Geometry of the sample frequency spectrum and the perils of demographic inference

The sample frequency spectrum (SFS), which describes the distribution of mutant alleles in a sample of DNA sequences, is a widely used summary statistic in population genetics. The expected SFS has a strong dependence on the historical population demography and this property is exploited by popular statistical methods to infer complex demographic histories from DNA sequence data. Most, if not all, of these inference methods exhibit pathological behavior, however. Specifically, they often display runaway behavior in optimization, where the inferred population sizes and epoch durations can degenerate to 0 or diverge to infinity, and show undesirable sensitivity of the inferred demography to perturbations in the data. The goal of this paper is to provide theoretical insights into why such problems arise. To this end, we characterize the geometry of the expected SFS for piecewise-constant demographic histories and use our results to show that the aforementioned pathological behavior of popular inference methods is intrinsic to the geometry of the expected SFS. We provide explicit descriptions and visualizations for a toy model with sample size 4, and generalize our intuition to arbitrary sample sizes n using tools from convex and algebraic geometry. We also develop a universal characterization result which shows that the expected SFS of a sample of size n under an arbitrary population history can be recapitulated by a piecewise-constant demography with only k(n) epochs, where k(n) is between n/2 and 2n-1. The set of expected SFS for piecewise-constant demographies with fewer than k(n) epochs is open and non-convex, which causes the above phenomena for inference from data.Comment: 21 pages, 5 figure

Quantitative stray field imaging of a magnetic vortex core

Thin-film ferromagnetic disks present a vortex spin structure whose dynamics, added to the small size (~10 nm) of their core, earned them intensive study. Here we use a scanning nitrogen-vacancy (NV) center microscope to quantitatively map the stray magnetic field above a 1 micron-diameter disk of permalloy, unambiguously revealing the vortex core. Analysis of both probe-to-sample distance and tip motion effects through stroboscopic measurements, allows us to compare directly our quantitative images to micromagnetic simulations of an ideal structure. Slight perturbations with respect to the perfect vortex structure are clearly detected either due to an applied in-plane magnetic field or imperfections of the magnetic structures. This work demonstrates the potential of scanning NV microscopy to map tiny stray field variations from nanostructures, providing a nanoscale, non-perturbative detection of their magnetic texture.Comment: 5 pages, 4 figure

A multiprocessor based packet-switch: performance analysis of the communication infrastructure

The intra-chip communication infrastructures are receiving always more attention since they are becoming a crucial part in the development of current SoCs. Due to the high availability of pre-characterized hard-IP, the complexity of the design is moving toward global interconnections which are introducing always more constraints at each technology node. Power consumption, timing closure, bandwidth requirements, time to market, are some of the factors that are leading to the proposal of new solutions for next generation multi-million SoCs. The need of high programmable systems and the high gate-count availability is moving always more attention on multiprocessors systems (MP-SoC) and so an adequate solution must be found for the communication infrastructure. One of the most promising technologies is the Network-On-Chip (NoC) architecture, which seems to better fit with the new demanding complexity of such systems. Before starting to develop new solutions, it is crucial to fully understand if and when current bus architectures introduce strong limitations in the development of high speed systems. This article describes a case study of a multiprocessor based ethernet packet-switch application with a shared-bus communication infrastructure. This system aims to depict all the bottlenecks which a shared-bus introduces under heavy load. What emerges from this analysis is that, as expected, a shared-bus is not scalable and it strongly limits whole system performances. These results strengthen the hypothesis that new communication architectures (like the NoC) must be found

DNA-encoded nucleosome occupancy is associated with transcription levels in the human malaria parasite Plasmodium falciparum.

BackgroundIn eukaryotic organisms, packaging of DNA into nucleosomes controls gene expression by regulating access of the promoter to transcription factors. The human malaria parasite Plasmodium falciparum encodes relatively few transcription factors, while extensive nucleosome remodeling occurs during its replicative cycle in red blood cells. These observations point towards an important role of the nucleosome landscape in regulating gene expression. However, the relation between nucleosome positioning and transcriptional activity has thus far not been explored in detail in the parasite.ResultsHere, we analyzed nucleosome positioning in the asexual and sexual stages of the parasite's erythrocytic cycle using chromatin immunoprecipitation of MNase-digested chromatin, followed by next-generation sequencing. We observed a relatively open chromatin structure at the trophozoite and gametocyte stages, consistent with high levels of transcriptional activity in these stages. Nucleosome occupancy of genes and promoter regions were subsequently compared to steady-state mRNA expression levels. Transcript abundance showed a strong inverse correlation with nucleosome occupancy levels in promoter regions. In addition, AT-repeat sequences were strongly unfavorable for nucleosome binding in P. falciparum, and were overrepresented in promoters of highly expressed genes.ConclusionsThe connection between chromatin structure and gene expression in P. falciparum shares similarities with other eukaryotes. However, the remarkable nucleosome dynamics during the erythrocytic stages and the absence of a large variety of transcription factors may indicate that nucleosome binding and remodeling are critical regulators of transcript levels. Moreover, the strong dependency between chromatin structure and DNA sequence suggests that the P. falciparum genome may have been shaped by nucleosome binding preferences. Nucleosome remodeling mechanisms in this deadly parasite could thus provide potent novel anti-malarial targets