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We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected low MFEs. Generalized ensemble Markov-chain Monte Carlo methods allow us to explore the rare-event tail of the MFE distribution down to probabilities like $10^{-70}$ and to study the relationship between the sequence entropy and structural properties for sequence ensembles with fixed MFEs. Entropic and structural properties of those ensembles are compared with natural RNA of the same reduced MFE (z-score).
We perform numerical simulations to study the optimal path problem on disordered hierarchical graphs with effective dimension d=2.32. Therein, edge energies are drawn from a disorder distribution that allows for positive and negative energies. This i
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a systems components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment and network
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy ma
We carefully investigate the two fundamental assumptions in the Stillinger-Weber analysis of the inherent structures (ISs) in the energy landscape and come to conclude that they cannot be validated. This explains some of the conflicting results betwe
Local entropic loss functions provide a versatile framework to define architecture-aware regularization procedures. Besides the possibility of being anisotropic in the synaptic space, the local entropic smoothening of the loss function can vary durin