Graph theory algorithms have been proposed in order to identify, follow in time, and statistically analyze the changes in conformations that occur along molecular dynamics (MD) simulations. The atomistic granularity level of the MD simulations is maintained within the graph theoric algorithms proposed here, isomorphism is a key component together with keeping the chemical nature of the atoms. Isomorphism is used to recognize conformations and construct the graphs of transitions, and the reduction in complexity of the isomorphism has been achieved by the introduction of “orbits” and “reference snapshots.” The proposed algorithms are applied to MD trajectories of gas phase molecules and clusters as well as condensed matter. The changes in conformations followed over time are hydrogen bond(s), proton transfer(s), coordination number(s), covalent bond(s), multiple fragmentation(s), and H-bonded membered rings. The algorithms provide an automatic analysis of multiple trajectories in parallel, and can be applied to ab initio and classical MD trajectories alike, and to more coarse grain representations.
We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity then we present a -approximation algorithm for a special case in which all bins have the same capacities.
We present a new approach for the prediction of the coarse-grain 3D structure of RNA molecules. We model a molecule as being made of helices and junctions. Those junctions are classified into topological families that determine their preferred 3D shapes. All the parts of the molecule are then allowed to establish long-distance contacts that induce a 3D folding of the molecule. An algorithm relying on game theory is proposed to discover such long-distance contacts that allow the molecule to reach a Nash equilibrium. As reported by our experiments, this approach allows one to predict the global shape of large molecules of several hundreds of nucleotides that are out of reach of the state-of-the-art methods.
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