Decoding coalescent hidden Markov models in linear time

In many areas of computational biology, hidden Markov models (HMMs) have been used to model local genomic features. In particular, coalescent HMMs have been used to infer ancient population sizes, migration rates, divergence times, and other parameters such as mutation and recombination rates. As more loci, sequences, and hidden states are added to the model, however, the runtime of coalescent HMMs can quickly become prohibitive. Here we present a new algorithm for reducing the runtime of coalescent HMMs from quadratic in the number of hidden time states to linear, without making any additional approximations. Our algorithm can be incorporated into various coalescent HMMs, including the popular method PSMC for inferring variable effective population sizes. Here we implement this algorithm to speed up our demographic inference method diCal, which is equivalent to PSMC when applied to a sample of two haplotypes. We demonstrate that the linear-time method can reconstruct a population size change history more accurately than the quadratic-time method, given similar computation resources. We also apply the method to data from the 1000 Genomes project, inferring a high-resolution history of size changes in the European population.Comment: 18 pages, 5 figures. To appear in the Proceedings of the 18th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2014). The final publication is available at link.springer.co

Two-Locus Likelihoods under Variable Population Size and Fine-Scale Recombination Rate Estimation

Two-locus sampling probabilities have played a central role in devising an efficient composite likelihood method for estimating fine-scale recombination rates. Due to mathematical and computational challenges, these sampling probabilities are typically computed under the unrealistic assumption of a constant population size, and simulation studies have shown that resulting recombination rate estimates can be severely biased in certain cases of historical population size changes. To alleviate this problem, we develop here new methods to compute the sampling probability for variable population size functions that are piecewise constant. Our main theoretical result, implemented in a new software package called LDpop, is a novel formula for the sampling probability that can be evaluated by numerically exponentiating a large but sparse matrix. This formula can handle moderate sample sizes ($n \leq 50$) and demographic size histories with a large number of epochs ($\mathcal{D} \geq 64$). In addition, LDpop implements an approximate formula for the sampling probability that is reasonably accurate and scales to hundreds in sample size ($n \geq 256$). Finally, LDpop includes an importance sampler for the posterior distribution of two-locus genealogies, based on a new result for the optimal proposal distribution in the variable-size setting. Using our methods, we study how a sharp population bottleneck followed by rapid growth affects the correlation between partially linked sites. Then, through an extensive simulation study, we show that accounting for population size changes under such a demographic model leads to substantial improvements in fine-scale recombination rate estimation. LDpop is freely available for download at https://github.com/popgenmethods/ldpopComment: 32 pages, 13 figure

Numerical solution of kinetic SPDEs via stochastic Magnus expansion

In this paper, we show how the Itô-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space only by utilizing finite difference methods and vectorize the resulting equation exploiting its sparsity. As a benchmark, we will apply it to the case of the stochastic Langevin equation with constant coefficients, where an explicit solution is available, and compare the Magnus scheme with the Euler–Maruyama scheme. We will see that the Magnus expansion is superior in terms of both accuracy and especially computational time by using a single GPU and verify it in a variable coefficient case. Notably, we will see speed-ups of order ranging form 20 to 200 compared to the Euler–Maruyama scheme, depending on the accuracy target and the spatial resolution

Mathematical and physical approaches to infer absolute zenith wet delays from double differential interferometric observations using ERA5 atmospheric reanalysis

Atmospheric water vapor (WV) is one of the driving constituents of the atmosphere. The modelling and forecasting of WV and derived quantities like precipitable water is reliable on regional scales but challenging on small scales because of its high spatial and temporal variation. Interferometric synthetic aperture radar (InSAR) can be exploited to retrieve integrated atmospheric water vapor (IWV) from path delay observations along the radar line of sight. InSAR-derived IWV maps feature a very high spatial resolution but the double-differential interferometric observations only provide changes of IWV between acquisition times and with respect to a certain spatial reference. In this study we present a method to derive the absolute IWV by combining ERA5 numerical weather model data with differential path delay observations from InSAR time series. We propose different functional approaches to merge the regional trend of WV from ERA5 with the high resolution IWV signal from InSAR. We apply this to a Sentinel-1 Persistent Scatterer InSAR time series in the Upper Rhine Graben and validate against IWV observations at GNSS stations of the Upper Rhine Graben Network

Teaching a Minimally Structured Back-Progpagation Network to Recognise Speech Sounds

An associatve network was trained on a speech recognition task using continuous speech. The input speech was processed to produce a spectral representation incorporating some of the transformations introduced by the peripheral auditory system before the signal reaches the brain. Input nodes to the network represented a 150-millIsecond time window through which the transformed speech passed in 2-millisecond steps. Output nodes represented elemental speech sounds (demisyllables) whose target values were specified based on a human listener's ability to identify the sounds in the same input segment. The work reported here focuses on the experience and train on conditions needed to produce natural generalizations between training and test utterances

Other‐Sacrificing Options

I argue that you can be permitted to discount the interests of your adversaries even though doing so would be impartially suboptimal. This means that, in addition to the kinds of moral options that the literature traditionally recognises, there exist what I call other-sacrificing options. I explore the idea that you cannot discount the interests of your adversaries as much as you can favour the interests of your intimates; if this is correct, then there is an asymmetry between negative partiality toward your adversaries and positive partiality toward your intimates

Efficiently inferring the demographic history of many populations with allele count data.

The sample frequency spectrum (SFS), or histogram of allele counts, is an important summary statistic in evolutionary biology, and is often used to infer the history of population size changes, migrations, and other demographic events affecting a set of populations. The expected multipopulation SFS under a given demographic model can be efficiently computed when the populations in the model are related by a tree, scaling to hundreds of populations. Admixture, back-migration, and introgression are common natural processes that violate the assumption of a tree-like population history, however, and until now the expected SFS could be computed for only a handful of populations when the demographic history is not a tree. In this article, we present a new method for efficiently computing the expected SFS and linear functionals of it, for demographies described by general directed acyclic graphs. This method can scale to more populations than p reviously possible for complex demographic histories including admixture. We apply our method to an 8-population SFS to estimate the timing and strength of a proposed "basal Eurasian" admixture event in human history. We implement and release our method in a new open-source software package momi2