150,517 research outputs found
Axioms for infinite matroids
We give axiomatic foundations for non-finitary infinite matroids with
duality, in terms of independent sets, bases, circuits, closure and rank. This
completes the solution to a problem of Rado of 1966.Comment: 33 pp., 2 fig
What is Autonomy?
A system is autonomous if it uses its own information to modify itself and its environment to enhance its survival, responding to both environmental and internal stimuli to modify its basic functions to increase its viability. Autonomy is the foundation of functionality, intentionality and meaning. Autonomous systems accommodate the unexpected through self-organizing processes, together with some constraints that maintain autonomy. Early versions of autonomy, such as autopoiesis and closure to efficient cause, made autonomous systems dynamically closed to information. This contrasts with recent work on open systems and information dynamics. On our account, autonomy is a matter of degree depending on the relative organization of the system and system environment interactions. A choice between third person openness and first person closure is not required
Axiomatic Design of Space Life Support Systems
Systems engineering is an organized way to design and develop systems, but the initial system design concepts are usually seen as the products of unexplained but highly creative intuition. Axiomatic design is a mathematical approach to produce and compare system architectures. The two axioms are:- Maintain the independence of the functional requirements.- Minimize the information content (or complexity) of the design. The first axiom generates good system design structures and the second axiom ranks them. The closed system human life support architecture now implemented in the International Space Station has been essentially unchanged for fifty years. In contrast, brief missions such as Apollo and Shuttle have used open loop life support. As mission length increases, greater system closure and increased recycling become more cost-effective.Closure can be gradually increased, first recycling humidity condensate, then hygiene wastewater, urine, carbon dioxide, and water recovery brine. A long term space station or planetary base could implement nearly full closure, including food production. Dynamic systems theory supports the axioms by showing that fewer requirements, fewer subsystems, and fewer interconnections all increase system stability. If systems are too complex and interconnected, reliability is reduced and operations and maintenance become more difficult. Using axiomatic design shows how the mission duration and other requirements determine the best life support system design including the degree of closure
Matrix representations and independencies in directed acyclic graphs
For a directed acyclic graph, there are two known criteria to decide whether
any specific conditional independence statement is implied for all
distributions factorized according to the given graph. Both criteria are based
on special types of path in graphs. They are called separation criteria because
independence holds whenever the conditioning set is a separating set in a graph
theoretical sense. We introduce and discuss an alternative approach using
binary matrix representations of graphs in which zeros indicate independence
statements. A matrix condition is shown to give a new path criterion for
separation and to be equivalent to each of the previous two path criteria.Comment: Published in at http://dx.doi.org/10.1214/08-AOS594 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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