Experience versus talent shapes the structure of the Web.

We use sequential large-scale crawl data to empirically investigate and validate the dynamics that underlie the evolution of the structure of the web. We find that the overall structure of the web is defined by an intricate interplay between experience or entitlement of the pages (as measured by the number of inbound hyperlinks a page already has), inherent talent or fitness of the pages (as measured by the likelihood that someone visiting the page would give a hyperlink to it), and the continual high rates of birth and death of pages on the web. We find that the web is conservative in judging talent and the overall fitness distribution is exponential, showing low variability.

On rate-distortion models for natural images and wavelet coding performance.

Operational rate-distortion (RD) functions of most natural images, when compressed with state-of-the-art wavelet coders, exhibit a power-law behavior D alpha R(-gamma) at moderately high rates, with gamma being a constant depending on the input image, deviating from the well-known exponential form of the RD function D alpha 2(-xiR) for bandlimited stationary processes. This paper explains this intriguing observation by investigating theoretical and operational RD behavior of natural images. We take as our source model the fractional Brownian motion (fBm), which is often used to model nonstationary behaviors in natural images.

Multiple power-law structures in heterogeneous complex networks.

This paper develops a framework for analyzing and designing dynamic networks comprising different classes of nodes that coexist and interact in one shared environment. We consider ad hoc (i.e.

Scale-free and stable structures in complex ad hoc networks.

Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections and rewiring of existing links, we study ad hoc networks, where one also has to contend with rapid and random deletions of existing nodes (and, hence, the associated links). We first show that dynamics based only on the well-known preferential attachments of new nodes do not lead to a sufficiently heavy-tailed degree distribution in ad hoc networks. In particular, the magnitude of the power-law exponent increases rapidly (from 3) with the deletion rate, becoming infinity in the limit of equal insertion and deletion rates.