The targeting of chaotic trajectories uses the sensitive dependence on initial conditions to produce large (desired) changes to the trajectory using small perturbations. One important application is to directing spacecraft using very small amounts of fuel, relying on the (Hamiltonian) chaos of the three body problem consisting of the spacecraft, earth, and moon or other planet. Another applicat...

Given a DNF formula φ with n variables, DNF counting is the problem finding the number of satisfying assignments for φ. Note that in general satisfiability for DNF is easy as we need only satisfy a single clause, but the counting problem is hard. Indeed, if we could do this, then given any 3-CNF formula f with n variables, we could take its negation, count how many satisfying assignments its ne...

Not long after taxonomists recognized that among the saprolegniaceous fungi there were homologous groups possessing similar devices for insuring reproduction, they began industriously arranging these groups into hierarchical clusters to suggest relationships. Although the resulting phylogenetic schemes were fashioned around the relatively simple structure of the individual species, mycologists ...

Sociologists understand the term ‘organization’ in very broad terms to mean any structure by which social life and behaviour are managed. The term is more narrowly understood to mean formal organizations with a bureaucratic structure. Some formal organizations process ‘clients’, like schools and police stations, where the principal purpose is the management of people and their needs. Others are...

Slide 1 Marx was very critical of Malthus. He said that an abstract law of population did not exist for men (Marx, 1974). All historical modes of production have their own special laws of population which are valid only within their limits. Marx discussed the law of population, applicable to capitalist mode of production in chapter XXV of Capital, entitled, “The General Law of Capitalist Accumu...