On the Complexity of Role Colouring Planar Graphs, Trees and Cographs

We prove several results about the complexity of the role colouring problem. A role colouring of a graph $G$ is an assignment of colours to the vertices of $G$ such that two vertices of the same colour have identical sets of colours in their neighbourhoods. We show that the problem of finding a role colouring with $1< k <n$ colours is NP-hard for planar graphs. We show that restricting the problem to trees yields a polynomially solvable case, as long as $k$ is either constant or has a constant difference with $n$, the number of vertices in the tree. Finally, we prove that cographs are always $k$-role-colourable for $1<k\leq n$ and construct such a colouring in polynomial time

Growth and Containment of a Hierarchical Criminal Network

We model the hierarchical evolution of an organized criminal network via antagonistic recruitment and pursuit processes. Within the recruitment phase, a criminal kingpin enlists new members into the network, who in turn seek out other affiliates. New recruits are linked to established criminals according to a probability distribution that depends on the current network structure. At the same time, law enforcement agents attempt to dismantle the growing organization using pursuit strategies that initiate on the lower level nodes and that unfold as self-avoiding random walks. The global details of the organization are unknown to law enforcement, who must explore the hierarchy node by node. We halt the pursuit when certain local criteria of the network are uncovered, encoding if and when an arrest is made; the criminal network is assumed to be eradicated if the kingpin is arrested. We first analyze recruitment and study the large scale properties of the growing network; later we add pursuit and use numerical simulations to study the eradication probability in the case of three pursuit strategies, the time to first eradication and related costs. Within the context of this model, we find that eradication becomes increasingly costly as the network increases in size and that the optimal way of arresting the kingpin is to intervene at the early stages of network formation. We discuss our results in the context of dark network disruption and their implications on possible law enforcement strategies.Comment: 16 pages, 11 Figures; New title; Updated figures with color scheme better suited for colorblind readers and for gray scale printin

Effect of Conidia Germination on Infection of Brown Planthopper (BPH) by Insect Fungi

Conidia of insect fungi actively invade BPH [brown planthopper]. After a conidium lands on the insect cuticle, germination takes about 8 to 16 h, depending on the temperature and relative humidity. After the germination, tuber is formed, the conidium produces specific chitinase enzymes to dissolve the insect cuticle. This allows the fungus to enter the insect body cavity, where further fungus growth occurs. At the end of the infection cycle, the mycelium sporulates on the outside of the insect. Conidia produced on the cadaver can infect healthy BPH initiating epizootics of the fungus. To test infection, 50 adult alate BPH were used for treatment. Insect were dipped in the conidia solution for about 60s and transferred to filter paper to drain. Control insects were dipped in Tween 80 solution. Insects were incubated on potted rice plants in mylar cages. Half the cages were covered with plastic bags for 2.5 h immediately after fungi application to raise RH to saturation. All pots were kept in a greenhouse at 25-30 deg C (day) and 15-20 deg C (night) for 5 d. Live and infected (dead and fungi-covered) insects were counted. Mortality due to fungus infection was calculated. The results show lessening, but not significantly different mortality with increasing fungus conidia treatment. Pregermination of the fungus Beauveria bassiana conidia and 2 h incubation at saturated RH did not increase BPH infection

Orbital assembly and maintenance study

The requirements, conceptual design, tradeoffs, procedures, and techniques for orbital assembly of the support structure of the microwave power transmission system and the radio astronomy telescope are described. Thermal and stress analyses, packaging, alignment, and subsystems requirements are included along with manned vs. automated and transportation tradeoffs. Technical and operational concepts for the manned and automated maintenance of satellites were investigated and further developed results are presented

Orbital assembly and maintenance study. Executive summary

A sound, practical approach for the assembly and maintenance of very large structures in space is presented. The methods and approaches for assembling two large structures are examined. The maintenance objectives include the investigation of methods to maintain five geosynchronous satellites. The two assembly examples are a 200-meter-diameter radio astronomy telescope and a 1,000-meter-diameter microwave power transmission system. The radio astronomy telescope operates at an 8,000-mile altitude and receives RF signals from space. The microwave power transmission system is part of a solar power satellite that will be used to transmit converted solar energy to microwave ground receivers. Illustrations are included