Quick Detection of High-degree Entities in Large Directed Networks

In this paper, we address the problem of quick detection of high-degree entities in large online social networks. Practical importance of this problem is attested by a large number of companies that continuously collect and update statistics about popular entities, usually using the degree of an entity as an approximation of its popularity. We suggest a simple, efficient, and easy to implement two-stage randomized algorithm that provides highly accurate solutions for this problem. For instance, our algorithm needs only one thousand API requests in order to find the top-100 most followed users in Twitter, a network with approximately a billion of registered users, with more than 90% precision. Our algorithm significantly outperforms existing methods and serves many different purposes, such as finding the most popular users or the most popular interest groups in social networks. An important contribution of this work is the analysis of the proposed algorithm using Extreme Value Theory -- a branch of probability that studies extreme events and properties of largest order statistics in random samples. Using this theory, we derive an accurate prediction for the algorithm's performance and show that the number of API requests for finding the top-k most popular entities is sublinear in the number of entities. Moreover, we formally show that the high variability among the entities, expressed through heavy-tailed distributions, is the reason for the algorithm's efficiency. We quantify this phenomenon in a rigorous mathematical way

Probing Amphotericin B Single Channel Activity by Membrane Dipole Modifiers

The effects of dipole modifiers and their structural analogs on the single channel activity of amphotericin B in sterol-containing planar phosphocholine membranes are studied. It is shown that the addition of phloretin in solutions bathing membranes containing cholesterol or ergosterol decreases the conductance of single amphotericin B channels. Quercetin decreases the channel conductance in cholesterol-containing bilayers while it does not affect the channel conductance in ergosterol-containing membranes. It is demonstrated that the insertion of styryl dyes, such as RH 421, RH 237 or RH 160, in bilayers with either cholesterol or ergosterol leads to the increase of the current amplitude of amphotericin B pores. Introduction of 5α-androstan-3β-ol into a membrane-forming solution increases the amphotericin B channel conductance in a concentration-dependent manner. All the effects are likely to be attributed to the influence of the membrane dipole potential on the conductance of single amphotericin B channels. However, specific interactions of some dipole modifiers with polyene-sterol complexes might also contribute to the activity of single amphotericin B pores. It has been shown that the channel dwell time increases with increasing sterol concentration, and it is higher for cholesterol-containing membranes than for bilayers including ergosterol, 6-ketocholestanol, 7-ketocholestanol or 5α-androstan-3β-ol. These findings suggest that the processes of association/dissociation of channel forming molecules depend on the membrane fluidity