The complexity of Drosophila innate immunity

Metazoans rely on efficient mechanisms to oppose infections caused by pathogens. The immediate and first-line defense mechanism(s) in metazoans, referred to as the innate immune system, is initiated upon recognition of microbial intruders by germline encoded receptors and is executed by a set of rapid effector mechanisms. Adaptive immunity is restricted to vertebrate species and it is controlled and assisted by the innate immune system. Interestingly, most of the basic signaling cascades that regulate the primeval innate defense mechanism(s) have been well conserved during evolution, for instance between humans and the fruit fly, Drosophila melanogaster. Being devoid of adaptive signaling and effector systems, Drosophila has become an established model system for studying pristine innate immune cascades and reactions. In general, an immune response is evoked when microorganisms pass the fruit fly’s physical barriers (e.g. cuticle, epithelial lining of gut and trachea), and it is mainly executed in the hemolymph, the equivalent of the mammalian blood. Innate immunity in the fruit fly consists of a phenoloxidase (PO) response, a cellular response (hemocytes), an antiviral response, and the NF-κB dependent production of antimicrobial peptides referred to as the humoral response. The JAK/STAT and Jun kinase signaling cascades are also implicated in the defence against pathogens.

On the extension complexity of combinatorial polytopes

In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete problems including subset-sum and three dimensional matching. We then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors. Using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs, including those used in quantum information and suspensions of cubic planar graphs.