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In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. A polytree (or directed tree or oriented tree or singly connected network) is a directed acyclic graph (DAG) whose underlying undirected graph is a tree
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Shape theory is a branch of topology, which provides a more global view of the topological spaces than homotopy theory. The two coincide on compacta dominated homotopically by finite polyhedra. Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory. Shape theory was reinvented, further developed and promoted by the Polish mathematician Karol Borsuk in 1968. Actually, the name shape theory was coined by Borsuk.
There is a natural notion of occurrence of contiguous pattern in such trees. We describe a way, given a set of generators and a set of patterns, to enumerate the trees avoiding this last. The method is built around inclusion-exclusion formulas forming a system of equations on formal power series of trees, and composition operations of trees. This does not require particular conditions on the set of patterns to avoid. We connect this result to the theory of nonsymmetric operads. Syntax trees are the elements of such free structures, so that any operad can be seen as a quotient of a free operad. Moreover, in some cases, the elements of an operad can be seen as trees avoiding some patterns.
Our purpose in this Chapter is to address the psychometric properties of several self-report measures of procrastination. In Chapter 9 we presented a theory-based, structured therapeutic program aimed at reducing procrastination. This time-limited program was primarily relevant to treatment of procrastinating college students. The premises regarding the etiologies of procrastination that we introduce in this book were used to shape the content of those interventions.
Risk tolerance, Social influence. Users’ perceived susceptibility and severity of malicious IT. A safeguarding measure's effectiveness, costs, and users' self-efficacy toward it. Technology Threat Avoidance Theory (TTAT) explains why and how individual IT users engage in threat avoidance behaviors. Unlike most studies that have examined IT security at the organizational level, TTAT provides a framework at the individual user level