We present a semiempirical model for calculating electron transport in atomic-scale devices. The model is an extension of the extended Hückel method with a self-consistent Hartree potential that models the effect of an external bias and corresponding charge rearrangements in the device. It is also possible to include the effect of external gate potentials and continuum dielectric regions in the device. The model is used to study the electron transport through an organic molecule between gold surfaces, and it is demonstrated that the results are in closer agreement with experiments than ab initio approaches provide. In another example, we study the transition from tunneling to thermionic emission in a transistor structure based on graphene nanoribbons.

Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present an evolutionary algorithm for reconstruction of graphs from their Laplacian spectra. Through a stochastic process of mutations and selection, evolving test networks converge to a reference graph. Applying the method to several examples of random graphs, clustered graphs, and small-world networks, we show that the proposed stochastic evolution allows exact reconstruction of relatively small networks and yields good approximations in the case of large sizes. [13]. Much effort is invested in the understanding how the structure of a network is mapped to its function and determines its operation. On the other hand, in applications ranging from bioengineering to neurosciences one also needs to design networks with a given function or reconstruct a network from its dynamics. Taking into account the great complexity of network dynamics, explicit solutions of such inverse problems of graph theory are difficult. But graph reconstruction may also be achieved without any knowledge of rules, by running an artificial evolution process through which a network learns to generate certain dynamics by adjusting its internal organization. Indeed, evolutionary algorithms are known to yield efficient solutions for complex optimization problems [14]. For the problem of graph reconstruction, such an approach has previously been proposed [15,16].In this Letter, we present an evolutionary algorithm and apply it to reconstruct graphs from their Laplacian spectra. Random graphs, small-world networks and networks with cluster organization are considered. We show that for relatively small graphs, exact reconstruction within a reasonable evolution time is possible. For larger graphs, the evolution leads to a network which provides a good approximation of the target graph. Both the spectral properties as well as other characteristic features of the reference network, such as the diameter, clustering coefficient, and the average degree, are well reproduced by the approximately reconstructed graph.Any graph G can be described by its adjacency matrix A such that A ij = 1 if the nodes i and j are connected, and A ij = 0 otherwise. A Laplacian spectrum of the graph G is defined [4] as the set of eigenvalues λ i of the matrix T with elements T ij = A ij − m i δ ij where m i = N j=1 A ij is the degree of node i and δ ij is the Kronecker symbol.

A simple flow network model of biological signal transduction is investigated. Networks with prescribed signal processing functions, robust against random node or link removals, are designed through an evolutionary optimization process. Statistical properties of large ensembles of such networks, including their characteristic motif distributions, are determined. Our analysis suggests that robustness against link removals plays the principal role in the architecture of real signal transduction networks and developmental genetic transcription networks.

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