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Agglomerative Percolation in Two Dimensions
Claire Christensen, Golnoosh Bizhani, Seung-Woo Son +2
We study a process termed "agglomerative percolation" (AP) in two dimensions. Instead of adding sites or bonds at random, in AP randomly chosen clusters are linked to all their nei…
Irreversible Aggregation and Network Renormalization
Seung-Woo Son, Golnoosh Bizhani, Claire Christensen +2
Irreversible aggregation is revisited in view of recent work on renormalization of complex networks. Its scaling laws and phase transitions are related to percolation transitions s…
Random Sequential Renormalization of Networks I: Application to Critical Trees
Golnoosh Bizhani, Vishal Sood, Maya Paczuski +1
We introduce the concept of Random Sequential Renormalization (RSR) for arbitrary networks. RSR is a graph renormalization procedure that locally aggregates nodes to produce a coar…
Sequence alignment, mutual information, and dissimilarity measures for constructing phylogenies
Orion Penner, Peter Grassberger, Maya Paczuski
Existing sequence alignment algorithms use heuristic scoring schemes which cannot be used as objective distance metrics. Therefore one relies on measures like the p- or log-det dis…
Lower Bounds on Mutual Information
David V. Foster, Peter Grassberger
We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show…
The Interacting Branching Process as a Simple Model of Innovation
Vishal Sood, Myléne Mathieu, Amer Shreim +2
We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed wi…