturally and linguistically diverse sample. This work explores how crowdsourcing can be used to annotate corpora, helping establish developmental milestones relevant to multiple languages and cultures. Lower inter‐annotator reliability on the crowdsourcing platform, relative to more traditional in‐lab expert annotators, means that a larger number of unique annotators and/or annotations are required, and that crowdsourcing may not be a suitable method for more fine‐grained annotation decisions. Audio clips used for this project are compiled into a large‐scale infant vocalization corpus that is available for other researchers to use in future work

Genetic Architecture of Flowering-Time Variation in Arabidopsis thaliana

The onset of flowering is an important adaptive trait in plants. The small ephemeral species Arabidopsis thaliana grows under a wide range of temperature and day-length conditions across much of the Northern hemisphere, and a number of flowering-time loci that vary between different accessions have been identified before. However, only few studies have addressed the species-wide genetic architecture of flowering-time control. We have taken advantage of a set of 18 distinct accessions that present much of the common genetic diversity of A. thaliana and mapped quantitative trait loci (QTL) for flowering time in 17 F2 populations derived from these parents. We found that the majority of flowering-time QTL cluster in as few as five genomic regions, which include the locations of the entire FLC/MAF clade of transcription factor genes. By comparing effects across shared parents, we conclude that in several cases there might be an allelic series caused by rare alleles. While this finding parallels results obtained for maize, in contrast to maize much of the variation in flowering time in A. thaliana appears to be due to large-effect alleles

Uniformity in the Wiener-Wintner theorem for nilsequences

We prove a uniform extension of the Wiener-Wintner theorem for nilsequences due to Host and Kra and a nilsequence extension of the topological Wiener-Wintner theorem due to Assani. Our argument is based on (vertical) Fourier analysis and a Sobolev embedding theorem.Comment: v3: 18 p., proof that the cube construction produces compact homogeneous spaces added, measurability issues in the proof of Theorem 1.5 addressed. We thank the anonymous referees for pointing out these gaps in v

A Coastal Cline in Sodium Accumulation in Arabidopsis thaliana Is Driven by Natural Variation of the Sodium Transporter AtHKT1;1

The genetic model plant Arabidopsis thaliana, like many plant species, experiences a range of edaphic conditions across its natural habitat. Such heterogeneity may drive local adaptation, though the molecular genetic basis remains elusive. Here, we describe a study in which we used genome-wide association mapping, genetic complementation, and gene expression studies to identify cis-regulatory expression level polymorphisms at the AtHKT1;1 locus, encoding a known sodium (Na+) transporter, as being a major factor controlling natural variation in leaf Na+ accumulation capacity across the global A. thaliana population. A weak allele of AtHKT1;1 that drives elevated leaf Na+ in this population has been previously linked to elevated salinity tolerance. Inspection of the geographical distribution of this allele revealed its significant enrichment in populations associated with the coast and saline soils in Europe. The fixation of this weak AtHKT1;1 allele in these populations is genetic evidence supporting local adaptation to these potentially saline impacted environments