BACKGROUND: Genome-wide prediction has become the method of choice in animal and plant breeding. Prediction of breeding values and phenotypes are routinely performed using large genomic data sets with number of markers on the order of several thousands to millions. The number of evaluated individuals is usually smaller which results in problems where model sparsity is of major concern. The LASSO technique has proven to be very well-suited for sparse problems often providing excellent prediction accuracy. Several computationally efficient LASSO algorithms have been developed, but optimization of hyper-parameters can be demanding. RESULTS: We have developed a novel automatic adaptive LASSO (AUTALASSO) based on the alternating direction method of multipliers (ADMM) optimization algorithm. The two major hyper-parameters of ADMM are the learning rate and the regularization factor. The learning rate is automatically tuned with line search and the regularization factor optimized using Golden section search. Results show that AUTALASSO provides superior prediction accuracy when evaluated on simulated and real bull data compared to the adaptive LASSO, LASSO and ridge regression implemented in the popular glmnet software. CONCLUSIONS: The AUTALASSO provides a very flexible and computationally efficient approach to GWP, especially when it is important to obtain high prediction accuracy and genetic gain. The AUTALASSO also has the capability to perform GWAS of both additive and dominance effects with smaller prediction error than the ordinary LASSO.

We study combinatorial parameters of a recently introduced bootstrap percolation problem in finite projective planes. We present sharp results on the size of the minimum percolating sets and the maximal nonpercolating sets. Additional results on the minimal and maximal percolation time as well as on the critical probability in the projective plane are also presented.

The Internet routing ecosystem is facing compelling scalability challenges, manifested primarily in the rapid growth of IP packet forwarding tables. The forwarding table, implemented at the data plane fast path of Internet routers to drive the packet forwarding process, currently contains about half a million entries and counting. Meanwhile, it needs to support millions of complex queries and updates per second. In this paper, we make the curious observation that the entropy of IP forwarding tables is very small and, what is more, seems to increase at a lower pace than the size of the network. This suggests that a sophisticated compression scheme may effectively and persistently reduce the memory footprint of IP forwarding tables, shielding operators from scalability matters at least temporarily. Our main contribution is such a compression scheme which, for the first time, admits both the required information-theoretical size bounds and attains fast lookups, thanks to aggressive level compression. Although we find the underlying optimization problem NP-complete, we can still give a lightweight heuristic algorithm with firm approximation guarantees. This allows us to squeeze real IP forwarding tables, comprising almost 500, 000 prefixes, to just about 140-200 KBytes of memory within a factor of 2-3 of the entropy bound, so that forwarding decisions take only 8-10 memory accesses on average and updates are supported efficiently. Our compression scheme may be of more general interest, as it is applicable to essentially any prefix tree.