Distortion of genealogical properties when the sample is very large

Study sample sizes in human genetics are growing rapidly, and in due course it will become routine to analyze samples with hundreds of thousands if not millions of individuals. In addition to posing computational challenges, such large sample sizes call for carefully re-examining the theoretical foundation underlying commonly-used analytical tools. Here, we study the accuracy of the coalescent, a central model for studying the ancestry of a sample of individuals. The coalescent arises as a limit of a large class of random mating models and it is an accurate approximation to the original model provided that the population size is sufficiently larger than the sample size. We develop a method for performing exact computation in the discrete-time Wright-Fisher (DTWF) model and compare several key genealogical quantities of interest with the coalescent predictions. For realistic demographic scenarios, we find that there are a significant number of multiple- and simultaneous-merger events under the DTWF model, which are absent in the coalescent by construction. Furthermore, for large sample sizes, there are noticeable differences in the expected number of rare variants between the coalescent and the DTWF model. To balance the tradeoff between accuracy and computational efficiency, we propose a hybrid algorithm that utilizes the DTWF model for the recent past and the coalescent for the more distant past. Our results demonstrate that the hybrid method with only a handful of generations of the DTWF model leads to a frequency spectrum that is quite close to the prediction of the full DTWF model.Comment: 27 pages, 2 tables, 14 figure

Paying for Market Quality

One way to improve the liquidity of small stocks is to subsidize the providers of liquidity. These subsidies take many forms such as informational advantages, priority in trading with incoming order flow, and fee rebates for limit order traders. In this study, we examine another type of subsidy – directly paying liquidity providers to provide contractual improvement in liquidity. Our specific focus here is the 2002 decision by the Stockholm Stock Exchange to allow listed firms to negotiate with liquidity providers to set maximum spread widths and minimum depths. We find, for a sample of stocks that entered into such an arrangement, a significant improvement in market quality with a decline in quoted spreads and an increase in quoted depth throughout the limit order book. We also find evidence that suggests that there are improvements beyond those contracted for. In addition, both inter and intraday volatility decline following the entry of committed liquidity providers for these stocks. Traders benefit by the reduced costs as well as by the ease of finding liquidity as seen in the increased trade sizes. We also find that a firm’s stock price subsequent to entering into the agreement rises in direct proportion to the improvement in market quality Thus, we find overwhelming evidence of liquidity benefits to listed firms of entering into such contracts which suggests that firms should consider these market quality improvement opportunities as they do other capital budgeting decisions and that there are residual benefits beyond those contracted for.No keywords;

GAASP: Genetic Algorithm Based Atomistic Sampling Protocol for High-Entropy Materials

High-Entropy Materials are composed of multiple elements on comparatively simpler lattices. Due to the multicomponent nature of such materials, the atomic scale sampling is computationally expensive due to the combinatorial complexity. We propose a genetic algorithm based methodology for sampling such complex chemically-disordered materials. Genetic Algorithm based Atomistic Sampling Protocol (GAASP) variants can generate low and well as high-energy structures. GAASP low-energy variant in conjugation with metropolis criteria avoids the premature convergence as well as ensures the detailed balance condition. GAASP can be employed to generate the low-energy structures for thermodynamic predictions as well as diverse structures can be generated for machine learning applications