Refine
Year of publication
- 2014 (20) (remove)
Document Type
- ZIB-Report (8)
- Article (6)
- In Collection (5)
- In Proceedings (1)
Language
- English (20)
Is part of the Bibliography
- no (20)
Keywords
- directed networks (2)
- metastability (2)
- Alanine dipeptide (1)
- Coarse graining (1)
- Electric field (1)
- Floquet theory (1)
- Girsanov Theorem (1)
- Importance Sampling (1)
- Markov states model (1)
- Module identification and classification (1)
Institute
We employ the adaptive resolution approach AdResS, in its recently developed Grand Canonicallike version (GC-AdResS) [Wang et al. Phys.Rev.X 3, 011018 (2013)], to calculate the excess chemical potential, $μ^{ex}$, of various liquids and mixtures. We compare our results with those obtained from full atomistic simulations using the technique of thermodynamic integration and show a satisfactory agreement. In GC-AdResS the procedure to calculate $μ^{ex}$ corresponds to the process of standard initial equilibration of the system; this implies that, independently of the specific aim of the study, $μ^{ex}$, for each molecular species, is automatically calculated every time a GC-AdResS simulation is performed.
The problem of decomposing networks into modules (or clusters) has gained much attention in recent years, as it can account for a coarsegrained description of complex systems, often revealing functional subunits of these systems. A variety of module detection algorithms have been proposed, mostly oriented towards finding hard partitionings of undirected networks. Despite the increasing number of fuzzy clustering methods for directed networks, many of these approaches tend to neglect important directional information. In this paper, we present a novel random walk based approach for finding fuzzy partitions of directed, weighted networks, where edge directions play a crucial role in defining how well nodes in a module are interconnected. We will show that cycle decomposition of a random walk process connects the notion of network modules and information transport in a network, leading to a new, symmetric measure of node communication. Finally, we will use this measure to introduce a communication graph, for which we will show that although being undirected it inherits all necessary information about modular structures from the original network.
Techniques for finding metastable or almost invariant sets have been investigated, e.g., for deterministic dynamical systems in set-oriented numerics, for stochastic processes in molecular dynamics, and for random walks on complex networks. Most prominent algorithms are based on spectral apporaches and identify metastable sets via the doimant eigenvalues of the transfer operator associated with the dynamical system under consideration. These algorithms require the dominant eigenvalues to be real-valued. However, for many types of dynamics, e.g. for non-reversible Markov chains, this condition is not met. In this paper we utilize the hitting time apporach to metastable sets and demonstrate how the wellknown statements about optimal metastable decompositions of reversible chains can be reformulated for non-reversible chains if one switches from a spectral approach to an exit time approach. The performance of the resulting algorithm is illustrated by numerical experiments on random walks on complex networks.
In recent years Markov State Models (MSMs) have attracted a consid-
erable amount of attention with regard to modelling conformation changes
and associated function of biomolecular systems. They have been used
successfully, e.g., for peptides including time-resolved spectroscopic ex-
periments, protein function and protein folding , DNA and RNA, and
ligand-receptor interaction in drug design and more complicated multi-
valent scenarios. In this article a novel reweighting scheme is introduced
that allows to construct an MSM for certain molecular system out of an
MSM for a similar system. This permits studying how molecular proper-
ties on long timescales differ between similar molecular systems without
performing full molecular dynamics simulations for each system under con-
sideration. The performance of the reweighting scheme is illustrated for
simple test cases including one where the main wells of the respective en-
ergy landscapes are located differently and an alchemical transformation
of butane to pentane where the dimension of the state space is changed.
We investigate the problem of finding modules (or clusters, communities) in directed networks. Until now, most articles on this topic have been oriented towards finding complete network partitions despite the fact that this often is unwanted. We present a novel random walk based approach for non-complete partitions of the directed network into modules in which some nodes do not belong to only one of the modules but to several or to none at all. The new random walk process is reversible even for directed networks but inherits all necessary information about directions and structure of the original network. We demonstrate the performance of the new method in application to a real-world earthquake network.
Life Sciences
(2014)