Genes and proteins are organized on the basis of their particular mutual relations or according to their interactions in cellular and genetic networks. These include metabolic or signaling pathways and protein interaction, regulatory or co-expression networks. Integrating the information from the different types of networks may lead to the notion of a functional network and functional modules. To find these modules, we propose a new technique which is based on collective, multi-body correlations in a genetic network. We calculated the correlation strength of a group of genes (e.g. in the co-expression network) which were identified as members of a module in a different network (e.g. in the protein interaction network) and estimated the probability that this correlation strength was found by chance. Groups of genes with a significant correlation strength in different networks have a high probability that they perform the same function. Here, we propose evaluating the multi-body correlations by applying the superparamagnetic approach. We compare our method to the presently applied mean Pearson correlations and show that our method is more sensitive in revealing functional relationships.

We present a detailed calculation of the magnetic couplings between nearest-neighbor and nextnearest-neighbor coppers in the edge-sharing geometry, ubiquitous in many cuprates. In this geometry, the interaction between nearest neighbor coppers is mediated via two oxygens, and the Cu-O-Cu angle is close to 90 • . The derivation is based on a perturbation expansion of a general Hubbard Hamiltonian, and produces numerical estimates for the various magnetic energies. In particular we find the dependence of the anisotropy energies on the angular deviation away from the 90 • geometry of the Cu-O-Cu bonds. Our results are required for the correct analysis of the magnetic structure of various chain, ladder and lamellar cuprates.

We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.

We investigate electron transfer processes in donor-acceptor systems with a coupling of the electronic degrees of freedom to a common bosonic bath. The model allows to study many-particle effects and the influence of the local Coulomb interaction U between electrons on donor and acceptor sites. Using the non-perturbative numerical renormalization group approach we find distinct differences between the electron transfer characteristics in the single-and two-particle subspaces. We calculate the critical electron-boson coupling αc as a function of U and show results for density-density correlation functions in the whole parameter space. The possibility of many-particle (bipolaronic) and Coulomb-assisted transfer is discussed. Introduction -Electron transfer (ET) is a fundamental process in chemistry, biology and physics, for example in corrosion of metals, charge transfer in semiconductors, enzymatic activities, cell metabolism, and photosynthesis [1,2]. The characterization of ET processes in bio-molecules is an important step towards an understanding of the biological function of many proteins and towards the possible construction of bio-molecular electronic devices or biosensors. Theoretical investigations of ET processes typically start from a two-site model for the electronic degrees of freedom at the donor and acceptor sites which are coupled via a tunneling matrix element t. The correlated dynamics of electrons and vibronic modes (phonons) is essential for the ET characteristics. If the phonons are treated classically, one arrives at the Marcus theory [3]. A quantum mechanical treatment of the phononic degrees of freedom [4] results in models related to the spin-boson model, in which the phonons are modeled by an infinite set of harmonic oscillators with a continuous spectral density J(ω) [5,6].