Background: Despite marked recent improvements in long-read sequencing technology, the assembly of diploid genomes remains a difficult task. A major obstacle is distinguishing between alternative contigs that represent highly heterozygous regions. If primary and secondary contigs are not properly identified, the primary assembly will overrepresent both the size and complexity of the genome, which complicates downstream analysis such as scaffolding.Results: Here we illustrate a new method, which we call HapSolo, that identifies secondary contigs and defines a primary assembly based on multiple pairwise contig alignment metrics. HapSolo evaluates candidate primary assemblies using BUSCO scores and then distinguishes among candidate assemblies using a cost function. The cost function can be defined by the user but by default considers the number of missing, duplicated and single BUSCO genes within the assembly. HapSolo performs hill climbing to minimize cost over thousands of candidate assemblies. We illustrate the performance of HapSolo on genome data from three species: the Chardonnay grape (Vitis vinifera), with a genome of 490 Mb, a mosquito (Anopheles funestus; 200 Mb) and the Thorny Skate (Amblyraja radiata; 2650 Mb). Conclusions:HapSolo rapidly identified candidate assemblies that yield improvements in assembly metrics, including decreased genome size and improved N50 scores. Contig N50 scores improved by 35%, 9% and 9% for Chardonnay, mosquito and the thorny skate, respectively, relative to unreduced primary assemblies. The benefits of HapSolo were amplified by down-stream analyses, which we illustrated by scaffolding with Hi-C data. We found, for example, that prior to the application of HapSolo, only 52% of the Chardonnay genome was captured in the largest 19 scaffolds, corresponding to the number of chromosomes. After the application of HapSolo, this value increased to ~ 84%. The improvements for the mosquito's largest three scaffolds, representing the number of chromosomes, were from 61 to 86%, and the improvement was even more pronounced for thorny skate. We compared the scaffolding results to assemblies that were based on PurgeDups for identifying secondary contigs, with generally superior results for HapSolo.

We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using Cartesian coordinates. We discuss the numerical techniques used in developing this code, and its performance on massively parallel and vector supercomputers. As a test case, we present evolutions for the first 3D black hole spacetimes. We identify a number of difficulties in evolving 3D black holes and suggest approaches to overcome them. We show how special treatment of the conformal factor can lead to more accurate evolution, and discuss techniques we developed to handle black hole spacetimes in the absence of symmetries. Many different slicing conditions are tested, including geodesic, maximal, and various algebraic conditions on the lapse. With current resolutions, limited by computer memory sizes, we show that with certain lapse conditions we can evolve the black hole to about t = 50M , where M is the black hole mass. Comparisons are made with results obtained by evolving spherical initial black hole data sets with a 1D spherically symmetric code. We also demonstrate that an "apparent horizon locking shift" can be used to prevent the development of large gradients in the metric functions that result from singularity avoiding time slicings. We compute the mass of the apparent horizon in these spacetimes, and find that in many cases it can be conserved to within about 5% throughout the evolution with our techniques and current 1 resolution.