Asha Rao

Identifying Influential Nodes in Bipartite Networks Using the Clustering Coefficient

The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities.

Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power

There has been much interest in mutually unbiased bases (MUBs) and their connections with various other discrete structures, such as projective planes, mutually orthogonal Latin squares (MOLS) etc. It has been conjectured by Saniga et al. (J Opt B Quantum Semiclass Opt 6:L19–L20, 2004) that the existence of a complete set of MUBs in ℂd is linked to the existence of a complete set of MOLS of side length d. Since more is known about MOLS than about MUBs, most research has concentrated on constructing MUBs from MOLS (Roy and Scott, J Math Phys 48:072110, 2007; Paterek et al., Phys Rev A 70:012109, 2009). This paper gives a simple algebraic construction of MOLS from two known constructions of MUBs in the odd prime power case.

Mutually orthogonal Latin squares from the inner products of vectors in mutually unbiased bases

Mutually unbiased bases (MUBs) are important in quantum information theory. While constructions of complete sets of d + 1 MUBs in C-d are known when d is a prime power, it is unknown if such complete sets exist in non-prime power dimensions. It has been conjectured that complete sets of MUBs only exist in if a maximal set of mutually orthogonal Latin squares (MOLS) of side length d also exists. There are several constructions (Roy and Scott 2007 J. Math. Phys. 48 072110; Paterek, Daki? and Brukner 2009 Phys. Rev. A 79 012109) of complete sets of MUBs from specific types of MOLS, which use Galois fields to construct the vectors of the MUBs. In this paper, two known constructions of MUBs (Alltop 1980 IEEE Trans. Inf. Theory 26 350-354; Wootters and Fields 1989 Ann. Phys. 191 363-381), both of which use polynomials over a Galois field, are used to construct complete sets of MOLS in the odd prime case. The MOLS come from the inner products of pairs of vectors in the MUBs.

Predicting item popularity: Analysing local clustering behaviour of users

Predicting the popularity of items in rating networks is an interesting but challenging problem. This is especially so when an item has first appeared and has received very few ratings. In this paper, we propose a novel approach to predicting the future popularity of new items in rating networks, defining a new bipartite clustering coefficient to predict the popularity of movies and stories in the MovieLens and Digg networks respectively. We show that the clustering behaviour of the first user who rates a new item gives insight into the future popularity of that item. Our method predicts, with a success rate of over 65% for the MovieLens network and over 50% for the Digg network, the future popularity of an item. This is a major improvement on current results.

Fast extraction of the backbone of projected bipartite networks to aid community detection

This paper introduces a computationally inexpensive method of extracting the backbone of one-mode networks projected from bipartite networks. We show that the edge weights in the one-mode projections are distributed according to a Poisson binomial distribution and that finding the expected weight distribution of a one-mode network projected from a random bipartite network only requires knowledge of the bipartite degree distributions. Being able to extract the backbone of a projection is highly beneficial in filtering out redundant information in large complex networks and narrowing down the information in the one-mode projection to the most relevant. We demonstrate that the backbone of a one-mode projection aids in the detection of communities.

New linear codes over Z/sub ps/ via the trace map

The trace map has been used very successfully to generate cocyclic complex and Butson Hadamard matrices and simplex codes over Z₄ and Z_2s. We extend this technique to obtain new linear codes over Z_ps. It is worth nothing here that these codes are cocyclic but not simplex codes. Further we find that the construction method also gives Butson Hadamard matrices of order p^sm

Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146.

Significance of likes: Analysing passive interactions on Facebook during campaigning

With more and more political candidates using social media for campaigning, researchers are looking at measuring the effectiveness of this medium. Most research, however, concentrates on the bare count of likes (or twitter mentions) in an attempt to correlate social media presence and winning. In this paper, we propose a novel method, Interaction Strength Plot (IntS) to measure the passive interactions between a candidate’s posts on Facebook and the users (liking the posts). Using this method on original Malaysian General Election (MGE13) and Australian Federal Elections (AFE13) Facebook Pages (FP) campaign data, we label an FP as performing well if both the posting frequency and the likes gathered are above average. Our method shows that over 60% of the MGE13 candidates and 85% of the AFE13 candidates studied in this paper had under-performing FP. Some of these FP owners would have been identified as popular based on bare count. Thus our performance chart is a vital step forward in measuring the effectiveness of online campaigning.

Influence Neighbourhoods in CiteSeer: A Case Study

We are interested in using purely network-based techniques to assist in matching instances across databases that can be represented as complex networks. In particular we are interested in the individuality of the influence neighbourhood of a node (the sub graph induced by its in-neighbours) in a directed network. We derive a paper citation network from the archived Cite Seer database and use this network as a case study of influence neighbourhoods. We show that papers can reliably be distinguished by their influence neighbourhoods.

A Family of Alltop Functions that are EA-Inequivalent to the Cubic Function

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (IEEE Trans. Inf. Theory 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called Alltop functions. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.