A Preferential Attachment Paradox: How Preferential Attachment Combines with Growth to Produce Networks with Log-normal In-degree Distributions.

Every network scientist knows that preferential attachment combines with growth to produce networks with power-law in-degree distributions. How, then, is it possible for the network of American Physical Society journal collection citations to enjoy a log-normal citation distribution when it was found to have grown in accordance with preferential attachment? This anomalous result, which we exalt as the preferential attachment paradox, has remained unexplained since the physicist Sidney Redner first made light of it over a decade ago. Here we propose a resolution. The chief source of the mischief, we contend, lies in Redner having relied on a measurement procedure bereft of the accuracy required to distinguish preferential attachment from another form of attachment that is consistent with a log-normal in-degree distribution. There was a high-accuracy measurement procedure in use at the time, but it would have have been difficult to use it to shed light on the paradox, due to the presence of a systematic error inducing design flaw. In recent years the design flaw had been recognised and corrected. We show that the bringing of the newly corrected measurement procedure to bear on the data leads to a resolution of the paradox.

Palindromic amplification of the ERBB2 oncogene in primary HER2-positive breast tumors.

Oncogene amplification confers a growth advantage to tumor cells for clonal expansion. There are several, recurrently amplified oncogenes throughout the human genome. However, it remains unclear whether this recurrent amplification is solely a manifestation of increased fitness resulting from random amplification mechanisms, or if a genomic locus-specific amplification mechanism plays a role. Here we show that the ERBB2 oncogene at 17q12 is susceptible to palindromic gene amplification, a mechanism characterized by the inverted (palindromic) duplication of genomic segments, in HER2-positive breast tumors. We applied two genomic approaches to investigate amplification mechanisms: sequencing of DNA libraries enriched with tumor-derived palindromic DNA (Genome-wide Analysis of Palindrome Formation) and whole genome sequencing (WGS). We observed significant enrichment of palindromic DNA within amplified ERBB2 genomic segments. Palindromic DNA was particularly enriched at amplification peaks and at boundaries between amplified and normal copy-number regions. Thus, palindromic gene amplification shaped the amplified ERBB2 locus. The enrichment of palindromic DNA throughout the amplified segments leads us to propose that the ERBB2 locus is amplified through the mechanism that repeatedly generates palindromic DNA, such as Breakage-Fusion-Bridge cycles. The genomic architecture surrounding ERBB2 in the normal genome, such as segmental duplications, could promote the locus-specific mechanism.