FSTruct: An Fst-based tool for measuring ancestry variation in inference of population structure

In model-based inference of population structure from individual-level genetic data, individuals are assigned membership coefficients in a series of statistical clusters generated by clustering algorithms. Distinct patterns of variability in membership coefficients can be produced for different groups of individuals, for example, representing different predefined populations, sampling sites, or time periods. Such variability can be difficult to capture in a single numerical value; membership coefficient vectors are multivariate and potentially incommensurable across groups, as the number of clusters over which individuals are distributed can vary among groups of interest. Further, two groups might share few clusters in common, so that membership coefficient vectors are concentrated on different clusters. We introduce a method for measuring the variability of membership coefficients of individuals in a predefined group, making use of an analogy between variability across individuals in membership coefficient vectors and variation across populations in allele frequency vectors. We show that in a model in which membership coefficient vectors in a population follow a Dirichlet distribution, the measure increases linearly with a parameter describing the variance of a specified component of the membership vector. We apply the approach, which makes use of a normalized Fst statistic, to data on inferred population structure in three example scenarios. We also introduce a bootstrap test for equivalence of two or more groups in their level of membership coefficient variability. Our methods are implemented in the R package FSTruct.

INCO-GAN: Variable-Length Music Generation Method Based on Inception Model-Based Conditional GAN

Deep learning has made significant progress in the field of automatic music generation. At present, the research on music generation via deep learning can be divided into two categories: predictive models and generative models. However, both categories have the same problems that need to be resolved. First, the length of the music must be determined artificially prior to generation. Second, although the convolutional neural network (CNN) is unexpectedly superior to the recurrent neural network (RNN), CNN still has several disadvantages. This paper proposes a conditional generative adversarial network approach using an inception model (INCO-GAN), which enables the generation of complete variable-length music automatically. By adding a time distribution layer that considers sequential data, CNN considers the time relationship in a manner similar to RNN. In addition, the inception model obtains richer features, which improves the quality of the generated music. In experiments conducted, the music generated by the proposed method and that by human composers were compared. High cosine similarity of up to 0.987 was achieved between the frequency vectors, indicating that the music generated by the proposed method is very similar to that created by a human composer.

New adaptive hysteresis band width control for direct torque control of induction machine drives

This paper presents a new adaptive hysteresis band control approach used in direct torque control (DTC) of the induction motor (IM) drives with the switching tables for the generation of PWM signals. Constant Hysteresis Direct torque control (CHB-DTC) method used the torque and stator flux errors to generate the stator voltage reference and frequency vectors for controlling the three-phase induction motor. The CHB-DTC gives better torque transient performance but it has large steady state ripples. To reduce torque and stator current ripples in CHB-DTC controlled induction motor drives a new adaptive hysteresis band control (AHB) approach is proposed, where the hysteresis band is adapted in real time with the stator flux and torque errors variation, instead of fixed bandwidth. Both classical CHB-DTC method and the proposed adaptive hysteresis band DTC (AHB-DTC) fed three induction motor have been simulated using Matlab/Simulink. The simulation results at different operating conditions over a wide speed range demonstrate the validity, effectiveness, and feasibility of the proposed scheme. The measurements showed that torque ripples were significantly decrease with the new AHB-DTC technique and better speed response in step up or down compared to the CHB-DTC.

Reconstruction of Rooted Directed Trees

Let T be a rooted directed tree on n vertices, rooted at v. The rooted subtree frequency vector (RSTF-vector) of T with root v, denoted by rstf(T, v) is a vector of length n whose entry at position k is the number of subtrees of T that contain v and have exactly k vertices. In this paper we present an algorithm for reconstructing rooted directed trees from their rooted subtree frequencies (up to isomorphism). We show that there are examples of nonisomorphic pairs of rooted directed trees that are RSTF-equivalent, s.t. they share the same rooted subtree frequency vectors. We have found all such pairs (groups) for small sizes by using exhaustive computer search. We show that infinitely many nonisomorphic RSTF-equivalent pairs of trees exist by constructing infinite families of examples.

FST and the Triangle Inequality for Biallelic Markers

The population differentiation statistic FST, introduced by Sewall Wright, is often treated as a pairwise distance measure between populations. As was known to Wright, however, FST is not a true metric because allele frequencies exist for which it does not satisfy the triangle inequality. We prove that a stronger result holds: for biallelic markers whose allele frequencies differ across three populations, FST never satisfies the triangle inequality. We study the deviation from the triangle inequality as a function of the allele frequencies of three populations, identifying frequency vectors at which the deviation is maximal. We also examine the implications of the failure of the triangle inequality for the four-point condition for groups of four populations. Next, we examine the extent to which FST fails to satisfy the triangle inequality in genome-wide data from human populations, finding that some loci have frequencies that produce deviations near the maximum. We discuss the consequences of the theoretical results for various types of data analysis, including multidimensional scaling and inference of neighbor-joining trees from pairwise FST matrices.

Probe Efficient Feature Representation of Gapped K-mer Frequency Vectors from Sequences using Deep Neural Networks

How to extract informative features from genome sequence is a challenging issue. Gapped k-mers frequency vectors (gkm-fv) has been presented as a new type of features in the last few years. Coupled with support vector machine (gkm-SVM), gkm-fvs have been used to achieve effective sequence-based predictions. However, the huge computation of a large kernel matrix prevents it from using large amount of data. And it is unclear how to combine gkm-fvs with other data sources in the context of string kernel. On the other hand, the high dimensionality, colinearity and sparsity of gkm-fvs hinder the use of many traditional machine learning methods without a kernel trick. Therefore, we proposed a flexible and scalable framework gkm-DNN to achieve feature representation from high-dimensional gkm-fvs using deep neural networks (DNN). We first proposed a more concise version of gkm-fvs which significantly reduce the dimension of gkm-fvs. Then we implemented an efficient method to calculate the gkm-fv of a given sequence at the first time. Finally, we adopted a DNN model with gkm-fvs as inputs to achieve efficient feature representation and a prediction task. Here, we took the transcription factor binding site prediction as an illustrative application. We applied gkm-DNN onto 467 small and 69 big human ENCODE ChIP-seq datasets to demonstrate its performance and compared it with the state-of-the-art method gkm-SVM. We demonstrated that gkm-DNN can not only improve the limitations of high dimensionality, colinearity and sparsity of gkm-fvs, but also make comparable overall performance compared with gkm-SVM using the same gkm-fvs. In addition, we used gkm-DNN to explore the representation power of gkm-fvs and provided more explanation on how gkm-fvs work.