Cops and robbers on dynamic graphs: Offline and online case

We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the underlying graph of the model. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n2k+1T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs, i.e., with at most linear number of edges. We prove λ +1 cops suffice to capture the robber in any underlying graph with n-1+λ edges. Further, we define a family of underlying graphs with n-1+λ edges where λ -1 cops are necessary (and sufficient) for capture. © Springer Nature Switzerland AG 2020

Gapless genome assembly of Colletotrichum higginsianum reveals chromosome structure and association of transposable elements with secondary metabolite gene clusters

Background: The ascomycete fungus Colletotrichum higginsianum causes anthracnose disease of brassica crops and the model plant Arabidopsis thaliana. Previous versions of the genome sequence were highly fragmented, causing errors in the prediction of protein-coding genes and preventing the analysis of repetitive sequences and genome architecture. Results: Here, we re-sequenced the genome using single-molecule real-time (SMRT) sequencing technology and, in combination with optical map data, this provided a gapless assembly of all twelve chromosomes except for the ribosomal DNA repeat cluster on chromosome 7. The more accurate gene annotation made possible by this new assembly revealed a large repertoire of secondary metabolism (SM) key genes (89) and putative biosynthetic pathways (77 SM gene clusters). The two mini-chromosomes differed from the ten core chromosomes in being repeat-and AT-rich and gene-poor but were significantly enriched with genes encoding putative secreted effector proteins. Transposable elements (TEs) were found to occupy 7% of the genome by length. Certain TE families showed a statistically significant association with effector genes and SM cluster genes and were transcriptionally active at particular stages of fungal development. All 24 subtelomeres were found to contain one of three highly-conserved repeat elements which, by providing sites for homologous recombination, were probably instrumental in four segmental duplications. Conclusion: The gapless genome of C. higginsianum provides access to repeat-rich regions that were previously poorly assembled, notably the mini-chromosomes and subtelomeres, and allowed prediction of the complete SM gene repertoire. It also provides insights into the potential role of TEs in gene and genome evolution and host adaptation in this asexual pathogen

Carbon Footprint: Concept, Methodology and Calculation

Carbon footprint (CF) is nowadays one of the most widely used environmental indicators and calculations of CF have been recently in very high demand. Many approaches, methodologies and tools, from simplified online calculators to other more scientific and complex life-cycle based methods, have been developed and are available for estimations. CF evaluations are, in general, focused on products and organizations, but calculation approach have been developed also for specific themes/sectors, such as for instance cities, individuals, households, farms, etc. This chapter is aimed at giving an updated and comprehensive overview on the concept of CF, and also on methodologies, technical standards, protocols and tools for its calculation. Attention is focused on the two main and usual scopes of CF assessment, i.e. products and organizations, but also on other relevant specific study subjects, also discussing methodological differences and issues.5n