Influence maximization, defined by Kempe, Kleinberg, and Tardos (2003), is the problem of finding a small set of seed nodes in a social network that maximizes the spread of influence under certain influence cascade models. In this paper, we propose an extension to the independent cascade model that incorporates the emergence and propagation of negative opinions. The new model has an explicit parameter called quality factor to model the natural behavior of people turning negative to a product due to product defects. Our model incorporates negativity bias (negative opinions usually dominate over positive opinions) commonly acknowledged in the social psychology literature. The model maintains some nice properties such as submodularity, which allows a greedy approximation algorithm for maximizing positive influence within a ratio of 1 − 1/e. We define a quality sensitivity ratio (qs-ratio) of influence graphs and show a tight bound of Θ( n/k) on the qs-ratio, where n is the number of nodes in the network and k is the number of seeds selected, which indicates that seed selection is sensitive to the quality factor for general graphs. We design an efficient algorithm to com- * Author affiliations and emails: W. pute influence in tree structures, which is nontrivial due to the negativity bias in the model. We use this algorithm as the core to build a heuristic algorithm for influence maximization for general graphs. Through simulations, we show that our heuristic algorithm has matching influence with a standard greedy approximation algorithm while being orders of magnitude faster.

Antibodies elicited by protein therapeutics can cause serious side effects in humans. We studied immunogenicity of a recombinant fusion protein (FPX) consisting of two identical, biologically active, peptides attached to human Fc fragment. EpiMatrix, an in silico epitope-mapping tool, predicted promiscuous T-cell epitope(s) within the 14-amino-acid carboxy-terminal region of the peptide portion of FPX. On administration of FPX in 76 healthy human subjects, 37% developed antibodies after a single injection. A memory T-cell response against the above carboxy-terminus of the peptide was observed in antibody-positive but not in antibody-negative subjects. Promiscuity of the predicted T-cell epitope(s) was confirmed by representation of all common HLA alleles in antibody-positive subjects. As predicted by EpiMatrix, HLA haplotype DRB1*0701/1501 was associated with the highest T-cell and antibody response. In conclusion, in silico prediction can be successfully used to identify Class II restricted T-cell epitopes within therapeutic proteins and predict immunogenicity thereof in humans.

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