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INTRODUCTION During the independent process of cereal evolution, many trait shifts appear to have been under convergent selection to meet the specific needs of humans. Identification of convergently selected genes across cereals could help to clarify the evolution of crop species and to accelerate breeding programs. In the past several decades, researchers have debated whether convergent phenotypic selection in distinct lineages is driven by conserved molecular changes or by diverse molecular pathways. Two of the most economically important crops, maize and rice, display some conserved phenotypic shifts—including loss of seed dispersal, decreased seed dormancy, and increased grain number during evolution—even though they experienced independent selection. Hence, maize and rice can serve as an excellent system for understanding the extent of convergent selection among cereals. RATIONALE Despite the identification of a few convergently selected genes, our understanding of the extent of molecular convergence on a genome-wide scale between maize and rice is very limited. To learn how often selection acts on orthologous genes, we investigated the functions and molecular evolution of the grain yield quantitative trait locus KRN2 in maize and its rice ortholog OsKRN2 . We also identified convergently selected genes on a genome-wide scale in maize and rice, using two large datasets. RESULTS We identified a selected gene, KRN2 ( kernel row number2 ), that differs between domesticated maize and its wild ancestor, teosinte. This gene underlies a major quantitative trait locus for kernel row number in maize. Selection in the noncoding upstream regions resulted in a reduction of KRN2 expression and an increased grain number through an increase in kernel rows. The rice ortholog, OsKRN2 , also underwent selection and negatively regulates grain number via control of secondary panicle branches. These orthologs encode WD40 proteins and function synergistically with a gene of unknown function, DUF1644, which suggests that a conserved protein interaction controls grain number in maize and rice. Field tests show that knockout of KRN2 in maize or OsKRN2 in rice increased grain yield by ~10% and ~8%, respectively, with no apparent trade-off in other agronomic traits. This suggests potential applications of KRN2 and its orthologs for crop improvement. On a genome-wide scale, we identified a set of 490 orthologous genes that underwent convergent selection during maize and rice evolution, including KRN2/OsKRN2 . We found that the convergently selected orthologous genes appear to be significantly enriched in two specific pathways in both maize and rice: starch and sucrose metabolism, and biosynthesis of cofactors. A deep analysis of convergently selected genes in the starch metabolic pathway indicates that the degree of genetic convergence via convergent selection is related to the conservation and complexity of the gene network for a given selection. CONCLUSION Our findings show that common phenotypic shifts during maize and rice evolution acting on conserved genes are driven at least in part by convergent selection, which in maize and rice likely occurred both during and after domestication. We provide evolutionary and functional evidence on the convergent selection of KRN2/OsKRN2 for grain number between maize and rice. We further found that a complete loss-of-function allele of KRN2/OsKRN2 increased grain yield without an apparent negative impact on other agronomic traits. Exploring the role of KRN2/OsKRN2 and other convergently selected genes across the cereals could provide new opportunities to enhance the production of other global crops. Shared selected orthologous genes in maize and rice for convergent phenotypic shifts during domestication and improvement. By comparing 3163 selected genes in maize and 18,755 selected genes in rice, we identified 490 orthologous gene pairs, including KRN2 and its rice ortholog OsKRN2 , as having been convergently selected. Knockout of KRN2 in maize or OsKRN2 in rice increased grain yield by increasing kernel rows and secondary panicle branches, respectively. 

Entering commands on touchscreens can be noisy, but existing interfaces commonly adopt deterministic principles for deciding targets and often result in errors. Building on prior research of using Bayes' theorem to handle uncertainty in input, this paper formalized Bayes' theorem as a generic guiding principle for deciding targets in command input (referred to as "BayesianCommand"), developed three models for estimating prior and likelihood probabilities, and carried out experiments to demonstrate the effectiveness of this formalization. More specifically, we applied BayesianCommand to improve the input accuracy of (1) point-and-click and (2) word-gesture command input. Our evaluation showed that applying BayesianCommand reduced errors compared to using deterministic principles (by over 26.9% for point-and-click and by 39.9% for word-gesture command input) or applying the principle partially (by over 28.0% and 24.5%). 

Interference alignment (IA) is widely regarded as a promising interference management technique for wireless networks and its potential is most profound in interference-intensive environments. This motivates us to study IA for multicast communications in multi-hop MIMO networks, which are rich in interference by nature. We develop a set of linear constraints that can characterize a feasible design space of IA for multicast communications. The set of linear constraints constitutes a simple mathematical model of IA that allows us to conduct cross-layer multicast throughput optimization in multi-hop MIMO networks, but without getting involved into the onerous signal design at the physical layer. Based on the mathematical model of IA, we formulate a multicast throughput maximization problem and develop an approximation solution that can achieve (1−ϵ)-optimality. Simulation results show that the use of IA can significantly increase the multicast throughput in multi-hop MIMO networks and the throughput gain increases with the volume of multicast traffic and the number of antennas.