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Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are sufficiently high to affect network structure on short time scales. For instance, more than 100 interactions may be added to the yeast network every million years, a substantial fraction of which adds previously unconnected proteins to the network. Highly connected proteins show a greater rate of interaction turnover than proteins with few interactions. From these observations one can explain ? without natural selection on global network structure ? the evolutionary sustenance of the most prominent network feature, the distribution of the frequency P(d) of proteins with d neighbors, which is a broad-tailed distribution. This distribution is independent of the experimental approach providing nformation on network structure.
The determination of protein functions is one of the most challenging problems of the post-genomic era. The sequencing of entire genomes and the possibility to access genes co-expression patterns has moved the attention from the study of single prote
From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that ne
Aligning protein-protein interaction (PPI) networks of different species has drawn a considerable interest recently. This problem is important to investigate evolutionary conserved pathways or protein complexes across species, and to help in the iden
We study the time until first occurrence, the first-passage time, of rare density fluctuations in diffusive systems. We approach the problem using a model consisting of many independent random walkers on a lattice. The existence of spatial correlatio
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure