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The dynamics of disease transmission strongly depends on the properties of the population contact network. Pair-approximation models and individual-based network simulation have been used extensively to model contact networks with non-trivial properties. In this paper, using a continuous time Markov chain, we start from the exact formulation of a simple epidemic model on an arbitrary contact network and rigorously derive and prove some known results that were previously mainly justified based on some biological hypotheses. The main result of the paper is the illustration of the link between graph automorphisms and the process of lumping whereby the number of equations in a system of linear differential equations can be significantly reduced. The main advantage of lumping is that the simplified lumped system is not an approximation of the original system but rather an exact version of this. For a special class of graphs, we show how the lumped system can be obtained by using graph automorphisms. Finally, we discuss the advantages and possible applications of exact epidemic models and lumping.

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This review describes the state-of-the-art of material derived from the forest sector with respect to its potential for use in the packaging industry. Some innovative approaches are highlighted. The aim is to cover recent developments and key challenges for successful introduction of renewable materials in the packaging market. The covered subjects are renewable fibers and bio-based polymers for use in bioplastics or as coatings for paper-based packaging materials. Current market sizes and forecasts are also presented. Competitive mechanical, thermal, and barrier properties along with material availability and ease of processing are identified as fundamental issues for sustainable utilization of renewable materials.

We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this “deterministic” representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

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Necrotic cell death is a common feature in numerous human neurodegenerative disorders. In the nematode Caenorhabditis elegans, gain-of-function mutations in genes that encode specific ion channel subunits such as the degenerins DEG-1 and MEC-4, and the acetylcholine receptor subunit DEG-3 lead to necrotic-like degeneration of a subset of neurons. Neuronal demise caused by ion channel hyperactivity is accompanied by intense degradation of cytoplasmic contents, dramatic membrane infolding and vacuole formation; however, the cellular pathways underlying such processes remain largely unknown. Here we show that the function of three autophagy genes, whose yeast and mammalian orthologs are implicated in cytoplasmic self-degradation, membrane trafficking and the cellular response to starvation, contributes to ion-channel-dependent neurotoxicity in C. elegans. Inactivation of unc-51, bec-1 and lgg-1, the worm counterparts of the yeast autophagy genes Atg1, Atg6 and Atg8 respectively, partially suppresses degeneration of neurons with toxic ion channel variants. We also demonstrate that the TOR-kinase-mediated signaling pathway, a nutrient sensing system that downregulates the autophagy gene cascade, protects neurons from undergoing necrotic cell death, whereas nutrient deprivation promotes necrosis. Our findings reveal a role for autophagy genes in neuronal cell loss in C. elegans.