MUEGANO: A divide and conquer algorithm to overcome memory limitations when assembling shotgun projects

When assembling a large quantity of reads in a genomic shotgun project a serious limitation is the amount of random access memory (RAM) of the computers used in the project. This arises because all assembling programs must look at all the overlaps between reads at the same time, using RAM in order to construct contigs, and the memory of the computer can be filled up during this step, causing the abortion of the assembling process.
Here we propose an algorithm that is capable of overcoming any memory limitation by using redundancy of processing and thus producing an increase in computing time but overcoming the memory limitation.
The proposed algorithm consists in dividing the reads in a set of groups which size is half the maximum capability in memory of the computer used and performing assembling for all the possible combination pairs of such groups. After eliminating the redundancy of the set of contigs obtained in the previous step, the process is iterated until a set of contigs of manageable size is obtained such that the set can be handled by the assembler in a final step.
Each step of the procedure increases the time of computing from k to approximately k + k(k-1)/2, but in many practical cases only one step is needed to finish the assembling process. The procedure is suitable for any kind of assembler and was successfully applied to the assembly of a very large set of reads from the maize genome

Skinner-Rusk approach to time-dependent mechanics

The geometric approach to autonomous classical mechanical systems in terms of a canonical first-order system on the Whitney sum of the tangent and cotangent bundle, developed by R. Skinner and R. Rusk, is extended to the time-dependent framework

Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication

This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the exponential convergence of the proposed algorithm under (i) strongly connected and weight-balanced digraph topologies when the local costs are strongly convex with globally Lipschitz gradients, and (ii) connected graph topologies when the local costs are strongly convex with locally Lipschitz gradients. When the local cost functions are convex and the global cost function is strictly convex, we establish asymptotic convergence under connected graph topologies. We also characterize the algorithm's correctness under time-varying interaction topologies and study its privacy preservation properties. Motivated by practical considerations, we analyze the algorithm implementation with discrete-time communication. We provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication. Building on this result, we design a provably-correct centralized event-triggered communication scheme that is free of Zeno behavior. Finally, we develop a distributed, asynchronous event-triggered communication scheme that is also free of Zeno with asymptotic convergence guarantees. Several simulations illustrate our results.Comment: 12 page